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

ZEMAX un-organized tips

I have to do extensive ZEMAX work to start my semi-new job. Had some non-sequential mode experience but now I really have to use sequential mode, and optimization and tolerancing functions. The first two tasks are aspheric collimating lens for diode and fiber-coupling. Now let me start to accumulate the little rules/tips of ZEMAX:

1. When defining a sequential system, the first parameter to set is aperture. Some aperture types are:
a. Float by stop size: defined by the radius of the stop surface. This type of aperture is used when the stop surface is a real, unchangeable aperture buried in the system, for example, fiber coupling.
b. Object cone angle: defined by the half-angle in degrees of the marginal ray in object space. This can be used when designing a collimating lens for a diode laser.
(Ref[1], page 63)

2. Afocal system [2]. The strict definition of an afocal system is a system in which both object and image conjugates are at infinity. For example, a laser beam expander in which both input and output beams are collimated. In Zemax, as long as the image conjugate is at infinity, the system is afocal. For example, when designing a diode collimating lens, one will choose "Afocal image space" in Aperture settings:


3. Apodization type. This describes amplitude variation of the pupil illumination. Gaussian apodization is what a laserist often uses:

A(ρ) = exp(-Gρ2)

Here ρ is the normalized pupil coordinate, i.e., ρ = 0~1 from the center to the edge of the pupil. 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). So the marginal ray represents the 1/e² ray.
(Ref[1] page 64)

Marginal ray: is the ray that travels from the center of the object, to the edge of the entrance pupil, and onto the image plane.
(Ref[1] page 30)


References:
[1] ZEMAX user's guide Jan 2003
[2] Mark Nicholson, ZEMAX users' knowledge base - How to design afocal systems. http://www.zemax.com/kb/articles/36/1/How-to-Design-Afocal-Systems/Page1.html