# Why does a (laser) light beam not disperse?

## Main Question or Discussion Point

Does anyone know where I can find a derivation how/why a light beam disperses? I'd like to see some sort of solution to Maxwell's equations for a finite width EM wave in free space.

If the beam is a linear superposition of frequencies and Maxwell's equations are linear, does a laser beam disperse less than an equivalent beam of normal light?

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HallsofIvy
Homework Helper
First, a laser beam does disperse, just not as much as "regular" lights. Laser beams are very closely 'collimated', much like a search light so it doesn't disperse very much to begin with. But the key to laser light is that it is NOT a "linear superposition of frequencies". The difference between laser light and "regular" light is that the laser's light is restricted to a very short range of frequencies (the ideal would be one frequency but that, strictly speaking, is not possible).

So can laser light be described by a classical EM wave of a single frequency or do you require quantum mechanics?
I'd like to calculate this in detail with actually solutions to Maxwell's equation. From undergrad studies I know calculations for waves in free space and wave guides. Not sure what's the easiest way to consider a finite width beam in free space. Any references?

Why should a mixture of frequencies disperse more than each of them individually?

Andy Resnick
The lowest mode laser beam is well described as a Gaussian. A google search for "gaussian beam propogation" or "abcd matrix" should pull up something useful.

Laser light is usually well described classically.

Redbelly98
Staff Emeritus
Homework Helper
Just a question, aren't we really talking about diffraction in this thread? Dispersion is what results from a variation in speed (or equivalently, refractive index) with wavelength.

Andy Resnick