Thermal lens effect simulation

When a powerful Gaussian beam propagates into an absorbing medium, it heats the center, creating a temperature gradient and thus an index gradient. This gradient deflect the light rays in a divergent way.

effect of a diverging lens on a Gaussian beam

This phenomenon known as "thermally induced GRIN lens effect" or "thermal lens effect" has been described analytically for thin medium [98][99]. Here, I extend this to a thick medium through a Gaussian beam propagation simulation.

Usage

The code contains a GaussianBeam module and a GrinLens module. Here I explain an example code for generating the following figure. You will find other examples in the gaussian-beam folder along with generated figures.

First, we import the needed code and define the parameters of the simulation (defaults parameters can be found in the grinlens.jl file).

include("./grinlens.jl")
using .Grinlens

exppows = [0.213, 0.248, 0.284, 0.319, 0.355] # experimental powers in watt
P = map(p -> Parameters(P=p, l=1e-6, w0=4e-6, n=1.33), exppows) # parameter vector

Then, we apply the propagation on the parameter vector we just generated.

O = propagate.(P) # run the simulation for these parameters

Then we use the observables we need to plot our figure (cosmetic code removed). The units are S.I. and are documented in the grinlens.jl file, thus the conversion in mm/µm.

using Plots
plot()
for (i,pow) in enumerate(exppows) # loop over results
    plot!((P[i].steps).*1e3, + O[i].wonlens.*1e6) # mm / µm
end
title!("beam profiles")
xlabel!("position in tank (mm)")
ylabel!("beam width at 1/e (µm)")

Don't hesitate to file an issue for any comment or question.

Comparison with measurements

This numerical model fits well with my experimental measurements as described in my PhD manuscript.

comparison of numerical simulation with real world measurements

References

References from my PhD thesis:

[98] J. R. Whinnery (1974); Laser measurement of optical absorption in liquids https://pubs.acs.org/doi/abs/10.1021/ar50079a003.

[99] J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto & J. R. Whinnery (1965); Long‐Transient Effects in Lasers with Inserted Liquid Samples http://aip.scitation.org/doi/10.1063/1.1713919