## Journal

Week 9 | Week 8 | Week 7 | Week 6 | Week 5 | Week 4 | Week 3 | Week 2 | Week 1

### Week 9

#### Friday, August 12, 2005

Today is the last official day for the LTC's Summer 2005 students. We spent the morning setting up a laser show which involved shining 4 different laser beams at a CD shard which was glued onto a latex glove (which was stretched over the speaker). After gazing up at the dancing laser beams and using liquid nitrogen to show the converging and diverging beams, we decided to watch a movie and get pizza. Three pizzas (eggplant, sicilian, and broccoli with garlic) were ordered while Amol, Maaneli, and Moon came with me to get my speakers for the movie. We ended up deciding to watch "Death to Smoochy", which was quite funny. By the time the movie was over, people had to leave, thus ending this summer at the Laser Teaching Center.

#### Thursday, August 11, 2005

Today, Amol and I worked on our data from yesterday's experiment. In the morning, we worked out how to convert the equation we derived to look like our data (so that it could be used as a fit). Once we got it, we tweaked our parameters (thickness d and index of refraction n2) until it fit our data best. For the most part, we left the index of refraction as 1.518 (the same index of refraction as the index of refraction matching fluid) and finally found ourselves with a thickness of 0.233 mm, which is close to our measured value.

Amol and I meant to experimentally determine whether the optical pathlength is constant across the entire face of the coverslip, but ran into several complications. We decided to use a linear CCD array (same type as Lindsey is using) in order to observe the movement of the fringes, but couldn't get the camera to work with the digital oscilloscope. We still had no results when tested with an analog oscilloscope and after asking for Lindsey's help. When Dr. Noé took a look at it, it still appeared to be broken--so he tested out Lindsey's camera (which did work). When this working camera was moved to our setup, it suddenly decided to stop working. The rest of the afternoon was spent trying to figure out the problem with the cameras. From an initial assessment, it appears that both of their voltage regulators are not outputting any voltage, which could be a problem.

#### Wednesday, August 10, 2005

This morning, the LTC had a communal talk, discussing everyone's projects and where we're going. Amol and I continued setting up our tilt to fringe shift experiment, deciding to use a photodetector and voltmeter to record our data. Jon and Danielle came to visit in the early afternoon and we all went to Lawan for lunch. Afterwards, we all showed them what we were working on and Amol and I started taking data. We took about 80 data points and typed it into Excel. From the looks of it, our sample rate wasn't high enough towards the end, but should still work fine for fitting it to a theoretical curve.

#### Tuesday, August 9, 2005

This morning, Amol and I re-completed our derivation of the phase change of light after passing through a tilted surface. We compared our results to a paper Hal referred us to to make sure that we were getting it right finally. With these initial equations:

We find the change in optical path length:

Which can be rearranged and simplified to solve for the number of fringe shifts as a function of angle:

Where m is the number of fringe shifts, d is the thickness of the sample, &lambda is the wavelength of the laser, &theta is the angle of incidence, φ is the angle of refraction, n1 is the index of refraction of the surrounding environment, and n2 is the index of refraction of the sample. As for the variables used earlier on, L is a fixed distance between two distant points, Lf is the distance travelled through n1, and df is the distance travelled through n2.

Otherwise, we had our last pizza lunch in which Kiko Galvez from Colgate University came down to talk to us about his work with OV's (specifically, composite optical vortices). Afterwards, he came to the lab and looked at what all of us are working on. Amol and I also spent some time setting up our experiment for measuring the phase shift of a rotated coverslip. Tomorrow we will hopefully complete the experiment and continue with our analysis of our coverslip surface data.

#### Monday, August 8, 2005

Today was mainly a day of re-organization. Amol and I got Matlab installed on the Windows computer and went over what we need to finish:

• Convert θx and θy into a total tilt, &thetatot.
• Re-derive the phase shift equation for a tilted sheet of plastic (and compare it to the solution found from the paper Hal gave us).
• Experimentally find the relationship between rotation angle (of a microscope coverslip) and phase shift using an interferometer (a Michelson interferometer will double the effect since it passes through it twice, as opposed to the C.J. interferometer).
• Complete the data analysis in Matlab using the information found above.

Amol and I are hoping to complete the first three things mentioned above tomorrow, if not all four.

