Why does a (laser) light beam not disperse?

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Discussion Overview

The discussion centers on the behavior of laser light in terms of dispersion and diffraction, particularly in comparison to regular light. Participants explore the theoretical underpinnings, including references to Maxwell's equations and the characteristics of laser beams.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks a derivation related to the dispersion of light beams and questions whether a laser beam disperses less than normal light due to its linear superposition of frequencies.
  • Another participant asserts that laser beams do disperse, but to a lesser extent than regular light, emphasizing that laser light is not a linear superposition of frequencies and is restricted to a narrow range of frequencies.
  • A question is posed regarding whether laser light can be described as a classical electromagnetic wave of a single frequency or if quantum mechanics is necessary for its description.
  • One participant mentions that the lowest mode laser beam can be described as a Gaussian and suggests searching for "gaussian beam propagation" for further information.
  • A participant questions whether the discussion is more about diffraction rather than dispersion, noting that dispersion involves variations in speed with wavelength.
  • Another participant confirms the distinction between diffraction and dispersion, stating that laser light, being nearly monochromatic, exhibits significantly less dispersion compared to broadband radiation.
  • A resource is shared that is suggested to contain valuable information on lasers and dispersion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of laser light and its dispersion characteristics, with no consensus reached on the definitions or implications of dispersion versus diffraction.

Contextual Notes

There are unresolved questions regarding the mathematical treatment of finite width beams in free space and the implications of frequency mixtures on dispersion.

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

Laser light is usually well described classically.
 
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.
 
Good catch- yes, diffraction and dispersion are entirely different.

Laser light, being nearly monochromatic, displays significantly less dispersion in optical systems than braodband radiation.
 

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