Laser Beam Collimation

This post discusses one question: how to achieve the best collimation of a laser beam?

To collimate a laser diode or fiber's output using a lens, a common belief is to make the output beam's waist location as distant as possible form the lens.  For example, see Saleh and Teich [1].  Well, this is only approximately correct.

The best collimation is achieved when the output beam has either:
(1) the smallest divergence angle; or
(2) the largest waist size; or
(3) the longest Rayleigh range.
The above three conditions are equivalent, i.e., achieving any single one means the other two are achieved simultaneously.

To reach the above conditions, the input waist needs be at exactly the object focal plane of the collimating lens. Then the output beam waist will be at exactly the conjugate (image) focal plane [2]:

Figure 1: Geometry of the perfect collimation.

I plot the output waist location (relative to the image focal plane) and the output waist diameter as a function of the input waist location (relative to the object focal plane). This plot shows that (a) output waist size is at maximum and (b) waist location is at the image focal plane when input beam waist is at the object focal plane. (Assuming input beam waist diameter = 5 um, lens focal length = 10 mm, wavelength = 1 um.)

Figure 2: Output beam properties vs. input beam waist location. Notice my custom sign rule: if "relative to" is at left of the reference point, the sign is plus. For example, positive waist location means it is at the left side of the focal plane.

This figure also indicates that the output beam's waist location cannot be placed at infinity.  The farthest distance one can make is when the input beam's waist is located at Z_R + f from the lens (Z_R is input beam's Rayleigh range and f is focal length). This is the common belief that the best collimation should be reached; however, the output waist size is not the largest.



References:
[1] Saleh and Teich, Fundamentals of Photonics, 2nd Ed. Page 90.
[2] Sidney A. Self, "Focusing of spherical Gaussian beams," Applied Optics 22, 658 (1983).