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### Week 8

#### Friday, August 5, 2005

From 9:30am until 3:30pm, the REU talks were given. Maaneli and I were lucky enough to be the first two to go (at least we got them done early). Probably the most notable talk was given by Michael and Eugene, presenting their spark chamber which was only completed the day before. Otherwise not much happened today.

#### Thursday, August 4, 2005

This morning, Amol and I typed in all our data from the night before and went over them, correcting incorrect data points (either from my misreading them or as typos). At this point, we moved to the SINC Site in order to use Matlab (for data analysis). We came up with some really pretty looking plots (including a 3D scatter plot), but still need some additional work on the data. I spent the night in my room starting and completing my PowerPoint presentation for Friday.

#### Wednesday, August 3, 2005

Today, Amol and I completed the tedious task of recording all 430 data points on our screen. However, we quickly realized that the greater task of measuring all the points lay just ahead. So, we stayed in the lab till late at night recording all the data points. Amol stayed over in Maaneli's room because it had gotten so late.

#### Tuesday, August 2, 2005

Amol and I started taking our first data today. It was prefaced by taking painstaking measurements in order to ensure that the data would be read correctly (measuring the angle of the mirror, distance from the screen, and alignment of the laser beam). After this, we placed a mirror where the spiral phase plate would go and checked where x0 (the position of the beam when the reflected surface is exactly parallel to the screen) was. We then measured the deflection of the beam after turning the calibration knobs five complete turns, comparing the actual deflection with our predicted value. At first, these two values were within a tenth of an inch (less than 10% error), so we went back and remeasured our constants. We came back with a more accurate reading of the angle of the mirror θm which put our measurement within 0.02" of the theoretical value.

After our pizza lunch, where we all discussed the current progress of our projects, Amol and I started taking data. It was pretty slow and painstaking and only got 84 data points (20% complete) done before I started working with Dr. Noé on my now complete abstract. Tomorrow we will finish taking data and hopefully measure all the data points.

#### Monday, August 1, 2005

Today I spent some time writing my REU abstract as well as moving forward with our scanning experiment. At this point we have gotten everything set up and ready to go minus a sheet of Plexiglas for mounting the graph paper on. My goal for tomorrow is to finish getting all the data from this experiment and input it into a text file (for evaluation in Matlab). Based on some initial tests, it appears like the data should be very interesting--I'm really looking forward to getting some real data to work with.

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### Week 7

#### Friday, July 29, 2005

Today Amol and I, using liquid nitrogen vapor, took a number of pictures of our interferometer, spiral phase plate, and optical vortices. I also did some work preparing for scanning the phase plate with a laser.

#### Thursday, July 28, 2005

Today I spent my time calculating the math behind scanning the spiral phase plate. The complications arise from two sources:

1. In order for the reflected beam (from the spiral phase plate) not to be obstructed by the mirror from where the incident beam came, an angle must be introduced (such that the incident beam is not normal upon the surface of the spiral phase plate). This means that the measured X and Y values (as projected onto a screen) will not be related to the horizontal and vertical tilt of the phase plate surface in a simple way.
2. The surface of the spiral phase plate is bent. This means that the position of the reflected spot on a distant screen depends on:
1. Tilt in the X-direction (θpx)
2. Tilt in the Y-direction (θpy)
3. The exact location in space (X, Y, Z)
which amounts to five variables. This creates a problem because I don't know enough information to be able to solve for θpx and θpy.

At this point, I'm pretty sure I've gotten the final equations that satisfy the first problem. However, my only choice for solving the second issue is by using an approximation (which I used in my calculations). That is, assume that the spiral phase plate exists in only two-dimensions while still having a θpx and θpy vary along the surface. I made equations for testing this approximation and will need to evaluate them tomorrow.

#### Wednesday, July 27, 2005

This morning, we finished cleaning up the lab in preparation of the REU tour. At noon, Maaneli and I went to our last weekly REU meeting where we were told about what we need to do for the REU symposium on August 5th. Afterwards, we migrated downstairs (with the exception of a few who slipped out for lunch) to the LTC where we all presented what we are working on.

After lunch, we were shown around the lab where Jose works and got to see a lot of large and expensive machinery, something we're not so used to in the laser lab. By the time we got back, several people had already left, leaving an almost empty lab. Tomorrow there should be fewer distractions, allowing me to get moving on collecting data.

