Abstract

The line width of a well-stabilized laser operating far above threshold is determined by random fluctuations of the phase. This paper discusses several types of experiments which can give information about the details of this phase random process. In order to study the laser phase noise experimentally the laser signal (containing phase noise only) must be passed through some type of interferometer which will convert the phase noise to intensity noise. The various properties of this derived intensity noise which may then be determined are its probability density, first and second moments, autocorrelation function, and spectrum. These measurable quantities depend on two factors; the first and more fundamental is the joint probability distribution for the change in phase in a given time. The second factor is the manner of operation of the interferometer in changing phase to intensity noise. We discuss both two-beam and multiple-beam interferometers and derive theoretical expressions for the above-mentioned properties of the output intensity fluctuations. It is interesting that although in both cases the output intensity fluctuations are nongaussian random processes, it is nevertheless possible to derive a number of useful theoretical results.

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  1. J. A. Armstrong and A. W. Smith, Phys. Rev. Letters 14, 68 and 208 (1965); also A. W. Smith and J. A. Armstrong, Phys. Letters 16, 38 (1965).
  2. J. A. Armstrong and A. W. Smith, Phys. Rev. 140, A155 (1965).
  3. C. Freed and H. A. Haus, Appl. Phys. Letters 6, 85 (1965); also C. Freed and H. A. Haus, Phys. Rev. 141, A287 (1966).
  4. F. T. Arecchi, A. Berne, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).
  5. D. E. McCumber, Phys. Rev. 141, A306 (1966).
  6. H. Risken, Z. Physik 186, 85 (1965).
  7. J. A. Armstrong and A. W. Smith, Appl. Phys. Letters 4, 196 (1964); see also Ref. 2 above.
  8. L. Mandel, Phys. Rev. 138, B753 (1965).
  9. H. Hodara, Proc. IEEE 53, 696 (1965).
  10. A. Blaquiere, Ann. Radioelec. 8, 36, 153 (1953).
  11. R. J. Glauber, in Quantum Optics and Electronics, C. DeWitt, A. Blandin, C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 169.
  12. W. E. Lamb, Jr., in Quantum Optics and Electronics, C. DeWitt, A. Blandin, C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 379.
  13. W. Magnus and F. Oberhettinger, Special Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949), p. 98.
  14. P. Connes, J. Phys. Radium 19, 262 (1958).

Arecchi, F. T.

F. T. Arecchi, A. Berne, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

Armstrong, J. A.

J. A. Armstrong and A. W. Smith, Phys. Rev. Letters 14, 68 and 208 (1965); also A. W. Smith and J. A. Armstrong, Phys. Letters 16, 38 (1965).

J. A. Armstrong and A. W. Smith, Phys. Rev. 140, A155 (1965).

J. A. Armstrong and A. W. Smith, Appl. Phys. Letters 4, 196 (1964); see also Ref. 2 above.

Berne, A.

F. T. Arecchi, A. Berne, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

Blaquiere, A.

A. Blaquiere, Ann. Radioelec. 8, 36, 153 (1953).

Bulamacchi, P.

F. T. Arecchi, A. Berne, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

Connes, P.

P. Connes, J. Phys. Radium 19, 262 (1958).

Freed, C.

C. Freed and H. A. Haus, Appl. Phys. Letters 6, 85 (1965); also C. Freed and H. A. Haus, Phys. Rev. 141, A287 (1966).

Glauber, R. J.

R. J. Glauber, in Quantum Optics and Electronics, C. DeWitt, A. Blandin, C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 169.

Haus, H. A.

C. Freed and H. A. Haus, Appl. Phys. Letters 6, 85 (1965); also C. Freed and H. A. Haus, Phys. Rev. 141, A287 (1966).

Hodara, H.

H. Hodara, Proc. IEEE 53, 696 (1965).

Lamb, Jr., W. E.

W. E. Lamb, Jr., in Quantum Optics and Electronics, C. DeWitt, A. Blandin, C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 379.

Magnus, W.

W. Magnus and F. Oberhettinger, Special Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949), p. 98.

Mandel, L.

L. Mandel, Phys. Rev. 138, B753 (1965).

McCumber, D. E.

D. E. McCumber, Phys. Rev. 141, A306 (1966).

Oberhettinger, F.

W. Magnus and F. Oberhettinger, Special Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949), p. 98.

Risken, H.

H. Risken, Z. Physik 186, 85 (1965).

Smith, A. W.

J. A. Armstrong and A. W. Smith, Phys. Rev. 140, A155 (1965).

J. A. Armstrong and A. W. Smith, Phys. Rev. Letters 14, 68 and 208 (1965); also A. W. Smith and J. A. Armstrong, Phys. Letters 16, 38 (1965).

J. A. Armstrong and A. W. Smith, Appl. Phys. Letters 4, 196 (1964); see also Ref. 2 above.

Other

J. A. Armstrong and A. W. Smith, Phys. Rev. Letters 14, 68 and 208 (1965); also A. W. Smith and J. A. Armstrong, Phys. Letters 16, 38 (1965).

J. A. Armstrong and A. W. Smith, Phys. Rev. 140, A155 (1965).

C. Freed and H. A. Haus, Appl. Phys. Letters 6, 85 (1965); also C. Freed and H. A. Haus, Phys. Rev. 141, A287 (1966).

F. T. Arecchi, A. Berne, and P. Bulamacchi, Phys. Rev. Letters 16, 32 (1966).

D. E. McCumber, Phys. Rev. 141, A306 (1966).

H. Risken, Z. Physik 186, 85 (1965).

J. A. Armstrong and A. W. Smith, Appl. Phys. Letters 4, 196 (1964); see also Ref. 2 above.

L. Mandel, Phys. Rev. 138, B753 (1965).

H. Hodara, Proc. IEEE 53, 696 (1965).

A. Blaquiere, Ann. Radioelec. 8, 36, 153 (1953).

R. J. Glauber, in Quantum Optics and Electronics, C. DeWitt, A. Blandin, C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 169.

W. E. Lamb, Jr., in Quantum Optics and Electronics, C. DeWitt, A. Blandin, C. Cohen-Tannoudji, Eds. (Gordon and Breach, New York, 1965), p. 379.

W. Magnus and F. Oberhettinger, Special Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949), p. 98.

P. Connes, J. Phys. Radium 19, 262 (1958).

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