Constructing a Confocal Fabry-Perot Interferometer Michael Dapolito and Eric Wu Laser Teaching Center Department of Physics and Astronomy, Stony Brook University Stony Brook, NY 11794 July 9, 2018 Introduction We have built a confocal Farby-Perot interferometer (FPI) to be used in the STI- RAP experiment for the Metcalf Research Group. A confocal FPI is an optical cavity consisting of two highly reflective mirrors, separated at a variable distance that is approximately equal to their shared radius of curvature. A piezoelectric transducer (PZT) ring actuator is used to scan over the free spectral range of the cavity. The free spectral range is the distance between subsequent resonance peaks and is given, in terms of frequency, by: f = c (1) 4L where c is the speed of light and L is the cavity length. These peaks arise when the resonant condition of the cavity is met, leading to completely constructive interference of the transmitted beams. The cavity exploits the many reflections of a single input beam, giving rise to interference. When light is incident on the first mirror, most of the light will be continually reflected while some will be partially transmitted through the second mirror. Successively transmitted beams will interfere either constructively or destructively. Completely constructive interference occurs when the distance traveled by the light is equal to an integer multiple of the wavelength. This condition is given by the equation: L = nλ (2) 2cosθ where L is the cavity length, λ is the wavelength of the light source, and θ is the angle of incidence. 1 Procedure Our confocal FPI consists of a piece of invar in the shape of a cylindrical shell, that was drilled in the machine shop located in the basement of Stony Brooks Physics Building. The 1
invar has a length of 3.85 inches, an outer diameter of one inch, and an inner diameter equal to 3/8 inch. Using epoxy, we attached a concave mirror with a diameter of half an inch and a focal length of 50 millimeters to one side of the invar, with the reflective side facing towards the cavity. Attached to the other end of the invar is the surface of a 2-millimeterthick, low voltage (V max = 200 V) PZT ring, with the second mirror epoxied onto the PZT. The mirrors have an NIR dielectric coating for a wavelength range of 750-1100 nm. They were purchased through a custom order from Thorlabs, Inc and the PZT was ordered from Michromechatronics, Inc. In order to test the Fabry-Perot prior to installment, we coupled 800.31 nm light from a Technoscan Ti:Sapphire laser into the cavity and applied a DC ramp voltage to the electrodes of our PZT, making micron-sized adjustments to the cavity length. For the ramp voltage, we used a driver to supply 82 volts with a frequency of 20 Hz to the PZT. 2 Specifications Figure 1: A schematic of the Fabry-Perot Interferometer with components: 1. Invar: Length = 97.799 mm, OD = 25.4 mm, ID = 9.525 mm 2. Concave Mirrors: Diameter = 12.7 mm, Radius of Curvature = 100 mm, NIR Dielectric Coating for λ = 750-1100 nm 3. PZT: Model No. NAC2124, OD = 15mm, ID = 9 mm, H = 2 mm, V max = 200 V, Free Stroke = 2.8 µm, Blocking Force = 4750 N, Capacitance = 470 nf 4. BNC Connector 2
Figure 2: Completed Fabry-Perot interferometer (side view) Figure 3: Completed Fabry-Perot interferometer (top view) The free spectral range (FSR) was calculated using eq. 1 given in the Introduction. The finesse was calculated using the approximation: F = π (R) 1 R (3) where R is the mirrors reflectivity. Lastly, the full width at half maximum (FWHM), or line width, was calculated from: F W HM = λ2 (1 R) 4πL (4) (R) This is derived from the definition of the finesse, which is the ratio of the FSR to the FWHM. Using the above equations, we obtained: Free Spectral Range: FSR = 750 MHz Finesse: F = 312.58 Line Width: FWHM = 2.4 MHz 3
3 Results Figure 4: Set up used to test the FPI Figure 5: FPI output Figure 6: FPI output - two peaks on the same ramp Measuring the line width from both Fig. 5 and Fig. 6 and then taking their average value, we obtain 26 MHz. This is approximately an order of magnitude away from the expected value of 2.4 MHz. This is most likely due to the loss of resolution from using a picture of 4
the oscilloscope screen, as opposed to directly using the osilloscope display, to calculate the line width. 4 Conclusion For our project, we constructed a confocal scanning Fabry-Perot interferometer. To build the interferometer, we used two concave mirrors that have a radius of curvature equal to 100 mm and are coated for 750-1100 nm, a low-voltage piezoelectric actuator ring with V max = 200 V, and a piece of invar. The invar is used due to its low coefficient of thermal expansion. After drilling through the center of the invar, we used epoxy to attach the mirrors and PZT to the ends of the invar. We then tested the FPI using a light source of λ = 800.31 nm and a driving voltage of 82 V with a frequency of 20 Hz. The FPI scanned as expected, however, we do not know what is causing the asymmetry in consecutive resonance peaks as shown in Fig. 5 and Fig. 6. 5