|Ph.D Thesis||Department of Physics|
|Supervisors:||Prof. Moiseyev Nimrod|
|Prof. Orenstein Meir|
|Prof. Emeritus Mann Ady|
The aim of the performed research is to study the propagation of the electromagnetic waves in non-uniform optical waveguides, using approaches and numerical methods that were developed in the field of quantum mechanics, especially interaction of matter with time-dependent fields. The study is based on the analogy between the refractive index inhomogeneities along the propagation axis in optical waveguides and the time-dependent potential created by laser fields in quantum mechanical processes. The analogy between the time-dependent Schroedinger equation (TDSE) and the paraxial wave equation was used for bridging between the control of processes of interaction of quantum particles with laser fields and the control of optical field propagation in weakly guiding optical devices.
The mechanism of chaos-assisted tunneling in the field of quantum chemistry was transformed to propose the intermediate-mode-assistant directional coupler (IMADC), in which the exchange of power between two identical coupled waveguides is controlled using an embedded periodic structure along the $z$-direction. The power exchange control is based on a symmetry of optical modes and results from the interaction of lowest-order waveguide modes with high-order modes. The propagation of light in a waveguide with periodic variations of refractive index, which constitutes IMADC, was previously made in the framework of the paraxial approximation using the (t,t') method. A numerical method for the solution of the wave equation for optical waveguides with long-range periodic inhomogeneities enables one to perform the exact analysis of the coupler. The method is based on a calculation of the Bloch waves and their matching with the ideal modes of a uniform waveguide.
Another quantum-mechanical mechanism -- STIRAP (stimulated Raman adiabatic passage) was used to propose non-evanescent adiabatic directional coupler. The coupling mechanism is also assisted by the intermediate auxiliary mode which, however, remains unexcited in the power transfer process. The proposed device couples the zero-order mode of two asynchronous waveguides through the intermediate auxiliary mode using an embedded periodic structure along the $z$-direction. The adiabatic switching and the chosen order of the gratings provide a very robust mechanism of the optical power transfer, insensitive to the variations of the grating periods or a wavelength of the light.
The non-hermitian formalism was developed in order to describe analytically the non-evanescent adiabatic directional coupler with large changes in refractive index.
We show that the slowly varying envelope approximation is hidden behind the rotating wave approximation, which implies that slowly varying envelope condition has to be satisfied.
A directional coupling mechanism between different waveguides in a periodic array of waveguides was suggested. The optical power transfer between two different waveguides is mediated by the coupling between zero-order modes of two of the waveguides and the second band of the periodic structure. Analytical solutions for the no-detuning (narrow band) and far-from-resonance cases were presented. The far-from-resonance case was shown to resemble a simple two-mode system with complete optical power transfer between the two waveguides, coupled by localized gratings. The transfer is mediated by the second band of the periodic structure. The transition length depends strongly on the shape of the perturbation, and depends exponentially on the distance between the waveguides. Yet it allows one to transfer power from one waveguide to another at such distances, for which the transition via directional tunneling mechanism is impossible.