Abstract

The sensitivity of a recently reported optical-fiber ring interferometer as a gyroscope has been analyzed. Photomixing SNRs were derived for the detection schemes. Noise sources due to the Rayleigh, Brillouin, Mie, and core–cladding interface light scattering processes are assessed quantitatively. Optimum gyroscope sensitivities are discussed via numerical examples for optical wavelengths λ = 0.633 μm and λ = 1.1 μm and both spontaneous and stimulated noises. Results show that (a) to reduce trapped scattered light by a factor of 100, mode stripping is essential, (b) λ = 1.1 μm is a more promising wavelength to use, and (c) high optical power operation, where the only noise is due to stimulated Brillouin scattering, gives better sensitivity than the low-power case. Examples show that at λ = 0.633 μm, the achievable sensitivities are 0.0078 deg/h at 2 mW and 0.0009 deg/h at 81 mW; and at λ = 1.1 μm, they are 0.0025 deg/h at 2 mW and 0.0007 deg/h at 14.4 mW. These calculated sensitivities are better than those of current laser ring gyroscopes.

© 1979 Optical Society of America

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    [Crossref]
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  7. The modulation frequency of this interferometer was set as high as 20 kHz so that low-frequency noise effects such as mechanical vibration-induced noise (1/f noise in detection) were eliminated by narrow bandpassing. R. L. Forward (Hughes Research Laboratories) has pointed out the inadequacy of using the result of Ref. 6 in a dc detection system; private communication.
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    [Crossref]
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    [Crossref]
  43. D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  49. Rich and Pinnow did not give the polarization state of the light when giving the value 0.4 dB/km. Our calculations based on their formula [Eq. (1)] and Schroeder’s result in values only one-half as large if linear polarization is assumed. We conclude that 0.4 dB/km would be correct for unpolarized light, which is what we presume now.
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    [Crossref]
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    [Crossref] [PubMed]
  55. See, e.g., H. Gamo, S. S. Chuang, R. E. Grace, IEEE J. Quantum Electron. QE-3, 243 (1967); S. S. Chuang, H. Gamo, J. Opt. Soc. Am. 59, 505 (1969).
    [Crossref]
  56. For a good review of magnetooptical materials, see W. G. Tabor, “Magneto-Optic Materials,” in Laser Handbook, F. T. Arecchi, E. O. Schulz-DuBois, Eds. (North-Holland, Amsterdam, 1972), Chap. D4.
  57. H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
    [Crossref]
  58. J. J. Hsieh, J. A. Rossi, J. P. Donnelly, Appl. Phys. Lett. 28, 709 (1976).
    [Crossref]
  59. T. Kimura, K. Daikoku, Opt. Quantum Electron. 9, 33 (1977).
    [Crossref]
  60. K. M. van Vliet, Appl. Opt. 6, 1145 (1967).
    [Crossref] [PubMed]
  61. A. van der Ziel, Proc. IEEE 58, 1178 (1970).
    [Crossref]
  62. J. Hanlon, S. F. Jacobs, Appl. Opt. 6, 577 (1967).
    [Crossref] [PubMed]
  63. C. Smit, C. T. J. Alkemade, W. F. Muntjewerff, Physica 29, 41 (1963).
    [Crossref]
  64. J. J. Brophy, Phys. Rev. 166, 827 (1968); J. Appl. Phys. 41, 2913 (1970); W. E. Purcell, J. Appl. Phys. 43, 2890 (1972).
    [Crossref]
  65. R. C. LeCraw, IEEE Trans. Magn. MAG-2, 304 (1966); C. D. Mee, Contemp. Phys. 8, 385 (1967); M. V. Chetkin, V. S. Solomatin, Sov. Phys. Solid State 8, 2708 (1967); V. V. Danilov, I. A. Deryngin, I. S. Melishchuk, V. D. Tronko, Radio Eng. Electron. Phys. USSR 15, 314 (1970); H. Takeuchi, I. Mikami, S. Taniguchi, J. Appl. Phys. 46, 3626 (1975).
    [Crossref]
  66. R. G. Smith, Appl. Opt. 11, 2489 (1972).
    [Crossref] [PubMed]
  67. The case with pump depletion has been worked out most recently by J. A. Yeung, A. Yariv for the stimulated Raman scattering in an optical fiber, IEEE J. Quantum Electron. QE-14, 347 (1978).
    [Crossref]

1978 (1)

The case with pump depletion has been worked out most recently by J. A. Yeung, A. Yariv for the stimulated Raman scattering in an optical fiber, IEEE J. Quantum Electron. QE-14, 347 (1978).
[Crossref]

1977 (7)

T. Kimura, K. Daikoku, Opt. Quantum Electron. 9, 33 (1977).
[Crossref]

V. Vali, R. W. Shorthill, Appl. Opt. 16, 290 (1977).
[Crossref] [PubMed]

J. A. Bucaro, H. D. Dardy, E. F. Carome, Appl. Opt. 16, 1761 (1977).
[Crossref] [PubMed]

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

S. S. Budrin, A. V. Goncharov, A. V. Samuilov, L. M. Kuchikyan, Sov. J. Opt. Technol. 44, 12 (1977).

H. F. Mahlein, Appl. Phys. 13, 137 (1977).
[Crossref]

E. M. Dianov, A. A. Manenkov, A. I. Ritus, Sov. J. Quantum Electron. 7, 841 (1977).
[Crossref]

1976 (3)

