PhotonicsSHA-2D: Modeling of Single-Period Multilayer Optical Gratings and Metamaterials

By Xingjie Ni1, Zhengtong Liu1, Fan Gu1, Marcos Gabriel Pacheco2, Joshua Borneman1, Alexander V. Kildishev3

1. Purdue University 2. University of Texas at El Paso 3. Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA

Frequency domain simulation of single-period multilayer gratings and optical metamaterials upon TE/TM plane-wave incidence at arbitrary angles

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Version 0.9.7 - published on 02 Mar 2015

doi:10.4231/D36H4CR41 cite this

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PhotonicsSHA-2D: Modeling of Single-Period Multilayer Optical Gratings and Metamaterials employs the 2-dimensional spatial harmonic analysis (2D SHA) method to model the optical responses of single-period multilayer gratings. The incident wave is a plane wave with arbitrary incident angles (with either TE or TM polarization), and the output results are the complex transmission and reflection coefficients for the zero diffraction order. The database of optical elemental materials stored in PhotonicsDB is integrated into this tool.

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The GUI of PhotonicsSHA-2D was developed using Qt and Qwt library. The solver was developed in C with LAPACK.


  • Xingjie Ni ... Graduate SURF mentor, TM solver development, GUI development, PhotonicsDB integration, overall testing
  • Zhengtong Liu ... TE solver developement, overall testing
  • Fan Gu ... SURF Fellow, GUI development
  • Marcos Gabriel Pacheco ... SURF Fellow, GUI development
  • Alexander V. Kildishev ... Advising SURF Professor, Initial GUI development and TM solver prototyping
  • Acknowledgements

  • Dmitrii S. Zakharov ... Initial GUI prototyping
  • Michael McLennan, Derrick Kearney, Steven Clark ... nanoHUB training and support


[1] K. Knop, "Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves," J. Opt. Soc. Am., Vol.68, No.9, 1206-1210 (1978).

[2] Alexander V. Kildishev and Uday K. Chettiar, "Cascading Optical Negative Index Metamaterials," ACES Journal, Vol.22 No.1, 172-182 (2007).

[3] P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A, Vol.13, No.4, 779-784 (1996).

[4] G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A, Vol.13, No.5, 1019-1023 (1996).

[5] Lifeng Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A, Vol.13, No.5, 1024-1035 (1996).

[6] Lifeng Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A, Vol.13, No.9, 1870-1876 (1996).


[1] Z. Liu, K.-P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, A. V. Kildishev, “SHA Modeling of Gold Gratings for Oblique Light Incidence”, Quantum Electronics and Laser Science Conference (QELS), May 17-21, 2010, San Jose, CA, USA.

[2] Zhengtong Liu, Kuo-Ping Chen, Xingjie Ni, Vladimir P. Drachev, Vladimir M. Shalaev, and Alexander V. Kildishev, "Experimental Verification of Two-Dimensional Spatial Harmonic Analysis with Oblique Light Incidence", submitted.

Cite this work

Researchers should cite this work as follows:

  • Xingjie Ni; Zhengtong Liu; Fan Gu; Marcos Gabriel Pacheco; Joshua Borneman; Alexander V. Kildishev (2015), "PhotonicsSHA-2D: Modeling of Single-Period Multilayer Optical Gratings and Metamaterials," (DOI: 10.4231/D36H4CR41).

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