S4: Stanford Stratified Structure Solver

By Jiarui Kang; Xufeng Wang1; Peter Bermel1; Chang Liu1

1. Purdue University

S4 is a frequency domain code to solve layered periodic structures. Internally, it uses Rigorous Coupled Wave Analysis (RCWA; also called the Fourier Modal Method (FMM)) and the S-matrix algorithm.

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Version 1.11 - published on 13 Aug 2014

doi:10.4231/D35T3G11T cite this

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S4 is a frequency domain code to solve layered periodic structures. Internally, it uses Rigorous Coupled Wave Analysis (RCWA; also called the Fourier Modal Method (FMM)) and the S-matrix algorithm. S4 was developed by Victor Liu of the Fan Group in the Stanford Electrical Engineering Department. http://www.stanford.edu/group/fan/S4/#main The S4sim Nanohub tool was developed at Purdue University as an analysis of optical propagation in the generalized 3D structure much more quickly than many alternatives. However, the original tool is hard to use. So the goal is to make it more accessible, especially for experimentalists in PV community.This tool allowed the user to click into the parameters including the number of layers and material for each layer and to define a multi-layers structure. The original complicated coding process was totally replaced. This tool then output data for the structure, which helped making the structure clear. General overview of transfer matrix methods: http://web.ics.purdue.edu/~pbermel/ece595/Lectures/ECE%20595%20-%20Lecture%2026.pdf S-matrix methods: http://web.ics.purdue.edu/~pbermel/ece595/Lectures/ECE%20595%20-%20Lecture%2027.pdf S-matrix calculations on 3D systems, including an introduction to S4: http://web.ics.purdue.edu/~pbermel/ece595/Lectures/ECE%20595%20-%20Lecture%2028.pdf

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Dr. Bermel is a tenure-track assistant professor of electrical and computer engineering at Purdue. He has published a total of 24 peer-reviewed original research articles on fundamental material science and engineering, including simulations and experiments on electromagnetic and quantum mechanical systems. Including scientific reviews, conference proceedings, and patents, he has published a total of 40 technical documents. His work has been cited a total of 1614 times, for an h-index value of 15. Peter's primary research goal is to improve the performance of photovoltaic, thermophotovoltaic, and nonlinear systems using the principles of nanophotonics.


Purdue University Prof. Peter Bermel Graduate Student Xufeng Wang Undergraduate Student Jiarui Kang Undergraduate Student Chang Liu In collaboration with: Prof. Mark Lundstrom Prof. Muhammad Ashraf Alam Prof. Jeff Gray

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This project was sponsored by the Bay Area Photovoltaic Consortium, a Department of Energy project with Prime Award number DE-EE0004946.

Cite this work

Researchers should cite this work as follows:

  • 1. Victor Liu and Shanhui Fan, "S4: A free electromagnetic solver for layered periodic structures," Computer Physics Communications 183, 2233-2244 (2012) http://dx.doi.org/10.1016/j.cpc.2012.04.026. 2. Michael Ghebrebrhan, Peter Bermel, Yehuda Avniel, John D. Joannopoulos, Steven G. Johnson, "Global optimization of silicon photovoltaic cell front coatings", Optics Express 17, 7505 (2009).
  • Jiarui Kang, Xufeng Wang, Peter Bermel, Chang Liu (2014), "S4: Stanford Stratified Structure Solver," https://nanohub.org/resources/s4sim. (DOI: 10.4231/D35T3G11T).

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