M. H. Reeve, M. C. Brierley, J. E. Midwinter, K. I. White, Opt. Quantum Electron. 8, 39 (1976).
[Crossref]

V. Vali, R. W. Shorthill, Appl. Opt. 15, 1099 (1976).
[Crossref] [PubMed]

J. J. Hsieh, J. A. Rossi, J. P. Donnelly, Appl. Phys. Lett. 28, 709 (1976).
[Crossref]

1975 (1)

1974 (6)

E. G. Rawson, Appl. Opt. 13, 2370 (1974).
[Crossref] [PubMed]

A more refined version of the refraction and reflection at the core–cladding interface was given more recently by J. P. Dakin, W. A. Gambling, Opt. Commun. 10, 195 (1974). Because we are interested in the first-order effects, we have chosen Stone’s formula for symmetric scattering. Dakin and Gambling’s formula, which takes into account the effects of depolarization, transverse intensity distribution in the core, and the finite angular width of the propagating beam will, of course, be used when more refined calculations are needed.
[Crossref]

See, e.g., A. W. Snyder, D. J. Mitchell, Electron. Lett. 10, 11 (1974); K. Petermann, Opt. Quantum Electron. 9, 167 (1977); D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[Crossref]

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

D. Gloge, Appl. Opt. 13, 249 (1974).
[Crossref] [PubMed]

T. C. Rich, D. A. Pinnow, Appl. Opt. 13, 1376 (1974).
[Crossref] [PubMed]

1973 (6)

H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
[Crossref]

H. Melchior, J. Lumin. 7, 390 (1973).
[Crossref]

J. Schroeder, R. Mohr, P. B. Macedo, C. J. Montrose, J. Am. Ceram. Soc. 56, 510 (1973).
[Crossref]

J. Stone, Appl. Opt. 12, 1824 (1973).
[Crossref] [PubMed]

D. B. Keck, R. D. Maurer, P. C. Schultz, Appl. Phys. Lett. 22, 307 (1973).
[Crossref]

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
[Crossref]

1972 (6)

1971 (6)

1970 (2)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
[Crossref]

A. van der Ziel, Proc. IEEE 58, 1178 (1970).
[Crossref]

1969 (2)

1968 (1)

J. J. Brophy, Phys. Rev. 166, 827 (1968); J. Appl. Phys. 41, 2913 (1970); W. E. Purcell, J. Appl. Phys. 43, 2890 (1972).
[Crossref]

1967 (5)

J. Hanlon, S. F. Jacobs, Appl. Opt. 6, 577 (1967).
[Crossref] [PubMed]

See, e.g., H. Gamo, S. S. Chuang, R. E. Grace, IEEE J. Quantum Electron. QE-3, 243 (1967); S. S. Chuang, H. Gamo, J. Opt. Soc. Am. 59, 505 (1969).
[Crossref]

B. Brixner, J. Opt. Soc. Am. 57, 674 (1967).
[Crossref]

K. M. van Vliet, Appl. Opt. 6, 1145 (1967).
[Crossref] [PubMed]

R. J. Post, Rev. Mod. Phys. 39, 475 (1967).
[Crossref]

1966 (2)

W. R. C. Rowley, IEEE Trans. Instrum. Meas. IM-15, 146 (1966).
[Crossref]

R. C. LeCraw, IEEE Trans. Magn. MAG-2, 304 (1966); C. D. Mee, Contemp. Phys. 8, 385 (1967); M. V. Chetkin, V. S. Solomatin, Sov. Phys. Solid State 8, 2708 (1967); V. V. Danilov, I. A. Deryngin, I. S. Melishchuk, V. D. Tronko, Radio Eng. Electron. Phys. USSR 15, 314 (1970); H. Takeuchi, I. Mikami, S. Taniguchi, J. Appl. Phys. 46, 3626 (1975).
[Crossref]

1965 (1)

1963 (1)

C. Smit, C. T. J. Alkemade, W. F. Muntjewerff, Physica 29, 41 (1963).
[Crossref]

1956 (1)

R. D. Maurer, J. Chem. Phys. 25, 1206 (1956).
[Crossref]

Alkemade, C. T. J.

C. Smit, C. T. J. Alkemade, W. F. Muntjewerff, Physica 29, 41 (1963).
[Crossref]

Bisbee, D. L.

Blagidze, Y. M.

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

Brierley, M. C.

M. H. Reeve, M. C. Brierley, J. E. Midwinter, K. I. White, Opt. Quantum Electron. 8, 39 (1976).
[Crossref]

Brixner, B.

Brophy, J. J.

J. J. Brophy, Phys. Rev. 166, 827 (1968); J. Appl. Phys. 41, 2913 (1970); W. E. Purcell, J. Appl. Phys. 43, 2890 (1972).
[Crossref]

Brown, R. B.

R. B. Brown, NRL Memorandum Report 1871 (Naval Research Laboratory, Washington, D. C., 1968), pp. 19–22.

Bucaro, J. A.

