inverse square law and "perfect" laser
Gary Jefferson
the diameter of the laser beam increases linearly (at distance), or is
there something else fundamental going on to decrease light energy as
it travels?
I suppose another way to ask the same question is, in a perfect vacuum,
do all the photons that a central source emits make it to the edge of
some distant sphere, or are there other effects that cause the photon
waves to dissipate or interfere (e.g, cancel out) as they travel?
Phil Hobbs
The inverse square law is a statement of the conservation of energy, so
it applies strictly only in the absence of absorption (it can be patched
up to account for absorption too, but then it isn't an inverse square
law).
At distances large compared with ((beam diameter)**2)/(wavelength), the
angular pattern of the laser beam doesn't change with distance. If you
were to measure the total beam power hitting successively larger and
larger spheres, it would be the same, because we've assumed that there
is no absorption in between. However, the area would have gone up by
the square of the radius of the sphere. Hence the flux density (also
called irradiance, measured in W/m**2) has to go down by the same r**2
factor.
Cheers,
Phil Hobbs
John
I do not agree that laser light obeys the inverse square law.
Basically, the decrease in intensity as the inverse square of the
distance is a property of point sources. These sources emit uniformly
into all angles (hence the argument with spheres of increasing
diameters). However, a laser is essentially the farthest from a point
source that any light source could be (in the sense that its angular
divergence is the minimum possible consistent with diffraction, at
least for lasers with nice transverse beams). Said another way, lasers
emit into a very narrow angle range. So if you measure the intensity
of a beam with a photodiode (say) 1 inch from the laser and then 10
inches from the laser, you will not find 1/100th of the light with your
fixed area detector. If you do this same experiment with an
incandescent light bulb and make your closest measurement far enough
away (much, much greater than the size of the filament), you will
observe this square law decrease.
Also, there is nothing in the perfect vacuum that will prevent all the
energy from reaching your distant sphere. Interference can
redistribute energy (in space and time) but it will not make the energy
go away.
Hope this is helpful.
John
Salmon Egg
1164132208.2...@f16g2000cwb.googlegroups.com, "Gary Jefferson"
<garyjeff...@yahoo.com> wrote:
Although others have answered your question, they were not blunt enough.
Laser beams do not obey the inverse square. They obey the inverse square law
as an approximation for very large distances.
Bill
-- Fermez le Bush
redbelly
Just to add, trying to stay blunt: conservation of energy is the rule.
Laser intensity is inversely proportional to beam area. Only when the
beam area obeys the square-law will intensity obey the inverse-square
law.
Mark
Boxman
> Just to add, trying to stay blunt: conservation of energy is the rule.
> Laser intensity is inversely proportional to beam area. Only when the
> beam area obeys the square-law will intensity obey the inverse-square
> law.
>
> Mark
So for example with a typical low power He-Ne operating in Tem00 mode
the beam area is approximately (pi*(r^2)*(divergence angle^2))/4 where
r is the distance from the beam waist. In this case the beam area is
changing porportional to the square of the distance, so the irradiance
(power per unit area) is changing as the inverse of the distance
squared.
Strictly speaking the term intensity is being used as irradiance in the
previous posts, where as the proper definition of intensity is
power/solid angle which would remain constant beyond the beam waist of
the example He-Ne listed above since the solid angle that the laser
emits into doesn't change. So the intensity does not follow the
inverse square law, but the irradiance, in this case, will vary as the
inverse square.
Practically speaking it may be difficult to measure the inverse square
relation with a real detector and a real beam as the detector would
need to be small to not be underfilled by the beam at a reasonable
distance. A typical He-Ne beam waist might be 0.5 mm in diameter
which means a detector would need to be less than that to be overfilled
and show the inverse sqaure fall off with distance right away. If I'm
not mistaken most photodiode type laser power meters have large chips
to ensure that the detector is underfilled to get a proper power
measurement which means that even if the beam is expanding with
distance, the power readings won't show it until the detector is first
overfilled.