#### Tuesday, July 26, 2005

Today we had our third pizza lunch and listened to Jose Mawyin talk about FEMLab, a computer program that allows you to model all sorts of physical phenomena (stress in materials, heat transfer, light propagation, etc). This will be applicable for Amol and I in order to create a theoretical model of our spiral phase plate.

Otherwise, I spent some time taking nifty pictures of our interferometer using liquid nitrogen vapor to show the beams. Afterwards, I setup the device that will translate the spiral phase plate (so that it can be scanned by a laser). John Noé pointed out that using a lens to focus the beam onto the phase plate will produce a sharper reflection, which it did. I also made a new piece of Plexiglas for inserting into the phase plate which had flat edges (the piece we've been using up to now was a scrap piece with uneven edges). Tomorrow I will make the final setup for scanning the spiral phase plate.

#### Monday, July 25, 2005

This morning Nilus talked about his optical lever project. John Noé explained how he should organize it and had us come up with a one sentence definition for "optical lever". After lunch, I showed moon some more math regarding harmonic motion: a review of damped and undamped vibrations, as well as forced vibrations. At the very end, I showed her how this math equally describes a physical system (driving force, spring, mass, and damping force) and an RLC circuit (driving force, resistor, inductor, and capacitor).

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### Week 6

#### Friday, July 22, 2005

This morning, Amol and I finished up our equation for the number of fringe shifts from 0° to θ:

Where m is the number of fringe shifts, d is the thickness of the sample, &lambda is the wavelength of the laser, &theta is the angle of incidence, φ is the angle of refraction, and n2 is the index of refraction of the sample. As far as we know, this is the correct equation, exactly describing the added optical pathlength.

At 11 o'clock, we had a lecture from Hal on OpAmps and electronic circuits. Following this, Maaneli and I went to our REU talk, had lunch, and came back to the lab briefly before I had to leave for the weekend.

#### Thursday, July 21, 2005

This morning I setup a device which (theoretically) was supposed to translate an incident beam vertically and horizontally. It was comprised of two mirrors and an X-Y-Z adjustable mount. Upon testing it out, I realized that I had not fully thought it out--as the beam did not move at all. When Amol returned from his BNL visit, we set up a similar device based on his design. It appeared to work well except that the reflection off of the coverslip was faint and broadened the beam considerably (~2cm).

Later on Amol and I started to work out the formula for the phase change of light passing through a medium with thickness d and at an angle θ. We eventually reached an equation which output the number of fringes between 0° (normal) and θ (if it were to be tested with an interferometer). We have a couple of minor errors which we will take care of tomorrow. We also used Mathematica to plot this equation.

At the end of the day, we listened to Maaneli and Matt give a talk explaining their research about an OpAmp circuit. Even though they had to go back and rework their equations, we all learned something about OpAmps and circuits.

#### Wednesday, July 20, 2005

Amol and I made several adjustments to our setup today, as well as constructing a holder for our spiral phase plate. First, we expanded our beam by passing it through convex lenses with focal lengths of 25.4mm and 250mm. This expanded, fixed-width beam was much easier to deal with and allowed us to insert the spiral phase plate with better precision (aligning the center of the beam with the end of the cut). We then used a lens mount to hold our spiral phase plate and adjust the curvature. Amol and I made a trek to the Life Sciences building in an attempt to obtain thicker plastic coverslips. Unfortunately, every lab we came to only used glass coverslips.

This afternoon, we added a 50µ pinhole and iris into our interferometer to give us a cleaner (gaussian) beam. This did improve the quality a little bit, but did not improve our fork grating image dramatically. Starting tomorrow, Amol and I will start building a setup where we'll scan the spiral phase plate with a laser (translated in the horizontal and vertical directions) to measure the angle of deflection, thus modeling the surface of the warped coverslip.

#### Tuesday, July 19, 2005

This morning, Amol and I were relocated to a different optical table. This also corresponded with our deciding to dismantle our Sagnac setup and modify it. The setup is similar to the Sagnac except that each beam (after the initial split) hits its own mirrors as opposed to sharing the same elements. This allows us to modify each individual beam path with more control and lets us insert lenses in the different beam paths as we see fit. So, we cleared the back of the table in the lab's main room and cleared the white board for our use.