Budrin, S. S.

S. S. Budrin, A. V. Goncharov, A. V. Samuilov, L. M. Kuchikyan, Sov. J. Opt. Technol. 44, 12 (1977).

Carome, E. F.

Chagulov, V. S.

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

Chuang, S. S.

See, e.g., H. Gamo, S. S. Chuang, R. E. Grace, IEEE J. Quantum Electron. QE-3, 243 (1967); S. S. Chuang, H. Gamo, J. Opt. Soc. Am. 59, 505 (1969).
[Crossref]

Cummins, H. Z.

See the review article by H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” in Progress in Optics, Vol. 8E. Wolf, Ed. (North-Holland, Amsterdam, 1970).
[Crossref]

Daikoku, K.

T. Kimura, K. Daikoku, Opt. Quantum Electron. 9, 33 (1977).
[Crossref]

Dakin, J. P.

A more refined version of the refraction and reflection at the core–cladding interface was given more recently by J. P. Dakin, W. A. Gambling, Opt. Commun. 10, 195 (1974). Because we are interested in the first-order effects, we have chosen Stone’s formula for symmetric scattering. Dakin and Gambling’s formula, which takes into account the effects of depolarization, transverse intensity distribution in the core, and the finite angular width of the propagating beam will, of course, be used when more refined calculations are needed.
[Crossref]

Dardy, H. D.

Dianov, E. M.

E. M. Dianov, A. A. Manenkov, A. I. Ritus, Sov. J. Quantum Electron. 7, 841 (1977).
[Crossref]

Di-Domenico, M.

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
[Crossref]

Donnelly, J. P.

J. J. Hsieh, J. A. Rossi, J. P. Donnelly, Appl. Phys. Lett. 28, 709 (1976).
[Crossref]

Dyott, R. B.

R. B. Dyott, J. R. Stern, Electron. Lett. 7, 624 (1971).
[Crossref]

Dzhibladze, M. I.

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

Fabelinskii, I. L.

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968).
[Crossref]

Foward, R. L.

Fox, R.

Gambling, W. A.

A more refined version of the refraction and reflection at the core–cladding interface was given more recently by J. P. Dakin, W. A. Gambling, Opt. Commun. 10, 195 (1974). Because we are interested in the first-order effects, we have chosen Stone’s formula for symmetric scattering. Dakin and Gambling’s formula, which takes into account the effects of depolarization, transverse intensity distribution in the core, and the finite angular width of the propagating beam will, of course, be used when more refined calculations are needed.
[Crossref]

Gamo, H.

See, e.g., H. Gamo, S. S. Chuang, R. E. Grace, IEEE J. Quantum Electron. QE-3, 243 (1967); S. S. Chuang, H. Gamo, J. Opt. Soc. Am. 59, 505 (1969).
[Crossref]

Gloge, D.

Goncharov, A. V.

S. S. Budrin, A. V. Goncharov, A. V. Samuilov, L. M. Kuchikyan, Sov. J. Opt. Technol. 44, 12 (1977).

Grace, R. E.

See, e.g., H. Gamo, S. S. Chuang, R. E. Grace, IEEE J. Quantum Electron. QE-3, 243 (1967); S. S. Chuang, H. Gamo, J. Opt. Soc. Am. 59, 505 (1969).
[Crossref]

Hanlon, J.

Hosaka, T.

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

Hsieh, J. J.

J. J. Hsieh, J. A. Rossi, J. P. Donnelly, Appl. Phys. Lett. 28, 709 (1976).
[Crossref]

Hubbard, W. M.

Ito, S. I.

H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
[Crossref]

Jacobs, S. F.

Kapron, F. P.

Kawachi, M.

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

Kawana, A.

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

Keck, D. B.

D. B. Keck, R. D. Maurer, P. C. Schultz, Appl. Phys. Lett. 22, 307 (1973).
[Crossref]

Kimura, T.

T. Kimura, K. Daikoku, Opt. Quantum Electron. 9, 33 (1977).
[Crossref]

Kuchikyan, L. M.

S. S. Budrin, A. V. Goncharov, A. V. Samuilov, L. M. Kuchikyan, Sov. J. Opt. Technol. 44, 12 (1977).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, English translation by J. B. Sykes, J. S. Bell (Pergamon, New York, 1960), pp. 331–337.

LeCraw, R. C.

R. C. LeCraw, IEEE Trans. Magn. MAG-2, 304 (1966); C. D. Mee, Contemp. Phys. 8, 385 (1967); M. V. Chetkin, V. S. Solomatin, Sov. Phys. Solid State 8, 2708 (1967); V. V. Danilov, I. A. Deryngin, I. S. Melishchuk, V. D. Tronko, Radio Eng. Electron. Phys. USSR 15, 314 (1970); H. Takeuchi, I. Mikami, S. Taniguchi, J. Appl. Phys. 46, 3626 (1975).
[Crossref]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, English translation by J. B. Sykes, J. S. Bell (Pergamon, New York, 1960), pp. 331–337.

Lipson, S. G.

Macedo, P. B.

J. Schroeder, R. Mohr, P. B. Macedo, C. J. Montrose, J. Am. Ceram. Soc. 56, 510 (1973).
[Crossref]

Mahlein, H. F.

