Abstract

An optical communication channel is analyzed, in which a light beam is amplitude modulated at the source by a filter of continuously variable transmittance, and the detector counts the received photons. Such a communication channel has intrinsic noise limitations because there is not a one-to-one correspondence between the modulated beam power and the number of counts registered. The information rates achievable with single-mode and multimode lasers are evaluated as functions of the mean number <i>N</i> of detected photons per symbol, for several different input statistics. For large <i>N</i> the information rate increases logarithmically with N. It is shown that, when the symbol length is short, there is a minimum number of independent modes for which the multimode laser gives a greater information rate than the single-mode laser, if the laser power is equally divided among all the modes, and the power per mode is regarded as constant. However, for even moderate numbers of detected photons per symbol, this minimum number of modes is so great that the single-mode laser is to be preferred. When the light beam is derived from a thermal source, the information rate in the channel is, in effect, governed by the same equations as those for the single-mode laser, so long as the detector area is limited to a coherence area.

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  2. T. E. Stern, Trans. IRE IT-6, 435 (1960).
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  26. R. J. Glauber, Phys. Rev. 131, 2766 (1963).
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Bédard, G.

G. Bédard, J. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

Bolgiano, Jr., L. P.

L. P. Bolgiano, Jr. and L. F. Jelsma, Proc. IEEE 52, 218 (1964).

B. E. Goodwin and L. P. Bolgiano, Jr., Proc. IEEE 53, 1745 (1965).

Chang, J.

G. Bédard, J. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

Emde, F.

See for example, E. Jahnke and F. Emde, Tables of Functions, 4th ed. (Dover, New York, 1945).

Fillmore, G. L.

G. L. Fillmore and G. Lachs, IEEE Trans. IT-15, 465 (1969).

Francia, G. Toraldo di

G. Toraldo di Francia, Opt. Acta 2, 5 (1955).

Gabor, D.

D. Gabor, Phil. Mag. 41, 1161 (1950).

Glauber, R. J.

R. J. Glauber, Phys. Rev. 131, 2766 (1963).

R. J. Glauber, in Quantumn Optics and Electronics, edited by C. deWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.

Goodwin, B. E.

B. E. Goodwin and L. P. Bolgiano, Jr., Proc. IEEE 53, 1745 (1965).

Gordon, J. P.

J. P. Gordon, in Quantumn Electronics and Coherent Light, edited by C. H. Townes and P. A. Miles (Academic, New York, 1962), p. 156.

J. P. Gordon, in Advances in Quantum Electronics, edited by J. R. Singer (Columbia University Press, New York, 1961), p. 509.

J. P. Gordon, Proc. IRE 50, 1898 (1962).

J. P. Gordon, W. H. Louisell, and L. R. Walker, Phys. Rev. 129, 481 (1963).

Hisdal, E.

E. Hisdal, J. Opt. Soc. Am. 55, 1446 (1965); 57, 35 (1967) 59, 921 (1969).

Hodara, H.

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

Jahnke, E.

See for example, E. Jahnke and F. Emde, Tables of Functions, 4th ed. (Dover, New York, 1945).

Jelsma, L. F.

L. P. Bolgiano, Jr. and L. F. Jelsma, Proc. IEEE 52, 218 (1964).

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 50, 1166 (1960); 52, 493 (1962).

Keeping, E. S.

See, for example, J. F. Kenney and E. S. Keeping, Mathematics of Statistics, 2nd ed. (Van Nostrand, New York, 1951), Pt. II, Ch. 1.

Kelley, P. L.

P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).

Kenney, J. F.

See, for example, J. F. Kenney and E. S. Keeping, Mathematics of Statistics, 2nd ed. (Van Nostrand, New York, 1951), Pt. II, Ch. 1.

Kleiner, W. H.

P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).

Lachs, G.

G. L. Fillmore and G. Lachs, IEEE Trans. IT-15, 465 (1969).

Lasher, G. J.

G. J. Lasher, in Ref. 3, p. 520.

Louisell, W. H.

J. P. Gordon, W. H. Louisell, and L. R. Walker, Phys. Rev. 129, 481 (1963).

W. H. Louisell, A. Yariv, and A. E. Siegman, Phys. Rev. 124, 1646 (1961).

Mandel, L.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

L. Mandel and D. Meltzer, Phys. Rev. 188, 198 (1969).

L. Mandel, J. Opt. Soc. Am. 51, 797 (1961).

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).