After lunch we heard Harold Metcalf's talk on clocks, which was quite interesting. Afterwards, Amol and I got to work on setting up our new interferometer. We started by carefully aligning the laser and drawing a layout of the setup on our white board. This was followed by placing the mirrors and beam splitters in the correct locations, checking the tilt of each element as we went along. Once we had finished the initial setup, we spent some time finalizing the alignment so that we got an interference pattern. Initially we were having the problem that the two beams did not overlap completely (but rather, intersected at only one point). We eventually solved this by making slight adjustments to the beam splitters.

We started playing around with inserting lenses into the setup to modify the interference pattern and took pictures of the setup (a photos section of my website will be coming soon...). Some of our short term goals include:

• Finalize on what material will be used for our spiral phase plate (use the coverslips we have currently or try thicker ones, which must be obtained)
• Design and make the element that will hold the phase plate stationary (and modify its curvature).
• Finish our interferometer setup by expanding the original beam (two lenses) and focusing the final beam onto a screen.

Some of our long term goals include (as discussed with John Noé):

• Assuming an index of refraction of 1.5 for our coverslips, plot a graph of θ vs. # of fringes (how rotating the coverslip around a vertical axis will increase the optical path length).
• Measure the # of fringes while changing θ, thus determining the index of refraction experimentally.
• Bend the coverslip in only two dimensions (i.e. hold an uncut coverslip fixed on the left side and bent at a certain angle on the right side) and scan the surface with a laser from left to right, finding how the optical path length (and hence, the angle of the tangent line) changes along this curve. This will allow us to better understand what is physically happening when we bend the coverslip.
• Repeat the previous experiment, but deform the coverslip into a spiral phase plate and scan it with a laser in both the X and Y directions. This data can then be used to reconstruct the surface of the coverslip in Matlab or Mathematica.
• Repeat the previous two experiments but measure the deflection of the reflected beam. Using the concept of an optical lever, calculate the angle of the coverslip (at every point). This method may or may not be better than that which was described in the previous two points. If possible, it would be nice to complete both these methods and compare their results.

#### Monday, July 18, 2005

Today we had our second pizza lunch and discussed different project ideas. I will be working with Amol on producing optical vortices with a spiral phase plate and creating an OAM sorter (time permitting). I will also work with Moon on Mueller matrices (helping her with the math).

Otherwise, Amol and I continued to work on our experimental setup. Our current dilemma is creating some sort of device which does the following:

• Holds the phase plate
• Adjusts the bend of the phase plate
• Mounts to the table

We went to the machine shop to get this made, but realized that we needed a better idea of what we wanted (especially since we found out that it will cost almost \$40 to make). We would also like the phase plate to be thicker than the microscope coverslip that we've been using--such as using a thicker coverslip.

This afternoon I showed Moon some linear algebra, specifically:

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### Week 5

#### Friday, July 15, 2005

So I decided it was time to take some action with regards to this spiral phase plate. This morning I made a trip over to the machine shop and got some spare pieces of Plexiglas™ and made cracks in them (with the help of a hammer). Amol and I then got started on setting up a Sagnac interferometer for the experiment. We currently have it set up so that the two waves interfere and produce a pattern (staight lines). We now have to figure out a better method of creating a more precise crack, mounting the cracked Plexiglas™, and bending the crack to make it act like an adjustable spiral phase plate.

#### Thursday, July 14, 2005

This morning I did some reading on interferometry and the various types of interferometers. I found the Sagnac interferometer particularly intriguing, which was also used in this paper on making a spiral phase plate. I then played around with a photodetector and a beam splitter and found that the light coming out of it is pretty close to being 50-50. With the setup that I had, a direct beam saturated the output, so I used neutral density filters to reduce the intensity and obtain realistic results.