H. F. Mahlein, Appl. Phys. 13, 137 (1977).
[Crossref]

Malitson, I. H.

Manenkov, A. A.

E. M. Dianov, A. A. Manenkov, A. I. Ritus, Sov. J. Quantum Electron. 7, 841 (1977).
[Crossref]

Marcuse, D.

D. Marcuse, Appl. Opt. 14, 3021 (1975).
[Crossref] [PubMed]

D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).

Maurer, R. D.

D. B. Keck, R. D. Maurer, P. C. Schultz, Appl. Phys. Lett. 22, 307 (1973).
[Crossref]

F. P. Kapron, R. D. Maurer, M. P. Teter, Appl. Opt. 11, 1352 (1972).
[Crossref] [PubMed]

R. D. Maurer, J. Chem. Phys. 25, 1206 (1956).
[Crossref]

Melchior, H.

H. Melchior, J. Lumin. 7, 390 (1973).
[Crossref]

Mestvirishvili, A. M.

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

Midwinter, J. E.

M. H. Reeve, M. C. Brierley, J. E. Midwinter, K. I. White, Opt. Quantum Electron. 8, 39 (1976).
[Crossref]

Mikami, I.

H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
[Crossref]

Miller, L. R.

Mitchell, D. J.

See, e.g., A. W. Snyder, D. J. Mitchell, Electron. Lett. 10, 11 (1974); K. Petermann, Opt. Quantum Electron. 9, 167 (1977); D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[Crossref]

Miyashita, T.

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

Mohr, R.

J. Schroeder, R. Mohr, P. B. Macedo, C. J. Montrose, J. Am. Ceram. Soc. 56, 510 (1973).
[Crossref]

Montrose, C. J.

J. Schroeder, R. Mohr, P. B. Macedo, C. J. Montrose, J. Am. Ceram. Soc. 56, 510 (1973).
[Crossref]

Moss, G. E.

Muntjewerff, W. F.

C. Smit, C. T. J. Alkemade, W. F. Muntjewerff, Physica 29, 41 (1963).
[Crossref]

Nakahara, M.

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

Ostermayer, F. W.

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
[Crossref]

Pearson, A. D.

Perelman, M. E.

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

Pinnow, D. A.

T. C. Rich, D. A. Pinnow, Appl. Opt. 13, 1376 (1974).
[Crossref] [PubMed]

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
[Crossref]

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

Platt, W. K.

W. K. Platt, Laser Communication Systems (Wiley, New York, 1969), Chaps. 8 and 10.

Post, R. J.

R. J. Post, Rev. Mod. Phys. 39, 475 (1967).
[Crossref]

Rawson, E. G.

Reeve, M. H.

M. H. Reeve, M. C. Brierley, J. E. Midwinter, K. I. White, Opt. Quantum Electron. 8, 39 (1976).
[Crossref]

Rich, T. C.

T. C. Rich, D. A. Pinnow, Appl. Opt. 13, 1376 (1974).
[Crossref] [PubMed]

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
[Crossref]

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

Ritus, A. I.

E. M. Dianov, A. A. Manenkov, A. I. Ritus, Sov. J. Quantum Electron. 7, 841 (1977).
[Crossref]

Rossi, J. A.

J. J. Hsieh, J. A. Rossi, J. P. Donnelly, Appl. Phys. Lett. 28, 709 (1976).
[Crossref]

Rowley, W. R. C.

W. R. C. Rowley, IEEE Trans. Instrum. Meas. IM-15, 146 (1966).
[Crossref]

Rubinshtein, G. M.

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

Samuilov, A. V.

S. S. Budrin, A. V. Goncharov, A. V. Samuilov, L. M. Kuchikyan, Sov. J. Opt. Technol. 44, 12 (1977).

Sansalone, F. J.

Schroeder, J.

J. Schroeder, R. Mohr, P. B. Macedo, C. J. Montrose, J. Am. Ceram. Soc. 56, 510 (1973).
[Crossref]

Schultz, P. C.

D. B. Keck, R. D. Maurer, P. C. Schultz, Appl. Phys. Lett. 22, 307 (1973).
[Crossref]

Shamir, J.

Shorthill, R. W.

Smit, C.

C. Smit, C. T. J. Alkemade, W. F. Muntjewerff, Physica 29, 41 (1963).
[Crossref]

Smith, R. G.

Snyder, A. W.

See, e.g., A. W. Snyder, D. J. Mitchell, Electron. Lett. 10, 11 (1974); K. Petermann, Opt. Quantum Electron. 9, 167 (1977); D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
[Crossref]

Stern, J. R.

R. B. Dyott, J. R. Stern, Electron. Lett. 7, 624 (1971).
[Crossref]

Stone, J.

Swinney, H. L.

See the review article by H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” in Progress in Optics, Vol. 8E. Wolf, Ed. (North-Holland, Amsterdam, 1970).
[Crossref]

Tabor, W. G.

For a good review of magnetooptical materials, see W. G. Tabor, “Magneto-Optic Materials,” in Laser Handbook, F. T. Arecchi, E. O. Schulz-DuBois, Eds. (North-Holland, Amsterdam, 1972), Chap. D4.

