OSCAR a Matlab based optical FFT code

Optical simulation softwares are essential tools for designing and commissioning laser interferometers. This article aims to introduce OSCAR, a Matlab based FFT code, to the experimentalist community. OSCAR (Optical Simulation Containing Ansys Results) is used to simulate the steady state electric fields in optical cavities with realistic mirrors. The main advantage of OSCAR over other similar packages is the simplicity of its code requiring only a short time to master. As a result, even for a beginner, it is relatively easy to modify OSCAR to suit other specific purposes. OSCAR includes an extensive manual and numerous detailed examples such as simulating thermal aberration, calculating cavity eigen modes and diffraction loss, simulating flat beam cavities and three mirror ring cavities. An example is also provided about how to run OSCAR on the GPU of modern graphic cards instead of the CPU, making the simulation up to 20 times faster. 1. Overview of OSCAR OSCAR is a FFT code which is able to simulate Fabry Perot cavities with arbitrary mirror profiles. One of the key features of OSCAR is the possibility to easily modify the code to tailor specific simulation purposes. OSCAR is written with the Matlab scripting language, one can import/export files (mirror maps or cavity eigen modes profile for example), create a ring cavity, create batch file or plot 2D optical field with little programming skill. The core of the code is only 400 lines long (including comments) and the manual provides five detailed examples. The first version of OSCAR was written with the software IGOR[1] in 2005. This code was then translated to Matlab and used to calculate diffraction losses by Pablo Barriga[2]. Finally, the Matlab code has been rewritten to decrease the computational time and to add new functionality. OSCAR is mainly intended for people who want to quickly simulate only one cavity with non Gaussian fundamental eigenmodes or input beam. The code and the manual can also be used as an educational tool to understand how internally FFT code works. 1.1. Possible simulations OSCAR is a versatile tool to simulate Fabry Perot cavities. The following is a (non-exhaustive) list of the results which can be obtained with OSCAR: • calculate the Gouy phase shift between higher order optical modes. It may be useful for flat beams for example, where no analytical calculations of the Gouy phase shift has been derived yet 8th Edoardo Amaldi Conference on Gravitational Waves IOP Publishing Journal of Physics: Conference Series 228 (2010) 012021 doi:10.1088/1742-6596/228/1/012021 c © 2010 IOP Publishing Ltd 1 • calculate the coupling loss between the input beam and the cavity eigen modes in the case of mode mismatching • calculate the circulating beam (intensity and profile) for stable and also unstable cavities • calculate diffraction loss and eigen modes of a cavity with arbitrary mirror profiles and imperfect optics. 1.2. Restrictions OSCAR is designed to simulate anything which can be derived from the steady state, classical, optical field circulating inside a Fabry Perot cavity. It means OSCAR does not take into account radiation pressure or quantum effects. OSCAR (in the present version) can not simulate coupled cavities. For more complex simulation other FFT codes such as SIS[3] or darkF[4] exist. 2. Principle In this section, we briefly introduce the concept of optical simulations using the Fourier transform. Unfortunately, due to the limited length of this article, no demonstration is included but the justification can be found in the references or in the OSCAR manual. 2.1. Propagation of an arbitrary optical field It is possible to propagate any arbitrary coherent optical field under the paraxial approximation by the use of a Fourier transform. Typically such an operation requires 3 steps [5]: (i) Decomposition of the complex amplitude of the electric field into a sum of elementary plane waves. Mathematically, this step is achieved by a 2D Fourier transformation. (ii) Propagation of each plane wave, which is equivalent to adding a phase shift in the frequency domain. The phase shift depends of the distance of propagation and the spatial frequency of the plane wave. (iii) Recomposition of the electric field from the propagated plane waves. This step is in fact a 2D inverse Fourier transformation. The above 3 steps make up the basis of optical FFT codes. The pseudo code shown here allows the propagation in free space of any arbitrary optical field, independently of any optical basis (Hermite or Laguerre Gauss) or assumption on the beam shape. In optical FFT codes, only the propagation requires a transformation into the spatial frequency domain, all the other operations (e.g. reflection by a mirror or transmission through an aperture) are performed directly on the complex electric field. 2.2. Adding realistic optics The reflection by a mirror or the transmission through a lens can be described as a change in the optical field wavefront. For example, we can consider an input laser field Ei passing through an element inducing a wavefront distortion characterized by the optical path ∆OP (x, y). In this case, the transmitted field Et can be written as[6]: Et(x, y) = Ei(x, y)× exp (−jk∆OPL(x, y)) (1) with k the constant of propagation. An aperture used to represent finite size mirrors can also be easily implemented by a 2D transmission matrix A. Practically, an aperture A(x, y) is represented by a matrix of zeros and ones. A 0 at the position (x, y) indicates that the light is blocked (falls outside the mirror) and a 1 indicates that the light is fully reflected or transmitted. So once again, numerically, the reflection or transmission through a finite size mirror can be described as: 8th Edoardo Amaldi Conference on Gravitational Waves IOP Publishing Journal of Physics: Conference Series 228 (2010) 012021 doi:10.1088/1742-6596/228/1/012021