5.03.2007

By Way of Explanation

More work-related posts for you guys.

Oh-by the way, when I give "left/right" directions, I'm assuming your right. As you may recall from the bathrooms of your youths (or Enter the Dragon), when you put mirrors up to each other, you see some very strange things. If you tilt a few mirrors and form a little triangle, you see copies of things receding off into infinity (and MADNESS!!). That is an optical "resonator."

So, an optical resonator is a place where light bounces back and forth. It turns out that when you start to make these things small (like the size of light waves), only the light that fits into the resonator can rattle around in there.

Here's a picture to illustrate.



On the top left, we have a three-sided resonator, like you might form with your vantiy mirrors. We can imagine light following along the red path, coming back onto itself again and again. If we were to add more sides, and follow the arrow down, we'd see that each time the light turns, it makes a smaller turn in the seven-sided resonator than in the three-sided one. If we go farther, up the diagonal arrow, we find a twenty-sided resonator, and the light's turns are smaller still... taking the limit of that process to infinity and imagining a hollow cylinder with a mirrored inside surface, we form what's called a "Whispering Gallery Mode Resonator," (or WGM),so named for the Whispering Gallery at St. Paul's cathedral in London.

We see that the arrow from the twenty-sided resonator to the WGM resonator is wiggly, and that the WGM is full of "lobes." That sort of represents for you that we're making certain that the light has the right wavelength to "fit" inside!

Those are the kind of resonators I deal with at work. Here's a few Scanning Electron Microscope micrographs I took of one such resonator:



Along the bottom is an overview, looking down on a Silicon microdisk WGM resonator. That one is 100 micrometers in diameter-about the diameter of a human hair. Above that, you see a couple of detail pictures. The left one shows a bit closer, and the right, closer still. As you see, these disks are very thin. Around 200 nanometers.

Dealing with these is a bit of a pain. In order to get light into them, we bring a fiber optical cable quite close... so close, that the photons jump from the cable to the resonator. Here's a schematic that emphasizes a that.



In the top panel, we have a fiber optic cable running from left to right, carrying a rainbow of light. The circular thing in the middle is a top-view of a WGM resonator. As you can see, some colors of light jump off the fiber optic cable and swirl around in the WGM. I've exaggerated the degree to which the different colors are displaced, just for clarity. As you see, each of the colors is a wave, and each wave closes on itself. That's called the resonant condition-and is what I mean when I say that the light has to "fit:" at any given point, after a round trip, the electromagnetic wave has to look identical to how it looked beforehand!

Another thing we see is that after the WGM resonator, the fiber optic cable doesn't have any more "red," "green," or "blue" light. It's all stuck in the resonator. We can see that in the bottom panel, where the curve shows the transmission past the resonator as a function of wavelength. Right at "red," "green," and "blue," all of the light gets stuck in the resonator. The shapes there are called "Lorentzian curves." You see that each dip has a little width- well, that has to do with how much light gets absorbed in the resonator, or radiated out into the world, etc. The less that happens, the narrower each dip will be.

So, what does all that have to do with the crazy picture below?

Well, the shapes of the Whispering Gallery Modes are a little more complicated. It turns out that each of those is an electromagnetic wave. And there are a couple of different ways that the electric field part can be oriented. Each of those orientations gives rise to different specific properties. Moreover, a given orientation can also form more complicated mode patterns- each of which also gives rise to different properties. The picture below was made by recording the transmission versus wavelength (around 1500nm-invisible light) and then moving the fiber optic cable farther from the resonator an then recording the transmission versus wavelength and then movi.... Sorry. Pointing up is one electric field orientation, and pointing down is another.

I'm still not sure WTF was going on.

1 comment:

Anonymous said...

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Cheers
Christian, iwspo.net