Transmission line photonic crystals: a comparison of Green's formalism, lumped circuit element model, and finite element method

This chapter presents the modeling, using Advanced Design System (ADS) from Keysight Technologies and Finite Element Method (FEM) based on Comsol Multiphysics tools, of photonic circuits. We particularly report in this chapter a confirmation of the results reported in Chapters 9, 10, and 11 concerning Fano, electromagnetic induced transparency (EIT), electromagnetic induced absorption (EIA) resonances, demultiplexer design based on EIT resonance, and the properties of comb structures with or without a defect state. In this chapter, we focus on three models: (i) lumped circuit elements used by ADS, (ii) FEM analysis of telegrapher's equation using Comsol, and (iii) FEM analysis of electromagnetic waves equation using Comsol. A comparison of these model results with those obtained by the Green's formalism in Chapters 9, 10, and 11 shows a good agreement. The analytical Green's function formalism enables an in-depth understanding of the physics; whereas the use of software-aided design will enable making the design, optimization, and experimentation of new designs in the field of photonics and microwaves quicker.