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Power-Recycled Michelson Interferometer Resonating in Corner Station!

Power-Recycled Michelson Interferometer Resonating in Corner Station!

- Contributed by Fred Raab

Interferometer Configuration Last July we observed the first resonances of the power recycled Michelson interferometer in the corner station at the LIGO Hanford Observatory. LIGO uses an interferometer configuration (diagrammed at left), called a power-recycled Fabry-Perot-Michelson interferometer, to compare space along two perpendicular directions for evidence of gravitational waves. These gravitational waves will stretch space along one arm while space shrinks along the perpendicular arm. Two suspended mirrors along each arm form a structure, called an optical cavity, that traps the light in the arm for some time. Light enters the cavity through the input mirror (near the beam splitter), travels down the length of the arm to the end mirror, where it is reflected back to the input mirror. The input mirror has a large reflectivity and a small transmission. So light may enter the cavity, but once inside it is trapped for many round trips through the cavity before it can leak out again. This configuration is known as a Fabry-Perot cavity (explaining part of the interferometer's name). In LIGO-I, the trapped light retraces its path about fifty times, reproducing its oscillating pattern on each round trip. Here at Hanford, we began resonating light in each of our 2-km Fabry-Perot cavities last December and have been using them to characterize our optics. But until this summer we did not have all of the electronics and signal extraction optics set up, so we could resonate only one optical cavity in one arm at a time.

Power-Recycled Michelson Schematic Now all the components are in place to light up the entire interferometer. Our first move was to get running the power-recycled Michelson part of the interferometer, formed by the input mirrors, as well as the beam splitter and the recycling mirror. The diagram at right shows this part of the system, which is basically the full interferometer minus the end mirrors. To understand how this works, pretend the recycling mirror is absent. If there was no recycling mirror, light from the laser would be split by the beam splitter, forming two beams that reflect off the input mirrors and then return to the beam splitter. If the distances between these mirrors and the beam splitter are exactly the same, the light returning to the beam splitter will recombine into a beam that returns toward the laser, leaving the photodetector in the dark. If we move the mirror on the right farther away from the beam splitter, some light will spill onto the photodetector and less light will go back toward the laser. (The total of the energy going toward the laser and the energy going toward the photodetector will stay the same due to energy conservation.) If we continue moving the mirror on the right away from the beam splitter, the light hitting the photodetector will increase until the distances between the beam splitter and the two mirrors is different by a quarter of the light's wavelength. For our infrared light sources, the wavelength is 1/1000th of a mm, so a difference of 1/4000th of a mm will cause all of the light returning to the beam splitter to fall on the photodetector. This process of switching light between the two directions (toward the laser or toward the photodetector) depending on the mirror distances is called interference. If a laser is used for the light source, we call the device a laser interferometer.

We operate our interferometer with the photodetector in the dark, by using feedback to keep the mirrors in the correct places. The forces we feed back to the mirrors to maintain the photodetector in the dark can be recorded as a measure of what forces try to change the mirror separations. Imagine if someone blew air onto the mirror on the right. The mirror would start to move and light would start to fall on the photodetector. But then feedback would push the mirror back, erasing the light on the photodetector. (We push and pull on the mirrors by gluing magnets to them and running currents through coils near the mirrors. The same current can be run through a speaker, allowing us to listen to the forces on the mirror.)

To make this device as sensitive as possible, we would like to get as much light as possible returning to the beam splitter. For example, if we double the light returning to the beam splitter, we get the same amount of light on the photodetector with half as much displacement of the mirror on the right. This is where the recycling mirror comes in handy. Since we balance the interferometer with darkness on the photodetector, all the light returns toward the laser. Now lasers work well emitting light, but they do not handle receiving light very well. So to avoid disturbing the laser, we need to keep the returned light from reaching it. We do this by inserting a partially reflecting mirror between the laser and the beam splitter. This is the recycling mirror. When placed exactly the correct distance from the beam splitter, it traps the reflected light in the Michelson interferometer. This causes the laser light in the interferometer to build up to a high level. For the full LIGO-I system, recycling will cause the light to build up by about a factor of thirty.

When this occurs, we say that the power-recycled Michelson interferometer is resonating. That was our accomplishment for July. In August, we hope to get one of the 2-km-long arms resonating in addition to the power-recycled Michelson. Tune in next issue to see how things worked out.