6/11 - 6/17/2007

The REU program is a week old now, and I guess today should serve as a good point for a recap of the week's events and findings. It all started Monday night when Dr. Noe took us out to eat at a very nice Indian restaurant called the Curry Club. It was quite good and left me with some meals to heat up for the rest of the week.

On Tuesday Morning I met with the rest of the REU students over a breakfast with the professors after that the three other students working in Optics (Ian Mallory and Yancey) met with Dr. Metcalf and told him about ourselves. An article in the Tuesdays science times lead him to give a quick lecture on meta-materials. Meta-materials are materials artificially constructed in such a way so that their electric permeativity and magnetic permeability are negatively valued, this can result in the meta-material having a negative index of refraction. Which in turn means that for a certain meta-material, light at the right wavelength will appear to travel"backwards" i.e. the group velocity will be negative i.e. the direction of the time averaged Poynting vector will be anti-parallel to the phase velocity (!) pretty exiting, but not quite invisibility cloak material (although ripe with applicational purpose).

After lunch on Tuesday we talked with Dr. Noe about past projects and a little bit about how we were to make our web-pages. After this he had us go outside and burn holes in paper with a magnifying glass (a favorite childhood pastime). We made the following observations: (From lab notebook pg. 5)

Experiment A: Hold the magnifying glass perpendicular to the incident solar rays, focus the incident light to the smallest possible spot size on a piece of paper also perpendicular to the incident solar rays.

  1. It is difficult to ignite white paper (even on a June afternoon) since the white reflects most of the incident light, but the more absorbent black construction paper ignited quickly.
  2. When the magnifying glass is tilted so that it is not perpendicular to the sun's rays there is a "coma" distortion to the spot, i.e. the spot spreads out and gets a comet-like tail to it.
  3. The spot on the paper usually has a reddish ring at its edges, except when there is the previously mentioned coma distortion, then the ring is blue. This may be due to chromatic aberrations in the lens
  4. As the focused sunlight burns through the paper the smoke lets us see the focusing rays of light converging, then intersecting at the plane of the paper then diverging and casting an oval ring on the ground. The ring is filled with "dancing" colors due to the changing index of refraction of the air caused by the burning paper.
  5. The spot size of on the lane of the paper has a minimum size. It can be focused to a smaller spot size with the magnifying glass than it can be with a set of (positive lens) glasses. Note: the reading glasses have a longer focal length and a smaller diameter than the magnifying glass.

Experiment B: Repeat Experiment 1 at the edge of an afternoon shadow of the math/physics building.

  1. The spot on the paper got more red and smaller as we approached the shadow, with significant distance into the shadow, the top of the spot began to get cut off by a straight horizontal line.
Questions to be answered:
  • Why is there a minimum spot size and why does it change with focal length of lens?
  • Why do the colored rings around the spot change color when the lens is tilted off of perpendicular? Why are they there in the first place?
  • Why do we observe a dimming and reddening of the spot near the shadow and why does the top get "cut off"?
  • And what is always good to ask, are and how are these observations related?

Wednesday I sat in on a discussion with one of Dr. Metcalf's groups about the confocal Fabry Perot, which I had studied some before. I became interested when on Tuesday someone in the group was talking to me about why the free spectral range of the confocal Fabry-Perot was expressed as c/4L and not the normal mode spacing of c/2L. So I attempted a geometrical proof based on the "bow-tie shaped" ray path inside a confocal resonator. On Wednesday I also began to learn some Linux and html to start my web-page.

On Thursday Dr. Noe showed us the interferometer built previously in the Laser Teaching Center. He showed us a novel way of achieving very small mirror movements by attaching a rubber band to one of the mirrors and simply pulling on the rubber band (I suggest that you try this, it works surprisingly well). We then learned a bit about optical vortices (more to come on those) after that I read a bit in Pedrotti and Hecht.

Friday (more on Friday soon): solved magnifying glass problems, talked to Marty Cohen about AMO's and he showed me some materials that were around to start a project with AOM's. The physics keg gathering was at 4:30 after that I went to NYC for the weekend


So another week over and I haven't been able to start a main project yet but I have arranged with Dr. Cohen to talk some more about the Acousto Optic Modulators. In addition I have delved into a number of mini-explortions, worked on classifying the LTC's collection of HeNe lasers with Mallory and have discovered how the laser beam combiner works (a device that I will need if I do a project with the AOM's). I have also been working on preparing talks on geometrical optics which I will give on Tuesday the 26th and thursday the 28th.

