vtmmpy 1.0.1

A vectorized implementation of the transfer matrix method

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.

Mathematical background

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$$ \mathbf{M}{TM}^{(\ell)} = \begin{bmatrix} \cos(\beta\ell d_\ell) & \sin(\beta_\ell d_\ell)n_\ell^2/\beta_\ell \ -\sin(\beta_\ell d_\ell)\beta_\ell/n_\ell^2 & \cos(\beta_\ell d_\ell) \end{bmatrix} \hspace{1cm} \mathbf{M}{TE}^{(\ell)} = \begin{bmatrix} \cos(\beta\ell d_\ell) & \sin(\beta_\ell d_\ell)/\beta_\ell \ -\sin(\beta_\ell d_\ell)\beta_\ell & \cos(\beta_\ell d_\ell) \end{bmatrix} $$

$$ \mathbf{M} = \mathbf{M}^{(L)}\cdots\mathbf{M}^{(2)}\cdot\mathbf{M}^{(1)} $$

$$ r_{TM} = -\frac{\mathbf{M}{TM}^{-1}n_t^2\beta_i-\mathbf{M}{TM}^{-1}n_i^2\beta_t+i[\mathbf{M}{TM}^{-1}n_i^2n_t^2+\mathbf{M}{TM}^{-1}\beta_i\beta_t]}{\mathbf{M}{TM}^{-1}n_t^2\beta_i+\mathbf{M}{TM}^{-1}n_i^2\beta_t-i[\mathbf{M}{TM}^{-1}n_i^2n_t^2-\mathbf{M}{TM}^{-1}\beta_i\beta_t]} $$

$$ r_{TE} = -\frac{\mathbf{M}{TM}^{-1}\beta_i-\mathbf{M}{TM}^{-1}\beta_t+i[\mathbf{M}{TM}^{-1}+\mathbf{M}{TM}^{-1}\beta_i\beta_t]}{\mathbf{M}{TM}^{-1}\beta_i+\mathbf{M}{TM}^{-1}\beta_t-i[\mathbf{M}{TM}^{-1}-\mathbf{M}{TM}^{-1}\beta_i\beta_t]} $$

$$ t_{TM} = -\frac{2n_in_t\beta_i}{\mathbf{M}{TM}^{-1}n_t^2\beta_i+\mathbf{M}{TM}^{-1}n_i^2\beta_t-i[\mathbf{M}{TM}^{-1}n_i^2n_t^2-\mathbf{M}{TM}^{-1}\beta_i\beta_t]} $$

$$ t_{TE} = -\frac{2\beta_i}{\mathbf{M}{TM}^{-1}\beta_i+\mathbf{M}{TM}^{-1}\beta_t-i[\mathbf{M}{TM}^{-1}-\mathbf{M}{TM}^{-1}\beta_i\beta_t]} $$

Installation

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Pip

pip install vtmmpy 

Manual

git clone [e-mail]:AI-Tony/vtmmpy.git
cd vtmmpy/modules
mv vtmmpy.py <YOUR PATH OR PROJECT DIRECTORY> 

Usage

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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 addDesign() method.

materials = ["sio2", "tio2", "sio2", "tio2", "sio2"] 
thicknesses = [54, 92, 134, 112, 68] 

tmm.addDesign(materials, thicknesses)

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

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

tmm.summary() 
tmm.designs() 

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).
• The minimum number of dimensions for reflection() and transmission() is 2. Therefore, when printing/plotting results, an index must be provided.

Examples

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