Methods for Measuring the Wavelength of Light  

Yue (Sandy) Xu, Bayport - Blue Point High School, NY; Harold Metcalf
and John Noe, Laser Teaching Center, Department of Physics and
Astronomy, Stony Brook University.

This summer I have studied and experimented with a large number of
optics-related topics which related to past or current projects in the
Laser Teaching Center, or which just seemed interesting or useful.
Several of my mini-experiments had a common theme: investigating ways
to modify and precisely measure the wavelength of light. An example
of modifying the wavelength of light is doubling the frequency of
laser light through its interaction with a non-linear material.  I've
read a lot about this, but haven't yet done any experiments in this
area. Measuring the wavelength of light ("spectroscopy") is important
to operating lasers, and has many other applications as well.  Here I
investigated experimentally three methods, which are based on
diffraction, optical transforms, and interference, respectively.

First, I learned about the theory and applications of "diffraction
gratings," which are transparent or reflective optical surfaces with
many evenly-spaced lines.  Using these gratings, we can determine the
wavelength of light relatively accurately, if correct measurements are
made. First I used a red HeNe laser with a well-known wavelength to
measure the period, or spacing, of the lines in my grating. I then
used the calibrated grating to measure the wavelength of green light
from a laser pointer. The result was 537 nm, which is only about 1%
different from the expected value 532 nm. Later I repeated the
measurements with the HeNe laser several more times, with the grating
tilted at various angles to the laser beam instead of perpendicular to
it. This way, I obtained the spacing distance between the grooves to
be 1338.2 nm, with an estimated percentage error of only 0.37%.

I next used a different type of diffraction grating, a Ronchi ruling,
to observe periodic images produced by the Talbot effect, continuing
experiments started by an undergraduate summer student, Allison
Schmitz. In the setup, a beam of diverging light, obtained by passing
light from a HeNe laser through a thin optical fiber, was shined at
the Ronchi grating. A CCD camera, connected to a computer, was used to
observe the images formed by the grating. The Talbot Effect basically
states that the grating has many focal lengths f = nd^2/l, where n is
any integer, d is the spacing, and l is the wavelength of the
light. It's possible to get many very sharp images as long as the
object distance and the image distance satisfy the lens equation.  A
design for a "Talbot spectrometer" based on transforming these images
has been reported, but it seems difficult to get much precision by
this method.

Finally, I have recently used interference of light waves to make very
precise measurements in the wavelengths of light emitted by various
lasers, using a device called a Fabry-Perot spectrometer. The
spectrometer has two highly-reflective curved mirrors about 5 cm
apart, which form an "optical cavity." The exact distance can be
varied periodically (100 times a second) by applying a changing
high-voltage signal to a device called a PZT, which supports one of
the mirrors. Using the Fabry-Perot device it was possible to see
distinctly the separate modes of a HeNe laser, which are separated in
wavelength by only about one part in a million, and to observe shifts
in the modes as the laser warmed up. In the future I hope to learn
how to better match the laser light into the Fabry-Perot cavity, and 
to use the spectrometer to study light from a tunable diode laser. 
 
This research was supported by the Simons Foundation and NSF Grant
PHY 00-98044.