Mini-experiments et al:

  • Photodetector, sunlight intensity on earth calculation and calculation of quantum efficieny (in my lab-book).
  • Ulexite (TV Rock) angle calculations of light cones emiited from the crystal- there is more than just the fiber optic phenomenon going on here.
  • Played with some derivations from QED by Richard Feynman and did some extra calculations with the phasor diagrams (also in lab-book).
  • Experimented with finding laser modes from a green (543nm) HeNe coupled to a single mode (10micrometer) and a multi-mode (100 micrometer) fiber optic cable. Explored the effect of a linear polarization on the output modes.
  • Set up an airy diffraction pattern with a 633nm Hene and a 100 micrometer pinhole using a plano-convex lens to focus the laser on the pinhole for a brighter image. Question: What happens if the light sent through the hole is in a non-Guasian mode, say an optical vortex? Since the phase of the light in the vortex mode will be out of phase with itself in such a way that as the ring of light (that constitutes the vortex mode) is traversed in a circle each point is slightly out of a phase with the next point such that opposite sides of the ring are always 180 degrees out phase with eachother. This would mean that what were dark rings before would now become bright rings and so on, but would something else happen due to the changing phase around the cirlce - say a spiral pattern? Perhaps I can do a Fourier Transform on the hole pattern with the appropriate phase realtionship of the incident beam and find an answer theoretically.Though I think I will try it experimentally too. I guess its nothing that a little more thining won't solve - we'll see.

Thoughts on the beam combiner: The beam combiner operates quite simply, it consists of three coated mirrors for red green and violet light inputs, when the input lasers are properly aligned a single white beam emerges from the fourth face of the device. The task would be to design a way to mount the input lasers to the input mirrors, the hardware at the input mirror interface seemes to be built in a way that suggests this line of appproach (there are screw mounts of some type). This device would be useful for creating a multi-wavelength beam to manipulate with the AOM.

Thoughts on the talk: I will be talking on Geometrical Optics and then the Matrix Method. I plan to cover Fermat's Principle and the paraxial approximation. With these I can derive the laws of reflection and refraction (Snell's law). From these I can derive an expression for reflection and refraction at spherical interfaces and from this derive the lens maker's equation and the thin lens equation. For The second talk I plan to discuss ray tracing in the thick lens or optical system case there by introducing the cardinal points and planes. I will then explain how the matrix method works and derive the three most useful matrices- Translation, reflection and refraction. After that I can talk about analysis of the cardinal points and optical systems (and the thisck lens) using the matrix method.

6/25/07 - 6/29/07

Thien an gave me a tour of the Metcalf lab, I spent and hour or two talking to Jonathon who described to me the Rydberg project and to Jason who told me about the lithography set-up. (much more on this later) Then I made some optical vortices (!) and sent them throught a pinhole. Results and set-up next time - mallory is giving her talk now.


Ahh it is July (!). I've been away from the lab for a few days but I've been doing a lot with The Optical Vortex diffraction pattern both on paper and in the lab. Tomorrow I am going to talk to Marty Cohen about the AOM's so right now I'm reading through a paper that Dr. Noe e-mailed me on the Two Phonon Absorption. I promise that I'll get back to this entry soon enough, until then, I am going to play with the optical tweezers that hamsa put a optical vortex through. Optical Optical Optical.


On Friday I met with Marty and we went over the aims of the experiment outlined in the two phonon absorption paper, discussed the equipment that I would need and discussed further experimentation that could be done with the AOM's. My initial goals are to become familiar with working with the AOM's by conducting this first experiment as outlined in the Two Phonon Response paper. From here with the experience from the first experiment, I hope to branch off into other studies on nonlinearities in Acousto-Optic devices. To help stimulate ideas I am going to find and read Marty Cohen's paper that he published in 1970 while working at Bell Labs. I beleive that It discusses the effect of setting up a second harmonic in the crystal (if it doesn't I would like to investigate this). I am also reading Isomet's application note manuals (see my links page) to get familiar with the technincal aspect of working with the AOM devices. A continual investigation into AOM theory should also continue stimulating ideas to test out through experiment.

