ksenia weber 3D PR IN TED M ICRO -OPT IC S : MATER IAL S , METHODS AND APPL ICAT IONS 3D Printed Micro-Optics: Materials, Methods and Applications Von der Fakultät Mathematik und Physik der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung vorgelegt von Ksenia Weber aus Novosibirsk Hauptberichter: Prof. Dr. Harald Giessen Mitberichter: Prof. Dr. Peter Michler Prüfungsvorsitzender: Prof. Dr. Maria Daghofer Tag der mündlichen Prüfung: 08.03.2022 4. Physikalisches Institut der Universität Stuttgart 2022 Ksenia Weber: 3D Printed Micro-Optics: Materials, Methods and Applications Für mich! ...nämlich der Fall, daß zwei Lichtquanten, deren Frequenzsumme gleich der Anregungsfrequenz des Atoms ist, zusammenwirken, um das Atom anzuregen. — Maria Göppert-Mayer, Über Elementarakte mit zwei Quantensprüngen ABSTRACT Additive manufacturing, or 3D printing, is a powerful fabrication method that unlocked a previously unknown level of design freedom. By adding new material in a layer-by-layer fashion, complex three-dimensional struc- tures can be created rapidly and reliably. The technology has the potential to revolutionize engineering and manufacturing in the 21st century with possible applications including rapid prototyping, custom manufacturing or robotics. Femtosecond two-photon 3D printing is the additive manufacturing tech- nology that oers the smallest achievable feature sizes by far. It enables the fabrication of complex micrometer-sized structures from a photopolymer material. The approach relies on the non-linear optical eect of two-photon absorption, which gives it an innate advantage over all other lithography techniques in terms of versatility and resolution. A tightly focused fem- tosecond pulsed near-infra-red laser beam is moved through a liquid pho- topolymer that is transparent at the laser’s fundamental wavelength. Due to the extremely high light intensity in the volumetric focal spot of the beam, the so-called voxel, two-photon absorption results in selective curing of the photopolymer. As a result, arbitrary three-dimensional structures can be created by moving the voxel through the resist. It has been shown that femtosecond 3D printing is capable of producing high-quality, complex micro-optical elements that can be used for a variety of possible applications. Examples include, but are not limited to: illumination optics, aspheric, toric and free-form lenses, beam shaping optics, photonic crystals, waveguides and multi-lens imaging objectives. In this thesis, we expand the emerging eld of 3D printed micro-optics with novel materials, fabrication methods and applications. By doing so, we break down barriers that have previously substantially hindered the technology. For example, we overcome the restriction to transparent pho- topolymers as fabrication materials by developing techniques to produce light-blocking apertures. Furthermore, we extend the range of available optical properties by introducing 3D printable high-index nano-composite materials. Moreover, we explore innovative scientic applications of the 3D printing method by using it to develop two single-mode ber based photonic vii devices: an orbital-angular momentum and a single-photon quantum-light source. Finally, we analyze our 3D printing process in terms of alignment and positioning accuracy to further boost our fabrication capabilities. Our work paves exciting new avenues in the diverse eld of femtosecond 3D printing with possible applications ranging from sensing technology, robotics, camera miniaturization and optical trapping all the way to quantum communication. As such, it opens the door for many more novel develop- ments in the years to come. viii DEU TSCHE ZUSAMMENFAS SUNG Additive Fertigung, oder auch 3D Druck ist eine vielseitige Herstellungs- methode, deren Erndung eine zuvor ungeahnte Designfreiheit erönet hat. Durch das schrittweise Hinzufügen von neuem Material in einzelnen Lagen können komplexe dreidimensionale Strukturen präzise und zuverläs- sig produziert werden. Die Technologie hat das Potential die Konstruktion und Herstellung von komplexen Teilen im Einundzwanzigsten Jahrhundert zu revolutionieren. Mögliche Anwendungen erstrecken sich dabei auf die schnelle Herstellung von Prototypen und Einzelanfertigungen oder auch Robotertechnik. Femtosekunden Zwei-Photonen 3D Druck ist die additive Fertigungs- methode die mit Abstand die höchste Auösung bietet. Sie ermöglicht die Herstellung von komplexen Mikrometer großen Strukturen aus einem Pho- topolymermaterial. Die Technologie basiert auf dem nichtlinearen Eekt der Zwei-Photon-Absorption, welcher ihr einen einzigartigen Vorteil über alle anderen Lithographiemethoden in Bezug auf die Vielseitigkeit und das Auf- lösungsvermögen verleiht. Ein stark fokussierten, Femtosekunden gepulster, nah-infrarot Laserstrahl, wird durch ein üssiges Photopolymer bewegt, welches bei der fundamentalen Laserellenlänge vollständig transparent ist. Aufgrund der extrem hohen Lichtintensität in dem dreidimensionalen La- serfokus, dem sogenannten Voxel, kommt es zu Zwei-Photonen-Absorption, wodurch das Material selektiv belichtet wird. Daraus resultiert, dass beliebi- ge dreidimensionale Strukturen hergestellt werden können, indem man den Laserstrahl entlang einer festgelegten Trajektorie durch das Polymer bewegt. Es hat sich gezeigt, dass Femtosekunden 3D Druck in der Lage ist qualitativ hochwertige, komplexe mikro-optische Elemente herzustellen, die für eine Vielzahl von möglichen Anwendungen verwendet werden können. Beispiele beinhalten, sind aber nicht beschränkt auf: Beleuchtungsoptiken, asphäri- sche, torische und Freiformlinsen, Strahl-formende Optiken, photonische Kristalle, Wellenleiter und mehrlinsige Abbildungsobjektive. In dieser Arbeit erweitern wir das aufkommende Feld der 3D-gedruckten Mikro-Optiken umneueMaterialien, Herstellungsmethoden undAnwendun- gen. Dadurch überwinden wir Hürden, welche diese Technologie in der Ver- gangenheit maßgeblich eingeschränkt haben. Beispielsweise erweitern wir ix den Katalog an verfügbaren Materialien welche bislang fast ausschließlich auf durchsichtige Photopolymere beschränkt waren, indem wir Techniken zur Herstellung von undurchsichtigen Blenden entwickeln. Des Weiteren vergrößern wir die Bandbreite der verfügbaren optischen Eigenschaften von Femtosekunden 3D-druckbaren Materialien, indem wir neuartige Nanokom- positamaterialien herstellen. Außerdem untersuchen wir innovative neue Anwendungen des Femtosekunden 3D Drucks indem wir zwei Single-Mode fasergekopplete Lichtquellen entwickeln: eine Orbital Angular Momentum- und eine Einzelphotonen-Quanten-Lichtquelle. Abschließen analysieren wir unseren 3D-Herstellungsprozess in Bezug auf seine Ausrichtung- und Posi- tioniergenauigkeit um dessen Leistungsfähigkeit noch weiter zu verbessern. Unsere Arbeit beschreitet aufregende neue Wege in dem vielseitigen Feld des Femtosekunden Zwei-Photonen 3D Drucks, wobei mögliche An- wendungsfelder sich von Sensortechnologie, über die Miniaturisierung von Kameras, der Robotertechnik, und optischen Fallen, bis hin zu Quanten- kommunikationstechnologien erstreckt. Sie önet damit die Tür für viele weitere Entwicklungen und Einsatzmöglichkeit in den kommenden Jahren. x CON TEN TS 1 introduction 7 1.1 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 fundamentals 13 2.1 Multi-Photon Absorption . . . . . . . . . . . . . . . . . . . . 14 2.2 Two-Photon Polymerization . . . . . . . . . . . . . . . . . . 19 3 fabrication 35 3.1 Femtosecond 3D Printing Setup . . . . . . . . . . . . . . . . 35 3.2 Design and Printing Process . . . . . . . . . . . . . . . . . . 38 3.3 Sample Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 42 4 tailored nanocomposites 47 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 The Maxwell-Garnett-Mie Eective Medium Theory . . . . . 50 4.3 Nanocomposite Material Fabrication . . . . . . . . . . . . . . 50 4.4 Characterization of Optical Properties . . . . . . . . . . . . . 51 4.5 Fabrication Parameters for Nanocomposite Structures . . . . 54 4.6 Characteriziation of 3D Printed Nanocomposite Structures . 58 4.7 3D Printed Nanocomposite Imaging Lenses . . . . . . . . . . 62 4.8 Nanocomposite Based Achromatic Doublet . . . . . . . . . . 64 5 distortion-free hypergon wide-angle objective 67 5.1 Design and Fabrication . . . . . . . . . . . . . . . . . . . . . 68 5.2 Absorptivity of Aperture Stop . . . . . . . . . . . . . . . . . 71 5.3 Imaging Performance . . . . . . . . . . . . . . . . . . . . . . 74 6 electroless silver plating 77 6.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.2 Characterization of Ag Structures . . . . . . . . . . . . . . . 80 6.3 Femtosecond Laser Plated Beam-splitter . . . . . . . . . . . . 85 6.4 Femtosecond Laser Plated Plasmonic Antennas . . . . . . . . 86 6.5 Direct Laser Writing of a Metallic Aperture . . . . . . . . . . 88 7 orbital angular momentum light 93 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.2 Design of Spiral Phase-plates . . . . . . . . . . . . . . . . . . 94 7.3 OAM Light Generation . . . . . . . . . . . . . . . . . . . . . 96 8 fiber coupling of qantum light sources 101 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 xi 8.2 Design and Fabrication . . . . . . . . . . . . . . . . . . . . . 103 8.3 Quantum Dot Emitters . . . . . . . . . . . . . . . . . . . . . 107 8.4 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 9 positioning accuracy of 3d printing process 121 9.1 Lateral Positioning Accuracy . . . . . . . . . . . . . . . . . . 121 9.2 Positioning Accuracy of Fiber-Coupling System . . . . . . . 124 10 conclusion 133 11 outlook 137 a test targets 141 b fabrication parameters 145 List of Acronyms 153 List of Figures 159 List of Tabels 161 bibliography 163 acknowledgments 185 xii P UBL ICAT IONS Parts of this thesis and associated work have been published in scientic journals, have been submitted to a journal, are being prepared for publication, and/or have been presented at national and international conferences. journal publications P1 Marc Sartison, Ksenia Weber, Simon Thiele, Lucas Bremer, Sarah Fis- chbach, Thomas Herzog, Sascha Kolatschek, Michael Jetter, Stephan Reitzenstein, Alois Herkommer, Peter Michler, Simone L. Portalupi, and Harald Giessen "3D printed micro-optics for quantum technology: Optimized coupling of single quantum dot emission into a single mode ber", Light: Advanced Manufacturing 2, 6 (2021), DOI 10.37188/lam.2021.006. P2 Ksenia Weber, Daniel Werdehausen, Peter König, Simon Thiele, Michael Schmid, Manuel Decker, Peter William de Oliveira, Alois Herkommer, and Harald Giessen "Tailored nanocomposites for 3D printed micro-optics", Optical Materials Express 10, 2345 (2020), DOI 10.1364/OME.399392. P3 Lucas Bremer, Ksenia Weber, Simon Thiele, Michael Schmidt, Arsenty Kaganskiy, Sven Rodt, Alois Herkommer, Marc Sartison, Simone L. Por- talupi, Peter Michler, Harald Giessen, and Stephan Reitzenstein "Quantum dot single-photon emission coupled into single-mode bers with 3D printed micro-objectives", APL Photonics 5, 106101 (2020), DOI 10.1063/5.0014921. 