Scanning, spherical-mirror Fabry-Perot interferometer: An upper-division optics laboratory experiment

American Journal of Physics

Volumn 65, Issue 3, 1997, Pages 202-213

  Nachman, Paul ^a,b   Bernstein, Aaron C ^a,c  

^a NEW MEXICO STATE UNIVERSITY   (United States)

^b NORTHROP GRUMMAN CORPORATION   (United States)

^c UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031507443     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18572     Document Type: Article

References (67)

1. K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: A laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
2. S. R. Mallinson, "Wavelength-selectable filters for single-mode fiber WDM systems using Fabry-Perot interferometers," Appl. Opt. 26, 430-436 (1987).
3. M. Bertolotti, Lasers and Masers: An Historical Approach (Adam Hilger, Bristol, 1983), p. 104.
4. A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
5. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), 6th ed., pp. 329-341.
6. R. L. Fork, D. R. Herriott, and H. Kogelnik, "A scanning spherical mirror interferometer for spectral analysis of laser radiation." Appl. Opt. 3, 1471-1485 (1964).
7. Examples: A. G. Podoleanu and I. M. Popescu, "Some simple experimental studies using a passive cavity coupled to a He-Ne laser cavity for practice in a quantum electronics laboratory," Am. J. Phys. 57, 646-654 (1989); J. C. Amato, R. E. Williams, and H. Helm, "An inexpensive, easy to build Fabry-Perot interferometer and its use in the introductory laboratory," Am. J. Phys. 59, 992-994 (1991); J. J. Monzon and L. L. Sanchez-Soto, "On the concept of absorption for a Fabry-Perot interferometer," Am. J. Phys. 64, 156-163 (1996).
8. Examples: A. G. Podoleanu and I. M. Popescu, "Some simple experimental studies using a passive cavity coupled to a He-Ne laser cavity for practice in a quantum electronics laboratory," Am. J. Phys. 57, 646-654 (1989); J. C. Amato, R. E. Williams, and H. Helm, "An inexpensive, easy to build Fabry-Perot interferometer and its use in the introductory laboratory," Am. J. Phys. 59, 992-994 (1991); J. J. Monzon and L. L. Sanchez-Soto, "On the concept of absorption for a Fabry-Perot interferometer," Am. J. Phys. 64, 156-163 (1996).
9. Examples: A. G. Podoleanu and I. M. Popescu, "Some simple experimental studies using a passive cavity coupled to a He-Ne laser cavity for practice in a quantum electronics laboratory," Am. J. Phys. 57, 646-654 (1989); J. C. Amato, R. E. Williams, and H. Helm, "An inexpensive, easy to build Fabry-Perot interferometer and its use in the introductory laboratory," Am. J. Phys. 59, 992-994 (1991); J. J. Monzon and L. L. Sanchez-Soto, "On the concept of absorption for a Fabry-Perot interferometer," Am. J. Phys. 64, 156-163 (1996).
10. In this paper, we are exclusively concerned with FPIs used in scanning operation, wherein the optical pathlength L between an interferometer's mirrors is varied systematically with time. Such a FPI serves as a variablefrequency optical filter and transmits light whenever the instrument's filter function is scanned across any frequency present in the incident beam. (This basic picture is complicated by mode-matching considerations, as discussed in the text.) In another type of operation, a flat-flat FPI with fixed L will transmit concentric rings of light when illuminated with a diverging or converging beam. The fine structure in these rings can be used for high-resolution studies of pulsed light sources. See, for example, D. C. MacPhcrson, R. C. Swanson, and J. L. Carlsten, "Quantum fluctuations in the stimulated-Raman-scattering linewidth," Phys. Rev. Lett. 61, 66-69 (1988).
11. K. D. Möller, Optics (University Science Books, Mill Valley, 1988), pp. 101-105; R. D. Guenther, Modern Optics (Wiley, New York, 1990), pp. 106-115; F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, 1993), 2nd ed. pp. 236-238. These authors all write the transmission. script T sign in a form that appears different from - but is equivalent to - our Eq. (1). Note that the Pedrottis introduce a "co- efficient of finesse" in addition to the usual "finesse."