Takeuchi, H.

H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
[Crossref]

Taniguchi, S.

H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
[Crossref]

Teter, M. P.

Tynes, A. R.

Vali, V.

van der Ziel, A.

A. van der Ziel, Proc. IEEE 58, 1178 (1970).
[Crossref]

van Vliet, K. M.

White, K. I.

M. H. Reeve, M. C. Brierley, J. E. Midwinter, K. I. White, Opt. Quantum Electron. 8, 39 (1976).
[Crossref]

Yariv, A.

The case with pump depletion has been worked out most recently by J. A. Yeung, A. Yariv for the stimulated Raman scattering in an optical fiber, IEEE J. Quantum Electron. QE-14, 347 (1978).
[Crossref]

Yeung, J. A.

The case with pump depletion has been worked out most recently by J. A. Yeung, A. Yariv for the stimulated Raman scattering in an optical fiber, IEEE J. Quantum Electron. QE-14, 347 (1978).
[Crossref]

Appl. Opt. (19)

Appl. Phys. (1)

H. F. Mahlein, Appl. Phys. 13, 137 (1977).
[Crossref]

Appl. Phys. Lett. (4)

D. B. Keck, R. D. Maurer, P. C. Schultz, Appl. Phys. Lett. 22, 307 (1973).
[Crossref]

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. Di-Domenico, Appl. Phys. Lett. 22, 527 (1973).
[Crossref]

J. J. Hsieh, J. A. Rossi, J. P. Donnelly, Appl. Phys. Lett. 28, 709 (1976).
[Crossref]

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 48, 3233 (1969).

Electron. Lett. (3)

See, e.g., A. W. Snyder, D. J. Mitchell, Electron. Lett. 10, 11 (1974); K. Petermann, Opt. Quantum Electron. 9, 167 (1977); D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[Crossref]

R. B. Dyott, J. R. Stern, Electron. Lett. 7, 624 (1971).
[Crossref]

Single-mode optical fiber with loss below 1 dB/km between λ = 1.0 μm and λ = 1.1 μm has been reported by A. Kawana, T. Miyashita, M. Nakahara, M. Kawachi, T. Hosaka, Electron. Lett. 13, 188 (1977) and in Digest of Topical Meeting on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D. C., 1977), pp. 275–278.
[Crossref]

IEEE J. Quantum Electron. (2)

See, e.g., H. Gamo, S. S. Chuang, R. E. Grace, IEEE J. Quantum Electron. QE-3, 243 (1967); S. S. Chuang, H. Gamo, J. Opt. Soc. Am. 59, 505 (1969).
[Crossref]

The case with pump depletion has been worked out most recently by J. A. Yeung, A. Yariv for the stimulated Raman scattering in an optical fiber, IEEE J. Quantum Electron. QE-14, 347 (1978).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

W. R. C. Rowley, IEEE Trans. Instrum. Meas. IM-15, 146 (1966).
[Crossref]

IEEE Trans. Magn. (1)

R. C. LeCraw, IEEE Trans. Magn. MAG-2, 304 (1966); C. D. Mee, Contemp. Phys. 8, 385 (1967); M. V. Chetkin, V. S. Solomatin, Sov. Phys. Solid State 8, 2708 (1967); V. V. Danilov, I. A. Deryngin, I. S. Melishchuk, V. D. Tronko, Radio Eng. Electron. Phys. USSR 15, 314 (1970); H. Takeuchi, I. Mikami, S. Taniguchi, J. Appl. Phys. 46, 3626 (1975).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-18, 608 (1970).
[Crossref]

J. Am. Ceram. Soc. (1)

J. Schroeder, R. Mohr, P. B. Macedo, C. J. Montrose, J. Am. Ceram. Soc. 56, 510 (1973).
[Crossref]

J. Appl. Phys. (1)

H. Takeuchi, S. I. Ito, I. Mikami, S. Taniguchi, J. Appl. Phys. 44, 4789 (1973).
[Crossref]

J. Chem. Phys. (1)

R. D. Maurer, J. Chem. Phys. 25, 1206 (1956).
[Crossref]

J. Lumin. (1)

H. Melchior, J. Lumin. 7, 390 (1973).
[Crossref]

J. Opt. Soc. Am. (4)

Opt. Commun. (1)

A more refined version of the refraction and reflection at the core–cladding interface was given more recently by J. P. Dakin, W. A. Gambling, Opt. Commun. 10, 195 (1974). Because we are interested in the first-order effects, we have chosen Stone’s formula for symmetric scattering. Dakin and Gambling’s formula, which takes into account the effects of depolarization, transverse intensity distribution in the core, and the finite angular width of the propagating beam will, of course, be used when more refined calculations are needed.
[Crossref]

Opt. Quantum Electron. (2)

M. H. Reeve, M. C. Brierley, J. E. Midwinter, K. I. White, Opt. Quantum Electron. 8, 39 (1976).
[Crossref]

T. Kimura, K. Daikoku, Opt. Quantum Electron. 9, 33 (1977).
[Crossref]

Phys. Rev. (1)

J. J. Brophy, Phys. Rev. 166, 827 (1968); J. Appl. Phys. 41, 2913 (1970); W. E. Purcell, J. Appl. Phys. 43, 2890 (1972).
[Crossref]