On Monday Marty came by again and we gathered the rest of the needed equipment and I spent a while setting things up. Mallory got me a 5.4mw 632.8nm HeNe, I liberated a dual channel power supply (to power the RF driver) from an adjacent sonoluminesence setup. I built a translational and rotational stage from some optical mounting equipment laying around. I then coupled the RF output to an o-scope to monitor the driver operation. After setting-up, Marty and I turned on the power to the RF driver but ran into a problem. We didn't see any frequency on the o-scope and the power supply/driver was acting strangely. As I increased the voltage towards 28 volts, the current pegged and limited the voltage to a few volts...(have to go take a picture one moment)...So it seemed as though there was something shorted in the driver's power supply. This large current was also making the driver get extremely hot. To check if soemthing was shorted we measured the input impedence at the driver's power supply leads but found a large impedance of over 6 Mega Ohms. Marty and I were stumped so I e-mailed John Kump at crystal technology, told him our problem and asked for advice.

But the next morning before I heard back from John Kump, I powered up the driver and well... it worked (but not quite at first). At first, I got a sine wave on the o-scope giving me about 200MHz, but it was rather attenuated, and the driver was still getting hot because there was about 1 amp running through the driver at 28 volts. I let the driver run for short periods of time and tried to align the AOM to view a deflected beam...(to bo continued Yancey is giving a talk). So to make a long story short, I finally found a deflected beam when I had the idea to attenuate the zeroth order beam by having it fall on a black peice of tape on the screen. Without the bright zeroth order beam washing out the deflected beam, I found the deflected beam and optimised the angle of the AOM for deflection into the first order beam. I verified that this weak spot was the deflected beam by varying the RF frequency and observing the changing deflection of the first order beam. I began investigating further by measuring the angle of defelction as a function of RF frequency. But before I could compare these values with the calculated angles, something happened (I don't know what - I am magic) The Rf driver stopped gettting hot and the output was amplified and the current dropped from 1 amp to 0.1 amps. Whatever happened this caused my deflected beam to be come brighter and deflect more. So I took my deflection angle vs. frequency data again and analyzed it but found an ugly systematic error in the angles. But I found two problems in my calculations that should soon remedy this:
  1. The o-scope has a 100MHz badnwidth and I am trying to read frequencies of 200Mhz and up.
  2. The AOM does not use a PbMoO4 crystal (which I thought it did) This means that the value for the sound velocity through the crystal will be different (the systematic discrepancy).
So for now I am going to retake the frequency data and recalculate theoretical angles with the new speed of sound figure in (... I am not sure yet). After this I will look at measuring and adjusting the RF power and measure intensities of the defelcted beam with a photodetector.


I have been so caught up in my work over the last week that I haven't given any time to my online journal. I have written about 40 pages in my lab book and made quite a bit of progress, but for now I will just note that the focus of my work has been designing and carrying out experiments to investigate the nature of some fascinating patterns that I came across last Wednsday as I was making some inital observations of the AOM diffraction pattern. They are apparently called Schaefer-Bergmann Patterns (although I call them shark-jaws because thats what I thought of when I first saw the patterns from the Tellurium Dioxide crystal). Once I finish some of these experiments investigating the sound behavior in the crystal I will be able to put up some pictures and give some detailed accounts that I have written in my lab book. Until then... (P.S. I have also done some diffraction angle measurements, speed of sound measurements in the TeO2 and PbMoO4 AOM's and did some theoretical and experimental Fourier analysis of the AOM treating it as an aperature in the "4f" set-up. Oh and just to note, my Journal is written in reverse temporal order relative to the other journals on the site I fear that I must remedy this soon)


Ok so as promised I have about a weeks worth of lab work and 40 pages of thought to try and summarize. It is about 7:00pm and It has been a trying day so I figure that takeing some time to summarize all of my work so far in type will help me to collect, think, solve, and move on.

Last Wednsday I was finishing up some statistics and prpagation of error on my calculations of beam deflection angle vs. RF carrier frequency to verify that the defelcted spot taht I was seeing was indeed what I was looking for (it was a rather weak dot). Marty came by and I showed him my work and the defelcted beam, we both agreed that this spot was teh first order diffracted beam but hat something was wrong because the RF driver out put seemed way to weak and the device wasn't even getting warm anymore. So we rigged up a new driver (I measured its frequency range to be about 115-240 MHZ). Unitl that moment I had not seen how a AOM really works. Instead of one puny delfected spot I could see up to 7 intense defelcted beam orders on each side (!) (with the lights out of course). I examined the new pattern for a while and observed its dependence on the angle of incident laser light, but the most exciting part of the day came when I noticed...(the fire alarm is going off again err)...I wont keep you in suspense any longer, so as I was saying the most exciting part of the day came when I noticed (using the Crystal Tech 4210 TEO2 crystal) some light on the screen that was outside of the plane of diffracted beams. It was a faint pattern of light above and below the line of "expected" diffracted beams. I turned of the lights and adjusted the RF frequency until I clearly saw what looked like a shark's jaw connecting the second order deflected spots. Inside of this was an ellipse (almost circular) that connected the first order beams. It was evident that somehow the RF signal was driving sound wave patterns in the crystal that were deflecting the beam in much more elaborate patterns than what I had expected. Marty told me that these patterns were referred to as Schaefer-Bergmann patterns and they are now the focus of my studies. My main goal is to figure out what the sound waves are doing in the crystal to cause these specific deflections. I found that in the PbMoO4 crystal the patterns are not shark jaws but families of ellipses (possibly due to the birefringent nature of this crystal (although that is not the whole story since TeO2 is also birefringent)) this lead me to beleive that the specific S-B patterns that I see depend on the crystal type that I use and thus the sound wave behavior must depend on the crystal structure.