1 https://doi.org/10.37188/lam.2021.006 https://doi.org/10.1364/OME.399392 https://doi.org/10.1063/5.0014921 P4 Ksenia Weber, ZhenWang, Simon Thiele, Alois Herkommer, and Harald Giessen "Distortion-free multi-element Hypergon wide-angle micro- objective by femtosecond 3D printing", Optics Letters 45, 2784 (2020), DOI 10.1364/OL.392253. P5 Ksenia Weber, Felix Hütt, Simon Thiele, Timo Gissibl, Alois Herkommer, and Harald Giessen "Singlemode ber based delivery of OAM light by 3D direct laser writing", Optics Express 25, 19672 (2017), DOI 10.1364/OE.25.019672. P6 Andrea Toulouse, Simon Thiele, Kai Hirzel, Michael Schmidt, Ksenia Weber, Maria Zyrianova, Harald Giessen, Alois Herkom- mer, and Michale Heymann "Wrapped femtosecond direct laser writing mode", Submitted to Optics Letters P7 Lucas Bremer, Carlos Jimenez, Simon Thiele, Ksenia Weber, Sven Rodt, Alois Herkommer, Sven Burger, Sven Hoeing, Harald Giessen, and Stephan Reitzenstein "Numerical optimization of single-mode ber-coupled single- photon sources based on semiconductor quantum dots", Submitted to Optics Express P8 Julian Schwab, Ksenia Weber, Lucas Bremer, Stephan Reitzenstein, and Harald Giessen "Coupling light emission of single photon sources into single mode bers", In preparation P9 Ksenia Weber, Simon Thiele, Mario Hentschel, Florian Sterl, Alois Hermkommer, and Harald Giessen "Positional Accuracy of Direct Laser Written Quantum Emitter Fiber Couplers", In preparation 2 https://doi.org/10.1364/OL.392253 https://doi.org/10.1364/OE.25.019672 publications not directly linked to this thesis P10 Asa Asadollahbaik, Simon Thiele, Ksenia Weber, Aashutosh Kumar, Johannes Drozella, Florian Sterl, Alois Herkommer, Harald Giessen, and Jochen Fick "Highly ecient dual-bre optical trappingwith 3D printed diractive Fresnel lenses", ACS Photonics 7, 88 (2020), DOI 10.1021/acsphotonics.9b01024. P11 Fatemeh Kiani, Florian Sterl, Tsoulos Tsoulos, Ksenia Weber, Harald Giessen, and Giulia Tagliabue "Ultra-broadband and Omni-directional Perfect Absorber based on Copper Nanowire/Carbon Nanotube Hierarchical Structure", ACS Photonics 7, 366 (2020), DOI 10.1021/acsphotonics.9b01658. P12 Qi Ai, Lili Gui, Domenico Paone, Bernd Metzger, Martin Mayer, Ksenia Weber, Andreas Fery, and Harald Giessen "Ultranarrow Second-Harmonic Resonances in Hybrid Plasmon-Fiber Cavities", Nano Letters 18, 366 (2020), DOI 10.1021/acs.nanolett.8b02005. P13 Maxim L. Nesterov, Martin Schäferling, Ksenia Weber, Frank Neubrech, Harald Giessen, and Thomas Weiss "Line-currentmodel for linear and nonlinear optical properties of thin elongated metallic rod antennas", Journal of the Optical Society of America B 35, 1482-1489 (2018), DOI 10.1364/JOSAB.35.001482. P14 Frank Neubrech, Christian Huck, Ksenia Weber, Annemarie Pucci, and Harald Giessen "Surface-Enhanced Infrared Spectroscopy using Resonant Nanoanten- nas", Chemical Review 117, 5110 (2017), DOI 10.1021/acs.chemrev.6b00743. P15 Ksenia Weber, Maxim L. Nesterov, Thomas Weiss, Michael Scherer, Mario Hentschel, Jochen Vogt, Christian Huck, Weiwu Li, Martin Dressel, Harald Giessen, and Frank Neubrech "Wavelength Scaling in Antenna-Enhanced Infrared Spectroscopy: To- wards the Far-IR and THz Region", ACS Photonics 4, 45 (2017), DOI 10.1021/acsphotonics.6b00534. 3 https://doi.org/10.1021/acsphotonics.9b01024 https://doi.org/10.1021/acsphotonics.9b01658 https://doi.org/10.1021/acs.nanolett.8b02005 https://doi.org/10.1364/JOSAB.35.001482 https://doi.org/10.1021/acs.chemrev.6b00743 https://doi.org/10.1021/acsphotonics.6b00534 P16 Shahin Bagheri, Ksenia Weber, Timo Gissibl, Thomas Weiss, Frank Neubrech, and Harald Giessen "Fabrication of Square-Centimeter Plasmonic Nanoantenna Arrays by Femtosecond Direct Laser Writing Lithography: Eects of Collective Excitations on SEIRA Enhancement", ACS Photonics 2, 779 (2015), DOI 10.1021/acsphotonics.5b00141. conference contributions as presenting author C1 Ksenia Weber, Lucas Bremer, Sarah Fischbach, Simon Thiele, Mario Hentschel, Marco Schmidt, Arsenty Kaganskiy, Sven Rodt, Alois Herkommer, Marc Sartison, Simone L. Portalupi, Peter Michler, Stephan Reitzenstein, and Harald Giessen", "Quantum Dot Single-Photon Emission Coupled into Single-Mode Fibers with 3D Printed Micro-Objectives" CLEO Technical Conference, All-Virtual (2021), Conference presentation. C2 Ksenia Weber, Peter König, Simon Thiele, Alois Herkommer, Peter William de Oliveira, and Harald Giessen "High Index Materials for Femtosecond 3D Printing of Complex Micro-Optics", 83th Annual Meeting of the DPG and DPG Spring Meeting, München, Germany (2019), Conference presentation. C3 Ksenia Weber, Simon Thiele, Simon Ristok, Mario Hentschel, Alois Herkom- mer, and Harald Giessen "Coupling Single Mode Fibers to Single Quantum Emitters with Fem- tosecond 3D Printing Technology", 82th Annual Meeting of the DPG and DPG Spring Meeting, Erlangen, Germany (2018), Conference presentation. C4 Ksenia Weber, Simon Thiele, Timo Gissibl, Alois Herkommer, Simon Ristok, and Harald Giessen "Complex micro- and nano-optics by femtosecond 3D printing", ad3pa | International Workshop on Advanced 3D Patterning, Dresden, Germany (2017), Conference presentation. 4 https://doi.org/10.1021/acsphotonics.5b00141 C5 Ksenia Weber, Maxim L. Nesterov, Thomas Weiss, Michael Scherer, Mario Hentschel, Jochen Vogt, Christian Huck, Weiwu Li, Martin Dressel, Harald Giessen, and Frank Neubrech "Resonant Plasmonic Antenna-Enhanced Far-IR and Terahertz Spec- troscopy", 81th Annual Meeting of the DPG and DPG Spring Meeting, Dresden, Germany (2017), Conference presentation. C6 Ksenia Weber, Frank Neubrech, Michael Scherer, Mario Hentschel, and Harald Giessen "Towards Surface-Enhanced Terahertz Spectroscopy", 7th International Workshop on Terahertz Technology and Applications, Kaiser- slautern, Germany (2016), Conference presentation. C7 Ksenia Weber, Frank Neubrech, Mario Hentschel, Michael Scherer, and Harald Giessen "Towards Resonant Plasmonic Antenna-Enhanced Terahertz Spec- troscopy", 80th Annual Meeting of the DPG and DPG Spring Meeting, Regensburg, Germany (2016), Conference presentation. selected conference contributions as co-author C8 Asa Asadollahbaik, Simon Thiele, Ksenia Weber, Aashutosh Kumar, Johannes Drozella, Florian Sterl, Alois Herkommer, Jochen Fick, and Harald Giessen "Ecient mirco- and nanoparticle trapping by improved optical ber tweezers using 3D printed diractive optical elements", Optical Trapping and Optical Micromanipulation XVII, (2020), Conference pre- sentation C9 Asa Asadollahbaik, Simon Thiele, Ksenia Weber, Aashutosh Kumar, Johannes Drozella, Florian Sterl, Alois Herkommer, Jochen Fick, and Harald Giessen "Improved optical ber tweezers using 3D printed Fresnel lenses", Nanophotonics VIII, (2020), Conference presentation C10 Shahin Bagheri, Ksenia Weber, Timo Gissibl, Thomas Weiss, Frank Neubrech, and Harald Giessen "Fabrication of plasmonic nanoantennas by femtosecond direct laser writing lithography for surface-enhanced infrared absorption", META’15, the 6th International Conference on Metamaterials, Photonic Crystals and Plasmonics, New York, USA (2015), Conference poster presentation 5 C11 Shahin Bagheri, Ksenia Weber, Timo Gissibl, Frank Neubrech, and Harald Giessen "Fabrication of plasmonic nanoantennas by femtosecond direct laser writing lithography -eects of near eld coupling on SEIRA enhance- ment", Radio Science Conference (URSI AT-RASC), Gran Canaria, Spain (2015), Confer- ence presentation C12 Frank Neubrech, Shahin Bagheri, Ksenia Weber, Timo Gissibl, and Harald Giessen "Fabrication of plasmonic nanoantennas by femtosecond direct laser writing lithography - eects of near eld coupling on SEIRA enhance- ment", 79th Annual Meeting of the DPG and DPG Spring Meeting, Berlin, Germany (2015), Conference presentation C13 Frank Neubrech, Shahin Bagheri, Ksenia Weber, and Harald Giessen "Fabrication of plasmonic nanoantennas by femtosecond direct laser writing lithography - eects of plasmonic coupling on SEIRA enhance- ment", The 5th International Topical Meeting on Nanophotonics and Metamaterials, Seefeld (Tirol), Austria (2015), Conference poster presentation 6 1 I N TRODUCT ION Additive manufacturing, or 3D printing, is the fabrication of a three- dimensional object from a digital model by sequentially depositing, joining or solidifying a material, usually done in a layer-by-layer fashion. In contrast to subtractive manufacturing techniques that rely on the removal of material from a solid block, e.g., via cutting, boring, drilling or grinding, 3D printing oers a much higher degree of design freedom. This enables the production of highly complex parts that would otherwise be impossible or extremely time- and cost-intensive to produce. Therefore, the technology opens entirely new doors in engineering and manufacturing. This includes applications like rapid prototyping, casting patterns and custom manufac- turing.[1] Figure 1.1.Hollow buckyball with rod structure inside. CADmodel (left) and 3D printed part produced with femtosecond two-photon 3D printing (right). The diameter of the printed buckyball is 400 μm. 7 introduction Multi-photon femtosecond lithography is an additive manufacturing tech- nology that enables the fabrication of complex three-dimensional structures on the micro- and nanometer scale.[2–7] A photosensitive material is ex- posed by a femtosecond-pulsed laser via a multi-photon absorption process. Since this non-linear optical eect is conned to the volumetric focal spot of the laser beam (the so called ’voxel’), arbitrary three-dimensional structures can be created by moving the focus through the resist. Figure 1.1 highlights the immense capabilities of the approach by presenting a 3D printed hollow buckyball encapsulating a rod structure. The ball is less than half a millimeter (400 μm) sized in diameter, with a minimum feature size of less than 10 μm. The top part of the rod is larger than the openings of the buckyball and contains several undercuts. This makes it impossible to create an equivalent structure via subtractive methods even at a much larger scale. To this day, no other technology is capable of reproducing such a design. Multi-photon lithography and especially its most commonly applied ver- sion two-photon lithography, which is also referred to as femtosecond 3D printing, has gained a lot of traction in recent years. Possible applications range from cellular tissue engineering,[8–10] over micro-uidics [11–13] and micro-mechanics,[14–16] all the way to micro-optics.[17–21] The lat- ter category more specically includes the fabrication of photonic crys- tals,[22–26] phase-plates,[27–30], optical waveguides,[26, 31, 32] as well as sub-millimeter sized imaging [33–35] and illumination optics.[36, 37] Such micro-optical elements, which are the focus of this thesis, play an important role in many real-world applications like sensing and camera miniaturiza- tion. Furthermore, they are highly desirable components for state-of-the-art technologies like self-driving cars, robotics and quantum communication which hold the potential to revolutionize the industries of tomorrow. Due to the additive nature of the 3D printing process, two-photon lithography possess an inherent advantage over other fabrication methods. Restrictions and challenges that are present in classical lens grinding techniques, like the manufacturing of aspheric or free-form surfaces, do not apply. Furthermore, alignment and assembly of multi-element systems becomes unnecessary, since all components can be printed in just one step. This makes two-photon lithography the ideal tool to produce complex micro-optical devices. So far, it has been demonstrated that micro-optical elements printed with femtosec- ond two-photon lithography possess excellent optical performance,[34, 38, 39] exhibiting high transparency,[40] shape accuracy,[40, 41] and surface quality with roughnesses on the order of just 10 nm.[41] However, in order to fulll the diverse demands of the manifold potential applications, a vast array of fabrication methods and materials still has to be developed. 8 introduction One of the biggest drawbacks of femtosecond 3D printing so far is the lim- ited amount of available materials. In classical optics, designers can choose from a large selection of glasses which all exhibit dierent optical prop- erties (refractive index, Abbe number, etc.). Besides that, components like apertures, lens tubes or mirrors are standard features of classical objective design. In the meantime, femtosecond 3D printing relies almost exclusively on transparent photopolymers whose optical properties only cover a very narrow range. Furthermore, due to the immense exibility of the approach, countless possible scientic applications remain yet to be explored. Figure 1.2. Microscope images representing some of the key results pre- sented in this thesis. (a) Spiral phase-plate on an optical ber enabling single- mode ber based delivery of orbital angular-momentum light. (b) Opaque metal aperture on a micrometer sized imaging lens directly printed via electroless metal plating. (c) Optical ber holder printed on a semiconductor quantum dot sam- ple. (d) Sub-millimeter sized wide-angle objective containing an integrated light- blocking aperture created via shadow evaporation. (e) Focusing lens on the tip of an optical ber used to couple single-mode bers to quantum emitters. (f) Images of spherical imaging lenses printed from dierent nano-composite materials. The nano-particle concentration (given at the bottom of each frame) and the refractive index increase from left to right. 