Lunch today was an interesting experience. Among a number of other things, we talked about:

• How to get a laptop by working for a large corporation
• How to get a job from CitiBank
• How to get into the Citigroup building with a hang glider and light saber
• The fact that I'm in the mafia and have killed two people
• Moon's two favorite words: contaminated and appreciate
• Who's hotter: Sean Connery or Orlando Bloom
• Coherent back scattering

When we got back to the lab we looked at a laser beam as it passed through a tank of water (with some of my mango lassi added in order to make the beam more visible). We also observed Nilus's Michelson interferometer and some of the effects from multiple reflections within the beam splitter

#### Wednesday, July 13, 2005

We had our first pizza lunch today and listened to Jan give a talk about his research. Afterwards, John Noé left (he'll be gone until Monday) while Marty stayed behind to watch over some of our projects. I went upstairs with Moon and Lindsey to show them the library and find a book on multivariable calculus for Moon.

I did some additional reading on HG and LG laser modes and looked at the paper titled, "Propagation Dynamics of Optical Vortices" (link to this on my links page). At this point I would like to start doing some hands on work with optical vortices because a lot of the writing on it is difficult to fully grasp without hands-on knowledge.

So, later on today, I started thinking about interferometers--which would be used to measure the phase of light around an optical vortex. When I pointed a laser beam into a beam splitter, it appeared that the transmitted light was considerably brighter than the reflected light. I tested this out with a photodetector and found, with Nilus's interferometer, that the two beams from the beam splitter read the same voltage. When I measured the light from the violet laser, the transmitted light read about 10.99V and the reflected light measured about 10.84V. Tomorrow I think I will do some reading about beam splitters and photodetectors (how to use them).

#### Tuesday, July 12, 2005

Today the physics REU students had a field trip to Brookhaven National Labs.

#### Monday, July 11, 2005

This morning I did some reading on an assortment of topics, including transverse laser modes, the faster-than-light phenomenon, and phase velocity. I also found a video of an example where the phase velocity is greater than the group velocity, but Amol found a better one. After explaining the derivation of the differential wave equation to Moon, John began today's lecture on describing a wave in exponential form. He demonstrated this through double slit diffraction and interference (adding two exponentials to describe the intensity of light at a particular point on a distant screen).

After a late lunch at Jasmine, I explained how to use differential equations to solve problems of simple harmonic motion (SHO) to Moon. This involved the method of substitution to solve second order ordinary differential equations with constant coefficients. As a homework problem, she will calculate the general equation of a horizontal mass and spring system with damping.

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### Week 4

#### Friday, July 8, 2005

This morning I continued thinking about the problem from yesterday and concluded that it could not be proven. Essentially, one only has to think about the situation where linearly polarized light goes through a polarizer at π/4 radians and another at π/2 radians. We know from experience that some light will get through, but doing the math, there will be no E field when it just goes through the second polarizer at π/2 radians--regardless of any constant in front of it. This happens because we represent light as a vector as opposed to a scaler (intensity), where the geometry isn't integral to the math.

After a long lunch at the SAC (we were waiting for the rain to stop), we ran back (through the rain) and did some logic riddles. This included one about pirates, as well as a number of others.

#### Thursday, July 7, 2005

This morning I read some more journal articles on optical vortices and John showed me the websites of some former students here at the lab that studied optical vortices. I will want to go through these more thoroughly in order to learn more about optical vortices.

A little after 11, Harold Metcalf came and talked about describing waves mathematically. We started with:

And got as far as:

By noon, when Matt, Amol, and Harold left, I explained the photoelectric effect after being asked about the particle nature of light. John then proceeded to explain when we should and should not think of light as a particle.

After lunch at Jasmine, I started to think about a problem which Lindsey, John, and Harold have been having: showing that a wave going through two polarizers is the same, mathematically, as the same wave going through the second polarizer times a constant. I thought that this should be fairly straightforward, especially when considering it using Malus's Law:

Where k=cos2(θ)=constant for a given θ. Of course, the proof wasn't this simple since the point of it was to do it using Jones Matrices to describe the polarizers. I soon found myself in a big trig mess and was going in circles. I will resume this problem tomorrow once my head stops spinning.

#### Wednesday, July 6, 2005

After doing some reading about optical vortices, John talked to us about the lab's DOS computer and the spreadsheet program it has. Maaneli and I then departed for our weekly REU talk titled, "Imaging the Surfaces of Rotating Stars".

After a lunch at Jasmine with my fellow REU students, I came back to the lab and read about various topics including birefringence, relative retardation, wave plates (full, half, and quarter), polarization, and angular momentum (of light). These were specific topics that I felt a little unclear about--which should help me when reading some of the articles I've been finding on vortices.

