TY  - THES
T1  - Coupled-mode theory for nonlinear multilayered structures and its applications in the design of all-optical devices
A1  - Grigoriev,Victor
Y1  - 2012/04/27
N2  - Photonic crystals offer a unique platform to construct all-optical devices and as an ultimate goal to develop photonic circuits for high-speed processing of light signals. The waveguides and microcavities created in the photonic crystals by a suitable choice of defects form the two basic elements which are used to design other components and devices with more complex functionality. The Coupled-Mode Theory (CMT) provides a theoretical framework for an efficient design of such devices. The main advantage of this theory is that it can reduce even very complex photonic structures to a uniform set of oscillators, which interact with the external signals and among each other through the scattering channels.

In spite of the fact that the CMT provides a higher-level analytical description of a system, which is very suitable for engineering purposes, it is mostly used in a phenomenological manner and requires a number of fitting parameters. The main goal of this work was to develop the CMT formalism in a systematic way by starting directly from the Maxwell equations and to provide a strong foundation for the usage of this theory in the modeling of nonlinear photonic structures. The CMT is a modal approach, and it can be applied without loss of generality to systems of any dimensionality. In this work an emphasis was made on studying the nonlinear optical properties of complex multilayered structures.

It is shown that the new formulation of the CMT describes equally well structures with periodic, quasiperiodic and even aperiodic arrangements of the layers. It is applicable for deep variations of the refractive index between the layers and takes into account correctly the influence of the boundaries for structures of finite length. Moreover, the nonlinear interactions can be easily included into the main equations, and this theory can be used both for the frequency and time domain simulations. This makes the CMT far superior to many other methods developed for the multilayered structures. In particular, it follows from the CMT that the transmission spectrum of quarter-wave structures can be described by exact analytical formulas which are valid in a broad spectral range. The knowledge of these formulas allows one to compute easily many other important characteristics such as the group delay experienced by the ultrashort pulses propagating through the structure or the photonic density of states.

A large part of this work is devoted to the applications of the CMT in the design of all-optical devices. It is considered how to create an optical diode by using the multistability of coupled nonlinear microcavities and the dependence of switching thresholds on the direction of incidence. The CMT not only provides a simple analytical model for this system, but also helps to choose the parameters of the microcavities so as to achieve a strong nonreciprocal behavior together with a negligible insertion loss. It is also shown how to use the self-pulsations in multilayered structures to convert a continuous wave signal into a regular train of ultrashort pulses. In this case, the CMT can be applied to describe the dynamics of the self-pulsations and to explain them as an infinite series of switching between bistable states due to the beating of modes.
KW  - Streutheorie
KW  - Optischer Resonator
KW  - Kerr-Effekt
KW  - Anharmonischer Oszillator
KW  - Optische Bistabilität 
CY  - Erlangen
PB  - Universitätsbibliothek der Universität Erlangen-Nürnberg
AD  - Universitätsstraße. 4, 91054 Erlangen
L2  - http://www.opus.ub.uni-erlangen.de/opus/volltexte/2012/3255
ER  -