group velocity

[kubalak]

I'm working on modeling a laser radar measurement through a window. The goal is to use it to measure hardware inside a cryostat. A laser radar uses frequency modulation to measure distance. The frequency of the return beam is measured and the distance is backed out of the frequency measurement. Because the measurement uses a frequency modulated beam, I need to look at the group velocity of the beam through the window. The velocity is not strictly c/n because of window dispersion.

I can write my own ray-tracing routine to take this into account by stopping the raytrace on the backside of the window and artificially adding a path length to account for the slower group velocity, but I can not get FRED to use my ray trace script instead of the built-in ray trace for optimization. When I test my optimization script it works but then during optimization it seems to ignore my raytrace. This method is also troublesome for gradient index materials, and when testing through a window into a cryostat the window sees a huge temperature (and index) gradient.

A better way would be to script a material to do it. I can write a user-scripted GRIN material, but the only way to set the velocity of transmitted light is to set the index artificially high, which then affects refraction as well as velocity. Is there any way to script a material to change the speed of light during transmission without using the index?

Is there any other way to look at group velocity than the methods I've outlined above?

Thanks,
-dave

[Molander]

I have had several times needed to use FRED to track pulse propagation. It seems to me that the simplest approach is just to trace two or more nearby wavelengths and then numerically do the derivatives to find the group delay, group velocity, group velocity dispersion or whatever else you need. Specifically for radar you're probably most interested in the group delay (i.e. pulse arrival time). This is the derivative with respect to omega, w, of the phase, phi, and phi = kz = w n z /c. nz of course is what FRED reports as path length of the ray.

One nice thing about this approach is that you don't have to do anything special at each element in the system. Just trace the various wavelengths through to the end and do the group delay calculation at the final detector.

You also mentioned the importance of getting the refraction right. If there is any significant bending the problem becomes more complicated due to spatial dispersion effects. The different wavelengths travel different paths. The pulse at any point is determined by the rays that end up at that point although they started at different points in the source. This can be handled in FRED script but is a real pain. Alternately you can just dump all the ray path lengths to a spreadsheet and do the calculation in Excel.

I hope this is useful.

[kubalak]

Thanks for the suggestion.

As a correction to my first post, I *can* get the FRED optimizer to use my raytrace routine. I don't know what I was doing when it wasn't working, but when I went back to work on it some more, everything came out copacetic.

I'll look at the suggestion you made. I happen to have a lot of information about the window material I'm using (fused silica), so the derivative calculations are fairly straightforward. The routine you suggested, however, could still make things easier in the long run.

Thanks!
-dave