Question

# Results for high frequency approximations

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Hello,

I am a new user of the OpticStudio software which arouses my curiosity!

The wave propagation can be solved with several models and the software offers several possibilities. The model based on the astigmatic Gaussian beams (beamlets) is very well interesting.

But, I found few years ago the relevant paper:

Gosse L., James F., Convergence results for an inhomogeneous system arising in various high frequency approximations, Numer. Math. 90: 721–753 (2002).

It is enough hard because the mathematics formulations are theoretic. However, the issue solving gives several possibilities to find the phase and the amplitude of the light wave together.

Numerical values for the phase and the amplitude of the smooth wedge.

Therefore, do we have this possibility with the OpticStudio? Compute the phase in order to see transparency images for instance?

Benoît.

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Userlevel 2
+1

Hi Plancoulaine,

OpticStudio provides 3 methods to model beam propagation. One is based on pure geometric ray trace. You can view the phase of the beam using the Wavefront map which shows you the optical path difference of a pupil ray relative to either the chief ray or the centroid. The second is the Paraxial Gaussian or the Skew Gaussian model.  The Paraxial Gaussian computes the propagation and transformation of a rotationally symmetric Gaussian beam using two paraxial rays in a meridional plane as given by Arnaud in "Hamiltonian Theory of Beam Mode Propagation” and Siegman in “Lasers”. The Skew Gaussian can model an off-axis propagation of the beam and the beam parameters are computed using real rays and account for astigmatism. The third method is the Physical Optics Propagation (POP) where the propagation is modeled by propagating wavefronts through your optical system. The physical optics model is generally more accurate at predicting the detailed amplitude and phase structure of the beam. You can find a detailed explanation on how POP works in the help documentation at The Analyze Tab (sequential ui mode) > Laser and Fibers Group > About Physical Optics Propagation.

I’m not familiar with the paper you’ve quoted above. Could you please elaborate a bit more on what you are trying to model here? Maybe a drawing or a lens file can help.

Best,

Hui

Hello Hui,

Thank you for your precious information.

Yes, the physic propagation module (POP) gives very good irradiance images, no problem (I tested with the knife-edge). The pure geometric ray trace with the “Jacobi-Hamiltonian” and especially the “method of characteristics” is also very good to find the light rays and the phase on the wave surfaces. I think the two modules compute independently the results but perhaps, it is not exact.

Therefore, it not is very easy to establish directly relationships between the intensity and the phase. The very simple example attached shows the Gaussian beams with the intensity superposed with the phase which are computed together. In particular, we see enough well the Rayleigh length impact on the Gaussian beams.

Kind regards, Benoît.