I will get into the specific experiments that I have been conductiong tomorrow since it is getting late, but I would like to note that at the moment I am analyzing the patterns that I have traced on graph paper. With these pattern traces I have accurately measured the speed of sound along the main axis of sound wave propagation for TeO2 and PbMoO4 and I am attempting to use them to build a picture of the velocities of sound in the crystal with respect to direction of sound propagation, this should help me construct a picture of the crystal structure as seen by the sound waves. I have also been attempting some of the theory myself with help from a paper by Uchida entitled "Schaefer-Bergmann diffraction patterns due to the abnormal Bragg reflection in birefringent media" In the Journal of Quantum electronics (volume 7 page 160 1971). Marty and I have also been discussing the nature of these patterns back and forth, so for now I will keep thinking and report back here in the morning. But before I go, check out the link at the bottom of the physics heading on my links page, It is a surface wave in TeO2 and is similar to the "shark jaw" pattern, peculiar no? Soon we shall see.


So today was the weekly Wednsday luncheon, our speakers were Danny Minkin and Simone who talked to us about their recent work on creating a mathematical model of 2 mirror alignment (or walking the beam). I had four pieces of pizza as usual and we talked about LN2 bombs, It was a great meeting, we discussed everyon'e's project status and Dr. Metcalf had suggestions all around.

As for my work with the AOM's... I progressed mostly experimentally but as for the theoretical anlysis I have let it settle for another day, I suppose that tonight I will begin collecting my thoughts again on what these sounds wavs are really doing inside of those crystals and what the laser light thinks of this to project such interesting patterns. But as I said I did run a few more littel experiments today where I investigated the patterns as a function of position of incidnet light on the crystal. I found that as the beam moves away from the center line of the crystal the usual deflected beam spots split apart. As the incident beam moves away from the transducer towards the absorber the central spots get dimmer (there is less interaction with the main saound wave set up by the transducer?). So considering this I put the beam incident on teh uppermost right corner and low and behold I got a much better veiw of the S-B patterns (!) Now I could not only see the first order patterns but also the larger second order patterns surrounding the originals. This confirmed my thought that the patterns are made up of several shapes which repeat themselves in several orders which are concentric with the originals but whose edges lie at the same positions as the usual defelcted beam spots. For example, the TeO2 shark jaw pattern consists of two shapes, the shark jaw and the inner ellipsoid. The first (or zeroth order) shark jaw is centered around the zeroth order beam spot and its edges lie on the second order beam spots. The first (or zeroth order) ellipsoid shape is centered around the zeroth order beam spot and its edges lie upon the first order beam spots. The second order shark jaw is then centered still on the zeroth order beam spot but it is now larger and its edges are on the (3rd or 4th cannot remember -maybe I don't know yet) order defelcted beam spot. The second order ellipsoid is still centered aroudn teh zeroth order beam spot but is larger and its edges now lie on the second order beam spots in such a way that it nearly circumscribes the first order shark jaw. So as I've said, a lot of observations and not too many explanations yet... I am working on it. Oh and I forgot to mention that I could get better views of the S-B patterns not only becuase of teh new alignment but also because I switched to a 12.4 mW laser after I noticed the the new alignmetn was helping me out. I took some better pictures today of the TeO2 patterns and plan to get some of teh PbMoO4 patterns tomorrow morning. I will post these pictures as soon as I learn how. Until then...


