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Modelling of Pulse Propagation in Nonlinear Photonic Structures
Sterkhova, Anna ; Richter, Ivan (oponent) ; Samek, Ota (oponent) ; Petráček, Jiří (vedoucí práce)
The demand for more effective data-storage and faster signal processing is growing with every day. That is why the attention of the scientists is focused on the all-optical devices, which can improve the above mentioned requirements. Microring optical resonators are among the state of art devices, that are under consideration. There is a variety of numerical techniques to simulate processes occurring while the optical signal propagates in the microring resonator structure. They differ in its calculation effectivity, used approximations and possibilities of application. The aim of this work was to develop two simple and practical numerical methods for simulation of pulse propagation in nonlinear waveguide structures. It was also demanded, that opposed to the commonly known and frequently used finite-difference time-domain (FD-TD) method, the newly developed techniques could be easily applicable for the study of nonlinear structures based on microring resonators. That is why developed methods use some approximations, namely the slowly varying envelope approximation. The methods advantage is high speed and low requirements of computational resources. Both techniques are based on observation that waveguide structures that use microring optical resonators can be considered as composed of single waveguides and waveguide couplers. The first numerical technique solves coupled partial differential equations, which describe pulse envelope propagation in the structure. This method uses the “up-wind” scheme, which is suitable for the partial differential equations that describe the wave propagation. The second developed technique is derived from the first one. The difference between methods is in the treatment of the coupling between two waveguides. If in the first method the coupling is considered as the real one, distributed on the given length, in the second method the coupling is considered to be concentrated in one point. Due to this approximation it is possible to integrate the appropriate equations and achieve significant increase of calculation speed. Quasianalytical character of the second method enables also easy identification of different types of steady-state solutions. Due to these properties the second method was used to study spontaneous generation of optical pulses in the structures, consisting of coupled ring resonators. Both methods, which were developed during this work, represent fast and physically illustrative alternatives to the FD-TD, so it can be expected that these methods can play an important role during the research of nonlinear waveguide structures.
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Modelling of Pulse Propagation in Nonlinear Photonic Structures
Sterkhova, Anna ; Richter, Ivan (oponent) ; Samek, Ota (oponent) ; Petráček, Jiří (vedoucí práce)
The demand for more effective data-storage and faster signal processing is growing with every day. That is why the attention of the scientists is focused on the all-optical devices, which can improve the above mentioned requirements. Microring optical resonators are among the state of art devices, that are under consideration. There is a variety of numerical techniques to simulate processes occurring while the optical signal propagates in the microring resonator structure. They differ in its calculation effectivity, used approximations and possibilities of application. The aim of this work was to develop two simple and practical numerical methods for simulation of pulse propagation in nonlinear waveguide structures. It was also demanded, that opposed to the commonly known and frequently used finite-difference time-domain (FD-TD) method, the newly developed techniques could be easily applicable for the study of nonlinear structures based on microring resonators. That is why developed methods use some approximations, namely the slowly varying envelope approximation. The methods advantage is high speed and low requirements of computational resources. Both techniques are based on observation that waveguide structures that use microring optical resonators can be considered as composed of single waveguides and waveguide couplers. The first numerical technique solves coupled partial differential equations, which describe pulse envelope propagation in the structure. This method uses the “up-wind” scheme, which is suitable for the partial differential equations that describe the wave propagation. The second developed technique is derived from the first one. The difference between methods is in the treatment of the coupling between two waveguides. If in the first method the coupling is considered as the real one, distributed on the given length, in the second method the coupling is considered to be concentrated in one point. Due to this approximation it is possible to integrate the appropriate equations and achieve significant increase of calculation speed. Quasianalytical character of the second method enables also easy identification of different types of steady-state solutions. Due to these properties the second method was used to study spontaneous generation of optical pulses in the structures, consisting of coupled ring resonators. Both methods, which were developed during this work, represent fast and physically illustrative alternatives to the FD-TD, so it can be expected that these methods can play an important role during the research of nonlinear waveguide structures.
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