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Re: combining laser beams



Bob referenced:

"Paradox Concerning Superposition of Identical (Infinite) Plane Waves",
L.S.Kothari, AJP 38, pg 268, Feb 1970.

The "paradox" is this: If we add two beams of equal energy, we expect
(by energy conservation) to get a beam of double the energy. But for
two coherent beams in phase, we actually get four times the energy
(since you have to add amplitudes before squaring).

The suggested resolution is to consider adding two plane waves with
slightly different frequencies. Averaging the energy quadrupling
where they're in phase with the energy nulling where they're out of
phase now gives the expected energy doubling. In the limit as the
frequency difference goes to zero, it takes an infinite distance to
move from the in-phase to the out-of-phase locations. But since these
are monochromatic plane waves, you've got infinity to work with.

Now I suppose we extend this to real laser diodes as follows. They
can't be exactly monochromatic because their coherence length isn't
infinite. Hence it's not possible for them to be in phase everywhere.
So energy gains at one place will balance energy losses elsewhere.
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/