```Lab #4 - Transverse Modes
ECE 482/582
Goals:
1. Learn and demonstrate proper alignment techniques for a conventional cavity laser.
2. Force a HeNe laser into many different transverse modes by altering the gain in
various places within the gain region.
3. Study the transverse mode intensity profiles of a HeNe laser
4. Polarize an unpolarized laser using a Brewster angle window inside the cavity.
5. Explore cavity stability limits
6. Confirm changes of Gaussian TEMoo beam parameters with cavity length.
Kuhn, Laser Engineering, Chapter 4: sections 4.1 – 4.3, Appendix A.3
Other Resources:
Kogelnik and Li, Laser Beams and Resonators, Proc. IEEE, vol. 54, no.10, pp. 1312-1329,
Oct.1966 [Link to pdf of paper on class web site]
Ramo, Fields and Waves in Communication Electronics, Chapter 14
Preparatory Questions:
1. What is Brewster’s angle for a zinc titania glass cover slip (n = 1.523 @ sodium D
line, 589 nm) using a HeNe laser at 632.8 nm?
2. Explain why the paraxial approximation can be used when solving the wave equation.
3. (Extra Credit) Use Maple, Mathematica or another tool to plot several lower order
cylindrical [and/or rectangular] modes given by equation 4.18 [or 4.20] in Kuhn’s
textbook.
Laboratory Experiment:
You will be working with a special, larger bore-size HeNe laser plasma tube to allow you to
produce the higher order transverse modes of the laser cavity. Be careful with the setup.
Many parts are fragile and high voltage is involved. Do not touch the red lead
connection from the power supply to the laser gain tube. It will be at ~1000 Volts DC
when operating and could be lethal if touched while you are grounded. [It is shielded
by the Lexan tube to make accidental contact impossible.]
Procedure:
1. Using the post mounted iris as a “target”, align the “guide” HeNe laser output to be
directly along the optical rail and parallel to the tabletop. [Note: This guide laser is
borrowed from Physics and is polarized. It has been mounted so that the electric
field polarization direction is perpendicular to the table top. You can use this laser
beam reflection to determine Brewster’s angle for the glass cover slip.]
2. Mount the laser gain tube inside its protective Lexan cylinder onto the far end of the
optical rail positioning the front surface of the 100% reflecting flat mirror (on the
anode [ + HV ] end of the plasma tube) directly at the end of the rail at position 0.0
cm. [Then the rail readings correspond directly to the laser cavity length.]
3. Using the 3 nylon screws on both ends of the Lexan tube, carefully adjust the position
of the laser plasma tube (without the power on to the plasma) to be perfectly coaxial
to the “guide” laser beam. This is the most critical, and tedious, adjustment of the
process. You will have to dim the lights a bit and look carefully at the reflection
from the 100% mirror coming back to the alignment laser and also at the small
amount of light transmitted through the “100% mirror.” When properly aligned,
the reflected laser beam should go directly back into the HeNe alignment laser and
there should be a very dim, but clear, red spot centered within a very dim circular
ring from the far end of the tube. At this point the plasma gain tube is coaxial with
the alignment laser beam and parallel to the rail.
[ NOTE: [1] – [3] SHOULD BE DONE WHEN YOU ARRIVE. You
should check the alignment to verify that it is still aligned.]
4. Now place the laser output mirror (radius of curvature = 45 cm, reflectivity = 99%
at 632.8 nm) on the rail with the front surface of the mirror positioned about 40-43
cm from the 0.0 cm position. Since the front surface of the mirror (the curved,
reflecting surface) reflects 99% of the HeNe laser light and the back surface is
antireflection (AR) coated, you will see only a bright reflected spot from the front
surface reflecting back toward the alignment laser. Use the “xy”-positioners on the
laser mirror mount to reflect the beam directly back into the alignment laser. At this
point, the two laser mirrors on the laser should be very close to resonant optical
alignment.
5. Now block the alignment laser beam with a piece of cardboard, paper, etc. Be
careful not to bump the alignment laser or beam steering mirrors. Turn on the
power supply to the laser gain tube by switching the switch on the grey metal box.
Be careful not to touch the red lead inside the head. [Turning on the laser power
supply creates a short 8 kV “start” pulse to break down the HeNe gas inside the gain
tube. Following this pulse, a d.c. voltage of ~1000 V @ ~2 mA current is maintained
to sustain the plasma discharge. This provides the pump to keep the gain above
threshold.] At this point, your laser may begin lasing as evidenced by a bright red
spot on a paper in front of the alignment laser. If not, try “rastering” the xy
adjustment knobs on the output mirror mount by first turning the “x” knob back and
forth by a small amount coming back to its initial position. If you see no lasing,
then turn the “y” knob a small amount one direction (Remember which way you
turned it and about how much!) and repeat the “x” back and forth adjustment. If no
lasing, turn “y” a bit more in the same direction and repeat the “x” rocking. If no
lasing, go back to the original “y” position and try a small turn the other direction. If,
after rastering the beam around, you still see no lasing, turn on (or unblock) the HeNe
alignment laser and check your alignment again.
