Sigma Xi Poster Presentation :: Apr. 3rd, 2008
So being a member of Sigma Xi every year I get to present some work that I have been doing to members of Marquette’s Sigma Xi. A good mixture of students and teachers are there.
This is my master’s thesis up to this date.
Sidabras, J.W., Richie, J.E., Hyde, J.S., “A Numerical and Analytical Approach to Coupling to Waveguide Evanescent Modes”, Sigma Xi Poster Presentation, April 3, 2008.
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April 6th, 2008 at 1:30 am
nice work! Those rectangular results really look good. Did the 2.5 factor multiplier on the width of the slot come by trial and error, or was that derived from something?
April 6th, 2008 at 9:51 am
Trial and error. The problem is the equilvelence principle says that all of your field is in the area of your source. And that is it. For a wide slot, you can imagine the error in this assumption is only a small percentage. But, for a very small slot the error is on the order of the slot width. Hence why I had to use the 2.5. But even with the 2.5 I make the assumption that the field is a step function. Which never happends in reality. So by using a Gaussian function with about the same width as the slot (variance) you estimate what is really happening, and I get 0.98% error (the purple line in Fig. 5). By toying around with the variance I’ve gotten it down to 0.54%, but that is just rediculous.
I basically assume Ansoft is truth.
April 6th, 2008 at 11:22 am
Have you tried a varying the width? That might allow you to extract a relationship between this multiplier and the slot width - either extracting an expression or by curve fitting.
April 6th, 2008 at 8:57 pm
Basically the top graph is what I have. So you can see by representing it as a uniform step function there is 50% error or so. Now as you make the slot larger the gaussian roll off still exists it just doesn’t account for as much error.
I talked to my advisor about “is there a better way than equivelence principle. And as far as we know, there isn’t.
Blue is ideal (step), purple is “real” gaussian.
April 6th, 2008 at 10:21 pm
I see what you’re saying — as the guassian gets wider, it fits more closely to a step. There might even be a simple geometric way of approximating the multiplier term.
For example, in the top figure, you can clearly see how the error on the sides of the pulse and the guassian are gong to lead to error. So if you can work out some way to relate the two areas, you can then be able to say, for a given width, what the multiplier should be.
By the way, you use a step — is there a way to do this using other waveforms? Just because it’s equivalence doesn’t mean it has to be a step function. Although a step function will simplify the analysis.
April 7th, 2008 at 8:24 am
Oh of course. If you notice on Fig. 5, the Orange dashed plot is using the 2.5 Unit Step function and gives 1.67% error. Now, the light purple is using a Gaussian function, which closely represents the function that is actually occuring according to ansoft. The error there is 0.98%. (And if I tweak it, i can get it to 0.58%).
There may be a geometric way to approximate it, the problem is I’m not sure how to properly do that. Especially when there becomes multiple slots. I haven’t done this yet but that 2.5 multiplier + the mutual coupling between slots may not be correct. The multiplier may be something different. I’m hoping that it isn’t, because the steps I want to take are:
1) solve line integral for multiple slots
2) convolve with gaussian to perfect integration
3) adjust relative intensities with mutual coupling matrix
If step 2 isn’t right, then I will have to tweak it for n number of slots, which just makes the problem more difficult.