Physica (1)

C. Smit, C. T. J. Alkemade, W. F. Muntjewerff, Physica 29, 41 (1963).
[Crossref]

Proc. IEEE (1)

A. van der Ziel, Proc. IEEE 58, 1178 (1970).
[Crossref]

Rev. Mod. Phys. (1)

R. J. Post, Rev. Mod. Phys. 39, 475 (1967).
[Crossref]

Sov. J. Opt. Technol. (1)

S. S. Budrin, A. V. Goncharov, A. V. Samuilov, L. M. Kuchikyan, Sov. J. Opt. Technol. 44, 12 (1977).

Sov. J. Quantum Electron. (2)

Y. M. Blagidze, M. I. Dzhibladze, A. M. Mestvirishvili, M. E. Perelman, G. M. Rubinshtein, V. S. Chagulov, Sov. J. Quantum Electron. 3, 335 (1974).
[Crossref]

E. M. Dianov, A. A. Manenkov, A. I. Ritus, Sov. J. Quantum Electron. 7, 841 (1977).
[Crossref]

Other (16)

Rich and Pinnow did not give the polarization state of the light when giving the value 0.4 dB/km. Our calculations based on their formula [Eq. (1)] and Schroeder’s result in values only one-half as large if linear polarization is assumed. We conclude that 0.4 dB/km would be correct for unpolarized light, which is what we presume now.

The conversion factor is 1 cm−1 = 4.33 × 105 dB/km.

M. Balkanski, R. C. C. Leite, S. P. S. Porto, Eds., Proceedings of Third International Conference on Light Scattering in Solids (Wiley, New York, 1976), Chap. 10, pp. 621–630; Chap. 11, pp. 673–687.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, English translation by J. B. Sykes, J. S. Bell (Pergamon, New York, 1960), pp. 331–337.

For a good review of magnetooptical materials, see W. G. Tabor, “Magneto-Optic Materials,” in Laser Handbook, F. T. Arecchi, E. O. Schulz-DuBois, Eds. (North-Holland, Amsterdam, 1972), Chap. D4.

See Ref. 14, Chap. 10, Eqs. (10-45) and (10-13).

See the review article by H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” in Progress in Optics, Vol. 8E. Wolf, Ed. (North-Holland, Amsterdam, 1970).
[Crossref]

W. K. Platt, Laser Communication Systems (Wiley, New York, 1969), Chaps. 8 and 10.

This is certainly not true for a multimode fiber for it has been observed that speckled patterns are formed at the output of such a fiber.

For linearly polarized input waves, the output waves from a long single-mode fiber may acquire some degree of ellipticity in their polarization states due to stress birefringence or deviation of the core cross section from a perfectly circular shape. However, these effects are most likely reciprocal. Therefore, in keeping with the assumption of reciprocity in fiber losses, we feel that it is reasonable at this time to put aside the question on polarization.

There is Raman scattering that has a much larger frequency shift. Because its scattering coefficient is 10–20 times smaller than Brillouin scattering, we will not consider it here.

By free space we mean either a vacuum or a homogeneous non-dispersive medium in which the optical system is submerged.

The fringe shift in a fringe pattern caused by the phase difference Δϕ is just Δϕ/2π.

R. B. Brown, NRL Memorandum Report 1871 (Naval Research Laboratory, Washington, D. C., 1968), pp. 19–22.

The modulation frequency of this interferometer was set as high as 20 kHz so that low-frequency noise effects such as mechanical vibration-induced noise (1/f noise in detection) were eliminated by narrow bandpassing. R. L. Forward (Hughes Research Laboratories) has pointed out the inadequacy of using the result of Ref. 6 in a dc detection system; private communication.

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1

Optical setup of the ring interferometer for the analysis.

Fig. 2
Fig. 2

Optical mixing technique for the phase difference measurement.

Fig. 3
Fig. 3

Direct optical beams in clockwise (CW) and counterclockwise (CCW) directions in a fiber inducing other scattered components: forward peak, Brillouin, and Rayleigh. Except for the direct beams, the phases of the others are random.

Fig. 4
Fig. 4

Differential detection scheme with balanced inputs to eliminate common-mode noises adaptable to the optical setup of Fig. 1.

Fig. 5
Fig. 5

Definition of coordinates and scattering fiber elements of (a) forwardscattering and (b) backscattering processes for the derivation of scattered light distribution laws.

Fig. 6
Fig. 6

Distribution laws for all the scattering components considered for a fiber with attenuation coefficients αT = 0.43 dB/km at λ = 1.1 μm (solid lines) and αT = 4 dB/km at λ = 0.633 μm (broken lines). Due to attenuation, the forwardscattered light components rise first as fiber length is increased, reach maxima, and then decay, whereas the backscattered components rise continuously to saturation. The direct beam attenuates much more slowly in the case of λ = 1.1 μm than it does for λ = 0.633 μm, while backscattered noises saturate to about the same level.

Fig. 7
Fig. 7

Signal-to-noise degradation due to scattered light components in a fiber as a function of optical fiber length L. For a perfect fiber with zero loss, the S/N is purely signal quantum-noise limited and is equal to 1 here. Curve (1) is for λ = 1.1 μm (0.43 dB/km); curve (2) is for λ = 0.633 μm (4 dB/km). So, at longer wavelength, the degradation is much less significant.

