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PPML - Periodically Patterned Multi Layer

version 1.2 (1.34 MB) by Simone Zanotto
Electromagnetic properties of patterned multilayers based on RCWA (Rigorous Coupled Wave Analysis)


Updated 21 May 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].

Three groups of functions are available: one is for 1-d patterns under TM polarization, another is for 1-d anisotropic (biaxial) patterns, the third for certain 2-d patterns.

For 1-d TM 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

The proper factorization rules [c,d] make the code extremely performing, and fully suitable for the simulation of metal components (plasmonic gratings).
Out-of-plane uniaxial materials can be treated.

For 1-d biaxial media, the following function is available:
i) amplitude, phase and polarization of transmitted diffracted waves

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 1.2 (see below). For some of them, you can find the corresponding tutorial in the software package.

Publications based on PPML 1.2

1. S. Zanotto, F. Sgrignuoli, S. Nocentini, D. Martella, C. Parmeggiani, D. S. Wiersma, "Multichannel remote polarization control enabled by nanostructured Liquid Crystalline Networks", to be published in Applied Physics Letters (2019)
2. S. Zanotto, G. C. La Rocca, and A. Tredicucci, “Understanding and overcoming fundamental limits of asymmetric light-light switches”, Optics Express 26, 3, 3618 (2018).
3. 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", Advanced Optical Materials 2017, 5, 1600732 (2017)
4. 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)
5. 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)
6. 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)
7. 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)
8. 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)
9. 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)
10. 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)
11. 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)
12. 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 (5)

kang chen

Thank you for your helpful work!
If possible, could you please answer my question?
When I simulate a MIM metasurface(Cu and Al2O3), there is a absorption peak locating at mid-infrared region.
But the result of FDTD is different from this code's. The results from various methods maybe have some difference, while I think 0.5um( peak position) can not be ignored.
Thank you for your attention to this matter.


S.Q. Li



The current version supports biaxial anisotropic permittivities in the 1-d pattern geometry (stripe array), under arbitrary polarization and incidence angle.

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 R2018b
Compatible with any release
Platform Compatibility
Windows macOS Linux