Efficient Sensitivity Analysis and Design Optimization of Photonic Devices - Swillam, Mohamed A. (My University, 2008)
In this thesis, we propose efficient approaches for design optimization of passive and active photonic devices. These approaches are based on utilizing gradient based optimization algorithms for efficient optimization of photonic devices. Some of the proposed approaches obtain the required gradient (sensitivity) information efficiently using adjoint variable method (AVM) applied directly to the exploited numerical techniques. Other approaches are based on formulating the design problem as an optimization problem using convex programming. These approaches utilize the gradient-based interior point method (IPM) for solving the design.
The AVM aims at efficiently obtaining the sensitivity information using the numerical technique. This technique requires a solution of an additional simulation of the adjoint system. The information obtained from the original and the adjoint simulation is sufficient to obtain the response and the sensitivity of the response with respect to all the design parameters. The AVM technique differs for different numerical method.
The obtained sensitivity using the AVM approach is not only useful for exploiting gradient based optimization for design optimization, but also for yield and tolerance analyses of the newly proposed designs.
We proposed a second order accurate approach to obtain the sensitivity information using finite difference time domain (FDTD) technique. This approach utilizes the AVM to efficiently obtain the sensitivity information. This approach is exploited for efficiently obtaining the sensitivity of the power reflectivity and coupling coefficient of various devices. This approach has been also utilized for obtaining the sensitivity of the dispersion characteristics of different guided wave structures.
We also introduce a novel approach for sensitivity analysis of photonic devices using the beam propagation method (BPM). This approach is simple and easy to implement. It exploits the existing factorization of the system matrices for efficient calculation of the sensitivity of the required objective function. This approach is also utilized for sensitivity analysis of the vectorial modal properties of different guided wave structures. This approach is also exploited for sensitivity analysis of various surface plasmon devices.
This AVM approach is also exploited to propose a novel design of an optical switch with wide working wavelength band and compact size. The switch is based on the self imaging theory in multimode waveguide with a refractive index has approximate parabolic profile. The design problem is formulated as two stage optimization procedure. The optimization algorithm exploits the efficiently obtained sensitivity information from a BPM simulation. The final design has interesting characteristics.
An efficient approach is also proposed to obtain the sensitivity of the energy levels and wavefunctions of different quantum structures obtained using time dependent and time independent Schrodinger equation. This approach is exploited for design optimization of different quantum well lasers.
We also propose a convex formulation for the design problem of multilayer optical coatings. This formulation allows for efficient design of structures with large number of layers in fractions of a second without an initial design.
Pages (41,133,161,209) were omitted from the thesis as they were completely blank pages.
Keywords: optimization, photonic devices, sensitivity, gradient