9 introduction In this thesis, we develop new materials, methods and applications for 3D printed micro-optics produced via femtosecond two-photon lithography. Figure 1.2 illustrates the scope of this thesis by presenting some of the key results of our work. Figure 1.2a, 1.2d and 1.2f represent the materials and methods part of this thesis. Here we can see highly opaque apertures integrated into 3D printed micro-objectives via electroless metal plating (Figure 1.2b) and electron-beam shadow evaporation (Figure 1.2d). In Fig- ure 1.2f, we see a striking illustration of how the optical property restrictions of photopolymers were overcome. Shown are the images of four otherwise identical spherical imaging lenses printed from dierent nanocomposite materials. Those composites are a mixture of a conventional photopolymer and high-index nano-particles. As the concentration of nanoparticles in- creases from left to right, the refractive index of the material rises, resulting in a reduction of the image size. In the remainder of the gure, we see exemplary images representing the novel applications explored within this work. Figure 1.2a and Figure 1.2e show micro-optical components that were directly printed onto the tip of single-mode bers. On the one hand, we see a spiral phase-plate pattern that enables the straightforward ber based delivery of orbital-angular momentum light in Figure 1.2a. On the other hand, a numerical aperture matched focusing lens used to couple quantum emitters to single-mode bers is presented in Figure 1.2e. The corresponding 3D ber holder used to precisely mount and align the ber to the emitter is shown in Figure 1.2c. Together, these images represent not only the large range of diverse topics covered within this thesis, but also the versatility of femtosecond 3D printing in general. 1.1 thesis outline In this thesis, we present new materials, methods and applications for micro-optical systems produced with femtosecond 3D printing. The thesis starts with a theory section that introduces fundamental concepts underly- ing the fabrication process like multi-photon absorption and two-photon polymerization in Chapter 2. Chapter 3 includes a detailed description of the 3D printing setup and process from the design to the nished part. In Chapter 4, we present novel nano-composite materials, as a way to overcome the restriction in terms of optical properties that are opposed 10 1.1 thesis outline by conventional photopolymers. We demonstrate that these materials are suitable to print high performance micro-optics and that their optical properties are deterministically adaptable by controlling the concentration of nano-particles. In Chapter 5, we present a multi-lens wide-angle Hypergon objective at a sub-millimeter scale with an integrated light-blocking aperture. Dierent approaches based on shadow evaporation are shown and compared to each other. Excellent and distortion free wide-angle imaging performance is achieved. In Chapter 6, we introduce electroless metal plating, as a way to directly print metallic structures using two-photon lithography. We investigate dierent possibilities of how such structures can be utilized in micro-optical systems. This includes the creation of directly printed metal apertures, beam splitters, mirrors and even plasmonic nanoantennas. In Chapter 7, delivery of orbital angular-momentum light by a single- mode ber is shown. To this end, a staircase phase-plate is 3D printed onto the end of an optical ber. Light that exits the ber, passes the phase-plate and picks up varying degrees of orbital-angular momentum (𝑙 = 1, 𝑙 = 2, 𝑙 = 3). In Chapter 8, we present a new concept for an integrated quantum light source enabled by two-photon lithography. An optical ber holder is 3D printed onto a semiconductor quantum dot sample. A two-lens micro-optical system is designed to eciently guide the emission of the quantum dot into the single mode-ber yielding a highly compact, integrated device. Finally, in Chapter 9, we address the alignment accuracy of our 3D printing process which plays a major role in ecient ber-coupling of small emitters like quantum dots. In the end, we discuss ways to mitigate these errors in the future. 11 2 F UNDAMEN TALS When Maria Göppert-Mayer rst wrote about "an absorption event caused by the collective action of two or more photons, all of which must be present simultaneously to impart enough energy to drive a transition" in her 1931 doctoral dissertation titled "Über Elementarakte mit zwei Quan- tensprüngen",[42] it was merely a theoretical concept. It should take over 30 years and the invention of an entirely new light source, the laser, until multi-photon absorption was rst experimentally veried. In 1961, Kaiser and Garrett rst detected two-photon uorescence in a europium-doped crys- tal.[43] Another twenty years later, in 1981, manufacturing of 3-dimensional structures from photopolymers emerged when Hideo Kodama invented a new layered approach to stereolithography.[2] After that, it did not take researchers quite as long anymore to realize that multi-photon absorption oered immense advantages to 3D structuring, enabling unknown design freedom and sub-diraction limited resolution. It was in 1997, when Maruo et al. presented three-dimensional microfabrication with two-photon-absorbed photopolymerization [3] to the world - the technology that is the very basis of this thesis. In this chapter, we give an overview of the fundamental principles un- derlying femtosecond two-photon 3D printing. To this end, multi-photon absorption in general and two-photon polymerization in particular are dis- cussed in detail. 13 fundamentals 2.1 multi-photon absorption The underlying mechanism of femtosecond 3D printing is multi-photon absorption (MPA). MPA is a non-linear optical process during which an energy transition is driven by two or more photons. The most common form of MPA used in 3D printing and the one utilized in this work, is two-photon absorption (TPA). A general illustration of this process is shown in Figure 2.1. Two photons with energies ℎ𝜈1 and ℎ𝜈2 are absorbed simultaneously and induce an electronic transition form the ground state |𝑔〉 to an excited state |𝑒2〉 of the same parity. The absorption can be followed by a non-radiative deexcitation to a lower energetic state |𝑒1〉 and a subsequent uorescent emission at an energy ℎ𝜈3 < ℎ𝜈2 +ℎ𝜈1. This phenomenon is known as two photons excited uorescence and is also illustrated in Figure 2.1. Figure 2.1. Typical energy level scheme of two-photon absorption (TPA). Red and green arrows represent the two photons that are (almost simultaneously) absorbed during the (non-degenerate) two-photon absorption process with energies ℎ𝜈1 and ℎ𝜈2. |𝑔〉 is the ground state, while |𝑒1〉 and |𝑒2〉 denote excited states of the molecule. Here, |𝑔〉 → |𝑒2〉 is the two-photon allowed transition. In general, there are two types of TPA: degenerate and non-degenerate. In the degenerate case, the two photons, which are absorbed, are of the same frequency. In the non-degenerate case, the photons exhibit dierent frequencies. Furthermore, absorption of two (or more) photons can take place either sequentially or simultaneously. In the case of sequential TPA, the excitation takes place via a real intermediate state. This, however, im- plies that the respective material is absorptive at the photon’s wavelength. As a result, sequential TPA is merely a surface eect which follows the 14 2.1 multi-photon absorption Beer–Lambert law.[44] It is thus not relevant for the volumetric 3D fabri- cation techniques described in this thesis. In simultaneous TPA however, excitation takes place via a virtual state, since no resonant intermediate state exists at the respective energy level. The material is thus transparent at the light’s frequency and the photons can therefore penetrate deeply into it. Since virtual states have extremely short lifetimes, the two-photon absorption process can only be completed if a second photon arrives (al- most) simultaneously. In order for this to happen at a substantial rate, very high light intensities are necessary. Two-photon femtosecond 3D printing, which is the focus of this thesis, is based on the degenerate, simultaneous two-photon absorption process. There are various technical applications which rely on TPA, including laser-spectroscopy,[45] two-photon (confo- cal) microscopy,[46] up-converted lasing,[47] autocorrelation based pulse characterization,[48] and most importantly in relation to this work, micro- fabrication which includes the printing of three-dimensional structures via two-photon polymerization.[4, 49, 50] The scaling laws of TPA can be obtained by the following considerations: When an electric eld 𝐸 permeates a material, it induces a polarization 𝑃 that can be described by a Taylor series expansion as: 𝑃 = 𝑃0 + 𝜒 (1)𝐸 + 𝜒 (2)𝐸2 + 𝜒 (3)𝐸3 +… (2.1) where 𝜒𝑖 is the 𝑖-th order susceptibility. This susceptibility is a complex quantity that is composed of its real part, the (nonlinear) refraction 𝜒 (𝑖) 𝑟𝑒𝑎𝑙 and its imaginary part, the (nonlinear) absorption 𝜒 (𝑖) imag. In general, Equation 2.1 is a tensor equation. Here however, it is written in its scalar form for simplicity. We now consider the optical theorem [51] which relates the imaginary part of an all-optical process of perturbation order 𝑗 to a process involving charge carriers of perturbation order 𝑗/2.[52] In perturbation theory, the order of a 𝜒 (𝑖) process is 𝑗 = 𝑖 + 1 (with 𝑖 being the order of the susceptibility). TPA is a second order electronic transition process, meaning that 𝑗/2 = 2 and thus 𝑖 = 𝑗 − 1 = 3. One can therefore conclude that TPA is related to the third order susceptibility 𝜒 (3) of a material. TPA is closely related to Raman scatting, as both are third order non- linear processes. In fact, the relationship between the selection rules of Raman and IR spectroscopy is the same as for the selection rules between one- and two-photon absorption. In the case of centrosymmetric molecules this means that one- and two-photon absorption allowed transitions are mutually exclusive. This can easily be understood by recalling the fact that 15 fundamentals the two states involved in a TPA process are of the same parity. A transition between these states is therefore not a dipole transition and would thus be forbidden in one-photon absorption. Since two molecular states are either of the same or of opposite parities, any possible transition is either one- or two-photon allowed but never both. In non-centrosymmetric molecules however, selection rules can be more complex. Next, we want to discuss the energy absorption in a two-photon ab- sorption process. In general, the energy exchange rate of a light matter interaction per volume is given by: 𝑑𝑊 𝑑𝑡 = 〈𝑬 · 𝑷〉 (2.2) From this we can conclude that the energy absorption rate of a (degenerate) TPA process is given by:[53] 𝑑𝑊 𝑑𝑡 = 8𝜋2𝜔 𝑛2𝑐2 𝐼 2 · 𝐼𝑚 ( 𝜒 (3) ) , (2.3) where 𝐼 and 𝜔 are the incident light’s intensity and frequency respectively, 𝑛 is the refractive index of the material and 𝑐 is the speed of light in vacuum. Here we can see and important nding, namely that the TPA rate depends quadratically on the light’s intensity. Furthermore, we learn that the capabil- ity of a material to exhibit TPA mainly depends on its 𝐼𝑚(𝜒 (3) ) value. This quality is called the TPA cross section 𝜎2 and is dened by the number of photons 𝑛photons absorbed per time: 𝑑𝑛photons 𝑑𝑡 = 𝜎2𝑁𝐼 2 ℎ2𝜈2 . (2.4) Here, 𝑁 is the density of the molecules the material is composed of. The two-photon absorption cross section 𝜎2 in units of cm4/GW can thus be written as: 𝜎2 = 8𝜋2ℎ𝜈2 𝑛2𝑐2 𝐼𝑚 ( 𝜒 (3) ) . (2.5) Alternatively, 𝜎2 can be expressed in units of GM (Göppert-Mayer), which is a tribute to Maria Göppert-Mayer. This is done via multiplication with the photon energy ℎ𝜈 : 𝐺𝑀 = 10−50 cm4/photon ·molecule (2.6) 16 2.1 multi-photon absorption A value of 1GM means that given a photon ux of 1 photon per second and 1 cm2 in a material with density of 1 molecule per cm3, 1050 photons will be absorbed over a distance of 1 cm.