12. K. D. Möller, Optics (University Science Books, Mill Valley, 1988), pp. 101-105; R. D. Guenther, Modern Optics (Wiley, New York, 1990), pp. 106-115; F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, 1993), 2nd ed. pp. 236-238. These authors all write the transmission. script T sign in a form that appears different from - but is equivalent to - our Eq. (1). Note that the Pedrottis introduce a "co- efficient of finesse" in addition to the usual "finesse."
13. K. D. Möller, Optics (University Science Books, Mill Valley, 1988), pp. 101-105; R. D. Guenther, Modern Optics (Wiley, New York, 1990), pp. 106-115; F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, 1993), 2nd ed. pp. 236-238. These authors all write the transmission. script T sign in a form that appears different from -but is equivalent to - our Eq. (1). Note that the Pedrottis introduce a "co-efficient of finesse" in addition to the usual "finesse."
14. 2
15. Another approach was taken by J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, "The PEPSIOS purely interferometric high-resolution scanning spectrometer. I. The pilot model," Appl. Opt. 2, 875-885 (1963).
16. W. S. Gornall, "The world of Fabry-Perots," Lasers & Applications, July, 1983, pp. 47-52.
17. Values of script F sign approaching two million have been reported by G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, "Measurement of ultralow losses in an optical interferometer," Opt. Lett. 17, 363-365 (1992). Also see Ref. 1.
18. See, for example, A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986), pp. 626-649.
19. Mode families consisting of Laguerre - Gaussian functions fulfill the same role (i.e., complete sets of solutions to the paraxial wave equation) as the Hermite-Gaussian functions and are sometimes more convenient. A tutorial experiment that displays conversion between low-order members of the two family types is described by M. Padjett, J. Arlt, N. Simpson, and L. Allen, "An experiment to observe the intensity and phase structure of Laguerre-Gaussian modes," Am. J. Phys. 64, 77-82 (1996).
20. See Ref. 14, pp. 682-686. An interferometric demonstration of the Gouy effect is discussed by P. Nachman, "Mach-Zehnder interferometer as an instructional tool," Am. J. Phys. 63, 39-43 (1995).
21. 00 mode is not quite correct.
22. m.
23. 0 will, for a given FPI cavity, increase with the wavelength. Over the wavelength ranges of interest in this experiment, this is of no concern. Further, in most cases, the spot size of a tunable laser's beam would have the same wavelength dependence, thus compensating for this effect of wavelength variation on the cavity's modes.
24. In a few instances (such as placing the interferometer's mirrors in their mounts and making high-voltage electrical connections) where student missteps could be catastrophic for them or for the equipment, we deviate from our ideal and do some of the preparatory steps ourselves.
25. Melles Griot (1770 Kettering St., Irvine, CA 92714, 800-835-2626) polarized laser head model 05-LHP-121 and power supply model 05-LPL-340-065. Suitable "new surplus" lasers and power supplies are often available, at substantially lower cost, from Meredith Instruments (P.O. Box 1724, Glendale, AZ 85301, 800-722-0392) and MWK Industries (1269 W. Pomona, Corona, CA 91720, 800-356-7714).
26. C. E. Wieman and L. T. Hollberg, "Using diode lasers for atomic physics," Rev. Sci. Instrum. 62, 1-20 (1991).
27. However, diode lasers are now available with attached cylindrical optics that might ease mode-matching problems. Consult Blue Sky Research (4030 Moorpark Ave., Suite 123, San Jose, CA 95117, 408-983-0471). Further, Teledyne-Brown Engineering (Electro-Optical Products Group, P.O. Box 070007, Huntsville, AL 35807, 800-933-2091) now offers a slip-on "collimator/corrector" for common laser diodes that is claimed to sculpt their outputs into more-tractable beams.
28. Aerotech (101 Zeta Drive, Pittsburgh, PA 15238, 412-963-7470) gimbal laser mount GLM-1 attached to Newport Research Corp. (1791 Deere Ave., Irvine, CA 92714, 800-222-6440) platform model 300-P and rod model 45.
29. ESCO Products (171 Oak Ridge Drive, Oak Ridge, NJ 07438, 800-922-3726) mirror model D410000.
