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Compare how much a coherent laser visible green light beam spreads out with a incoherent green light beam.

Physics Asked on November 29, 2020

Suppose I am mathematically modeling a visible green laser pointer beam which starts from the ground and ends up a half mile or full mile in the sky, projected upon an aircraft window 2 inches thick. How much will the ground-borne visible green laser pointer beam spread out in the final 2 inches between the front and back pane of the aircraft window? Please compare this result with that for an incoherent visible light green beam originating from the ground.

The reason I ask this question is to solve one of society’s problems where commercial aircraft are grounded due to laser pointers sent from the ground near airports?

I just read the following 2 Stack Overflow articles which discuss some of the physics and equations necessary to solve my question:Physics of Focusing a Laser

Can radio waves be formed into a pencil beam?
Thank you.

3 Answers

It totally depends on the type of incoherence. If the source is spatially incoherent, it will spread by an angular amount corresponding to the angular size of the source as seen from the final beam- forming element, plus the amount that a beam formed from a spatially coherent source would experience. Temporal coherence doesn't really matter in your scenario. The presence of a clean thick pane of glass, at normal incidence, will not significantly affect either the beam size or its divergence.

Answered by S. McGrew on November 29, 2020

Assume your incoherent light comes from a source smaller than the window and spreads out to cover the window. Then its angular divergence, defined as the angle between the light on the left edge and the light at the right edge, or the width of the window over the distance to the plane.

$$ Delta phi = w_{rm{window}}/d_{rm{plane}}$$

Any beam in these conditions will keep its overall beam divergence. A good laser might be smaller than the window at that distance. If so, the divergence in the window is given by that beam divergence. If larger, see formula above.

But I agree with the commentators: in any case, the effect of divergence as the beam goes through the glass is negligible.

Answered by Bob Jacobsen on November 29, 2020

@anna v, a theoretical physicist from Greece, wrote on Physics Stack Exchanges 3 years ago, "Coherence matters because it retains the angles , there is spacial coherence. With incoherent light there is large divergence.One could not shine incoherent light on the moon, for example. The incoherent spot on the unit sphere will diverge and enlarge proportional to r^2 as the radius grows. A laser beam spot due to coherence enlarges slowly as can be found in various links". – anna v Jul 3 '12 at 18:47 in this URL, How can a laser pointer have range of several kilometers in atmosphere?

The answer to my question is, The incoherent spot on the unit sphere will diverge and enlarge proportional to r^2 as the radius grows. Therefore: 1/2 mile = 804.5 meters 2 inches thickness = 5 centimeters So, (804.55 meters) * (804.55 meters) - (804.5 meters) * (804.5 meters) = 80 square meters difference which equates to the radius of the incoherent spot on the unit sphere growing by 5 meters over the final 2 inches of the aircraft cockpit window. I must admit that this result may needs to be corrected because it is relative to the unit sphere. Please correct me if you have the time.

Answered by Frank on November 29, 2020

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