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Vectorized transfer matrix method (TMM) for computing the optical reflection and transmission of multilayer planar stacks
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vtmm (vectorized transfer matrix method)

vtmm is a vectorized implementation of the transfer matrix method for computing the optical reflection and transmission of multilayer planar stacks. This package is in beta.

The vtmm package supports some of the same functionality as the tmm Python package developed by Steven Byrnes. However, in vtmm all operations are vectorized over angles / wavevectors as well as frequencies. Due to the small size of the matrices involved in the transfer matrix method (2 x 2), such vectorization results in significant performance gains, especially for large structures and many frequencies / wavevectors.

In some cases we have observed approximately two orders of magnitude difference in execution time between the two implementations (see below). The much lower execution time in vtmm may be useful for applications which require many evaluations of the reflection and transmission coefficients, such as in fitting or optimization.


Currently vtmm uses Tensor Flow as its backend. This means that gradients of scalar loss / objective functions of the transmission and reflection can be taken for free. At a later time a numpy backend may be implemented for users that do not need gradient functionality and/or do not want Tensor Flow as a requirement.


The entry point to vtmm is the function tmm_rt(pol, omega, kx, n, d). See the example below for a basic illustration of how to use the package.

import tensorflow as tf
from vtmm import tmm_rt

pol = 's'
n = tf.constant([1.0, 3.5, 1.0]) # Layer refractive indices 
d = tf.constant([2e-6]) # Layer thicknesses 
kx = tf.linspace(0.0, 2*np.pi*220e12/299792458, 1000) # Parallel wavevectors
omega = tf.linspace(150e12, 220e12, 1000) * 2 * np.pi # Angular frequencies

# t and r will be 2D tensors of shape [ num kx, num omega ]
t, r = tmm_rt(pol, omega, kx, n, d)


See tests/ for a comparison between vtmm and the non-vectorized tmm package. The benchmarks shown below are for len(omega) == len(kx) == 50 and 75 timeit evaluations.

python -W ignore ./tests/
Single omega / kx benchmark
vtmm: 0.2432 s
tmm:  0.0401 s

Large stack benchmark
vtmm: 0.7811 s
tmm:  79.8765 s

Medium stack benchmark
vtmm: 0.4607 s
tmm:  52.2255 s

Small stack benchmark
vtmm: 0.3367 s
tmm:  41.0926 s
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