Modeling and photonic Simulation:RSM

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 :

La géométrie à deux dimensions du composant d’optique intégrée à modéliser est d’abord échantillonnée en une succession de segments de guides droits. Chaque guide droit dont le profil d’indice de réfraction peut être une fonction continue sera lui aussi approximé en un guide équivalent plan multicouche. Le champ électromagnétique d’excitation défini sur le plan d’entrée du composant est projeté sur l’ensemble des modes guidés et rayonnés du premier tronçon de guide droit. Afin de garder l’aspect entièrement vectoriel de la méthode, cette projection doit se fait sur les modes incidents et réfléchis. Le champ à l’extrémité de ce segment de guide droit est alors calculé simplement en propageant le champ issu de chacun des modes incidents et réfléchis. Ce champ sert alors de nouveau champ d’excitation pour le tronçon de guide suivant pour lequel la même opération est répétée. Cela jusqu’à atteindre l’extrémité du composant. Pour les composants présentant des réflexions, on utilise une approche itérative en procédant par allers-retours de l’entrée jusqu’à l’extrémité du composant où sur ces faces on rappelle les conditions aux limites.

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

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  Geometry

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  Overlap of the plots of field (color) and refractive index (gray)

• Mach-Zehnder interferometer in on state

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  Geometry

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  Overlap of the plots of field (color) and refractive index (gray)

• Photonic crystal

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  Geometry

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  Overlap of the plots of field (color) and refractive index (gray)

• Micro lens

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  Geometry

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  Overlap of the plots of field (color) and refractive index (gray)

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/ . In all this project, we wanted to keep every where the general aspect of the problem. The geometry of the waveguide and the excitation conditions mist stay arbitrary. We are working now to port this Mac OS X software to Windows.

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.

[4] http://camfr.sourceforge.net/

[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.