Some more Research Related Stuff

I will talk about a few things in this post:  (1) Initial thoughts on my research project, (2) other things that I have been doing at work, and (3) some other reading that I have been doing that is optics related.

So the main idea of my project is as follows: say you have a mirror and you shine light at it. There are two things that happen. First, only a percentage of this light is reflected. Second, the light is delayed. The amount of reflection and delay differ for different frequencies (i.e. red light and blue light are reflected differently). It is easy to measure reflectivity but it is hard to measure delay. There is a (somewhat complicated) relationship between these two quantities. The issue is that to calculate delay from reflectivity, you must know the reflectivity for all different frequencies. My current understanding is that my goal is to approximate the delay using only some (but not all) knowledge of the reflectivity. (Ex. you might get a pretty accurate answer by just using the reflectivity data for visible light and not other frequencies like ultraviolet). 

Overall, I am pleased with this project. It combines theory and experiment in a nice way for me. The approximations that I will need to make require me to both know a lot of math and understand the trends in the actual reflectivity data. The math that I have learned in the past year that is related to approximating integrals and integral transforms may be useful for my projection. Additionally, the approximations that I make will require me to understand the trends of the actual data. I will have to know what data can easily be measured and what areas cannot be neglected even if it would be mathematically convenient to do so. 

Anyways, at my first real day of work. Franck introduced us to a program called IMD that simulates multilayer mirrors. For now, we are just looking at a periodic mirror of Mo and a-Si. We are varying the number of times we repeat layers of those two substances, the ratio of those two substances, the thickness of the period and the roughness (i.e. there is some error involved in making the mirrors so we introduce some error into the sizes of the layers). Then we are looking at the reflectivity as a function of wavelength. By bragg's law, we know that the maximum should be around double the period of the multilayer mirror. 

Another thing that I noticed yesterday is that when you look at these plots, there is a maximum and the center, but then there are local maxima on the higher wavelength side of the global max. After playing around with this, I noticed that when you increase the number of layers, then the number of ripples increases. When you change the incidence angle, the ripples are on different sides of the central maximum.  This isn't too important, but it was fun to play around with a bit. In order to see the ripples, you have to put the reflectivity on a log scale.

I also asked more about automating the process of using the program to simulate the multilayer mirrors. It would be nice to generate a reflectivity graph, then feed that result into a loop, and then adjust the layers with some method and then see what the new reflectivity would be. Apparently one of the people here made a program that simulates the reflectivity in matlab. Depending on the nature of my project, it might be worthwhile for me to either learn matlab or to learn how to make the program in mathematica. 

After we played around with things, our professor came in and talked to us for a bit. I hope that he continues to check up on us and see how we are doing. He seems very knowledgable about the program that we were using. He also explained complex reflectivity to me. The idea is that if you have a light pulse that reflects off a surface, then you get the same frequency with a different amplitude and phase. It turns out that if you represent the incoming wave as a complex exponential, then the math works out nicely and when you divide the outgoing complex exponential by the incoming exponential, you get a complex number whose magnitude is the ratio of the amplitudes and the argument is the phase difference. This is an interesting representation. 

I have been having so many experiences that I haven't had the time to talk about the physics related stuff that I have been doing. For the past few days, I have been taking some time to read a long paper on general attosecond physics. The main thing that it talked about was the specifics behind high harmonic generation and the simulated raman scattering schemes for generating short pulses. I focused more on the high harmonic generated because it seems like my lab is going to focus on that light in that range. 

The other interesting things that I have been reading about involve measuring these attosecond pulses. Since they are so short, you need to generate new methods to measure them. One idea is streaking. So what I read about was that you have a light pulse and you send that through a photocathode. This knocks off electrons. Then you have a rapidly varying electric field and so the electrons excited by the start of the pulse are moved a different amount by the electric field than the electrons excited by the electric field later in the pulse. This converts the image of the pulse into electrons. The intensity of the pulse is measured through the number of electrons. I don't think that this can be done with attosecond pulses because a professor said that this is more useful on the order of picoseconds. I am not sure if there are streaking cameras that can measure attosecond pulses. However, apparently these apparatuses are very expensive. 

The other stuff that I have been reading about is related to the methods of FROG and SPIDER.  (Again we see the crazy acronyms that have become standard in this area of physics).  FROG stands for frequency resolved optical gating. I don't really understand what this is doing, but here are some general ideas. This method splits the beam up into two parts. Then one can use mirrors so that the second pulse is delayed in a controlled fashion. Then the pulses are able to interact in a nonlinear medium. I asked the professor/researcher that has been showing me around about this. 

So some things that he explained to me were as follows:   There is a model of a medium where we consider the atoms like little oscillators. When you subject these oscillators to an external EM field, they oscillate with the same frequency as the field however there is a phase delay. These oscillators emit photons at the same frequency. Since this is happening over many little oscillators, this accumulated phase delay over a distance can just be thought of as the light pulse traveling slower in the medium.  Then he proceeded to talk about in a nonlinear medium that at the start, the potential for an electron is parabolic as we might expect from a first order Taylor expansion but when we get into higher order terms, the potential becomes wider than one might expect. That is to say, if the external EM field has a high amplitude, then there is a nonlinear effect and there is an additional phase delay because the potential widens. So the idea here is that if the amplitude changes as a function of position, then the wave separates itself.   Loosely speaking, you could imagine that if you have a known pulse and an unknown one, then when you put it through this nonlinear medium, you could deduce something about the unknown pulse based on how much it slows down.

The FROG says that given two split pulses where we vary the time delay, then we can find the autocorrelation of the original pulse. However, there is something additional that we can get that is more than an autocorrelation. The things that I do not understand are: what are we physically measuring when we do the frog experiment. I asked John a bit about this and he gave me the explanation above that vaguely, you can imagine that in a nonlinear medium, you get some terms that are the product of the electric fields instead of just the sum. Another thing that I don't understand is what information you can extract from the autocorrelation of an electric field.

There is also something called SPIDER. I need to read more about this, but the idea is that it is another method that is used to measure the pulses.   One of the problems of these methods that some people have problems with is that you are using your own signal to probe the signal. All of these things are fuzzy in my head now but it seems that it isn't that important that I understand them for my project.