I devoted today to a collection of observations, posing of questions and construction of a theory. At the end of the day I have completed all three of these and now intend to rework what I have done many times over to see if it a consistent interpretation. Tonight I plan to do this and present what I have come up with tomorrow. For now I can say though that I have worked backwards from the S-B pattern in TeO2 to create a diffraction grating that should cause the observed beam deflections and resulting pattern. If I can verify that this is a physically possible pattern as far as the crystal is concerned (which it seems to be so far since the theoretical grating is nearly identical to the surface wave patterns in TeO2) and that it does indeed create the observed S-B pattern, then I think that I will be in buisness for the time being. More on this tomorrow...

It is 8:00 and I had a quick idea. Since I am now more interested in the actual shapes in the S-B pattern (since they will tell my what the sound waves in the crystal will look like) and not the extra orders that I was curious about before, I decided to use an adjustable iris to block out everything but the first order shapes of the S-B pattern and put a thin horizontal piece of black tape across the iris to block out the main order of bright spots. I quickly ran back and set that up and observed a nice clean S-B pattern that I can look at more tomorrow. (Although I think that I already have traced all of the important features of these patterns, there may be something that I haven't caught sight of yet so it is always good to push for better and better resolution). Anyway I feel pretty good about the patterns that I have generated theoretically for the TeO2 shapes, I will keeping checking it over and then start on one for the PbMoO4 tommorrow. Hopefully Marty and I will also meet and discuss.


So on Friday I caught a train at 4:00 so I didnt have time to write online about the day's findings. I will summarize what I've been working on since friday morning. Thursday night Marty emailed me an interesting paper on Schaefer Bergmann patterns in lithium niobate entitled, "Optical diffraction studies of sound waves in lithium niobate" from the Journal of Physics D: Applied Physics (Vol. 9 Page 999 (1976)). The paper was interesting in that it described the methods that I had been attempting earlier to image the sound in the crystal by using a 4f Fourier set-up. It also discussed a similar Fourier set-up, blocking out all but the first order deflected light at the spectrum plane that is useful for imaging the S-B patterns. In addition to this paper I have also accquired paper from those cited in the Uchida S-B paper and two others. Currently I am working with teh following papers:
  • "Schaefer-Bergmann diffraction patterns due to the abnormal Bragg reflection in birefringent media" by Uchida for a theoretical discussion of the patterns.
  • "Acoustic Diffraction of Light in Anisotropic Media" by Dixon for some more theoretical treatment of the diffraction process in the crystal.
  • "Brillouin Scattering in Birefringent Media" by Hope for some more theory (although I'm not sure how useful this one will be yet).
  • "Optical diffraction studies of sound waves in lithium niobate" by W S Goruk, R Normandin, P J Vella and G I Stegeman for some interesting experimental methods and pictures.
  • "Optical Properties of Single-Crystal Paratellurite (TeO2)" by Uchida for the velocities and indicies of refraction in TeO2.
  • " Physical Properties of Lead Molybdate Relevant to Acousto-Optic Device Applications" by G. A. Coquin, D. A. Pinnow, and A. W. Warner for acoustic velocities and indicies of refraction in PbMoO4.
Today, I also checked out three books from the library on Acousto-Optics and wave propagation in elastic solids to figure out how the waves were being set-up in the crystal to cause the patterns. I have:
  • "Acousto-Optics" by J.Sapriel
  • "Wave Motion in Elastic Solids" by Karl F. Graff
  • "Acoustics an vibrational Physics" by Stephens and Bate
So I am really getting into acoustics, but it has paid off, as of today I have beleive that I have a pretty good picture of what is going on inside the crystal.Basically, The transducer launches a longitudinal sound wave down the crystal axis, this wave hits the angled end of the crystal at teh absorber end and reflects. Due to the non-normal incidence of this reflection (the crystal end is angled) part of the wave reflects and stays in longitudinal form just as an analogous light wave would but some of teh sound wave mode converts at reflection into a shear wave. For now I will say that this mode conversion is due to a transverse component of the wave disturbance manifesting itself, but I am reading more on this to understand it better. In this manner longitudinal and shear acoustic wave modes are set up in all directions in teh crystal. Due to the specific structure and symetries in a given crystal the speeds of these waves will be a function of direction in the crystal. Also the shear wave will usually travel slower than the longitudinal wave and have a different directional dependence on speed. Since the deflection of the beam into the eventual S-B pattern depends on the index of refraction gradient in the crystal and the index of refraction gradient depends on wavelengths of the sound waves and these wavelengths are dependent on sound wave velocity which is a function of propagation direction and sound mode type this means that to understand the patterns I need only understand the mode cenversion that create the shear waves and the crystal proprties that determine the dependence of sound wave velocity with direction in teh crystal.

