Browsing by Author "Klaedtke, Andreas"

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Spatio-temporal non-linear dynamics of lasing in micro-cavities : full vectorial Maxwell-Bloch FDTD simulations
(2004) Klaedtke, Andreas; Hess, Ortwin (Prof. Dr.)
This work explores the ultra fast and non-linear effects in dielectric micro-cavities and micro-cavity lasers on the basis of full vectorial Maxwell-Bloch finite difference in time domain simulations. Micro-cavity lasers promise low lasing pump thresholds and ultra fast amplitude modulations. Micro-cavities with low pump thresholds may function as single photon sources which are required for quantum optic data processing. For the first time the full three dimensional complete polarisation dynamics during the initial transient of a lasing process in a micro-cavity are calculated and discussed. So called microdisks and microgears were chosen as the cavity geometries. In order to simulate the non-linear, ultra short effects in micro cavities, a three dimensional finite element in time domain (FDTD) code was set up, adapted to different types of computer architectures and verified. The FDTD algorithm describes the temporal evolution of the electromagnetic fields on a Yee type numerical grid by using the Faraday and the generalised Ampere law to calculate the fields at a new time step from the former time step in a leap frog like, second order accurate scheme. The Maxwell material equations introduce the polarisation into the FDTD algorithm. It is described for the first time in a semi-classical, self consistent three dimensional formalism by the discretised optical Bloch equations as separate difference equations. Resonators with distributed feedback (DFB resonators), including one or two dimensional corrugations, pose the first type of micro-resonator for which the numerical method is applied. This type of resonator is used in so called "plastic lasers" which are entirely made from organics in order to form extremely flexible and shapeable, large area light sources. The simulations in this work lead to qualitative results which give insight in the type of DFB mechanism, and they give quantitative results for DFB structures which are used in experiments. The last two chapters of this work deal with disk type lasers with length scales in the range of a few wavelengths. Starting with smooth shaped dielectric cylinders, cold cavity modes are computed and measured. The results are then compared to experiments and different theoretical computations from literature. Subsequently, the influence of a periodic modulation of the cylinder radius - which characterises the microgear laser - with variable depth on the properties of cold cavity modes in smooth shaped disks is studied. Quantitative investigations are performed on selected modes. These dielectric disks with a periodic modulation of the radius are called microgears. The simulations of the initial transient relaxation oscillation of the active material in microdisk lasers visualise the quasi stationary spatial hole burning process. But this initially static behaviour is immediately replaced by a rotational movement of the electromagnetic mode. We ascribe this effect to the continuous azimuthal degeneracy of the eigenmodes of the cold cavity and the non-linearity of the combined optical Maxwell-Bloch equations. The continuous azimuthal degeneracy is removed by the transition to the microgear geometry. The simulations of lasing in this kind of resonator shows a spatially static hole burning of the inversion from the first relaxation oscillations to the steady state lasing process. It is thereby demonstrated that the mode decomposition of a cold dielectric cavity is an indication of the properties which are to be expected of a lasing resonator, but proves to be insufficient to predict non-linear effects in micro and macro lasers.