Journal

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.

• 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.

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

6/18-6/22/07

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.

7/5/07

7/11/07

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.

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).

7/16/07

7/17/07

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.

7/18/07

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...

7/19/07

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.

7/23/07

• "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.

• "Acousto-Optics" by J.Sapriel
• "Wave Motion in Elastic Solids" by Karl F. Graff
• "Acoustics an vibrational Physics" by Stephens and Bate

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)

7/30/07

• 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)))

8/01/07