[54] The magnitude of 𝜎2 for a given molecule can be estimated based on the one-photon absorption cross-section 𝜎1 which is approximately identical to the geometrical cross-section (𝛥𝑆 ≈ 10−16 cm−2),[55] and the estimated lifetime of a virtual state 𝜏𝑉𝑆 ≈ 10−16 s.[56] The TPA cross section is then given by 𝜎𝑁 = 𝜎2 1𝜏VS [cm4s] ≈ 10−48.[57] Likewise, one can conclude that the probability ratio of TPA and three-photon absorption (3PA) is on the order of 10−32 cm2s. This shows that TPA is by far the most likely multi-photon absorption process. Next, we want to discuss the non-linear absorption coecient 𝛼 . Similarly to the polarization, this quality can be described by a Taylor series expansion: 𝛼 = 𝛼0 + 𝛼2𝐼 + 𝛼3𝐼 2 +…, (2.7) where 𝛼0, 𝛼2 and 𝛼3 are the linear, TPA and 3PA absorption coecients respectively and 𝐼 is the intensity of the light. The TPA coecient can be written in terms of the TPA cross section as: 𝛼2 = 𝜎2𝑁𝐴𝑑0 · 10−3 ℏ𝜔 , (2.8) with the Avogadro number 𝑁𝐴, the molar concentration 𝑑0 [𝑚𝑜𝑙/𝑑𝑚3] and the photon energy ℏ𝜔 . Whereas, the 3PA coecient can be written as: 𝛼3 = 𝜎2 · 10−32𝑁𝐴𝑑0 · 10−3 (ℏ𝜔)2 . (2.9) Higher order absorption coecients become relevant only for light inten- sities above 10 TW/cm2. However, since this value is far above the optical damage threshold of most dielectric materials, they can here be neglected.[57, 58] One should also note that at such high light intensities, dierent interac- tion eects take place. At high laser intensities and low frequencies, electrons can be excited via tunneling ionization.[59] In this case, the potential energy barrier of the molecule gets distorted by the strong laser eld in such a way that electrons can tunnel through it. The probability of each of these processes (MPA and tunneling ionization) can be obtained from the Keldysh paramater:[60] 𝛾 = 𝜔 𝑒 √︂ 𝑚𝑒𝑐𝑛𝜖0𝐸𝑔 𝐼 , (2.10) 17 fundamentals where 𝜔 is the laser frequency, 𝐼 is the laser intensity,𝑚𝑒 is the electron eective mass, 𝑒 is the fundamental electron charge, 𝑐 is the speed of light, 𝑛 is the refractive index of the material, 𝜖0 is the permittivity of free space and 𝐸𝑔 is the bandgap of the dielectric material. Based on this parameter, two dierent regimes can be identied. If 𝛾 > 0.5, tunneling ionization is more likely to occur, while in the case of 𝛾 < 0.5, MPA is more likely to occur. As one can see, the Keldysh parameter increases with the square-root of the intensity, making tunneling ionization more likely to become the dominant process at extremely high intensities. Here, we are only interested in cases where 𝛾 < 0.5 and thus MPA is the dominating force. Comparing Equations 2.8 and 2.9, we can once again see that the proba- bility of TPA far exceeds that of 3PA. Interestingly, under the right circum- stances, even the human eye is capable to see ultra short infra-red laser pulses, due to TPA processes taking place in the retina.[61] In contrast to that, 3PA typically requires extremely high light intensities above 100GW/cm2 to become signicant.[55] Therefore, applications that rely on MPA pro- cesses are mostly based on TPA, while applications of 3PA processes are less common. This includes the femtosecond 3D printing processes that this thesis is based on. In the following section, we will therefore focus on TPA as the trigger for photo-polymerization. 18 2.2 two-photon polymerization 2.2 two-photon polymerization Two-photon polymerization (TPP) is a photochemical process that relies on two-photon absorption. The technique is illustrated in Figure 2.2. A high numerical aperture (NA) microscope objective tightly focuses a femtosecond (fs) pulsed near infra-red (NIR) laser beam into a liquid photopolymer. There, two photons are absorbed simultaneously leading to a chemical reaction that solidies the previously liquid material. Figure 2.2. Principle of two-photon polymerization. Energy level diagram illustrating two-photon and one-photon absorption. (left) Scheme of two-photon polymerization process of a photopolymer via a fs-pulsed NIR laser beam. (right) Polymerization Process The materials used in TPP applications are usually negative photoresist. This means that parts that were exposed by light become insoluble to the photoresist developer (a chemical solvent), whereas for a positive photore- sist, the exposed parts become soluble to the developer. A scheme of the basic polymerization process is illustrated in Figure 2.3 by the example of polystyrene formation. During this specic polymerization reaction, the carbon-carbon 𝜋-bonds of the vinyl group are broken and replaced by new carbon-carbon 𝜎-bonds with another styrene monomer, resulting in a styrene chain (polystyrene). In general, a photopolymer (also known as a photoresist) is a substance that changes its physical properties when exposed to light - typically in 19 fundamentals Figure 2.3. Principle of polymerization illustrated by the creation of polystyrene. During the polymerization process, individual styrene monomers interconnect to form a polystyrene molecule. Figure based on Ref. [62]. the UV range. In classical one-photon polymerization (1PP) processes, a photoinitiator (PI) absorbs one UV photon through linear absorption. This mechanism is used in many well-known applications like UV- and stereo- lithography. Due to the absorptivity of the photoresist at UV wavelengths, the light can only penetrate a few micrometers into the resist,[7] making those processes inherently planar. In the case of UV-lithography, only 2.5 dimensional structures can be fabricated.[63, 64] Stereo-lithography on the other hand is a 3-dimensional layer-by-layer process. However, it requires fresh resin to be coated onto the top of the 3D printed structure for every new layer.[65] In the case of TPP however, the photopolymer is transparent at the laser’s fundamental wavelength, enabling it to deeply penetrate into the resist and setting the technology apart from 1PP based techniques. Due to the quadratic dependence of the energy transfer rate on the light’s intensity (see Equation 2.22) and the small TPA cross-section of most materials, only the focus of the laser beam actually exposes the photopolymer.[7] There, a combination of the extremely high peak intensities of fs-pulsed laser light (TW/cm2) and the tight focusing of the high NA objective, results in light intensities that are sucient for TPA to take place at a substantial rate. This volume around the laser focus is known as the voxel, which is short for volume pixel. The exact shape and size of the voxel depend on the process parameters and is discussed in detail in Section 2.2. By moving the voxel through the photoresist, complex 3-dimensional (3D) structures can be created (see Figure 2.4 for an illustration). 20 2.2 two-photon polymerization Figure 2.4. Scheme of direct laser writing.A 3-dimensional structure is created in a liquid photopolymer by moving the focus of a fs-pulsed laser beam through the resist. The chemical reaction that takes place during TPP can be broken down into three individual processes that are described by the following three rate equations:[66] PI 2ℎ𝜈𝑁𝐼𝑅−−−−−→ R· + R· (2.11) R· +M −−−→ RM· M−−−→ RMM·… M−−−→ RM𝑛 · (2.12) RM𝑛 · + RM𝑚 · −−−→ RM𝑛+𝑚R (2.13) In the rst step, represented by Equation 2.11, the PI simultaneously absorbs two NIR photons with energy ℎ𝜈NIR. The PI consequently decomposes to radicals (R·), which are highly reactive molecules with unpaired valence elec- trons (the "·" here represents the unpaired electron). This step is known as the initialization process. In the case of 1PP, only one photon with an energy level in the UV range is absorbed instead. In the second step (Equation 2.12) the radicals react with 𝑛-number of monomers (M), creating monomer radi- cals (RM𝑛 ·). These monomer radicals then combine with other monomers 21 fundamentals in a chain reaction. This step is known as the propagation process. At some point, two dierent monomer radicals RM𝑛 · and RM𝑚 · combine, forming a complete polymer chain RM𝑛+𝑚R (see Equation 2.11). Since there are no more unpaired valence electrons after this combination, the chain reaction comes to an end. This step is therefore known as the termination process. Due to the change in chemical structure, photopolymers shrink in size during polymerization. This leads to a deviation in shape of the 3D printed part com- pared to the computer model.[67, 68] Depending on the requirements of the applications, these deviations might have to be considered and the printed shape might have to compensate for the shrinkage. Since this is typically a non-trivial task, low-shrinkage photopolymers are highly desirable.[69] Here we should say that while the chemical reactions during polymer- ization are the same for 1PP and TPP, one should always keep in mind that fundamentally, these are dierent processes. TPP relies on the use of fs-pules laser light, while 1PP is typically performed with a UV lamp, a cw- or a long-pulsed laser. This can lead to notable dierences when comparing one-photon with two-photon exposed polymer structures, for example in regards to the optical properties.[70] Polymerization Threshold In order to be initiated, the polymerization process requires a certain con- centration of radicals being created in the photoresist. This means that given a specic irradiation time, there is a threshold of the laser intensity that needs to be surpassed to polymerize the resist. Figure 2.5 illustrates this concept. Here, we assume the irradiation laser to exhibit a perfect Gaussian beam prole. Due to the quadratic dependence of the absorption rate 𝑑𝑊 /𝑑𝑡 on the laser intensity 𝐼 (see Equation 2.3), we actually need to consider the intensity squared (𝐼 2) distribution of the beam, which is simply another Gaussian distribution with a narrower width. Therefore, TPP exhibits a smaller polymerization region than 1PP, resulting in an inherently higher resolution. Additionally, the threshold behavior of the photopolymer contributes to even smaller attainable feature sizes. As a result, femtosecond 3D printing can achieve resolutions far beyond the diraction limit.[71–73] 22 2.2 two-photon polymerization Figure 2.5. Light intensity (𝐼 ) and intensity squared (𝐼 2) of a Gaussian beam (𝐼 (𝑟 ) = 𝐼0𝑒𝑥𝑝 (−2𝑟 2/𝜔2 0)). The amplitude is set to 𝐼0 = 1 and the beam waist is 𝜔0 = 0.6. The dashed line marks the polymerization threshold. Above this value, photopolymerization takes place. The rectangles highlight the polymerized region for one-photon polymerization (1PP, blue) and two-photon polymerization (TPP, red). Resolution of Two-Photon Lithography The shape and dimension of the voxel play a crucial role in two-photon lithography, as it greatly inuences many important parameters, such as the resolution, the achievable writing speed and the surface roughness. There- fore, knowledge about the size of the voxel is of high interest. Voxels created by a focused Gaussian beam basically resemble an elongated spinning el- lipsoid with its lateral diameter 𝑑 being smaller than its axial length 𝑙 (see Figure 2.6).[74] In order to obtain an analytical expression for the voxel dimensions, we rst assume our writing laser to exhibit a Gaussian beam prole: 𝐼 (𝑟 , 𝑧) = 𝐼0 ( 𝜔2 0 𝜔 (𝑧)2 ) 𝑒 −2𝑟2 𝜔 (𝑧)2 (2.14) Here, 𝐼0 is the photon ux intensity at the center of the beam (𝑟 = 0, 𝑧 = 0),𝜔0 is the beamwaist and𝜔 (𝑧) is the radius of the beam at a propagation distance 𝑧, with 𝑧 = 0 located at the center of the beam. We should note that in reality, objective lenses contain apertures that block the outer parts of the laser beam leading to a deviation from the perfect Gaussian shape. However, these 23 fundamentals Figure 2.6. Longitudinal beam prole of focused Gaussian laser beam. Dashed white lines highlight the beam width. Solid white line highlights the TPP region (voxel). deviations are small enough to still consider the created focal spot intensity distributions to be approximately Gaussian.[75] Substantial deviations can occur due to self-focusing eects when lamentation arises.