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Kolmogorov lens in wave optics

Job Feldbrugge and Neil Turok

We consider lensing by a plasma whose electron density takes the form of a Gaussian random field with a Kolmogorov power spectrum: in the thin lens approximation, the lens is effectively two-dimensional and the power spectrum \(P(k)\propto k^{-{5\over 3}}\). This is a good model for twinkling produced by a turbulent medium.

The following picture shows a realization of the lens:

Fig. 1- A 2d Gaussian random lens with a Kolmogorov power spectrum.

We calculate the intensity pattern produced by this lens, comprising an intricate caustic network with diffraction fringes:

Fig. 2- The intensity pattern produced by lensing of the 2d Kolmogorov lens, for various lens strengths.

We also consider a 2d Gaussian random field with a power spectrum \(P(k)\propto k^{-1}\):

Fig. 3- A realization of a random lens with power spectrum \(P(k)\propto k^{-1}\).

The intensity pattern for this case are shown below, again for various lens strengths.

Fig. 4- The intensity pattern produced by a 2d plasma lens with power spectrum \(P(k)\propto k^{-1}\), for various strengths of the lens.