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PPML - Periodically Patterned Multi Layer

version (1.28 MB) by Simone Zanotto
Electromagnetic properties of patterned multilayers based on RCWA (Rigorous Coupled Wave Analysis)


Updated 14 Feb 2019

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Rigorous coupled wave analysis (RCWA) based on the scattering matrix (SM) algorithm is one of the most powerful tools for the electromagnetic simulation of patterned multilayer structures.
PPML - RCWA is a project which implements the SM-RCWA, based on the formalisms of [a-d].

Two groups of functions are available: one is for 1-d patterns, the other for 2-d patterns.
Not all the features available for 1-d patterns are available for 2-d ones, and vice-versa.

For 1-d patterns, currently available are functions for the calculation of
i) intensity reflectance, transmittance, and layer-by-layer absorbance
ii) the full 2x2 scattering matrix
iii) the E and S fields inside the structure

1-d patterns are only supported for TM-polarization, i.e., p-polarized incident waves belonging to the plane orthogonal to the pattern (see the Manual for details).
This specificity, together with the proper factorization rules [c,d], make the code extremely performing, and fully suitable for the simulation of metal components (plasmonic gratings).
Anisotropic materials can be treated.

For 2-d patterns, currently available are functions for the calculation of
i) polarization-resolved reflection coefficients

Allowed unit cell geometries are rectangular and L-shaped inclusions (see the Manual for details). The proper factorization rules are implemented [c,d], thus allowing for a fast convergence even in presence of metallic inclusions.

The present code is distributed for free, but we kindly ask you to cite its source and, if applies, the publications below.

Several publications are based on PPML 1.1 (see below). For some of them, you can find the corresponding tutorial in the software package.

Publications based on PPML 1.1

1. S. Zanotto. A. Blancato, A. Buchheit, M. Munoz-Castro, H.-D. Wiemhofer, F. Morichetti, and A. Melloni, "Metasurface reconfiguration through lithium ion intercalation in a transition metal oxide", to be published (2016)
2. S. Zanotto and A. Tredicucci, "Universal lineshapes at the crossover between weak and strong critical coupling in Fano-resonant coupled oscillators", Scientific Reports 6, 24592 (2016)
3. L. Baldacci, S. Zanotto, G. Biasiol, L. Sorba, and A. Tredicucci, “Interferometric control of absorption in thin plasmonic metamaterials: general two port theory and broadband operation”, Optics Express 23, 9202 (2015)
4. S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy feeding into strongly coupled systems and interferometric control of polariton absorption”, Nature Physics 10, 830 (2014)
5. J.-M. Manceau, S. Zanotto, T. Ongarello, L. Sorba, A. Tredicucci, G. Biasiol, and R. Colombelli, “Mid-infrared intersubband polaritons in dispersive metal-insulator-metal resonators”, Appl. Phys. Lett. 105, 081105 (2014)
6. J.-M. Manceau, S. Zanotto, I. Sagnes, G. Beaudoin, and R. Colombelli, “Optical critical coupling into highly confining metal-insulator-metal resonators”, Appl. Phys. Lett. 103, 091110 (2013)
7. S. Zanotto, R. Degl'Innocenti, J. Xu, G. Biasiol, L. Sorba and A. Tredicucci, “Ultrafast optical bleaching of intersubband cavity polaritons”, Phys. Rev. B 86, 201302(R) (2012)
8. S. Zanotto, R. Degl'Innocenti, G. Biasiol, L. Sorba and A. Tredicucci, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs”, Phys. Rev. B 85, 035307 (2012)
9. R. Degl'Innocenti, S. Zanotto, G. Biasiol, L. Sorba and A. Tredicucci, “One-dimensional surface-plasmon gratings for the excitation of intersubband polaritons in suspended membranes”, Solid State Comm. 151, 1725-1727 (2011)
10. S. Zanotto, G. Biasiol. R. Degl'Innocenti, L. Sorba and A. Tredicucci, “Intersubband polaritons in a one-dimensional surface plasmon photonic crystal”, Appl. Phys. Lett. 97, 231123 (2010)

References for the method
a. D. M. Whittaker & I. S. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures",
Phys. Rev. B 60, 2610 (1999).
b. M. Liscidini, D. Gerace, L. C. Andreani & J. E. Sipe, "Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media", Phys. Rev. B 77, 035324 (2008).
c. L. Li. "Use of Fourier series in the analysis of discontinuous periodic structures". J. Opt. Soc. Am. A 13, 1870 (1996)
d. Lalanne, Philippe, and G. Michael Morris, "Highly improved convergence of the coupled-wave method for TM polarization", JOSA A 13, 779 (1996).

Cite As

Simone Zanotto (2019). PPML - Periodically Patterned Multi Layer (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (3)

S.Q. Li


Ahmet Tüzen


Updated logo

Fixes an error in the manual ( pag. 2, k = k0*sqrt(eps_sup) )

Version 1.1. Updates the SM_1d_tm function (left-> right and right-> left transmittance with the correct phases)
and includes the 2d folder (for the simulation of certain 2-d patterns)

testing updates

MATLAB Release Compatibility
Created with R2014b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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