6. Once you get the laser lasing, adjust [by very small amounts] “x” and “y” to
maximize the laser output intensity. Then turn off the alignment laser and slide the
final turning mirror (carefully) out of the way, place the lens on the rail in the output
beam and expand the beam onto a white surface to show the transverse mode
structure more easily. Tweak the “x” and “y” knobs to try getting several different
transverse lasing modes. Sketch several of the modes you obtain into your lab
notebook. Keep adjusting the mirror to see if you can get several different “pure”
Hermite-Gaussian modes (or maybe even some cylindrical Laguerre-Gaussian
modes!). [It is difficult to get pure modes just by moving the mirror but sometimes
happens. Usually you get combinations of several pure modes at the same time.]
Identify these modes by number and sketch them into your notebook, too. Measure
the maximum power level you get from the laser with each mode pattern and note this
in your lab notebook along with the cavity length.
7. Check the polarization characteristics of the modes you are making by placing a
linear polarizer into the beam (outside the cavity!) and rotating it. If linearly
polarized, there should be one direction where the power is maximum and 90 degrees
from that direction, the power should be minimum – ideally, zero if perfectly
polarized and the measurement polarizer is also perfect. Are the modes you make
polarized? [Measure the polarization ratio (Pmax / Pmin) with the power meter.]
[You can measure the polarization of the alignment laser for practice.]
8. Determine the Brewster’s angle for the glass cover slip by rotating it in the alignment
laser beam until the reflection goes to zero. Now CAREFULLY place the glass
microscope cover slip into the beam inside the cavity (ie, between the laser gain tube
window and the output mirror) and adjust it to Brewster’s angle. [How will you know
when you have hit Brewster’s angle?] (You might have to move the glass window in
or out a bit to find a low-loss spot that will lase.) Check the polarization of the laser
mode using the sheet polarizer. Is it polarized now? What is the polarization ratio,
(Pmax / Pmin)? Did the transverse mode profile change with the polarizer? Why or
why not? Adjust to other transverse modes. Are they also polarized?
9. Remove the Brewster’s angle window and place the small iris inside the cavity. Try
to force the laser into the TEMoo mode by making the iris smaller. [This adds loss to
the larger diameter higher order TEM modes.] You will probably have to adjust the
mirror adjustment slightly and also the iris position with the xyz stage to make sure
the mode is going right through the center of the iris as you make it smaller. [Why
does the laser stop if the iris isn’t centered?]
10. For the TEMoo mode use the Beam Scan (“signal out” to scope) to measure the beam
intensity profile in the two main perpendicular directions. How do your measured
signals compare with what you would expect? You can also open the iris and verify
that the higher order modes are all larger than the TEMoo mode. Rotate the
Beam Scan to scan modes in different directions and sketch the “signal out” shape of
the power distribution of the modes you produce.
11. Remove the iris and put the rotating stage with the small, sharp needle point into the
center into the cavity with the needle tip barely into the laser beam. Use this
“forced zero” in the electric field (and, hence, the intensity pattern) to try forcing
certain higher order modes to lase. Try rotating the needle and forcing the transverse
mode pattern to also rotate. Why does this happen?
12. Remove all intra-cavity items (needle, Brewster’s angle glass, iris) and maximize the
laser output – all modes lasing. Now move the output mirror out 1-3cm to make the
cavity longer. If the beam goes out, adjust the xy mirror adjustments to make it lase
again. Keep moving to longer cavity lengths until you can no longer make the laser
lase by adjusting the mirror. At what length does lasing stop? How does this
length compare with the output mirror radius of curvature? Test the stability
criterion at this length. When should the cavity become unstable? What happens to
the lasing then? The gain inside the HeNe plasma tube hasn’t changed. In terms of
the gain curve and loss line, why does the lasing stop.
Questions to Answer: [Recall that M1 is flat and 100% reflecting while M2 is 99%
reflecting with radius of curvature = 45 cm. I bought it that way.]
1. You didn’t adjust the cavity length to any particular length, especially to orders of a
half wavelength. Why does the laser still lase for this arbitrary length?
2. Why does the laser quit lasing if the cavity length becomes more than 45 cm?
3. How do the “diameters” of the higher order modes compare with the TEMoo mode?
4. If the cavity length is 40 cm, what is wo, where is wo located, what is the radius of
curvature of the beam at the output mirror, what is zo, and what is the size of the
beam waist 1 m from the output mirror for a TEMoo mode beam?
5. Why do the sizes of the laser modes get larger for longer cavities and smaller for
shorter cavities?
6. How does the Brewster angle cover slip cause the laser to be polarized? Describe its
direction of polarization with a sketch and words.
7. Why does an iris force the laser to lase in the TEMoo mode?
8. What is the effect of the needle tip in the beam? Why?
Conclusion:
You are one of only a small number of people in the world who has aligned a HeNe laser
cavity, gotten it to lase, and observed the various transverse mode structures it can
produce! You polarized the laser using an intra-cavity Brewster window and forced the
laser into various transverse modes by adding loss with the needle or iris. You showed
how an unstable cavity is formed and its effect on the laser. Hopefully, you now have a
much better knowledge of how laser beams are formed in resonant cavities and what
transverse modes are.
Updated by T.K. Plant, October 22, 2011
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