Fig. 8
Fig. 8

The variation of the photodetector current as a function of the phase difference between the two signal beams. Maximum sensitivity points correspond to the points on the photodetector current curve where its slope has maximum values. Therefore, for small ±Δϕ, we need a dc phase bias of π/2 in order to ensure maximum sensitivity.

Fig. 9
Fig. 9

Typical solid-state detector noise spectrum (upper figure, InAs, Ref. 62), and photomultiplier noise spectrum (lower figure, Ref. 63) showing the effect of 1/f noise at low-frequency ends.

Fig. 10
Fig. 10

An example of the ac detection scheme for improvement of the ring interferometer sensitivity. A heterodyne technique evolving from the basic dc configuration shown in Fig. 1.

Fig. 11
Fig. 11

Another example of the ac detection scheme. A phase dc bias with modulation or a large ac modulation alone.

Fig. 12
Fig. 12

Another possible example of the ac detection scheme. A reciprocal gated-phase shifter amplitude-detection technique.

Tables (4)

Tables Icon

Table I Summary of Light Scattering Information in a Typical Fused Silica Fiber

Tables Icon

Table II Numerical Values of the Parameters Used to Evaluate the Optimum Fiber Length (an Example)

Tables Icon

Table III Quantum-Noise-Limited Performance a

Tables Icon

Table IV Values of the Parameters Used for the Evaluation of the Critical Pump Power in Eqs. (43) and (44)

Equations (53)