#### Tuesday, July 5, 2005

I was out today due to Jury Duty :-(

#### Monday, July 4, 2005

Happy 4th of July!

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### Week 3

#### Friday, July 1, 2005

After being told about Google Scholar, I was able to find a number useful articles relating to optical vortices, which can now be found on my links page. Otherwise, I looked over the Science Times until the day's concluding event--lunch at the Curry Club. Afterwards I departed for Baltimore.

#### Thursday, June 30, 2005

This morning Harold Metcalf talked to us about polarizers and imaginary numbers. We discussed the Euler Formula and how it can be used to derive most trig identities. Moon found a derivation of the Euler Formula by using integration (refer to the bottom of the page linked above), which is quite elegant.

After lunch I transcribed my calcutor program into C++, which can be downloaded here (compile at a command prompt by typing "g++ reflection.cpp" and run the executable by typing "./a.out"). The nice thing about this program is that it is many orders of magnitude faster (being on a computer rather than a calculator), which allows one to experiment with considerably more interfaces.

Otherwise, we spent most of the afternoon talking about various topics including the dispersion relation, phase and group velocity, reflection, and the feasibility of making a light saber. At this point, I would like to resume my research regarding optical vortices and singular optics as a potential project.

#### Wednesday, June 29, 2005

This morning I continued figuring out the problem from yesterday and realized that it was getting too complicated to reduce everything to one formula. So, I decided that it would be a fairly simple problem for a computer, using only two for loops.

At noon Maaneli and I left for our weekly REU meeting where we got a full tour of the Nuclear Structure Lab here at Stony Brook. After lunch at Jasmine and a visit to the bookstore, I made a program in my calculator and debugged it. It appears to be working correctly and yields pretty interesting results. It does reduce reflection, especially if a lot of layers are used. It should also be noted that it works for all wavelengths (it isn't wavelength specific like λ/4 anti-reflection coatings). However, as mentioned before, it would have limited applications. I would like to finish this problem up by making my program in C++, allowing me to run it on a computer (which would be a lot faster than my calculator) and be able to show it to viewers like yourself.

#### Tuesday, June 28, 2005

This morning John continued talking about optics--answering questions and explaining new topics--as well as some math tricks. I derived an equation for solving difficult square roots, which goes like this:

Where α is the nearest square to x (if x were 74, then α would be 81). This derivation of this equation utilized calculus and is only good when x is not small (where the curve of f(x)=√(x) is close to being linear).

When the fire alarm went off, we all went to lunch at the SAC and continued talking physics. Upon returning, we played around with a long spring which we used to demonstrate all types of waves. I found that it was possible to illustrate coupled oscillations--the energy in the system slowly oscillated between the different modes (transverse and longitudinal waves).

Otherwise, I spent the day working out the previously mentioned (June 23rd entry) problem of layers with consecutively larger indices of refraction. I setup a problem where n ranged from 1 to 1.5 in increments of 0.1. Normally (without multiple layers) 96% of the energy would be transmitted and 4% would be reflected. After working out the problem in depth, I came up with a transmission of 99.171015% and reflection of 0.826434% with 0.002551% unaccounted for (due to multiple reflections). I am currently in the process of making equations for the general case--which appeared promising at first (a definite pattern appeared)--but is taking longer (and more paper) than I thought.

#### Monday, June 27, 2005

The high school students have arrived! We spent today talking about a whole slew of optics related topics including diffraction, interference, reflection, polarization, stimulated emission, lasers, etc. We also got the third computer to work, which will help greatly this summer.

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### Week 2

#### Friday, June 24, 2005

Like most Fridays, not too much happened today. After having lunch at the Curry Club, Maaneli and I sat in on Harold Metcalf's group discussion. It was interesting to hear about all the different projects and what problems they were facing (and how they planned on dealing with them).

Otherwise I spent most of my time reading more about singular optics and optical vortices. It seems that the resources available online are not geared for people who know nothing about the topic. I feel like I know the "what" about optical vortices, but not the "how" and "why". For now, I will continue reading about it and see where it takes me.

#### Thursday, June 23, 2005

This morning I started by learning more about a couple of different laser & optics topics: laser cooling, Magneto-Optical Traps (MOT's), optical vortices, and photovoltaic cells. Then, at John Noé's suggestion, I setup my Poisson Spot from yesterday in order to take a picture of it. Now, yesterday's journal entry links to my picture.

