Tuesday, June 16, 2009

Plan for the Week

I spent the day today (Monday) looking over everything from the past few days and getting a plan for the week. I also spent some time taking notes on what Antoine showed me in the lab last Friday.

With one of their setups in the lab, there is a Si disc which is placed horizontally in a sample holder so that there is air on both the top and the bottom of the disc (i.e. the disc is not placed simply on another solid or liquid). A THz beam is incident on the surface and does two things -- reflects off the first interface (air/Si) AND transmits through the disc and then reflects back off the second interface (Si/air) and travels back through the initial interface (this is just reflection upon transmission). These two waves will differ in both phase and time.

The data we get out is of the initial pulse (off the air/Si interface) and then of the secondary pulse (off the Si/air interface) measured on a time scale. We can easily tell the thickness of the disc by knowing when the two pulses occur in time and what the speed of the wave is (or this is at least a rough estimate of thickness). Also note that the secondary pulse is inverted upon reflection.

After this initial collection, we are able to change the second interface to something like water. This will cause the reflected wave to change in amplitude relative to that same wave off the initial Si/air boundary. By saving the initial collection (showing the two pulses) and then collecting data again but with the second boundary being Si/water, we will see the two signals to agree with each other (aside from a little noise) for everything but the amplitude of the reflected wave off of this second boundary.

Once we have this data, we may use the Fresnel reflection and transmission expressions to determine index of refraction and dielectric properties of the (in this case) water (I think there are other properties which may be measured, though I am not aware of them currently). Also note that I think this operates around the Brewster angle for Si.

Now that I have spent some time looking over material from the previous week (and actually had a little time in the lab) I have a plan for this week.

- re-read article by the Japanese group to answer questions posed by John in last few posts
- read through the books on optics and diffraction to try and better understand why the current setup at LOB may not be the best
- continue a search for articles and other sources which may have alternative methods of profiling a beam
- learn more about beam optics and what may cause beams to be something other than Gaussian (i.e. what gives us a flat top beam, etc).

5 comments:

  1. Note that the experiment you describe is much the same as the one Galen described in that one class report I sent you. i.e., the one where we were looking at the thickness of the ceramic layer on the jet-engine turbine blade. However, we were not interested in the material after the last interface, because that was a metal. We mainly wanted to look for the difference in the timing between the front face and back interface reflections.

    A couple things to appreciate about this experiment:
    1) you can see why the sign of the second reflection is flipped by looking at the expression for reflection of electric field, r=(n_t-n_i)/(n_t+n_i). When you go into the Si, its index is greater than that of air, so r is positive. When you go from Si back into air, then n_i > n_t and r becomes negative.
    2) In order to get thickness information, you need to know the speed of the THz pulse, as you mentioned. This means that you need to know the index of the medium. So, if you know thickness, you can compute index, and if you know index, then you can compute thickness.
    3) If the materials being measured have a frequency dependence to their index in the THz regime (which will also make them lossy), then the second pulse, which has traveled through the medium, will not look simply like a smaller version of the pulse reflecting off the incident face of the medium. It will take on a different shape depending on which frequencies in the spectrum of the pulse are attenuated and delayed, and thus a more complex analysis must be performed to obtain the frequency dependent index. This is in contrast to just measuring the delay in two reflections in order to get the thickness information, for instance, on the sample. I imagine that LOB has the capability to perform such analysis.

    I believe the water at the second interface for your example experiment would have a frequency dependence for its index within the spectrum of their THz pulses. This could cause this reflected pulse to look somewhat different than the one when the 2nd interface is air rather than water.

    - John

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  3. I did in fact notice some of the similarities between this experiment and Galen's experiment with the blades -- though not nearly as much as you pointed out. I would like to go read through his report again, with this experiment in mind. A few questions/comments regarding your last comments (in accordance to your numbers):

    1. -

    2. You mention being able to get thickness from index of refraction and vice versa, given you know one. For example, what if we do not know either the index of the material or the thickness? I imagine it is pretty easy to have an approximate value for the index of refraction and from this tell the thickness, but what if the sample is something of an unknown index?

    3. This makes sense... I never thought of this effect. I actually think that our signal did not look (as I earlier put it) "simply decreased in amplitude" relative to the initial scan (before adding water). I would like to look into this more.

    Alex

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  4. Let me provide an answer for #2 above. The quick response is that you can't simply solve a one-step multiplication problem to get both thickness and index. This is too complicated to describe easily in a comment, but to explain briefly, you should be able to combine the known incident THz pulse with the reflection coefficients for the front and back face interfaces (assuming you know what materials are at the front and back of your unknown material) to obtain an index value for the unknown that can be used to compute amplitudes that match the experimentally measured THz amplitude values from the first two reflections off the material. This could be done by iteration, i.e., by initially choosing a value for index, then computing the amplitudes of the 1st and 2nd reflections, checking these vs. the experimentally measured reflections, then iterating the index until both computed amplitudes match the experimental ones. Following me? It would be easier if this could be explained in person.

    With that value for index in hand, one can then multiply the velocity of the THz pulse in the medium by that index to get a "round-trip" thickness of the material. This all relies on knowing the surrounding materials and having a material that is lossless and dispersion free. If it's not, the complexity ratchets up another degree. If there's scattering, because the unknown is, say, "chunky," then it may become nearly impossible to determone both thickness and index simultaneously.

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  5. John,

    I think I follow you pretty well here... so I assume you choose the value for the index to be what you would expect for such a material (i.e. choosing something around 3.4 for q material composed primarily of Si)? Then from there just iterate like you were saying until the computed values of amplitude converge to the experimental values?

    I think I understand this idea pretty well (I also recall reading about it a little for my senior project proposal). It would help still to talk about it via Skype, though.

    Alex

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