[76] However, since two-photon 3D printing is impossible to conduct under such conditions, we will not consider these cases here. Please note that in Equation 2.14 𝐼 (𝑟 , 𝑧) is the photon ux intensity. The regular light intensity that measures the power 𝑃 per area 𝐴 for a pulsed laser beam, which we will here call 𝐼 ∗, can be expressed as: 𝐼 ∗ = 𝑃 𝐴 = 𝐸 𝐴𝜏 W cm2 (2.15) with 𝐸 being the pulse energy, 𝜏 being the pulse width (full width at half maximum (FWHM) of the optical power versus time), ℎ being the Planck’s constant and 𝜈 = 𝑐/𝜆 being the frequency of the light. The photon ux intensity, which measures the number of photons per time and area is in turn given by:[77] 𝐼 = 𝐸 𝐴𝜏ℎ𝜈 photon cm2 · s . (2.16) Next, we consider the beam to be propagating along an optical axis 𝑧. This is illustrated in Figure 2.7. From Equations 2.14, 2.18 and 2.19 we can conclude 24 2.2 two-photon polymerization Figure 2.7. Radius of Gaussian beam 𝜔 as a function of the distance along the propagation direction 𝑧, as denoted in Equation 2.18.Here,𝜔0 is the beam waist, 𝑧𝑅 is the Rayleigh range, as given by Equation 2.19, 𝜃 is the total angular spread and 𝑏 is the depth of focus. Dashed blue lines represent the wavefronts at dierent 𝑧 positions. The inset shows the intensity distribution 𝐼 (𝑟 ) (see Equation 2.14), at a given 𝑧 position. that the shape of such a propagating Gaussian beam with wavelength 𝜆 can be fully described with knowledge of just one parameter: the beam waist 𝜔0. For a focused beam, this value is usually approximated by the expression 𝜔0 = 0.61𝜆/NA), based on the Rayleigh criterion. However, since TPP relies on high-NA microscope objectives (NA > 1), this relation is no longer valid, as the paraxial approximation cannot be applied. Instead, one can estimate the beam waist as follows:[78] 𝜔0 = 𝜆 𝜋NA √ 𝑛2 −𝑁𝐴2, (2.17) where 𝑛 is the refractive index of the immersion medium. In the case of dip-in lithography, which is mostly used throughout this thesis, this means the refractive index of the liquid photopolymer. The beam radius of a Gaussian beam at any position 𝑧 is then given by:[78] 𝜔 (𝑧) = 𝜔0 √︄ 1 + ( 𝑧 𝜋𝜔2 0 )2 , (2.18) and the Rayleigh length, which is dened as the distance along the propa- gation direction (measured from the waist), in which the laser beam’s area cross-section doubles is given by 25 fundamentals 𝑧𝑅 = 𝜋𝜔2 0 𝜆 . (2.19) Now that we can fully describe the behavior of the focused laser beam, we next have to consider the light intensity distribution around the focal spot. Based on Equation 2.16, we can estimate the average photon ux intensity in the focal plane to be: 𝐼f = 𝑃 𝜋𝜔2 0𝜏 𝑓 ℎ𝜈 (2.20) where 𝑃 = 𝐸/𝑓 is the average power and 𝑓 is the repetition rate of the pulsed laser beam. We here used the fact that in the focal plane, the beam radius is given by the beam waist 𝜔0 and thus the cross-section area of the beam in the focal plane is given by 𝐴 = 𝜋𝜔2 0 . The relationship between 𝐼0 and 𝐼f can then be expressed as:[79] 𝐼0 = 2𝑒2 𝑒2 − 1 𝐼f ≈ 2.3𝐼f (2.21) We can thus estimate 𝐼0, the peak intensity of the photon ux in the focal plane, with the simple knowledge of the basic laser parameters 𝑃 ,𝜏 , 𝑓 and 𝜆, as well as the NA of the utilized microscope objective and the refractive index of the immersion medium (see Equation 2.17). However, the voxel volume does not only depend on the properties of the laser beam, but also on the photoresist that is being polymerized. In general, polymerization takes place, once a certain threshold of radicals is being produced by the fs-pulsed light. The density of radicals 𝜌 can be obtained by solving the following rate equation:[6] 𝜕𝜌 𝜕𝑡 = (𝜌0 − 𝜌)𝜎2𝐼 2 (2.22) which is solved by 𝜌 = 𝜌0 (1 − 𝑒−𝜎2,𝑟 𝐼 2𝑡 ) (2.23) with 𝜎2,r = 𝜎2𝜂. (2.24) 26 2.2 two-photon polymerization Here, 𝜎2,r is the eective two-photon absorption cross-section for the genera- tion of radicals, while 𝜎2 is the standard two-photon absorption cross-section and 𝜂 is the eciency of the radical generation process. 𝜌0 is the primary photoinitiator particle density and 𝑡 is the exposure time. Please note that in Equation 2.22, we assume the initial density of radicals to be zero. Once the density of radicals 𝜌 (𝑟 , 𝑧) exceeds the polymerization threshold 𝜌th, the polymerization process is initiated. Since the polymerization threshold is reached only after many fs-laser pulses, we can assume the light intensity ux to be constant during one pulse: 𝐼 (𝑡) = 𝐼0.[6] Furthermore, we will ne- glect the losses of radicals between laser pulses. With these approximations, the diameter 𝑑 of the volxel can be estimated by taking the light intensity ux at the focal plane 𝐼 (𝑟 , 𝑧 = 0) = 𝐼0 · 𝑒 −2𝑟2 𝜔2 0 , (2.25) and inserting it into Equation 2.23 while imposing the condition that 𝜌 (𝑟 , 𝑧) ≥ 𝜌𝑡ℎ . We then obtain the intensity ux under which TPP is ini- tiated: 𝐼 (𝑟 , 𝑡) = 𝐼0𝑒 2𝑟2 𝜔2 0 = √︄ ln(𝜌0/(𝜌0 − 𝜌th)) 𝜎2,r𝑡 (2.26) By rearranging Equation 2.26, we nally arrive at the voxel diameter 𝑑 = 2𝑟 : 𝑑 (𝐼0,𝑚) = 𝜔0 √︄ ln ( 𝜎2,r𝐼 2 0𝑚𝜏 𝐶 ) (2.27) Here,𝑚 = 𝑓 𝑡 = 𝑡/𝜏 is the number of pulses and 𝐶 = ln[𝜌0 (𝜌0 − 𝜌𝑡 )] (2.28) is a constant that depends on the properties of the photopolymer. Likewise, one can express𝑑 in terms of the laser power 𝑃 and the exposure time 𝑡 to get a more intuitive representation of the dependence of the voxel dimensions on the laser properties: 𝑑 (𝑃 , 𝑡) = 𝜔0 √︄ ln ( 5.29 · 𝜎2,r𝑃2𝑡 (𝜋𝜔2 0ℎ𝜈)2 𝑓 𝜏𝐶 ) (2.29) 27 fundamentals In a similar fashion, we can obtain the voxel length 𝑙 by considering the axial intensity ux distribution 𝐼 (𝑟 = 0, 𝑧) = 𝐼0 · 𝜔2 0 𝜔 (𝑧)2 , (2.30) and combining it with Equations 2.18 and 2.19. We then obtain 𝑙 (𝐼0,𝑚) = 2𝑧𝑅 √︄( 𝜎2,r𝐼 2 0𝑚𝜏 𝐶 )1/2 − 1. (2.31) In analogy to the diameter, we can express the voxel length as a function of 𝑃 and 𝑡 as follows: 𝑙 (𝑃 , 𝑡) = 2𝑧𝑅 √︄( 5.29 · 𝜎2,r𝑃2𝑡 (𝜋𝜔2 0ℎ𝜈)2 𝑓 𝜏𝐶 )1/2 − 1 (2.32) In the next step, we want to calculate some typical voxel dimensions for our 3D printing setup. To this end, we choose the laser wavelength, the repetition rate and the pulse width according to the specications of the 3D printing machine used in this theses [80] (Photonic Professional GT, Nanoscribe GmbH). As a photopolymer, we choose IP-S, a commonly used photoresist throughout this thesis, which is also a product of the Nanoscibe GmbH. Finally, for the primary initiator particle density and the density of particle polymerization threshold, we use typical values for two-photon photopolymers which were taken from Ref. [6]. All numeric values can be found in Table 2.1. The process parameters that can be varied to adjust the voxel size during the writing are the laser power (𝑃 ) and the exposure time (𝑡 ) which is indirectly set via the scan-speed when using the galvanometric scanner of the Photonic Professional GT. Figure 2.8 shows the behavior of the voxel dimensions in dependence of the exposure times for some typical laser power values. It includes curves for three numerical apertures (1.4, 1.2 and 0.8) which correspond to the microscope objectives that were used in this work. All process parameters, including the utilized objectives for all structures presented within this thesis can be found in Chapter B of the Appendix. The rst thing that becomes evident when comparing the dierent graphs is that smaller NAs result in substantially larger voxels. Interestingly, the eect is more pronounced for the voxel length than for the diameter. For 28 2.2 two-photon polymerization Parameter Value Laser wavelength 𝜆 780 nm Refractive index of photopolymer 𝑛 1.505 [70] Pulse width 𝜏 100 fs Repetition rate 𝑓 80MHz Eective two-photon cross-section 𝜎2,r 3 · 10−55 cm4s Primary initiator particle density 𝜌0 2.4% [6] Density of particle polymerization threshold 𝜌th 0.25% [6] Table 2.1. Process parameters of femtosecond 3D printing used to analytically calculate the voxel dimensions. example, while the NA = 1.4 objective is capable of producing a voxel with a diameter of roughly 0.25 μm and a length of roughly 0.4 μm at laser power of 90mW and an exposure time of 0.4ms, the same process parameters result in a voxel with approximately twice the diameter but almost four times the length in the case of the NA = 0.8 objective. This has some in- teresting implications for femtosecond 3D printing. It means that smaller NA objectives retain a relatively small lateral resolution. At the same time, due to the nature of the layer-by-layer process, the axial resolution is not actually determined by the length of the voxel, but rather by the spacing of the layers. This fact will be discussed in Chapter 3.2. However, longer voxels can potentially enable much shorter fabrication times since they reduce the minimum number of layers that need to be printed to obtain a solid structure. Generally, the voxel dimensions are more sensitive to a change in laser power than in exposure time, due to the quadratic dependence on 𝑃 (see Equations 2.29 and 2.32). Besides that, it appears that the voxel length is more sensitive to changes in process parameters than the voxel diameter. To verify this fact, we now plot the voxel aspect ration 𝑙/𝑑 as a function of exposure time and laser power for dierent numerical apertures in Figure 2.9. As one can see, the aspect ratio increases both for increasing laser power and increasing exposure time. This means that the voxel length grows faster than the voxel diameter. The eect is more pronounced for a change in laser power than in exposure time. This is an interesting observation that needs to be kept in mind when choosing the process parameters for a specic 3D printing process. For example, when the goal is to reduce the fabrication time 29 fundamentals Figure 2.8. Scaling laws of voxel dimensions. Calculated voxel diameters (left) and lengths (right) for varying NAs and laser powers, as indicated in the gures. by using a longer voxel and thus reducing the number of layers, it would be more benecial to increase the laser power rather than the exposure time. 30 2.2 two-photon polymerization Figure 2.9. Scaling laws of voxel aspect ratio. Length divided by diameter (𝑙/𝑑) for xed laser power (𝑃 = 30mW) and varying NA values over exposure time (top) and for a xed exposure time (𝜏 = 0.5ms) and varying NA values over laser power (bottom). Dynamic Power Range As it is evident from Equations 2.27 and 2.31, the voxel dimensions depend both on the exposure time 𝜏 and the square of the light intensity 𝐼 2. The product of these two parameters is the laser dose (𝐼 · 𝜏). As discussed in the previous section, voxel length and diameter scale dierently, depending on which of the two laser dose parameters is tuned. However, in general, the size of the voxel increases with an increasing laser dose. Controlling the voxel size in femtosecond 3D printing is important, as it allows one to increase either the writing speed or the resolution, depending on the requirements of the process. There are, however, restrictions when it comes to varying the laser dose. The so-called dynamic power range is dened by the two-photon polymerization threshold and the laser-induced breakdown threshold of the respective photoresist.[81] Figure 2.10 illustrates the dynamic power range by showcasing micro-cubes that were written with varying laser doses. While an insucient laser dose (Figure 2.10a) leads to an only partially formed structure, an excessive laser dose (Figure 2.10c) results in micro-explosions 31 fundamentals Figure 2.10. Illustration of dynamic power range.Microscope images of pho- topolymer cube that was exposed (a) below the two-photon polymerization thresh- old, (b) within the dynamic power range and (c) above the laser-induced breakdown threshold. Scale bar: 100 μm. (bubbling) and defects. Only an appropriate laser dose leads to a well-dened, undamaged cube (Figure 2.10b). The photo-polymerization threshold of a photoresist is determined by the eciency of the radical generation process, as well as the reactivity of the produced radicals and the monomers. The laser-induced breakdown threshold is unrelated to TPA. Even though one would intuitively expect it to be a thermal process, for short-pulsed laser (< 1 ps), it is actually believed to be rooted in plasma generation.