Vectorized Transfer Matrix Method Python

The transfer matrix method (TMM) is an analytic approach for obtaining the reflection and transmission coefficients in stratified media. vtmmpy is a vectorised implementation of the TMM written in Python. It has a focus on speed and ease of use.

Installation

pip install vtmmpy 

Usage

Import the vtmmpy module.

import vtmmpy

Create an instance of the TMM class.

freq = np.linspace(170, 210, 30) 
theta = np.array(0, 60, 60) 

tmm = vtmmpy.TMM(freq, 
                theta, 
                f_scale=1e12, 
                l_scale=1e-9, 
                incident_medium="air", 
                transmitted_medium="air") 

• freq: a numpy array representing the spectral range of interest.
• theta: a numpy array of one or more angles of incidence.
• f_scale (optional): input frequency scale, default is terahertz.
• l_scale (optional): input length scale, default is nanometers.
• incident_medium (optional): incident medium, default is air.
• transmitted_medium (optional): transmitted medium, default is air.

Add multilayer metamaterial designs with the add() method.

materials   = ["Ag", "SiO2", "Ag", "SiO2", "Ag", "SiO2"] 
thicknesses = [15, 85, 15, 85, 15, 85] 

tmm.add(materials, thicknesses)

• materials: list of materials
• thicknesses: list of the corresponding material thicknesses

Internally, vtmmpy uses the regidx Python package to download refractive index data from refractiveindex.info for your choosen materials and spectral range. At this point, you will be presented with a few options corresponding to the data source ("Page" dropdown on refractiveindex.info). Study these carefully and refer to refractiveindex.info for more detailed information about how the data were obtained. Your choice here could greatly impact the accuracy of your results.

Optionally call the summary() and/or designs() methods to view the data currently held by the instance.

tmm.summary() 
tmm.designs() 

Additionally, the tmm.opticalProperties() method can be used to obtain a dictionary of optical properties of the materials entered in the frequency range specified.

props = tmm.opticalProperties()

print(props.keys()) # output: dict_keys(['air', 'SiO2', 'Ag'])
print(props["Ag"]["n"]) # ouput is the refractive index of Ag
print(props["Ag"]["beta"]) # ouput is the propagation constant of Ag

Calculate the reflection/transmission coefficients by calling the appropriate method. You should specify wether you want the transverse magnetic/electric polarization by supplying the "TM" or "TE" flag, respectively.

RTM = tmm.reflection("TM") 
RTE = tmm.reflection("TE") 
TTM = tmm.transmission("TM") 
TTE = tmm.transmission("TE") 

Tips:

• The reflection() and transmission() methods return both complex parts. Use Python's built-in abs() function to obtain the magnitude.
• The intensity is the square of the magnitude (eg. abs(reflection("TM"))**2).
• reflection() and transmission() return an ndarray with a minimum of 2 dimensions. The first dimension always corresponds to the number of designs. Therefore, when printing/plotting results, you must always index the first dimension (even if you only have 1 design).

Examples