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re: polarized lasers



Here is a more in-depth answer to my question of polarized lasers:

kyle

The mailer rejected my response because I am not a list member. Please
forward this message if you find it of interest to list subscribers.

Polarization of HeNe's

I understood this twenty years ago; let's see what I can
remember.

First consider the mode structure:

Helium -neon lasers operate with a stable optical cavity
formed by its two end mirrors. Along the line joining
the mirrors, the optical field forms a standing wave
pattern similar to that of standing waves on a string. In
the transverse plane, the pattern is Gaussian (G = exp[-
(r/a)^2]). Other forms are possible, but they will be
discussed only at the end. So we have a single
transverse form and longitudinally a standing wave
satisfying the mirror spacing L equal about
n(wavelength/2). The corresponds to a frequency
spacing of 150 Mhz for a 50 cm tube. The gain in the
HeNe is a neon transition that is Doppler broadened such
about a 400 MHz band of frequencies is above threshold.

(*** You should start to be wary at this point; I'm
fabricating numbers to make a point. Look for a
introduction to lasers by Jeff ? Hecht if you can find it.
Also call

Metrologic Instruments, Inc.
Coles Road at Route 42
Blackwood, NJ 08012
Tel: 609-228-8100
800-ID-METRO
Fax: 609-228-6673
Assert yourself. Make them mail one of their laser fact
books at no charge. also http://www.metrologic.com/)

Now life gets dynamic. The tube expands as it warms
and 'scans' through many wavelengths. You can
illustrate this by drawing a lot of vertical spikes even
spaced. The laser gain profile is a Gaussian (Doppler
broadened) profile. Draw a horizontal line representing
loss about 2/3's of the way up the Gaussian to represent
total loss. The modes the are in the Gain > Loss region
will oscillate or lase. The expansion translates the picket
fence of allowed modes through the gain profile. Modes
turn on as the enter the above threshold region and turn
off as they leave. This is why you see time dependence.
The modes will scan more rapidly just after you
energize the laser and more slowy as the temperature
equilibrates.

What does this have to do with polarization ?

More of life is never simple. The lasing modes derive
there gain from the same medium (excited atoms) and
therefore are in competition for the gain.
A new mode entering the gain profile can see just a little
more gain if its polarization is orthogonal to that of its
nearest neighbor. More available gain means that the
mode grows into that polarization and pretty much
maintains it as it translates across the gain profile. With
three modes you expect two of one polarization and one
of the other. As the tube ages and the gain drops, and
the effects are more dramatic. I would not expect a
new HeNe which has miirors sealed directly to the end
of the tube to exhibit 100 % polarization. This could
happen for sinle mode operation.

Was it always this way ?

Early (60's) mirror technology to produce mirror with
the high reflectivity (about 99%) required because the
HeNe has low gain where SOFT and easily damaged.
These soft mirrors could not be sealed to the ends of the
laser tube with being destroyed so glass Brewster
windows were attached and the mirrors were mounted
to the laser frame rather than to the laser tube. The
Brewster windows defined the polarzation. Later epxoy
was used to seal mirrors directly to the tube. Moisture
seeping in through the expoxy and gas leaking out
became the dominate lifetime limiters. The current
mirrors are very hard and are glass welded to the tubes
giving the current long tube lifetimes. Without the
Brewster windows, the polarization is random. The
choice of linear polarization MAY be related to small
misalignments of the optical axes of the end mirrors
defining a preferred plane.Argon ion lasers (and others)
still often used Brewster windows and hence operate
linearly polarized.


The about in the standing wave relation:

The about should be ignored for introductory
treatments; it is related to a Pi phase shift to the beam
as it goes through a focus or waist and expands again.
The are small corrections to this related to the
curvatures of the end mirrors. The statement that the
mode spacing is c/2L is an extremely good
approximation.

More on transverse structure:

Let's designate the transverse coordinates as x and y.
The transverse structure can be more complicated with
form such as x G and y G where G is the Gaussian.
The general form is Hm(x/a) Hn(y/a) G where the Hm's
are the Hermite polynomials fron the harmonic
oscillator in quantum mech. Again the rectangular
transverse structure may be due to a slight misalignment
of the optical axes of the mirrors defining a preferred
plane. The more complicated trasverse modes have a
larger spatial extend. The tube diameter is chosen to
avoid causing loss for the Gaussian mode, but to cause
some for the higher more complicated modes to they
will not lase and mess up the beam quality. I believe
that wall relaxation is important in the overall pumping
dynamics of a HeNe so you also keep the tube small so
the atoms that have lased will more quickly complete
their deexcitation to the ground state so they can be
repumped. Other lasers are seen operating in higher
transverse modes with circular symmetry. An argon
ion laser can operate in the (x + i y) G mode which is
referred to as the dreaded doughnut mode. It has zero
intensity on axis and is therefore everything a laser
beam should not be.

Modes are related to other issues such as the coherence
length for making holograms. A single mode laser has a
long coherence length while that of a multi-mode laser
is limited by the distance change over which operating
modes will shift in relative phase by Pi.

If anyone is interested in sources for HeNe tubes without
mirrors and with one or more Brewster windows, drop
me a line. They are not cheap, but they allow cavity
issues and higher transverse modes to be examined.

c


---------------------------
| Larry Tankersley |
| Physics Department 9C |
| U. S. Naval Academy |
| Annapolis, MD 21402-5026 |
| Phone: (410) 293-6653 |
| FAX - 3729 Message - 6650 |
| DSN 281-6653 |
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