[82] This is due to the extremely high local electric-eld intensities of the short laser pulses (TW/cm2) accelerating free electrons and starting an avalanche eect. During this process, more and more electrons are removed from their atomic shells. The generated plasma then absorbs, scatters and deects the incident laser beam which results in the before-mentioned defects. A large dynamic power range is obviously desirable to make the voxel size more tunable and the fabrication process less sensitive to errors. The most ecient way to achieve this goal is to use photoinitiators with a large two- photon absorption cross-section. Therefore, even though most initiators that are sensitive to one-photon absorption also exhibit two-photon absorption to a degree, specially optimized photoresists are typically used in femtosecond 3D printing. Aside from this, the choice of the irradiation laser’s wavelength also plays a role in the formation of the dynamic power range. Witzgall et al. [83] found that the two-photon polymerization threshold at 660 nm is approximately half of that at 700 nm and only about a fth of that at 800 nm with the laser induced breakdown threshold remaining basically unchanged. 32 2.2 two-photon polymerization Radical Quenching In the previous sections, we described the TPP process via the reaction Equations 2.11, 2.12 and 2.13. However, we should mention that other types of reactions can take place during laser irradiation which can inuence the voxel size.[84] Radical quenchers (Q) are molecules, like oxygen, that free radicals (R·) can react with, instead of reacting with monomers (M).[85] As a result, quenched radials RQ· are produced which can be deactivated by emitting either radiation or heat. The process can be expressed as follows: R· +Q −−−→ RQ·, (2.33) RQ· −−−→ RQ + h𝜈 or heat, (2.34) This means that photo-polymerization is hampered in the presence of radical quenchers. As a result, a higher photon ux intensity is needed to overcome the polymerization threshold of the density of radicals 𝜌th and the feature size of the voxel eectively decreases (see Equations 2.27 and 2.31). Thus, adding suitable radical quenchers to photo-active materials can be used to increase the resolution of TPP. For example, in the past, Takda et al. [86] improved the lateral resolution from 120 nm to 100 nm by increasing the concentration of the radical quencher in the photoresist SCR500 by 0.8 wt.% In a similar experiment, Park et al. [84] reached lateral resolutions of almost 100 nm in SCR500 using 2,6-di-tert-buty1-4-methylphenol (DBMP) as a radical quencher. Proximity Eect So far, we have discussed issues like feature sizes and damage threshold by considering the eect of an isolated voxel in a homogeneous unexposed photopolymer environment. However, in real 3D printing processes, the conditions are usually not that simple. In fact, these parameters depend not only on the photopolymer and the 3D printing system, but also on the proximity of features. For example, Saha et al. [87] found that the damage threshold power (for a xed writing speed) in a photoresist (IP-DIP) can decrease by as much as 47% when decreasing the distance of parallel 3D printed lines. This phenomenon is known as the proximity eect. There are, in fact, several dierent types of proximity eects in TPP that are both spatial and temporal in nature.[88] As a result, proximity eects are structure- dependent and vary with writing speed which makes it very challenging 33 fundamentals to account for them. The eect can, however, be compensated to a certain degree by adjusting the laser dose. The eects can be attributed to dierent types of cross-talk between adjacent features, namely diusion phenomena [89–91], the accumulation of laser dose [92] and an increase of the single- photon absorptivity in cured photoresists.[87] Besides the damage from micro-explosions, structures written in close proximity may also suer from linewidth broadening, sporadic connections and bending.[84, 93] This makes the fabrication of small separations below a couple hundred nanometers challenging. When designing parts or choosing process parameters for femtosecond 3D printing, the existence of the proximity eect always has to be kept in mind. 34 3 FABR ICAT ION All 3D printed structures presented in this work were produced with a commercial femtosecond two-photon direct laser writing system: The Pho- tonic Professional GT (Nanoscribe GmbH, Germany). This machine enables a precise, exible and straightforward fabrication process at a high resolution. In this chapter, the basic layout of the femtosecond 3D printing setup is introduced and the fabrication process is explained in detail. Furthermore, 3D printing on dierent substrates (wafers and optical bers) is discussed. 3.1 femtosecond 3d printing setup A scheme showing the dierent components of the Photonic Professional GT is shown in Figure 8.7. At its core, the machine consists of an inverted microscope with a high NA objective. The system is also equipped with a fs-pulsed (≈ 100 fs) NIR (780 nm) ber laser that operates at a repetition rate of 80MHz. In addition to that, it includes a mechanical (xy) stage for coarse and a piezoelectric (xyz) stage for ne positioning of the sample. A galvanometer- (galvo-)scanner is used to rapidly move the laser beam in the xy-plane when operating the machine in the so-called GalvoScanMode. An alternative writing mode called PiezoScanMode, in which the laser beam remains in one spot and the sample is moved via the piezo-stage, can also be used. However, the writing speed of the PiezoScanMode is too slow to feasibly fabricate any of the structures shown within this thesis and it was therefore not utilized. In order to move the voxel in the axial (z-) direction during fabrication, there are two possibilities. One can either use the piezo-stage to move the sample or the mechanical z-drive of the microscope to move the writing objective. When choosing one of these z-scan modes, one has to keep in mind that the piezo-stage has a maximum range of 300 × 300 × 300 μm. 35 fabrication The microscope z-drive on the other hand has a range of several millimeters, which is basically limitless in relation to the size of the structures we produce. The sample surface can be observed via the inbuilt CCD camera, even during the printing process. Figure 3.1. Schematic illustration of 3D printing setup (Photonic Profes- sional GT, Nanoscibe GmbH)when used in dip-in conguration.A fs-pulsed (≈ 100 fs, 80MHz repetition rate) NIR (780 nm) ber laser beam can be scanned in xy-direction with a galvanometric scanner composed out of two movable mirrors. The laser beam is then focused onto a substrate with a photopolymer drop applied to it via a high-NA microscope objective. For coarse alignment, the substrate can be moved via a mechanical translation-stage (xy). Precise alignment is achieved via a 3-dimensional (xyz) piezoelectric translation stage. Additionally, the distance be- tween substrate and objective in the z-direction can be adjusted with the microscope z-drive. Figure 8.7 shows the dip-in lithography conguration which was used throughout this thesis. In this mode, a drop of liquid photoresist is applied 36 3.1 femtosecond 3d printing setup onto the substrate and the high NA objective is submerged directly into it. The photoresist thus serves as an immersion medium. Magnication NA Immersion medium WD (μm) WFD (μm) 63x 1.4 Oil / photoresist 360 μm 450 μm 40x 1.2 Water 450 μm 500 μm 25x 0.8 Oil / photoresist 380 μm 800 μm 25x 0.8 Oil / photoresist 740 μm 800 μm 20x 0.5 Air 2100 μm - Table 3.1. Characteristics of microscope objectives used for 3D printing. Dierent microscope objectives can be used, depending on the requirements of the specic fabrication process. They are listed in Table 3.1. The most important dierences are the NA (see Chapter 2.2 for details on how the resolution of TPP depends on the numerical aperture), the working distance (WD), which is important in the case where several structures of a certain height, are printed next to each other, and the write eld diameter (WFD), which denes the maximum area that the laser beam can cover when moved by the galvo-scanner. The WFD values given in 2.2 were manually adjusted and therefore dier from those given in the ocial Photonic Professional GT manual.[80] The 63x objective oers the highest resolution with an NA of 1.4 (voxel diameter < 200 nm) while the 25x objectives enable the fabrication of substan- tially larger structures (WFD = 800 μm). One should add that it is possible to print structures larger than the write eld diameter by dividing the structure into several pieces and printing them sequentially. Between the printing steps, the sample is moved either via the piezo- or the mechanical stage. This technique is commonly known as stitching. In this way, structures with sizes of several millimeters in all three dimensions can be 3D printed.[94] However, in the case of micro-optics presented in this thesis, this method is not suitable as it results in displacements between the writing blocks and visible stitching marks where the blocks overlap, compromising the quality of the optical surfaces. 37 fabrication The 40x water immersion objective is used in the electroless metal plating experiments presented in Chapter 6. In that case, a water based precursor solution was used as the immersion medium. The 20x air objective can be used to inspect the sample before the printing process. This can help to, for example, nd specic areas on a wafer or locate an optical ber more easily than with a high-magnication immersion objective. Since it is not used for printing, no write eld diameter is given. Materials All structures presented in Chapters 5, 7 and 8 were printed using one of two commercially available acrylic photoresist: IP-S and IP-DIP (Nanoscibe GmbH, Germany). IP-DIP oers the highest resolution (feature sizes of ≈ 150 nm), while IP-S results in clearer structures and smoother surfaces, making it the material of choice for larger optics.[95] In Chapters 4 and 6, experimental 3D printing materials were prepared and characterized. Namely, in Chapter 4, IP resist based nanocomposites containing zirkonia (ZrO2) nanoparticles were used to produce high-index micro-optics and in Chapter 6, a water based Silver (Ag) precursor solution was used to print metallic structures. Details on the preparation and the properties of these materials can be found in the respective chapters. 3.2 design and printing process The fabrication process of any new structure starts with the creation of the necessary printing le. A basic scheme of this process is presented in Figure 3.2. First, the desired part is build in a computer-aided design (CAD) software (Autodesk Inventor Professional). When preparing an optical sys- tem, for example, the double lens objective shown in Figure 3.2a, the optical surfaces rst have to be designed in an optical simulation software (Zemax OpticStudio), before being exported to the CAD program. Subsequently, supporting structures have to be added to hold the lenses in place. After completing the design, the structure is exported in the standard triangle language (.stl) format. This le format consists of a raw triangulated surface of the CAD model and is commonly used in 3D printing and computer aided manufacturing applications. 