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Divergence Angle in POP

  • 8 February 2022
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Userlevel 2

Dear Experts,

in order to get an exact understanding of POP, I have stripped down a simulation to purely a POP simulation, i.e. without any optical element but a free-space propagation (Gaussian beam diffraction) over 1000m:

My  beam definition is

My beam waist is 21mm. Exploring that with the Beam File Viewer, this is a 21mm radius at 1/e². However, in the help file I find

 

 

where w_0y (omega) should be the same as Waist X?! According to these formulas this would be a 1/e radius (not squared), if I do the math right. Maybe w_0y is not equal to Waist X?

 

According to Teich/Saleh a 21mm 1/e² radius Gaussian beam should result in a divergence theta of (omega_0 is the 1/e² radius)

i.e. my beam should have a radius of 23.5mm after 1000m propagation.

Reading from the cross section in the image plane, I get around 31mm at 1/e², so a difference of 7.5mm to the expected 23.5mm.

It would be great to get a hint, if my modelling of such a minimal system, i.e. only the Gaussian beam diffraction, is correctly done in Zemax. I attach my file.

Many thanks. Any advice would be very welcome

Markus

 

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Best answer by Jeff.Wilde 8 February 2022, 19:30

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Userlevel 7
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Hi Markus,

Simply using the far-field divergence angle to estimate beam radius, when measured from the waist location, is an over-simplification.  The actual dependence is slightly more involved (see the Wikipedia page on the properties of a Gaussian Beam, or any reference on Gaussian beams):

 

Using this formula for your example yields a beam radius of 31.5 mm at z = 1000 m.  Another way to check your results is to use the Paraxial Gaussian Beam Data analysis function:

 

Regards,

Jeff

 

Userlevel 2

Jeff, thank you so much for your support! I gained some good insight into POP and improved my understanding of Gaussian beams :)

Markus

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