After lunch, I continued reading about various optics topics in hope of finding a research topic. After awhile I started thinking about gradient-index (GRIN) lenses and their reflection coefficient. My idea was that there would be less reflection if light went from air into a GRIN lens (assume it to span from n=1 to n=2) than if the light hit an n=2 lens directly from the air. I made a rough calculator program for my TI-89 to evaluate the transmission and reflection coefficients of a lens comprised of NUM layers, each with an increasing index of refraction. It looks like this:

``` :refl(A,B,X) :Prgm :ClrIO :abs(B-A)/X→NUM :1→T :For CT,0,NUM-1 :A+CT*X→N1 :(X/(2*N1+X))²→R :T*(1-R)→T :EndFor :Disp "T:" :Disp T :1-T→R :Disp "R:" :Disp R :EndPrgm ```

Where A is the starting index of refraction, B is the ending index of refraction, X is the index of refraction increment between layers, NUM is the number of layers, and R and T are the reflection and transmission coefficients respectively. While this program is quite basic and does not take into account multiple reflections, it was an encouraging start. Normally, the reflection coefficient from n=1 to n=2 is 0.111, but if this is done by passing through ten layers, each with index of refraction 0.1 greater than the one before, then the reflection coefficient is 0.0124--almost ten times less reflection. Continuing on, 100 layers gives a reflection coefficient of 0.001249--almost 100 times less. Anyway, I'm not completely sure whether this is bogus or not, nor whether it's been done before (couldn't seem to find anything from Google), so I'll have to pull out the old physics notes and do the problem out fully.

#### Wednesday, June 22, 2005

Today, many of the REU physics students gathered together for our first seminar of the summer; the talk: A New Approach to Introducing Quantum Mechanics - "The Einstein Way", by Prof. Goldhaber. As a rising junior who has taken Modern Physics and will be taking Intro. to Quantum this fall, I wasn't able to judge the effectiveness of his ideas, but still enjoyed listening to what he had to say.

Otherwise, I spent most of the day reading about physics and optics--primarily from HyperPhysics. This site, which I have found to be a useful reference in the past, helped me understand many optics related subjects. Via the numerous links that tie together related topics, I read about different types of lasers, laser applications, laser fusion, holography, polarization, Fresnel diffraction, doped semiconducters, and LED's. I was able to confirm some of this stuff in the lab--particularly, finding the Brewster Angle and observing a Poisson Spot.

I finished off the day by doing some research about the violet diode laser that was donated to our lab. Manufactured by Power Technology Inc., this PPM Laser Diode System requires 12VDC and appears to have a high power output.

#### Tuesday, June 21, 2005

This morning, John Noé talked to Maaneli and me about the coming high school students and what we need to be doing at this point. We also got to ponder the problem of using a fan, light detector, and oscilloscope to determine the diameter of a laser beam.

Otherwise, I made some finishing touches to my website, including the creation of this page. I also put my list of important Bash commands and Linux programs (mentioned in my June 13-20 journal entry) into an HTML file which you can also access at my links page.

Starting tomorrow, I will focus all my energy on finding a research topic which I will invest my time in here at the LTC.

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### Week 1

#### June 13-20, 2005

During the period of this week, I settled into the Laser Teaching Center. Besides spending time looking at John Noé's optics toys, I learned HTML (formerly, I've used Dreamweaver for making websites). I also refreshed my knowledge of Linux and compiled a list of important commands and programs that I found out about through John Noé and the internet. During this whole process, I became familiar with the ins and outs of Emacs and Linux and even made some of my own customizations. I would recommend inserting the below text into the .bash_profile file in your home directory for some useful aliases/customizations:

``` alias list='ls -lotr --color' alias lista='ls -lotrA --color' alias rm='rm -i' xclock -d -update 1 & ```

Otherwise, Maaneli and I spent some time organizing the lab, specifically going through and testing batteries and digital multimeters. We ended up with eight working (handheld) digital multimeters and one broken one. One important thing that I learned is that when a multimeter is giving readings that are incorrect, but proportional to the tested input, replacing the battery should solve the problem.

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Greg Caravelli
gjc at jhu.edu