Titlle: Recent Trends in Computational Photonics
Editors: Arti Agrawal, Trevor Benson, Richard DeLaRue, Gregory Wurtz
Chapter 1:
Guided wave interaction in photonic integrated circuits - a hybrid analytical / numerical approach to coupled mode theory
By: Manfred Hammer, University of Paderborn
Outline: Computational tools are indispensable in the field of photonic integrated circuits, for specific design tasks as well as for more fundamental investigations. Difficulties arise from the usually very limited range of applicability of purely analytical models, and from the frequently prohibitive effort required for rigorous numerical simulations.Hence we pursue an intermediate strategy. Typically, an optical integrated circuit consists of combinations of elements (waveguide channels, cavities) the simulation and design of which is reasonably well established, usually through more or less mature numerical solvers. What remains is to predict quantitatively the interaction of the waves (modes) supported by these elements. We address this task by a quite general, "Hybrid" variant (HCMT) of a technique known as Coupled Mode Theory. Using methods from the realm of finite-element numerics, the optical properties of a circuit are approximated by superpositions of eigen-solutions for its constituents, leading to good quantitative, reasonably low-dimensional, and easily interpretable models. This chapter describes the theoretical background, explains its limitations, hints at implementational details, and discusses a series of 2-D and 3-D examples that illustrate the versatility of the technique.
Keywords: Photonics, guided wave (integrated) optics, coupled mode theory,
numerical modeling.
Content:
1. Introduction motivation, background
2. Hybrid analytical / numerical coupled mode theory
setting: frequency domain, 3D / 2D ...
2.1 Coupled mode field template specifically for an example, general
2.2 Amplitude discretization specifically for an example, general
2.3 Projection & algebraic procedure
2.4 Remarks on theory and implementation avoiding heuristics, relation to numerics, scaling properties, types of basis fields, boundary conditions, spectral scans, material dispersion
2.5 Eigenfrequencies of composite systems "supermodes"; perturbational analysis
2.6 Variational approach: restriction of a functional
3. Examples, 2D
3.1 Basis elements modes of straight channels, bend modes, eigenmodes of cavities, WGMs
3.2 Straight parallel waveguides
3.2 Waveguide crossing
3.3 Waveguide Bragg reflector
3.4 Chains of coupled square cavities
3.5 Resonators with Ring and disc cavities, bend- and WGM templates
3.6 Coupled resonator optical waveguide
4. 3D HCMT
implementation, first results, outlook
4.1 ...
4.2 ...
5. Concluding remarks brief summary of results, additional comments
Chapter 2:
Finite Element Time Domain Method for Photonics
By: B M A Rahman, R Kabir, A Agrawal, City University London
Outline:
In this chapter we will discuss the development of a finite element based time domain approach, the use of perforated mesh to increase numerical efficiency and evaluation of numerical dispersions for both 2-D and 3-D photonic devices. Comparison of speed enhancement over the finite difference time domain method will be shown particularly comparing their numerical dispersions
