cgubbin / Nonlocal_SMMs

Calculations for Nonlocal Optical Response of N-Layer Polar Dielectric Stacks

Nonlocal Scattering Matrix Calculator

This module implements the nonlocal scattering matrix formalism available on the arXiv or behind a paywall. It allows you to calculate the reflectance of anisotropic planar semiconductor heterostructures. Documentation is available here. If you use the code please cite the paper!

Installation

This repository is packaged using Poetry. Having installed Poetry you can install the package and it's dependancies as:

$ git clone https://github.com/cgubbin/nonlocal_smms.git
$ cd nonlocal_smms
$ poetry install

Examples are demonstrated in Jupyter notebooks in /examples, to launch the notebook server run:

$ cd examples
$ poetry run jupyter notebook

Basic Usage

To create a simple heterostructure such as the nitride stack studied in the accompanying manuscript write

from nonlocal_smms.core import scattering_matrix

angle = 75  # Incident angle in degrees
wavenumbers = [x for x in range(750, 1050)]  # Sets a wavenumber range to probe
thickness = 1e-9  # Set the layer thickness
repetitions = 50  # Set the sublattice repeats

# Construct the heterostructure
sublattice = [['AlN', thickness], ['GaN', thickness]]  # Define the superlattice cell
superlattice = sublattice * repetitions
superlattice.insert(0, ['vacuum', 0])
superlattice.insert(len(superlattice), ['SiC4H', 0])

# Calculate the reflectance
rte, rtm = scattering_matrix(wavenumbers, superlattice, angle=angle)

Adding a Material to the Database

To add a material to the database follow this template:

from tinydb import TinyDB, Query

# Import the material database, you will need to change the import path depending
# on where you run the script
material_db = TinyDB(".../materials.json")

# Create a new material, in this case 3C-SiC. Note that frequencies are provided in wavenumbers
# while velocities (beta_) are provided in unitless form. They are the physical phonon velocity
# divided by the speed of light in vacuum.
new_material = {
  "beta_l": 3e-05, "beta_t": 3e-05, "beta_c": 5e-05, "rho": 3.21, "eps_inf_pa": 6.52,
  "eps_inf_pe": 6.52, "eps_0_pa": 9.7, "eps_0_pe": 9.7, "wto_pa": 797.4, "wto_pe": 797.5,
  "gamma": 4, "wlo_pa": 972.69, "wlo_pe": 972.7, "material": "SiC3C"
}

# Insert the new material into the database, automatically writing to file
material_db.insert(new_material)