lecture 9. optical elements rick k. r...
TRANSCRIPT
Ph 103c: The Physics of LIGO
Assigned Reading:
LECTURE 9. OPTICAL ELEMENTS
Lecture by Rick Savage
27 April 1994
Y. W. Winkler, K. Danzmann, A. Rudiger and R. Schilling, "Optical Problems in Interfereometric Gravitational Wave Antennas," in The Sixth Marcel Grossmann Meeting, eds. H. Sato and T. Nakamura (World Scientific, Singapore, 1991) , pp. 176-191.
H. A. E. Siegman, Lasers (University Science Books, Mill Valley CA, 1986), chapter 17 "Physical Properties of Gaussian Beams": Section 17.1 "Gaussian Beam Propagation," (pages 663-674) ; section 17.4 "Axial Phase Shifts: The Guoy Effect ," (pages 682-685), and section 17.5 "Higher-Order Gaussian Modes," (pages 685-691) . [This material was suggested reading in Lecture 4.] If you did not read it then, you should read it now.]
Suggested Supplementary Reading:
Z. D. Malacara, Optical Shop Testing (John Wiley and Sons, New York, 1978) , section 1.2, "Fizeau Interferometer," pp. 19-37.
AA. H. A. Macleod, Thin-Film Optical Filters, 2nd edition (Adam Hilger Ltd. , Bristol, 1986), "Introduction," pp. 1- 10.
SS. J. M. Elson, H. E. Bennett, and J. M. Bennett, "Scattering from Optical Surfaces," in Applied Optical Engineering, Vol. VII (Academic Press 1979), Chapter 7, page 191. [This is reproduced later, in connection with Lecture 15.]
1
A Few Suggested Problems
1. Gaussian Beam Propagation. The present conceptual design for the 4 km long LIGO arm cavities specifies that the input mirror be flat and the end mirror curved, with a radius of curvature of 6 km. The beam waist is therefore located on the flat input mirror and the spot size is significantly larger on the curved mirror than on the flat.
a. Consider employing a symmetrical curved-curved mirror configuration instead of the flat-curved geometry. What is the required radius of curvature of the mirrors (R1 = R2) to maintain the cavity g factor product at 9192 = 1/3?
b. Calculate the spot size at the beam waist and on the mirrors. What is the Rayleigh range for this configuration?
c. What factors might influence the decision to adopt either the flat-curved or the symmetrical, curved-curved geometry?
2. Scattering from mirror surface irregularities. Consider the following simple model for scattering from mirror surface irregularities. Represent the mirror surface height z = 1'( x , y) as a superposition of a number of spatially monochromatic terms. Assume, for the moment, that only one term is non-zero, and let that term have peak height a and wavelength A; i.e. set
J.'(x,y) = aC08(21rx/A).
Idealize the mirror to be of infinite extent and irradiated by a plane wave at normal incidence.
a. Show that the wave reflected from the surface has spatial sidebands that propagate at some angle 0 relative to the specularly reflected beam. What is O? [Hint: This can be regarded as an exercise in Fraunhofer diffraction (Why?); see, e.g., Section 7.3 of chapter 7, "Diffraction", of Blandford and Thorne, Applications of Classical Physics (which was passed out in Lecture 4).J
b. Find the power scattered into these sidebands as a function of the amplitude of the surface variation, a.
c. Generalize to find the total light scattered into all angles from a surface with a total rms irregularity a.
2
Lecture 9 Optical Elements
by Rick Savage, 27 April 1995
Savage lectured from the following transparencies. Kip has added a few annotations, based on Savage's lecture.
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TABLE 2
OPTICAL POWER AND INTENSITY AT VARIOUS COMPONENTS
component w (cm) Power (W ) Intensity (W Icm2)
¢> modulator 7 x 10-2 .. 4 X 102
isolator 5 x 10-'2 4 8 X 102
mode filter (flat) 1 x 10-1 4 X 103 2 X 105 ..
mode filter (curved) 2 x 10-1 4 X 103 6 X 10' telescope out. mir. 2.1 3 4 x 10-1
recycling mir. 2.1 8 x 101 1 X 101
beam spli t ter 2.1 8 x 101 1 X 101
arm cavity input mir, 2.1 4.5 x 103 6.7xl02 arm cavity far mir. 3.8 4.5 x 103 2 X 102
main frame laser 5 x 10-2 1 X 102 3 X 10'
6
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CHAPTER 17: PHYSICAL PROPERTIES OF GAUSSIAN BEAMS
FIGURE 17.20
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• Effects of temperature gradient:
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• These effects limit our ability to couple power into a cavity.
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Pathfinder Goals
Primary
• Specify performance requirements of large aperature optics.
• Evaluate industrial polishing, coating and measuring capabilities.
• Scope costs for fabrication of the LlGO optics.
Secondary
• Develop and determine the actual processes and techniques for fabrication and mensuration of LlGO optics.
LIGO~ 3
SPARES
MECHANICAL Q MEASUREMENTS
LIGO~
PATHFINDER PROCESS
+ POLISHER
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METROLOGY I 0.6328 IJ.I11
+ IN-HOUSE TESTING
+ COATING
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+ PATHFINDER COMPLETE
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