7.5.7. Transformation of high order Gauss modes.

7.5.7.1. From Hermite to Laguerre.

Beside the application of a spiral phase plate, it is also possible to transform Hermite Gauss into Laguerre Gauss laser modes with the help of a pair of cylindrical lenses. This so-called ‘astigmatic laser mode converter’ has been introduced by M.W. Beijersbergen et al. [1]. We used their experimental setup to demonstrate this in the Python script below [2] [3] .

M.W. Beijersbergen, L. Allen, H.E.L.O. van der Veen and J.P. Woerdman, Astigmatic laser mode converters and transfer of orbital angular momentum, Optics Comm. 96 (1993) 123.

(Source code, png, hires.png, pdf)

Conversion of a Hermite 3,3 mode

Conversion of a Hermite 1,3 mode

7.5.7.2. From Laguerre to Hermite.

The transformation from a Laguerre to a Hermite mode is also possible with this setup:

Conversion of a Laguerre 0,4 to a Hermite Gauss 4,4 mode

Conversion of a Laguerre 0,1 to a Hermite Gauss 1,1 mode

References:

[1]

M.W. Beijersbergen, L. Allen, H.E.L.O. van der Veen and J.P. Woerdman, Astigmatic laser mode converters and transfer of orbital angular momentum, Optics Comm. 96 (1993) 123.

Remarks:

[2]

We had to change some of the parameters used in the experiment slightly (d3, d4 and f2) to get a better mode matching.

[3]

The size of the Gauss beam in the resonator in its waist was calculated in the usual way. The effect of the outcoupler, which acts as a negative lens, was taken into account as well in the simulation.