The curved surface mirrors "trap" light in a stable, sometimes referred to as bow-tie, mode. There will be a build up of the light intensity inside the cavity whenever the round trip path length of the laser beam is equal to an integral number of wave lengths. These are called longitudinal modes. The frequency separation between the longitudinal modes is called the "Free Spectral Range" of the cavity and is given by the equation: Δƒ = c/4L.
Besides longitudinal modes, there are also transverse modes in an optical cavity. Transverse modes may be characterized by differences in the intensity of the light within a cavity in directions transverse to the direction of propagation. Usually, each transverse mode has a different wavelength. However, in a configuration called a confocal cavity, where each mirror has the same radius of curvature and the cavity length is equal to the radius of curvature, all transverse modes become degenerate and resonant at the same frequency.
A Fabry-Perot Interferometer is a "resonant cavity" for light which has many uses in the world of optics. Initially designed, in collaboration with Caltech, as an accessory for Diode Laser Spectroscopy, the TeachSpin Fabry-Perot Cavity can be used with any tunable laser operating in a wavelength range of 740 - 820 nm. The variable iris, shown in the photograph above, and used to align the beam, is part of the apparatus.
The Fabry-Perot Cavity itself consists of a 0.5 inch inner diameter aluminum tube with high reflectivity curved cavity mirrors at each end. The mirrors are mounted in adjustable lens tubes which allow students to control the cavity length. The mirrors that TeachSpin has used in this apparatus have a (power) reflection coefficient of R > 0.995 or 99.5%. We have included a brass spanner wrench which can be used to remove the retaining rings that hold the mirrors in place. This allows users the option of replacing or changing the mirrors quite easily.
For the TeachSpin apparatus, the optimum cavity length is roughly 20 cm giving a free spectral range of about 380 MHz. With careful adjustments, students can achieve a finesse over 100. This means that the instrument can be sensitive to frequency changes on the order of 1 MHz, out of an optical frequency of 400 million MHz.
In our application, the Fabry-Perot cavity is used primarily to calibrate the laser sweep and to observe sidebands on the current modulated laser output. Figure 1 shows the basic cavity set up. The curved surface mirrors are coated for high reflectivity while the outer flat surfaces are anti-reflection coated.
Students can adjust the cavity length and observe the collapse of the transverse modes.
Figure 2 shows the Doppler broadened absorption spectrum of natural rubidium vapor simultaneous with the Fabry-Perot transmitted light intensity. The overall decrease in the F-P output is due to the current modulation of the diode laser. This modulation affects both the laser output frequency and power. The length of our etalon cannot be modulated, therefore, the variation in the optical transmission is due to the frequency sweep of the laser.
To calibrate the Free Spectral Range, the student modulates the diode current using an RF signal generator. These data were taken with the low cost ELNCO SG-9000 signal generator sold with our Optical Pumping apparatus. This current modulation creates optical side bands that can easily be observed on the transmitted output of the F-P etalon.
Figure 3 shows the F-P output for the swept diode laser, where the oscilloscope sweep has been expanded to clearly observe the Free Spectral Range. Figure 4 shows the same sweep with a 60 MHz RF current modulation. Figure 5 shows data from the same configuration with 120 MHz modulation. Since the RF frequency can be measured with an electronic counter, the Free Spectral Range can be accurately and absolutely calibrated. Students should compare this calibration with the Free Spectral Range they can calculate from a crude measurement of the separation of the etalon mirrors.
This etalon has other applications as well. These include observing multimode behavior in the diode laser and external cavity locking of the diode laser. The reflected power from the cavity can be used to lock the diode laser to the cavity. Caltech's advanced lab has a good discussion of this.