Does the Inverse Square Law Apply to Lasers and Perfect Lasers?

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Discussion Overview

The discussion revolves around the applicability of the inverse square law to lasers, particularly in the context of "perfect lasers" versus real-world lasers. Participants explore theoretical implications, practical considerations, and the behavior of laser beams over distances, including applications in space.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the inverse square law does not apply to perfect lasers, as they would maintain a constant energy density along the beam without divergence.
  • Others argue that real lasers exhibit beam divergence, leading to a decrease in energy density over distance, which aligns with the inverse square law at significant distances.
  • A question is raised regarding what constitutes a "significant distance" in the context of laser applications, particularly for space-based weapons.
  • One participant notes that the inverse square law assumes isotropic radiation, while lasers have a far-field divergence angle that affects their irradiance profile.
  • Another participant mentions that averaging over a spherical surface at a distance can yield results consistent with the inverse square law, even for lasers.
  • There is a reference to literature suggesting that laser beams can remain coherent over distances before diverging, which may not conform to the inverse square law.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the inverse square law to lasers, with no consensus reached. Some support the idea that it applies under certain conditions, while others maintain that it does not for perfect lasers.

Contextual Notes

Discussions include assumptions about the nature of perfect lasers, the definition of significant distances, and the impact of beam divergence on energy density. The conversation also touches on the implications of laser use in space and the behavior of light in various contexts.

Who May Find This Useful

This discussion may be of interest to those studying laser physics, space applications of lasers, or anyone exploring the theoretical and practical aspects of light propagation and energy distribution.

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I've read from several sources that says the inverse square law doesn't apply to lasers, but I've been told that it does apply. Which is right?

Also if it does apply in today's lasers what about in a perfect laser?

Thanks.
 
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In a perfect laser beam the \frac 1 {r^2} law would not hold. The beam diameter would not change, you would have the same energy density at any point on along the beam.

HOWEVER. Perfect laser beams do not exist. Every real laser has a bit of beam divergence. If the beam is divergent, then at a significantly large distance you would measure a drop off in energy density according to \frac 1 {r^2}.
 
How long is a significant distance? 1 AU? I ask because I was discussing the application of lasers as weapons in space.
 
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Normally "perfect laser" doesn't require the wavelength to be so negligible compared to the beam waist..
 
Energy falling off "as 1/r2" is true for light expanding from the source in a sphere- the energy is spread across the entire surface of the sphere which area is increasing as r2.

If by "perfect laser" you meant "no spread at all", then the energy would not drop (except of course by absorption by space dust or whetever material was in its way).

If your laser has a spread angle of \theta (That would be a three dimensional "dihedral" angle) then the area over which it is spread at distance r from the origin would be \theta r^2 and so the strength would still fall off at a rate proportional to r2 (but the proportionality would be small for very small angles).
 
Whats Known About Very Small Return Waves Riding Back On Em Waves Or On Any Other Wave?
 
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I have a really good book about science for SF writers, written by Ben Bova (who is both a real scientist and a novelist). The section on lasers in space indicates some counter-intuitive behaviour. Something about the beam remaining coherent for quite some distance, then diverging at some rate that doesn't follow the inverse law.
I can't remember the details, and the book is back at my house. I'll try to find it after work and get back to you.
 
The inverse square law does not hold true because the inverse square law assumes the source is radiating isotropically. Lasers do however have a far-field divergence angle which can be used to calculate the irradiance profile some distance away. This far-field divergence angle depends on the wavelength of the laser and the minimum spot size of the beam.

Claude.
 
I ask because I was discussing the application of lasers as weapons in space.
On one of the Apollo missions, they left an array of mirrors, with each shaped like a cube sliced in half diagonally, so they would reflect from any direction. Earth based lasers can be pulsed at the mirrors, and it takes a bit before the reflection comes back.

http://science.nasa.gov/headlines/y2004/21jul_llr.htm

One of the advantages of being an old guy (55 years old), is being able to remember this stuff. At the time, major networks included snippets of videos of the laser beams being bounced off the mirrors.
 
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  • #10
Claude Bile said:
Lasers do however have a far-field divergence angle which can be used to calculate the irradiance profile some distance away. This far-field divergence angle depends on the wavelength of the laser and the minimum spot size of the beam.

That sounds familiar. I never got the chance to go back to the house today, but this might very well be what Bova was referring to.
 
  • #11
Jeff Reid said:
One of the advantages of being an old guy (55 years old)


Shouldn't you be dead by now? Bloody hell, but you're ancient!
 
  • #12
if you take the average on the whole spherical surface at a distance r, even for lasers, perfect ones, the inverse square law will hold. On average, though.

best wishes

DaTario
 
  • #13
Jeff Reid said:
On one of the Apollo missions, they left an array of mirrors, with each shaped like a cube sliced in half diagonally, so they would reflect from any direction.
Interestingly, these are the same type of things used on the masts of sailboats to make them more visible on radar.

http://www.marisafe.com/Store/viewItem.asp?ID=108010869&CID=10800000&FLT=108010869
 
  • #14
DaTario said:
if you take the average on the whole spherical surface at a distance r, even for lasers, perfect ones, the inverse square law will hold. On average, though.
Huh? That can also be said of a single cannonball, which is exactly the case for which you would prefer to say that the inverse square law doesn't apply.
 

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