Gaussian Beam Apodization in Zemax

When the light source in a Zemax model is a Gaussian laser beam, the apodization setting is important.

1. Definition.
From Zemax manual, light amplitude is

A(ρ) = exp(-Gρ2)

Here both A and ρ are the normalized parameters, i.e., they both equal to 0~1 within their full range. G is the apodization factor. If G = 1, the amplitude at the edge of the entrance pupil falls to 1/e of the center value (intensity falls to 1/e²).

2. Determine G value.
From equation:

I(ρ) = exp(-2Gρ2) = 1/exp[2(√ G ρ)2]

It is not difficult to see that entrance pupil (system's clear aperture) radius is √ G times the Gaussian beam's 1/e² radius.

For example, let's plot intensity I vs. ρ at different G values:

From this plot,
(1, blue curve) If G = 1, the Gaussian laser beam is clipped by the system clear aperture right at 13.5% (1/e²) of the peak value. For coherent sources like laser, diffraction will occur significantly.
(2, green curve) If G = 4, the system aperture is twice the size of the beam 1/e² width. This aperture will clip only 0.03% (1/e⁸) of the peak power and should suffice for most laser system.
(3, red curve) If G = 9, the system aperture is three times the size of the beam 1/e² width.

So, the apodization factor determines the Gaussian beam size relative to the system aperture size. If the designer knows both sizes, then setting the G value is easy. For example, for a simple system with a single-mode fiber source and a collimating lens, we know the NA of both. Then the apodization factor should be:

G =

NAlens2 NAfiber2

(1)

Note that the fiber NA in this equation is the 1/e² value. Fiber manufacturers define/measure their NA differently. For example, Corning datasheets give the NA at 1% value, which is 1.517 times larger.

References:
1. http://www.zemax.com/kb/articles/164/1/What-Does-the-Term-Apodization-Mean/Page1.html