30. For example, Thorlabs (P.O. Box 366, Newton, NJ 07860, 201-579-7227) kinematic mirror mount KM1HC and 1/2-in.-diam posts with associated hardware.
31. For example, Optics for Research (Box 82, Caldwell, NJ 07006, 201-228-4480) manufactures a wavelength-tunable Faraday isolator, model IO-5-VIR.
32. Inexpensive, surplus λ/4 plates for 633 nm, ∼1 cm diameter and antireflection coated, are sometimes available from vendors such as Meredith Instruments and MWK Industries, both in Ref. 22. Birefringent plastic waveplate material from Strainoptic Technology (108 W. Montgomery Ave., North Wales, PA 19454, 215-661-0100), part number PQW-4×4-HN, is also acceptable. We mount our λ/4 plate on a Thorlabs, in Ref. 27, model RSP1 rotary stage, with its rotation axis horizontal.
33. CVI Laser Inc. (200 Dorado Place S. E., Albuquerque, NM 87123, 505-296-9541) beamsplitter model PBS-633-100 mounted on Thorlabs, in Ref. 27, platform KM-B with clamp PMH.
34. Guenther, in Ref. 9, pp. 541-542.
35. Rolyn Optics Co. (706 Arrow Grand Circle, Covina, CA 91722, 818-915-5707) lens model 10.0450 held in Thorlabs, in Ref. 27, lens mount model LH1 and other standard 1/2-in.-diam mounting hardware.
36. Because of our coating specifications, such mirrors are custom items. We purchased ours from Virgo Optics (6736 Commerce Ave., Port Richey, FL 34668, 813-845-3402). CVI, in Ref. 30, is another supplier. A possible source of "free" mirrors is a defunct HeNe laser: We have heard that, in some instances, the mirrors can be gently removed, intact, with pliers. However, the output-coupler mirrors from most HeNes have transmissions of only a few tenths of a percent, so an interferometer built from two such mirrors will have a finesse that is inconveniently large for a student experiment. (The "high-reflector" mirrors from the other ends of HeNe tubes typically have even lower transmissions and are correspondingly less suitable for our purpose.) A reasonable compromise, in order to obtain a more-tractable finesse, might be to scavenge one mirror this way and purchase a single custom mirror of lower reflectivity. The mismatched reflectivities of the two mirrors will force the maximum transmission script F sign for the interferometer to be less than 1. Further, output couplers often are fabricated on substrates that have both surfaces curved. This will complicate the mode-matching calculations if such a mirror is used as the FPI's input port (see the Appendix).
37. Burleigh Instruments (Burleigh Park, Fishers, NY 14453, 716-924-9355) piezoelectric aligner translator PZ-81, mounting adapter PZ-80-1, and gimbal mount SG-201.
38. Newport, in Ref. 25, model 150.
39. New Focus (1275 Reamwood Ave., Sunnyvale, CA 94089, 408-738-8988) model 9809.
40. Thorlabs, in Ref. 27, model MB 175.
41. We used a 1 in. O.D., 7/8 in. I.D., 3/4 in. long piezo tube manufactured by Channel Industries, Inc. (839 Ward Drive, Santa Barbara, CA 93111, 805-967-0171). Another source is EDO Corp., 2645 South 300 West, Salt Lake City, UT 84115, 801-486-2115.
42. Burleigh, in Ref. 34, high-voltage op-amp PZ-70.
43. High-voltage monolithic op-amps that should be suitable for the purpose are available from Apex Microtechnology Corp. (5980 N. Shannon Road, Tucson, AZ 85741, 800-546-2739).
44. Power-One, Inc. (740 Calle Plano, Camarillo, CA 93010, 800-678-9445) model HB200-0.12-A. New surplus units are sometimes available from Herbach and Rademan (P.O. Box 122, Bristol, PA 19007, 800-848-8001).
45. K. B. MacAdam, A. Steinbach, and C. Wieman, "A narrow-bandwidth tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb," Am. J. Phys. 60, 1098-1111 (1992).
46. For example, Newport, in Ref. 25, linear translation stage model 421-1.
47. UDT Sensors, Inc. (12525 Chadron Ave., Hawthorne, CA 90250, 310-978-0516) planar diffused silicon photodiode model PIN-10D. This detector is sealed in a housing that attaches directly to BNC connectors.
48. Intor Inc. (1445 Frontage Rd., Socorro, NM 87801, 505-835-2200) 1-in.-diam, 633-nm interference filter with 10 nm bandpass and 45% peak transmission.