38 3.2 design and printing process Figure 3.2. Scheme of le creation for a 3D printing job. (a) CAD model of an exemplary micro-objective structure consisting of two lenses connected via supporting structures. (b) Side view of schematic representation of computer le processed for 3D printing (.gwl le format). Inset highlights the individual layers the structure is composed of with the slicing distance in between them. (c) Top view of the structure as shown in (b). Inset shows how each layer is made up of individual lines with a hatching distance in between them. Between two adjacent layers, the writing direction of the lines is oset by 90◦, resulting in the perceived chequerboard pattern. (d) Illustration of the 3D printing process. From left to right, an increasing amount of layers is added to the 3D rendering of the micro-objective until the entire structure is formed. In the next step, the .stl les are converted into general writing language .gwl les, a format native to the various Nanoscribe software solutions. This is done using the DeScribe (Nanoscribe GmbH) program. During the le conversion process, the closed surface of the .stl le is transformed into a number of parallel horizontal lines making up one layer of the 3- dimensional structure. The spacing between two such layers in the 3D model is referred to as slicing (see Figure 3.2b), while the spacing between 39 fabrication two adjacent lines within a layer is referred to as hatching (see Figure 3.2c). Several parameters need to be adjusted to t the specic 3D printing process. This includes the slicing and hatching distances, which mostly depend on the utilized objective and thus the resultant voxel size (see Chapter 2.2). Inuences like the proximity eect (see Chapter 2.2) can also impact the choice. Additionally, the angle oset between lines of adjacent layers has to be set. For the structures presented in this thesis, this value was kept at 90◦ (see enlarged area in Figure 3.2c). Finally, the method in which the voxel is moved between layers is chosen between the piezo- and the z-drive method. These modes were already discussed in the previous Section 3.1. DeScribe oers additional options, like a shell writing mode to reduce the writing time and a stitching mode to fabricate structures that are larger than the write eld of the microscope objective. However, since they are not relevant to the work presented within this thesis, they will not be discussed further. Before the actual printing, process parameter like the laser power (LP) and the scan-speed (SS) of the galvo-scanner also have to be dened. Suitable parameters were acquired via extensive experimental parameter sweeps and are listed in Chapter B of the Appendix for all structures presented within this thesis. Figure 3.2d shows a simulation of the structure being created during the printing process. Each line is written individually by scanning the laser focus along the predened trajectory with the galvo-scanner. After nishing one layer, the voxel is shifted in the vertical direction, by moving either the microscope objective with the z-drive, or the sample with the piezo-stage. This way, a 3-dimensional structure is created layer-by-layer. Voxel Overlap As discussed in Chapter 2.2, the voxel has a characteristic shape resembling an elongated ellipsoid. For high precision printing, this shape needs to be considered, as the quality of the fabricated structure strongly depends on the size and the spatial arrangement of the individual voxels. In order to obtain a solid structure consisting of fully polymerized photoresist, the voxels of adjacent lines and layers need to overlap to a certain extend (see Figure 3.3a). 40 3.2 design and printing process Figure 3.3. Voxel overlapping and step eect. (a) Illustration of voxels over- lapping when writing adjacent layers during 3D printing process. (b) Illustration of the step eect. One can quantify the degree of overlap between the voxels by dening an overlap parameter 𝛿 :[55] 𝛿 = 𝑑 −𝑑𝑥 𝑑 · 𝑙 −𝑑𝑧 𝑙 (3.1) where, 𝑑𝑥 is the distance of two voxels in x direction and 𝑑𝑧 is the distance in z direction (see Figure 3.3a). These values are equivalent to the hatching and slicing distances that were introduced in the previous section respectively. The overlap plays an important role for the achievable surface roughness 𝑅𝑎 , which is given by: 𝑅𝑎 = 1 𝑙𝑟 ∫ 𝑙𝑟 0 |𝑍 (𝑥) −𝑍0 |𝑑𝑥 ≈ 1 𝑛 𝑛∑︁ 𝑖=1 |𝑍𝑖 | (3.2) where 𝑙𝑟 is the scanning length, 𝑍 (𝑥) is the height at each point, 𝑍0 is the average height, 𝑛 is the number of samples and 𝑍𝑖 is the height at each sampling point. This value is extremely important for optical applications, as it is essentially a measure for the quality of an optical surface. A high surface roughness 𝑅𝑎 is equivalent to low quality optics. Additive manufacturing processes, in general suer from something called the step eect. The issue is illustrated in Figure 3.3b. Due to the layer-by-layer fashion in which the structure is created, its surface exhibits a step-like shape with the step height being dened by the thickness of the individual layers. This is directly related 41 fabrication to the size and overlap of the voxels. In order to obtain a smoother surface, smaller voxels and a larger overlap are required. Therefore, components that serve as optical surfaces, for example, lenses, need to be printed with a smaller hatching and slicing distance (typically in the order of 100− 200 nm) than components that merely serve as supporting structures. This, of course, impacts the fabrication time, which is directly proportional to the number of lines that are being written. For this reason, it can be benecial to set dierent hatching and slicing parameters for dierent parts of the 3D printed structure, especially when dealing with large objects. Examples for dierent writing parameters within the same structure can be found in Chapter B of the Appendix. 3.3 sample fabrication Femtosecond 3D printing is a highly exible technique that can be applied to a large variety of substrates. Within this thesis, two basic types were used: at substrates like glass slides and semiconductor wafers and optical bers. The fabrication details for each of them are described below. Fabrication on Wafer Substrates Before 3D printing, substrates are cleaned using 2-propanol and blow dried with nitrogen. In order to improve the adhesion of the resist, they are then treated in an O2-plasma for 30 − 60 s. Subsequently, substrates are mounted onto the sample holder and a drop of photoresist is applied onto them before the holder is inserted into the 3D printer. The substrate’s surface is found automatically using the inbuilt interface nder algorithm (Zeiss Denite Focus). Since this method relies on a sucient refractive index contrast between the substrate and the photoresist, there are cases in which the automatic interface nding fails. For example, large dierences in the reectivity of the surface, for examplemetallic structures on a semiconductor wafer, can interfere with the algorithm. In these cases, the surface has to be found manually by carefully adjusting the objective position via the manual z-drive. This task can be simplied by turning on the fs-pulsed laser and observing its reection on the substrates surface. In this case, it is important to keep the laser power low (< 5%) to prevent polymerization of the photoresist. 42 3.3 sample fabrication Figure 3.4. 3D printing on various substrates. Exemplary structures fabricated on (a) a glass substrate (b) a cuprous oxide (Cu2O) crystal (c) a semiconductor wafer with gold markers on top and (d) a semiconductor chip integrated onto a printed circuit board (PCB) with pre-attached bonding wires enclosed by the 3D printed material. Scale bar in inset: 200 μm. After the printing, unexposed photoresist is removed chemically in a de- veloper bath (mr-Dev 600, Microresist). The duration of the development process depends on the shape of the 3D printed structure. Gaps and cavi- ties (especially small ones), require more time for the resist to be properly washed out. For a structure without such features, a development time of 15min is typically sucient. For more complex structures, development times of several hours might be necessary. Figure 3.4 illustrates the large variety of possible substrates, highlighting the extreme exibility of the additive manufacturing approach. In Figure 3.4d printing was even carried out around preexisting bonding wires on a wafer sample. No special adaptations to the printing process had to be made in this case. However, depending on the type of substrate, adjustments might be necessary. On the one hand, for highly reective substrates the deployed laser dose is enhanced close to the surface due to back-reection of the laser. This might move the overall dose outside of the dynamic power range of the photoresist. On the other hand, highly absorptive substrates result in a large heat deposition close to the surface which can lead to micro-explosions and 43 fabrication degradation of the resist. In these cases, it can be necessary to reduce the deposited laser dose/heat by either reducing the laser power, increasing the scan-speed, or choosing a larger slicing distance, when printing the rst couple of layers on the surface. For example, in Figure 3.2c, the laser power was reduced from 70% to 50% when printing the rst 10 layers (20 μm) of the structure to adjust for the highly reective Au structures on the surface. Fabrication on Optical Fibers In this thesis, we rely on single-mode optical bers (SM 780HP, Thorlabs). To print on the ber tips, we rst strip o several centimeters of the protective coating and cleave o both ends of the ber. The facet that is going to be used for 3D printing is then rinsed with 2-Propanol and blow-dried with nitrogen for several seconds each. Subsequently, the ber is mounted in a standard V-groove ber holder (MDE 710, Elliot Martock) that is inserted into the 3D printing setup via a custom made holder. Figure 3.5. Illustration of fabrication process on optical bers. (a) Scheme of dip-in writing conguration. The optical ber is submerged into a drop of photoresist that was applied on top of the objective lens. (b) Microscope image showing the facet of a single-mode optical ber in the 3D printing setup. The back end of the ber is illuminated by a red LED making the ber core in the center light up. (c) Microscope image showing an example of an optical ber with a 3D printed structure on top of it. During this step, it is important to ensure that the ber does not protrude beyond the ber holder’s V-groove for more than a few millimeters. This is done to prevent bending or movement during the fabrication process. To improve the adhesion of the photoresist, the ber is either put into an 44 3.3 sample fabrication O2-plasma, or treated with a plasma pen (piezobrush® PZ3, relyon plasma GmbH) for 30 − 60 s directly before fabrication. 3D printing is performed in the dip-in conguration. To this end, a drop of photoresist is applied directly onto the writing objective before the ber tip is submerged into it. The process is illustrated in Figure 3.5a. After focusing on the ber facet using the built-in CCD camera, the back end of the ber is illuminated with a red LED, making the light-guiding ber core visible on the camera image. The core is then used as a reference point for the lateral alignment of the 3D printing machine. To align the center of the write eld with the center of the ber, the NIR laser is manually switched on at a low laser power and precisely overlapped with the center of the single-mode ber core using the piezo-stage. Figure 3.5b shows how the end facet of the optical ber looks during the alignment process. As one can see, the illuminated core is clearly visible in the center. After writing, the unexposed photoresist is removed in a development bath. Since only very small amounts of photoresist adhere to the ber, the development process is much shorter than for other substrates. In fact, if the 3D printed structure contains no cavities, development is typically completed after merely 30 s. However, longer development times are necessary for structures that do contain cavities. In Figure 3.5c, an example of a 3D printed structure on a ber tip in the form of a focusing lens is shown. 45 4 TA I LORED NANOCOMPOS I TE S In this chapter, we introduce nanocomposite materials based on the commonly used photopolymers IP-DIP and IP-S as polymer matrix and zirconium dioxide (ZrO2) nanoparticles. While optical polymers only cover a rather narrow range of optical properties, greatly limiting the design freedom of polymer optics, the refractive index and dispersion of these nano-inks can be purposefully tailored by varying the constituent materials and the volume fraction of the nanoparticles. Here, we demonstrate the suit- ability of nanocomposites as a platform of tailorable materials for 3D printed micro-optical elements and systems. In addition, we also use our nano-inks to systematically investigate the accuracy of the Maxwell-Garnett-Mie eective medium theory for dierent materials. Finally, we discuss what further steps are required to unlock the full potential of nanocomposites as next-generation optical materials and highlight that nano-inks are also promising materials for other applications. This chapter is mostly based on the following publication: Ksenia Weber, Daniel Werdehausen, Peter König, Simon Thiele, Michael Schmid, Manuel Decker, Peter William de Oliveira, Alois Herkommer, and Harald Giessen "Tailored nanocomposites for 3D printed micro-optics", Optical Materials Express 10, 2345 (2020), DOI 10.1364/OME.399392. 