Abstract

A method is presented for determining the aperture apodization functions needed to optimize any given product of powers of the even-order moments of the beam intensity in the near and far zones. The results are a generalization of previous work [Pure Appl. Opt.7, 1221 (1998)] that dealt only with the far-zone moments. These methods are applied to the problem of optimizing the so-called beam propagation factor, MP2.

© 1999 Optical Society of America

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  1. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
  2. P. Bélanger, Y. Champagne, C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
    [CrossRef]
  3. R. Martinez-Herrero, P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
    [CrossRef] [PubMed]
  4. H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
    [CrossRef]
  5. At the time this paper was written, A. E. Siegman maintained an extensive list of references on beam quality and characterization at the internet address http://www-ee.stanford.edu/~siegman/ .
  6. G. N. Lawrence, “Proposed international standard for laser-beam quality falls short,” Laser Focus World109–114 (July1994).
  7. R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995).
    [CrossRef]
  8. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964). See Sec. 50.
  9. G. Gbur, P. S. Carney, “Convergence criteria and optimization techniques for beam moments,” Pure Appl. Opt. 7, 1221–1230 (1998).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996). See Secs. 4.2 and 4.3.
  11. Equation (9) reduces to the differential equation found in Ref. 9 when νl=0 for all l.
  12. N. N. Lebedev, Special Functions and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1965).
  13. C. Lanczos, The Variational Principles of Mechanics, 4th ed. (Dover, New York, 1986).

1998 (1)

G. Gbur, P. S. Carney, “Convergence criteria and optimization techniques for beam moments,” Pure Appl. Opt. 7, 1221–1230 (1998).
[CrossRef]

1995 (1)

R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995).
[CrossRef]

1994 (2)

P. Bélanger, Y. Champagne, C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

G. N. Lawrence, “Proposed international standard for laser-beam quality falls short,” Laser Focus World109–114 (July1994).

1993 (1)

1992 (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

Bélanger, P.

P. Bélanger, Y. Champagne, C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Carney, P. S.

G. Gbur, P. S. Carney, “Convergence criteria and optimization techniques for beam moments,” Pure Appl. Opt. 7, 1221–1230 (1998).
[CrossRef]

Champagne, Y.

P. Bélanger, Y. Champagne, C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Gbur, G.

G. Gbur, P. S. Carney, “Convergence criteria and optimization techniques for beam moments,” Pure Appl. Opt. 7, 1221–1230 (1998).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996). See Secs. 4.2 and 4.3.

Lanczos, C.

C. Lanczos, The Variational Principles of Mechanics, 4th ed. (Dover, New York, 1986).

Lawrence, G. N.

G. N. Lawrence, “Proposed international standard for laser-beam quality falls short,” Laser Focus World109–114 (July1994).

Lebedev, N. N.

N. N. Lebedev, Special Functions and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1965).

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964). See Sec. 50.

Martinez-Herrero, R.

R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995).
[CrossRef]

R. Martinez-Herrero, P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
[CrossRef] [PubMed]

Mejias, P. M.

R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995).
[CrossRef]

R. Martinez-Herrero, P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
[CrossRef] [PubMed]

Paré, C.

P. Bélanger, Y. Champagne, C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Piquero, G.

R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995).
[CrossRef]

Siegman, A. E.

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

Weber, H.

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

Laser Focus World (1)

G. N. Lawrence, “Proposed international standard for laser-beam quality falls short,” Laser Focus World109–114 (July1994).

Opt. Commun. (2)

R. Martinez-Herrero, G. Piquero, P. M. Mejias, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995).
[CrossRef]

P. Bélanger, Y. Champagne, C. Paré, “Beam propagation factor of diffracted laser beams,” Opt. Commun. 105, 233–242 (1994).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

Pure Appl. Opt. (1)

G. Gbur, P. S. Carney, “Convergence criteria and optimization techniques for beam moments,” Pure Appl. Opt. 7, 1221–1230 (1998).
[CrossRef]

Other (7)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996). See Secs. 4.2 and 4.3.

Equation (9) reduces to the differential equation found in Ref. 9 when νl=0 for all l.

N. N. Lebedev, Special Functions and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1965).

C. Lanczos, The Variational Principles of Mechanics, 4th ed. (Dover, New York, 1986).

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

At the time this paper was written, A. E. Siegman maintained an extensive list of references on beam quality and characterization at the internet address http://www-ee.stanford.edu/~siegman/ .

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964). See Sec. 50.

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