L. Mandel, in Progress in Optics, II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 181.

L. Mandel, Proc. Phys. Soc. (London) 74, 233 (1959).

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

L. Mandel and E. Wolf, Phys. Rev. 149, 1033 (1966).

G. Bédard, J. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).

Meltzer, D.

L. Mandel and D. Meltzer, Phys. Rev. 188, 198 (1969).

Mollow, B. R.

B. R. Mollow and R. J. Walker, Phys. Rev. 160, 1076, 1097 (1967).

Shannon, C. E.

C. E. Shannon, Bell System Tech. J. 27, 376, 623 (1948).

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, Phys. Rev. 124, 1646 (1961).

Stern, T. E.

T. E. Stern, Trans. IRE IT-6, 435 (1960).

Sudarshan, E. C. G.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).

E. C. G. Sudarshan, Phys. Rev. Letters 10, 277 (1963).

Walker, L. R.

J. P. Gordon, W. H. Louisell, and L. R. Walker, Phys. Rev. 129, 481 (1963).

Walker, R. J.

B. R. Mollow and R. J. Walker, Phys. Rev. 160, 1076, 1097 (1967).

Wolf, E.

L. Mandel and E. Wolf, Phys. Rev. 149, 1033 (1966).

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, Phys. Rev. 124, 1646 (1961).

Other (33)

D. Gabor, Phil. Mag. 41, 1161 (1950).

T. E. Stern, Trans. IRE IT-6, 435 (1960).

J. P. Gordon, in Advances in Quantum Electronics, edited by J. R. Singer (Columbia University Press, New York, 1961), p. 509.

G. J. Lasher, in Ref. 3, p. 520.

J. P. Gordon, Proc. IRE 50, 1898 (1962).

J. P. Gordon, in Quantumn Electronics and Coherent Light, edited by C. H. Townes and P. A. Miles (Academic, New York, 1962), p. 156.

L. P. Bolgiano, Jr. and L. F. Jelsma, Proc. IEEE 52, 218 (1964).

B. E. Goodwin and L. P. Bolgiano, Jr., Proc. IEEE 53, 1745 (1965).

G. Toraldo di Francia, Opt. Acta 2, 5 (1955).

R. C. Jones, J. Opt. Soc. Am. 50, 1166 (1960); 52, 493 (1962).

E. Hisdal, J. Opt. Soc. Am. 55, 1446 (1965); 57, 35 (1967) 59, 921 (1969).

G. L. Fillmore and G. Lachs, IEEE Trans. IT-15, 465 (1969).

C. E. Shannon, Bell System Tech. J. 27, 376, 623 (1948).

See, for example, J. F. Kenney and E. S. Keeping, Mathematics of Statistics, 2nd ed. (Van Nostrand, New York, 1951), Pt. II, Ch. 1.

W. H. Louisell, A. Yariv, and A. E. Siegman, Phys. Rev. 124, 1646 (1961).

J. P. Gordon, W. H. Louisell, and L. R. Walker, Phys. Rev. 129, 481 (1963).

B. R. Mollow and R. J. Walker, Phys. Rev. 160, 1076, 1097 (1967).

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958).

L. Mandel, in Progress in Optics, II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 181.

L. Mandel, E. C. G. Sudarshan, and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).

P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).

R. J. Glauber, in Quantumn Optics and Electronics, edited by C. deWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.

L. Mandel and D. Meltzer, Phys. Rev. 188, 198 (1969).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

E. C. G. Sudarshan, Phys. Rev. Letters 10, 277 (1963).

R. J. Glauber, Phys. Rev. 131, 2766 (1963).

L. Mandel and E. Wolf, Phys. Rev. 149, 1033 (1966).

See for example, E. Jahnke and F. Emde, Tables of Functions, 4th ed. (Dover, New York, 1945).

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

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

L. Mandel, Proc. Phys. Soc. (London) 74, 233 (1959).

G. Bédard, J. Chang, and L. Mandel, Phys. Rev. 160, 1496 (1967).

L. Mandel, J. Opt. Soc. Am. 51, 797 (1961).

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