After understanding this, I plotted some velocities from my TeO2 pattern and compared them with the measured velocities in the Uchida TeO2 paper. I found that the velocites that measured from the shark jaw shape match up with the velociteis from the paper of shear waves in TeO2. The velocities associated with the ellipse in the TeO2 S-B pattern match up with the velocites of the longitudinal wave. This was rather exciting since it meant that The two shapes in my S-B pattern were being produced by a shear and a longitudinal wave and that these waves were created by the reflection and mode conversion process mentioned earlier. My plans are to now map out a complete velocity spread for both the TeO2 and the PbMoO4 S-B patterns. I will caclulate a velocity at every five degrees around the S-B pattern and plot velocity vs. direction of wave propagtion in the crystal. With this I can identify the wave types in each crystal and continue to build a more complete story of S-B pattern production in Acoust-Optic devices.(P.S. the pictures are coming soon and so is a correct ordering to my journal)


A lot has been going on since my last entry, but basically I have been...
  • Taking better pictures of the Schaefer-Bergmann patterns
  • Investigating the effects of incident beam polarization on the patterns
  • Observing deformation of the patterns with incident beam angle
  • Slaving over a ruler and graph paper to measure beam displacements as a function of acosutic wave propagation direction
  • Making graphs of acosutic wave velocity vs. acosutic wave propagation direction
  • Using "Maple" (see Links under mathematics) to calcualte a propagation of error for all of the velocity measurements
  • Trying to match my data with accepted acoustic velocites in TeO2 and PbMoO4 to build a picture of acoustic wave behavior in the crystal
  • Learning some elastics theory
  • Learning some acoustics thoery
  • Learning some more mathematics so that I can understand acoustics and elastics
  • Trying to make theoretical calculation of the wave velocites in the plane perpendicular to the incident laser beam
  • Writing and revising an abstract for my talk on friday with Marty and Dr. Noe
  • Wishing I had 8 more weeks to come to more conclusions and play with sound in crystals (everyday I discover something new or observe a new area to investigate and everyday I have no less than one less day (think about that (also think about if it is confusing to put parentheses inside parenthese)))
So there is the general break down for you. The problems that I am dealing with at the moment are apparent anomolies in the accepted acoustic wave velocites in TeO2 vs. my findings. I am finding similar acoustic velocites to within error allowances but the propagation directions of the cooresponding waves are still somewhat contradictory. I took two final traces today that utilize the latest in my techniques to observe reliable S-B data, by this I mean that I ensured normal laser light incidence, proper laser light polarization, and specific measurement and error analysis of important variables (distance form AOM to screen and RF frequency). I will use these final traces to measure velocity of each wave in each pattern for every 5 degrees around the pattern (as I have done 4 times now). These last traces should provide a more complete spread of velocities, be unbiased by pattern deformation and unknown error estimation, and confirm previous findings. I will plot the veolicity spreads in excel with error bars from my Maple calculations. After I do this (hopefully tonight) I will learn how to caculate the same velocity spreads using some elastics theory (I need to find expressions for the acosutic moduli in all directions in the specific crystal classes that TeO2 and PbMoO4 fall into). When all that is done I will prepare a talk and sleep friday on the way home. I also want to put my pictures up in the time remaining. P.S. Brookhaven National Lab tour tomorrow (!)


So I don't have much time since I need to put together a 10-15 minute talk and its corresponding power point presentation tonight, but it is worth writing that yesterday after the BNL tour I picked up a book called "crystal acoustics" by M.J.P. Musgrave (four names?) and learned some acoustics for a few hours with teh goal of learning how to calculate acosutic wave velocities in different directions in the crystal so I can compare them with my experimental measurements and determine what acosutic waves are causing teh S-B patterns. So as I was saying after a few hours of reading and thinking and playing with some equations in Maple (mathematics software), I figured out how to caclulate velocity curves for all directions of propagation in a plane of the crystal. With this new theoretical tool I can explore quite a bit more about the patterns (I just need more time here(!)), for example one of the many things it has lead me to so far is the confirmation of the long debated crystal axis orentation in the TeO2 (which was also confirmed by Crystal Technologies inc. today). Tomorrow I will put up the Maple code and describe this process along with a final statement of my findings and plans for future work on the subject that I may hopefully continue and present in the fall (never enough time).
Dan D'Orazio
June 2007
Laser Teaching Center