# Modeling and photonic Simulation:RSM

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## Modeling tool RSM :

- The Radiation Spectrum Method [1] (RSM) resolves the same problem than the generic Beam Propagation Method (BPM). It permits to simulate the propagation of light in an arbitrary shaped component of integrated optics. The RSM makes use of a modal approach whereas the others BPM mainly use finite difference or fast Fourier transform approaches. For this problem, both the device geometry (spatial distribution of the refractive index) and the excitation field (transverse distribution of both the electric and magnetic fields at the entrance of the component) have to be defined arbitrarily. In opposition with the FDTD (Finite Difference Time Domain method) where all kind of temporal and impulsionnal excitation is accepted, the RSM calculates only the harmonic established field. This tool makes use of the theoretical developments on the analytical normalization of the radiation modes of the 2D multilayer dielectric waveguidess [2], [3]. The main originality of the RSM compared to the concurrent modal tools (BPM_BEP, Camfr [4]) is that using this analytical normalization, it is no more necessary to close laterally the waveguide with metal walls. This gives a direct advantage in caclulation speed and makes the RSM compatible with a further speedup using fast Fourier transforms.

## Principle :

- The two-dimensional geometry of the integrated optical component to be modeled is first sampled in a succession of straight guide segments. Each straight guide whose refractive index profile may be a continuous function will also be approximated to a multilayer equivalent plane guide. The excitation electromagnetic field defined on the input plane of the component is projected on all the guided and radiated modes of the first straight guide section. In order to keep the entirely vectorial aspect of the method, this projection must be done on the incident and reflected modes. The field at the end of this straight guide segment is then calculated simply by propagating the field resulting from each of the incident and reflected modes. This field then serves as a new excitation field for the next guide section for which the same operation is repeated. This until reaching the end of the component. For components with reflections, an iterative approach is used by going back and forth from the input to the end of the component where on these faces the boundary conditions are recalled.

## Advantages :

- modal approach: this permits a physical understanding of the physical mechznisms that explain permet une interprétation physique du fonctionnement du composant étudié par l’analyse de l’évolution de la répartition de la puissance sur les différents modes (spectre des modes) en cours de propagation

- rigorous vectorial simulation : wide angle propagation, polarization effects, reflections

- high guiding conditions

- high calculation speed

## Limitations :

- harmonic established field : monochromatic excitation

- 2D modeling

- pure real refractive index materials

## Application examples:

- Mach-Zehnder interferometer in off state

- Mach-Zehnder interferometer in on state

- Photonic crystal

- Micro lens

## Available software :

- A development work has been initiated these recent years to transform the RSM calculation kernel issued of work in reference [1] to a friendly software. The main motivation was to obtain a very easy to use software that can demonstrate easily all the possibilities offered by the choice of a modal approach. At this date, a free licence software with a GUI (Graphical User Interface) is available and can be downloaded here : http://sourceforge.net/projects/rsmvisit/. Different versions are available for Windows, Mac OS X and ever an old version for MS-DOS 32 bits. In all this project, we wanted to keep everywhere the general aspect of the problem. The geometry of the waveguide and the excitation conditions must stay arbitrary.

- example taper waveguide simulation with the RSM visit software for Windows

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- example taper waveguide simulation with the RSM visit software for Mac OS X

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- example mirror waveguide simulation with the RSM visit software for Mac OS X

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Principal functions :

- -definition of the waveguide geometry of three different manners :
- CAD file (dxf)
- script
- proprietary file

- - excitation conditions :
- E and H fields for the fundamental mode of an input waveguide
- E and H field for a gaussian excitation
- sampled E and H field stored in a file for an arbitrary excitation

- - graphical outputs :
- refractive index plot (2d and 3D)
- propagation field plot (2D and 3D)
- plot for the spectrum of guided and radiation modes during the propagation in the device

- - saving of all the parameters for the current calculation

- - saving of the output data in files for the further treatment with other plotting software

## Bibliography:

- [1] P. Gérard, P. Benech, D. Khalil, R. Rimet, S. Tedjini, “Towards a full vectorial and modal technique for the analysis of integrated optics structures : the Radiation Spectrum Method (RSM)”, Optics Communications , Vol 140, july 1997, pp 128-145.

- [2] H. Ding, P. Gérard and P. Benech "Radiation modes of lossless multilayer dielectric waveguides". IEEE Journal of Quantum Electronics, Vol. 31, n°2, February 1995, pp 411-416.

- [3] P. Gérard, P. Benech, H. Ding and R. Rimet. "A simple method for the determination of orthogonal radiation modes in planar multilayer structures". Optics Communication 108, June 1994 , pp 235-238.

- [5] P. Gérard, “Vers une méthode du faisceau propagé modale et rapide : RSM-FFT”, actes de la conférence Journées Nationales de l’Optique Guidée, 12-14 novembre 2003, Valence, p231-233.

- [6] V. Raulot, P. Gérard, B. Serio, M. Flury, B. Kress, P. Meyrueis, “Modeling of the angular tolerancing of an effective medium diffractive lens using combined finite difference time domain and radiation spectrum method algorithms”, Optics Express, vol. 18, n°. 17, August 2010, p 17974-17982.

- [7] K. P. Fakhri, P. Benech “A new technique for the analysis of planar optical discontinuities : an iterative modal method”, Optics Communications, Vol. 177, 15 april 2000, pp 233-243.

- [8] P. Gérard, “Radiation modes of lossy or active slab waveguides”, Optics Communications , Vol 151, may 1998, pp 110-116.