49. At this point, the capacitance of the coaxial lines used for making connections (between photodiode and bias box and between bias box and 'scope) starts to be a significant fraction of the detection system's overall capacitance.
50. A useful discussion of these points can be found on pp. 3-9 of the Optoelectronics Components Catalog from UDT Sensors, in Ref. 44.
51. Newport, in Ref. 25, model XSD-34.
52. Technical Manufacturing Corp. (15 Centennial Drive, Peabody, MA 01960, 800-542-9725) tabletop model 78A-455 and flotation support system model 14-427-35.
53. The polarization could equally well be arranged so that the input light reflects 90° at the PBS. Then, if the platform on which the PBS sits and the laser mount have suitable angular adjustments, both steering mirrors could be omitted.
54. An iris diaphragm (e.g., Thorlabs, in Ref. 27, model ID25), centered in the outbound beam, is helpful in this operation and, later, in centering the mode-matching lens.
55. Assuming the polarization element is a PBS, we use this visual technique: rotate the λ/4 plate so that the dumped return beam is minimum; then rotate the waveplate another 45°, using the scale on the rotary stage. This approach is better than trying to pick out a maximum in the diverted light (hence a minimum in the light returning to the laser), since one's eye is more adept at locating a (nearly null) minimum than a (broad) maximum.
56. It is useful for the instructor to know in advance what incremental drive voltage corresponds to a FSR, in case the FPI fringe display on the oscilloscope is too cluttered for identifying the repetitive patterns. This is easily determined by using the PZT-scanned mirror in a Michelson interferometer, illuminated with the same wavelength as is used in the FPI experiment. The change in bias voltage on the PZT that is needed to shift the Michelson interferometer's output pattern by one fringe will also sweep the FPI through one FSR.
57. 00 mode. Hence, further adjustments are needed to complete mode-matching. In Fig. 6(c), the bright features within each repealed pattern are spaced consistently with the quoted separation of laser modes; accordingly, mode matching is essentially complete. (This chain of reasoning is useful only if the laser's entire frequency spread is smaller than the interferometer's FSR. HeNe lasers generally emit over a range of 1.5 GHz or less. Accordingly, the FPI would need to have L≤10 cm.)
58. See also R. Feinberg, "Observing the transverse modes of an optical resonator," Am. J. Phys. 50, 90 (1982).
59. The view of these patterns is improved by enlarging them: Insert a mirror in front of the detector to deflect the transmitted beam to the side, then place a short-focal-length lens in the deflected beam to rapidly diverge it for convenient observation on a card.
60. For example, A. Yariv, Quantum Electronics, 3rd Edition (Wiley. New York, 1989), p. 126.
61. See, for example, Melles Griot, in Ref. 22, "Introduction to the helium neon laser" in 1995/96 catalog, section 53.
62. The display at these higher dither frequencies often becomes annoyingly unstable: Fringes that occur just after a turnaround in the high-voltage ramp "bob up" to amplitudes characteristic of fringes seen with low-frequency dithers. This behavior arises because, immediately after a turn-around, the scanning mirror is still moving slowly, so the detection system confronts a "slow" fringe, which is doesn't distort.
63. This needs to be done with a load resistor small enough to avoid significant distortion of the fringe profiles. Compare Figs. 7(a) and 7(b), and refer to the discussion in Sec. IV D 1.
64. For example, National Photocolor Corp. (P.O. Box 320, Mamaroneck, NY 10543, 914-698-8111) 1 inch diameter, uncoated, laser-quality pellicle, model ST-LQ-UNC.
65. Surplus acousto-optic modulators, with associated driver electronics, are sometimes available from MWK Industries, in Ref. 22.
66. Contact, for example, Con-Optics, Inc. (87 Sandpit Road, Danbury, CT 06810, 203-743-3349).
67. D. Z. Anderson, J. C. Frisch, and C. S. Masser, "Mirror reflectometer based on optical cavity decay time," Appl. Opt. 23, 1238-1245 (1984).