Abstract

We show that when an arbitrary optical beam is decomposed into a superposition of Hermite–Gaussian functions, it is sufficient to record a number of intensity profiles sampled at various transverse planes to uniquely determine the relative modal weights. This result follows from the parity relation and the nature of the Gouy phase, in addition to the orthogonality of the Fourier-transformed intensity profiles associated with the Hermite–Gaussian modes.

© 2000 Optical Society of America

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1999 (2)

1998 (1)

1997 (2)

D. Burak, R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[CrossRef]

L. W. Casperson, D. G. Hall, A. A. Tovar, “Sinusoidal-Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A 14, 3341–3348 (1997).
[CrossRef]

1995 (1)

1993 (1)

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

1989 (1)

1986 (1)

1982 (3)

1980 (1)

F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” AIEE Trans. 47, 617–644 (1928).

Binder, R.

D. Burak, R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[CrossRef]

Borghi, R.

Buckman, A. B.

A. B. Buckman, Guided-Wave Photonics (Saunders College, New York, 1992).

Burak, D.

D. Burak, R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[CrossRef]

Casperson, L. W.

Champagne, Y.

Friberg, A. T.

Gasquet, C.

C. Gasquet, P. Witomski, Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Springer, New York, 1999).

Golub, M. A.

M. A. Golub, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Sov. J. Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Gori, F.

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., A. Jeffrey, ed. (Academic, Boston, 1994).

Guattari, G.

Hall, D. G.

Johnson, E. G.

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Lü, B.

Ma, H.

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” AIEE Trans. 47, 617–644 (1928).

Prokhorov, A. M.

M. A. Golub, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Sov. J. Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., A. Jeffrey, ed. (Academic, Boston, 1994).

Santarsiero, M.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Siegman, A. E.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif.1986).

Sisakyan, I. N.

M. A. Golub, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Sov. J. Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Soifer, V. A.

M. A. Golub, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Sov. J. Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Starikov, A.

Tervonen, E.

Thompson, G. H. B.

G. H. B. Thompson, Physics of Semiconductor Laser Devices (Wiley, New York, 1980).

Tovar, A. A.

Townsend, S. W.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Turunen, J.

Witomski, P.

C. Gasquet, P. Witomski, Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Springer, New York, 1999).

Wolf, E.

Wolf, W.

Zhang, B.

AIEE Trans. (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” AIEE Trans. 47, 617–644 (1928).

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

D. Burak, R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[CrossRef]

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

Opt. Lett. (3)

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Sov. J. Quantum Electron. (1)

M. A. Golub, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Synthesis of spatial filters for investigation of the transverse mode composition of coherent radiation,” Sov. J. Quantum Electron. 12, 1208–1209 (1982).
[CrossRef]

Other (7)

A. B. Buckman, Guided-Wave Photonics (Saunders College, New York, 1992).

G. H. B. Thompson, Physics of Semiconductor Laser Devices (Wiley, New York, 1980).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif.1986).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., A. Jeffrey, ed. (Academic, Boston, 1994).

C. Gasquet, P. Witomski, Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Springer, New York, 1999).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

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