Collimation

A point source placed at the front focal point of a lens emerges as a set of parallel rays; that is collimation, and the lens is a collimator. Real sources have finite size and real beams diffract, so a collimated beam is never perfectly parallel. For a laser beam the practical meaning is that the beam waist is large enough, and placed well enough, that the beam stays close to its waist size over the distance that matters. Collimated beams are what free-space optics on a bench, free-space links, fiber-to-fiber couplers and most instruments pass between their components.

Collimating a fiber output

The light leaving a single-mode fiber is close to a Gaussian beam with a waist at the fiber end equal to half the mode field diameter, $w_f$. A lens of focal length $f$ placed one focal length away produces a beam with waist radius and far-field half angle

For SMF-28-type fiber at 1550 nm ($w_f \approx 5.2$ µm) and an 11 mm aspheric lens, the output is 2.09 mm in $1/e^2$ diameter with a half-angle divergence of 0.47 mrad, and its Rayleigh range is 2.2 m. A longer focal length gives a larger, less divergent beam; the divergence is simply the fiber's mode radius divided by the focal length.

Best collimation for a given distance

If light must travel a distance $L$ between two collimators, the beam is kept narrowest everywhere by putting the waist midway and choosing its size so that the Rayleigh range equals $L/2$. That waist is $w_0 = \sqrt{\lambda L/(2\pi)}$, 0.50 mm for 1 m at 1550 nm; a larger beam then diverges less but starts bigger, and a smaller one grows faster. The same reasoning sets the beam size in fiber-to-fiber free-space couplers and in beam expanders for long paths.

Checking and adjusting

The lens-to-source distance is adjusted until the beam size is the same close to the collimator and several metres away, or, for a beam that should come to a waist at a set distance, until the waist lands there. A shear-plate interferometer is more sensitive: a wedged plate reflects two laterally shifted copies of the beam, whose interference fringes run parallel to a reference line only when the wavefront is flat. Autocollimation, reflecting the beam from a flat mirror back through the lens and checking that it refocuses on the source, is the classic method for lenses and fiber collimators.

References: A. E. Siegman, Lasers (University Science Books, 1986), Ch. 17; M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).