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I = E tcw E tccw * = ( E coh + E incoh ) ( E coh + E incoh ) * = E coh E coh * + E incoh E coh * + E coh E incoh * + E incoh E incoh * .
i = D I ,
i ¯ 1 = 1 τ 0 τ i 1 ( t ) d t ,
E cw E ccw ¯ = ½ A cw A ccw cos ( π + Δ ϕ ¯ , = - ½ A cw A ccw cos ( Δ ϕ ) ¯ ,
E cw 2 ¯ = A cw 2 cos 2 ( θ ) ¯ = ½ A cw 2 ¯ .
i ¯ 1 = D [ ½ ( I cw + I F P + I R F + I R B + I B O + I B π ) - ½ I cw cos ( Δ ϕ ) ] ,
i ¯ 2 = D α 1 [ ½ ( I cw + I F P + I R F + I R B + I B O + I B π ) + ½ I cw cos ( Δ ϕ ) ] ,
i T 1 a 1 i ¯ 1 d a = D a 1 [ ½ ( I cw + I F P + I R F + I R B + I B O + I B π ) - ½ I cw cos ( Δ ϕ ) ] = D [ ½ ( P cw + P F P + P R F + P R B + P B O + P B π ) - ½ P cw cos ( Δ ϕ ) ] ,
i T 2 a 2 i ¯ 1 d a = D α 1 [ ½ ( P cw + P F P + P R F + P R B + P B π + P B O ) - ½ P cw cos ( Δ ϕ ) ] ,
( S / N ) peak = D 2 G 2 P cw 2 R L / 4 2 q G 2 [ 1 2 ( P cw + P F P + P R F + P R B + P B O + P B π ) + D P b + I D ] + 4 k T B 0 ,
( S / N ) peak , 1 = ¼ D q B 0 P cw 2 ( P cw + P F P + P R F + P R B + P B O + P B π )
( S / N ) peak , 2 = ¼ α 1 D q B 0 P cw 2 ( P cw + P F P + P R F + P R B + P B O + P B π )
( S / N ) peak = / 4 1 D P cw q B 0 = ¼ η P cw h ν B 0 ,
i s i T 2 - i T 1 = D a 1 I cw cos ( Δ ϕ ) = D P cw cos ( Δ ϕ ) .
R L i S 2 = D 2 G 2 P cw 2 R L ,
R L i N 2 ¯ = ( i N 1 2 ¯ + i N 2 2 ¯ ) R L G 2 = 2 q B 0 G 2 R L D ( P cw + P F P + P R F + P R B + P B O + P B π ) ,
( S / N ) peak , diff = i S 2 ¯ i N 2 ¯ = D q B 0 P cw 2 2 ( P cw + P F P + P R F + P R B + P B O + P B π ) .
( S / N ) peak , diff = D q B 0 P cw 2 = ½ η P cw h ν .
P ( x ) = P i exp ( - α T x ) ,
d P ( x ) = - P ( x ) α s d x = - P i exp ( - α T x ) α s d x ,
d P ( x ) = - F P i exp ( - α T x ) α s d x .
d P s ( x ) = - F P i exp ( - α T x ) exp ( - α T ( x 1 - x ) ] α s d x = - F P i α s exp ( - a T x 1 ) d x .
P s ( x 1 ) = - F P i α s exp ( - α T x 1 ) x 1 .
P s ( L ) = - F P i α s exp ( - α T L ) L .
d P s ( x ) = - B P i exp ( - α T x ) α s exp [ - α T ( x - x 1 ) ] d x = - B P i α s exp ( α T x 1 ) exp ( - 2 α T x ) d x .
P s ( x 1 ) = - B P i α s exp ( α T x 1 ) x 1 L exp ( - 2 α T x ) d x = B P i 2 α s α T { exp [ - α T ( 2 L - x 1 ) ] - exp ( - α T x 1 ) } .
P s ( 0 ) = B P i 2 α s α T [ exp ( - 2 α T L ) - 1 ] .
Ω trap = 0 2 π d ϕ 0 θ 0 ( 1 + cos 2 θ ) sin θ d θ , = 4 π 2 [ / 3 4 - ( 1 n core - 1 3 n core 3 ) ] ,
Ω trap = 0 2 π d ϕ 0 θ 0 ( 1 + cos 2 θ ) sin θ d θ , = 4 π 2 [ / 3 4 - ( 1 clad n cone - n cald 3 3 n core 3 ) ] .
F Ω trap Ω total = ½ [ 1 - ¾ ( 1 n core + 1 3 n core 3 ) ]
F = ½ [ 1 - ¾ ( n clad n core + n clad 3 3 n core 3 ) ]
α S B = ( 8 3 ) ( π 3 λ 4 ) k T ( n 8 p 12 2 ρ V 2 ] ,
R 90 ° = π 2 λ 4 ( n 8 p 12 2 ) k T ( ρ V 2 ) - 1 .
α F P = ( ) α S R ,             α S R = α T - α S B - α F P ,
P cw / Π = P ccw / Π = exp ( - α T L ) P F P / Π = ( α S R ) L exp ( - α T L ) P R F / Π = ( 0.2 α S R ) L exp ( - α T L ) P R B / Π = ( 0.1 α S R / α T ) [ 1 - exp ( - 2 α T L ) ] P B O / Π = ( 0.2 α S B ) L exp ( - α T L ) P B π / Π = ( 0.1 α S B ) [ 1 - exp ( - 2 α T L ) .
( S / N ) peak = ¼ η h ν B 0 P cw 2 P cw + P F P + P R F + P R B + P B O + P B π ) = K f ( L ) ,
i T = D [ ½ ( P cw + P N ) - ½ P cw cos ( Δ ϕ + π / 2 ) ] = D [ ½ ( P cw + P N ) + ½ P cw sin ( Δ ϕ ) ] ,
Δ ϕ = ϕ cw - ϕ ccw = 4 π R L λ c Ω .
S = ¼ D 2 G 2 P cw 2 sin 2 ( Δ ϕ ) R L ,
( S / N ) = ¼ D 2 G 2 P cw 2 sin 2 ( Δ ϕ ) R L q G 2 [ D ( P cw + P N ) ] R L B 0 = ¼ ( η h ν B 0 ) P cw 2 P cw + P N sin 2 ( Δ ϕ ) = F ( L ) sin 2 ( 4 π R L λ c Ω ) ,
Ω = 1 β L sin - 1 { [ 1 / F ( L ) ] ( S / N ) } 1 / 2 .
Ω = 1 β L sin - 1 [ U ( L ) ] ,             d Ω d L = 1 β L 2 [ - sin U + L d U d L ( 1 - U 2 ) 1 / 2 ] .
U 0 = U ( L 0 ) ,             sin - 1 U 0 = L 0 ( 1 - U 0 2 ) 1 / 2 d U d L | L = L 0 .
U 0 = ( 4 h ν B 0 η Π ) 1 / 2 exp ( ½ α T L ) { 1 + ( A + B + C ) L 0 + ( B + C ) [ exp ( α T L 0 ) - exp ( - α T L 0 ) ] } 1 / 2 .
d U d L | L - L 0 = U 0 α T 2 [ 1 + H ( L 0 ) ] ,
H ( L 0 ) = ( A + B + C α T ) + ( B + C ) [ exp ( α T L 0 ) + exp ( - α T L 0 ) ] 1 + ( A + B + C ) L 0 + ( B + C ) [ exp ( α T L 0 ) - exp ( - α T L 0 ) ] , A = 1 5 α S R ,             B = 0.2 α S R ,             C = 0.2 α S B , B = 0.1 ( α S R ) / ( α T ) ,             C = 0.1 ( α S B ) / ( α T ) ,
P s ( 0 ) = P p ( L ) exp ( - α T L ) .
P s ( 0 ) = P p ( 0 ) exp ( - α T L ) .
P s ( 0 ) = ( π ) 1 / 2 2 ( ν s ν a ) ( k T ) ( Δ ν B ) [ ν 0 P p ( 0 ) α T A ] 1 / 2 × 0 L d ξ ( exp { - 2 α T ξ + γ 0 P p ( 0 ) A α T [ 1 - exp ( - α T ξ ) ] } ) ,
( S / N ) = 1 8 η P cw h ν B 0 sin 2 ( β L Ω ) ,
Ω min = [ 8 h ν B 0 η P p ( 0 ) ] 1 / 2 1 β exp ( ½ α T L ) L .
( S / N ) = 1 4 η P cw 4 ν B 0 sin 2 ( β L Ω ) ,
Ω min = [ 4 h ν B 0 η P p ( 0 ) ] 1 / 2 exp ( ½ Ω T L ) β L .

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