47 https://doi.org/10.1364/OME.399392 tailored nanocomposites 4.1 introduction In optical design, the use of materials spanning a wide range of optical prop- erties is a powerful tool for correcting both chromatic and monochromatic aberrations.[96] Therefore, such materials are a key ingredient of high- performance optical systems.[97] The quantities that are commonly used to quantify the optical properties of a material are the refractive index at the d-line 𝑛𝑑 = 𝜆𝑑 = 587.56 nm and the Abbe number 𝜈𝑑 = (𝑛d − 1)/(𝑛F + 𝑛C), where the subscripts F, d, C refer to the Fraunhofer spectral lines at 𝜆F = 386.12 nm, 𝜆d = 587.56 nm, and 𝜆C = 656.28 nm. [96] These deni- tions indicate that 𝑛d denotes the overall magnitude of the refractive index, whereas 𝜈d quanties its dispersion. To visualize the range that is encom- passed by optical glasses today, the green area in Figure 4.1 highlights the region in the Abbe diagram that is covered by the current Schott glass catalog.[98] However, all optical systems and technologies that rely on Figure 4.1. Abbe diagram of conventional optical polymers and glasses. Refractive index at the d-line 𝑛d = 𝑛(𝜆d = 587.56 nm) over the Abbe number 𝜈d) including photoresists (inks) for femtosecond 3D printing,[70] conventional optical polymers, and the glasses of the Schott glass catalog. The shaded areas show that polymers only cover a narrow range of optical properties, whereas glasses cover a much wider range. From left to right, the conventional polymers (purple stars) included in the gure are: PMMA, COP, Optorez, Styrene, SAN, PC, and PS. 48 4.1 introduction optical polymers, e.g. femtosecond 3D printing, suer from the fact that polymers only cover a narrow range of optical properties. Specically, as visualized by the blue area in Figure 4.1, polymers are restricted to much smaller refractive indices than optical glasses.[99–101] A promising ap- proach to overcome these limitations is incorporating nanoparticles made of high-refractive-index dielectric materials into a polymer as host matrix [102–104]. As visualized in Figures 4.2a and 4.2b, the much higher eective refractive index of such nanocomposites compared to conventional poly- mers, for example allows for increasing the performance of a lens while simultaneously decreasing its size. However, so far, experimental research Figure 4.2. Layout of (a) a conventional polymer lens and (b) a nanocomposite-enabled lens. Both lenses were designed in ZEMAX OpticStu- dio. The blue lines visualize the propagation of rays through the lenses. The nanocomposite-enabled lens is both thinner (𝑙nano < 𝑙conv) and enables a higher performance (𝑑nano < 𝑑conv) than the conventional lens. In these gures, 𝑑conv and 𝑑nano visualize the root mean square (RMS) spot size in the focal plane that can be obtained from the ray traces. into high-refractive-index nanocomposites was mostly restricted to thin coatings.[104] The suitability of nanocomposites as a material platform for optical elements and systems has not yet been experimentally demonstrated. Furthermore, the accuracy of the Maxwell-Garnett-Mie eective medium theory for predicting the eective refractive index and its dispersion has never been systematically investigated in experimental works. This is a key issue because, theoretically, an innite variety of nanocomposites exist and 49 tailored nanocomposites validated eective medium theories are consequently essential to guide the design of the most promising novel materials. 4.2 the maxwell-garnett-mie effective medium theory Here, we investigate nanocomposites which are composed of discrete nano- particles that are embedded into a polymer host matrix. The natural starting point to analytically determine the eective permittivity (𝜖e) of such materi- als is the Clausius-Mossotti equation. This equation treats the nanoparticles as polarizable entities with an electric dipole polarizability of 𝛼inc and reads [105] 𝜖e = 𝜖h 1 + 2 3𝑁𝜋𝛼inc 1 − 2 3𝑁𝜋𝛼inc , (4.1) where 𝜖h is the permittivity of the host matrix and 𝑁 is the nanoparticles’ number density. For spherical nanoparticles, the nanoparticles’ dipole polar- izability that appears in the Clausius-Mossotti Equation can be directly determined from Mie theory [106] as follows [107]: 𝛼inc = 𝑖 3(𝑑inc/2)3) 2𝑥3 𝑎1, (4.2) where 𝑎1 is the rst order Mie coecient, 𝑑inc is the diameter of the inclu- sions, and 𝑥 = √ 𝜖h𝜋𝑑scat−1 is the size parameter.[108] The Maxwell-Garnett- Mie eective medium theory can now readily be obtained by substituting Equation 4.2 into Equation 4.1. As a more intuitive measure, the volume fraction 𝛷 = 1 6𝜋𝑁𝑑3inc (4.3) can then be used instead of the number density (𝑁 ). Finally, if the material’s permeability remains negligible, its eective refractive index can be readily determined from 𝑛e = √ 𝜖e. 4.3 nanocomposite material fabrication To systematically demonstrate that nanocomposites can serve as a platform of novel tailored optical materials, we synthesized dierent nano-inks based 50 4.4 characterization of optical properties on IP-DIP and IP-S as host matrices. To this end, we mixed ZrO2 nanoparti- cles within a 50 wt.% PGMEA solution (PCPA, Pixelligent) into these two photoresists. These nanoparticles spherical-like shapes and a narrow size dis- tribution that peaks below a diameter of 10 nm. In addition, the nanoparticles are functionalized to avoid agglomeration in polymers with proprietary cap- ping layers that have been disclosed in several patent applications.[109–112] We performed the mixing of the constituent materials in a conical ask under constant stirring with a magnetic mixer. Subsequently, when homogeneous compounds were formed, we removed the solvent in which the nanoparticles were dispersed by concentrating the mixture under reduced pressure for several hours until the target weight (weight of mixture with all solvent evaporated) was reached. We rst performed this process for pure IP-DIP as the host material. In addition, we synthesized nano-inks based on a mixture of IP-S and 2-Hydroxy-3-phenoxypropylacrylat (HPPA [𝑛d = 1.528,𝜈d = 34]) at a 1:1 ratio as the host matrix, to achieve agglomeration-free blending of the nanoparticles in the matrix. This enables us to systematically analyze the inuence of the nanoparticle volume fraction on the optical properties of the nano-inks. 4.4 characterization of optical properties To characterize the optical properties of the nano-inks, we polymerized all materials with UV light and measured their refractive index prole using a commercial automated Pulfrich refractometer.[113] (ATR-L, Schmidt and Hänsch GmbH & Co.). Accordingly, Figure 4.3a displays the dispersion curves of the three IP-DIP based nano-inks and the pure host material, while Figure 4.3b displays the dispersion curves of the IP-S based nano-ink, pure IP-S and the IP-S/HPPA mixture that was used as the host material. In these gures, the crosses denote the measured data points, whereas the solid lines represent Cauchy functions that we tted to the experimental data. These ts enable us to accurately determine the 𝑛d and 𝜈d values of all materials from the measured data. In addition, the dashed blue lines in Figure 4.3a depict the predictions obtained from the EMT. It is evident that there is an excellent agreement between experimental data and theory. Note that we determined the volume fraction of each nano-ink from the EMT. To this end, we used Equation 4.1 and Equation 4.2 together with the refractive indices of ZrO2 and the respective host material.[114, 115] We then tted the resulting expression for 𝑛e to our experimental data by using the volume fraction𝛷 as the only free parameter. We used this approach 51 tailored nanocomposites because, in practice, the key question is whether the EMT can accurately predict what dispersion properties, that is 𝑛d and 𝜈d values, can be achieved by varying the volume fractions. To directly visualize the 𝑛d and 𝜈d values Figure 4.3. Dispersion curves of nanocomposites. Refractive index as a func- tion of the wavelength for (a) the three IP-DIP-based nano-inks and (b) nano-ink based on a mixture of IP-S and 2-Hydroxy-3-phenoxypropylacrylat as the host ma- terial at dierent volume fractions𝛷 of ZrO2 nanoparticles. The crosses denote the measured data points, the solid lines Cauchy ts, and the dashed lines the prediction of the eective medium theory (EMT). The volume fractions were determined from the EMT. Refractive index data for the pure IP photoresists was taken from Ref. [70]. of all nano-inks, Figure 4.4 depicts their locations in the Abbe diagram (orange stars). This gure indicates that the nano-inks are located well within the region that is normally only accessible using optical glasses. Specically, Figure 4.3 demonstrates that increasing the volume fraction of the nanoparticles systematically increases the magnitude of the refractive 52 4.4 characterization of optical properties Figure 4.4. Locations of dierent materials in the Abbe diagram. Here, 𝑛d = 𝑛(𝜆d = 587.56 nm) over Abbe number 𝜈d. In addition to the IP-DIP-based nano-inks the diagram includes a nano-ink that is based on a mixture of IP-S and 2- Hydroxy-3-phenoxypropylacrylat as the host material (𝛷 = 14.2%)). The dashed blue lines visualize the prediction from the EMT for a wide range of nano-inks that are composed of IP-DIP as well as the IP-S-mixture as the host materials and diamond, ZrO2 and TiO2 as the materials of the nanoparticles. These lines extend up to volume fractions of up to 35%. The shaded red area visualizes the region that is accessible by combining dierent nanoparticle materials in the same host. index. Furthermore, it is evident that the EMT predicts the 𝑛d and 𝜈d values that can be achieved by varying the volume fractions with high accuracy. The nding that the refractive indices of our nano-inks are much higher than those of the pure host materials shows that our nano-inks indeed overcome the restrictions of conventional polymers that we discussed in the introduction (see Figure 4.1). In fact, it is well known from aberration theory,[116] that materials of a high refractive index allow for reducing spherical aberration or, in combination with materials with a low refractive index, also allow for reducing the Petzval eld curvature.[117] In addition to the IP-DIP based nano-inks, the location of the IP-S based nano-ink in the Abbe diagram in Figure 4.4 demonstrates that dierent regions in the Abbe diagram can be accessed by combining dierent materials. It is evident that the IP-S based nano-ink is characterized by a higher Abbe number than the IP-DIP based nano-inks. In optical design, such materials with higher Abbe numbers are useful for reducing chromatic aberrations.[117] Furthermore, the dashed blue lines in Figure 4.4, which depict the predictions from the EMT for volume fractions between 0% and 35%, directly show that 53 tailored nanocomposites the EMT accurately predicts the locations of all nano-inks in the Abbe diagram. Specically, the Abbe numbers of all nano-inks deviate by less than 0.9% from those obtained from the EMT at the same value of 𝑛d. Both our experimental ndings and theoretical predictions hence demonstrate that the host matrix and the nanoparticle materials dene a trajectory in the Abbe diagram. Adjusting the volume fraction then allows for tuning the optical properties of the nano-inks along this trajectory. We chose a maximum volume fraction of 35% for our theoretical predictions because such volume fractions have already been achieved for thin lms.[112] In fact, building on the nding that the EMT is highly accurate, we can now use the EMT to investigate what locations in the Abbe diagram can be accessed by using dierent nanoparticle materials. To do so, the Abbe diagram in Figure 4.4 also includes diamond and TiO2 as nanoparticle materials. Accordingly, the corresponding dashed blue lines demonstrate that using these materials allows for accessing widely dierent regions of the Abbe diagram. This conrms that nanocomposites allow for the design of dispersion-engineered materials. In addition, the shaded red area illustrates that combining multiple nanoparticle materials within the same host allows for continuously tuning 𝑛d and 𝜈d within wide regions. We obtained this area by generali