This work belongs to the AIMS Lab, Indian Institute of Technology Bombay, prepared under the guidance of Professor Siddharth Tallur. The code has been employed to investigate the results published in our journal article :

Pallabi Das, Shlok Vaibhav Singh and Siddharth Tallur, Design and analysis of electro-optic modulators based on high contrast gratings in AlGaN/GaN heterostructures Semiconductor Science and Technology (IOP Publishing), 35.12, 125022, October 2020

The analytical model used was developed in C. J. Chang-Hasnain and W. Yang, High-contrast gratings for integrated optoelectronics," Advances in Optics and Photonics 4, 379-440 (2012)

Grating Analysis Code

This repository hosts the code for analysis of the some electromagnetic properties of Grating structures.

A grating waveguide is an optical waveguide where the waveguide is in form of periodic structures (1-D or 2-D), more can be read on wikipedia here. This is how our structure looks like:

The period of grating is denoted by Λ,θ is the angle of incidence k₀ denotes the wavevector of incident wave, we take surrounding medium to be air, so that n₀=1, we assume translational symmetry in y-axis so that φ=0, n_bar is the refractive index of bar, we assume that all refractive indices are real. Polarization can be TM or TE. Another variable needed is the duty cycle, or the fraction of space in each period of grating occupied by the bar, we denote this by η. All these variables describe the required physics needed to model the device.

Our interest lies in computing the reflectivity and the transmittivity exhibited by the structure for given values of (Λ,k₀,θ,n_bar, η). The reflected and transmitted power will further be divided into amongst various diffracted beams.

We now show the results obtained by our code, then we shall explain how to use the code and then performance issues and limitations will be demonstrated.

Results

Reflectivity Spectrum

The reflectivity spectrum obtained using our code with RCWA results superimposed for Benchmarking.

TE mode	TM mode

Field intensity profile

TE mode	TM mode

Code

The main code is HCG_central_node. The various callee and caller functions are shown:

Performance and issues

Functionality	Results benchmarked?	Source for benchmarking
TM mode reflectivity	☑	RCWA
TE mode reflectivity	☑	RCWA
TM mode field profile	☒
TE mode field profile	☑	Compated with Results in High-contrast gratings for integrated optoelectronics Connie J. Chang-Hasnain and Weijian Yang

References

• High-contrast gratings for integrated optoelectronics
  Connie J. Chang-Hasnain and Weijian Yang

This is the primary reference where the analytical derivation of the model is carried out.

• PPML-Periodically Patterned Multi Layer, Simone Zanotto