Abstract

A method is presented that expands the scheme of physical optics propagation beyond the Fresnel approximation to include beams that are nonparaxial. The formalism retains most of the calculation advantages of the Fresnel approach; i.e., it is based on a single Fourier transform step. The kernel of the new transformation is no longer separable in Cartesian coordinates; thus the formalism can account for astigmatic coupling effects originating purely from diffraction. The validity limits of the proposed algorithm are explored. Analytical expressions, numerical simulation results, and experimental data are compared.

© 2004 Optical Society of America

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2001 (1)

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

1999 (1)

1998 (1)

P. Varga, P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

1997 (2)

1996 (1)

1992 (1)

1991 (1)

1989 (1)

1983 (1)

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

1981 (1)

1975 (1)

L. Frank, “The properties of the Sommerfeld diffraction integral for a large aperture converging beam,” Optik (Stuttgart) 43, 149–157 (1975).

Agrawal, G. P.

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

Alonso, M. A.

An, Y.

Asatryan, A. A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Butler, D. J.

Engelberg, Y. M.

Y. M. Engelberg, S. Ruschin, “Coma aberration in diffraction from a narrow slit,” in Optical Modeling and Performance Predictions, M. A. Kahan, ed., Proc. SPIE5178, 112–123 (2003).

Fiengold, A.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Forbes, G. W.

Fradkin, Z.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Frank, L.

L. Frank, “The properties of the Sommerfeld diffraction integral for a large aperture converging beam,” Optik (Stuttgart) 43, 149–157 (1975).

Geron, A.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gordon, R. L.

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1974).

Hrynevych, M.

Kuchiki, S.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Landry, M. J.

Lawrence, G. N.

G. N. Lawrence, “Optical modeling,” in Applied Optics and Optical Engineering Series, R. R. Shanon, J. C. Wyant, eds. (Academic, San Diego, Calif., 1992), Vol. XI, pp. 125–200.

Lax, M.

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

Levy, J.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Liang, C.

Majer, D.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Matmon, G.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Mittas, A.

Ogura, A.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Ohta, K.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Oishi, I.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Rafaeli, E.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Rudman, M.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Rupert, J. W.

Ruschin, S.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Y. M. Engelberg, S. Ruschin, “Coma aberration in diffraction from a narrow slit,” in Optical Modeling and Performance Predictions, M. A. Kahan, ed., Proc. SPIE5178, 112–123 (2003).

Rutt, H. N.

Shekel, E.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Sheppard, C. J. R.

Shiraishi, K.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Southwell, W. H.

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).

Steane, A. M.

Tidhar, G.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Török, P.

P. Varga, P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

Varga, P.

P. Varga, P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

Vecht, J.

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).

Zeng, X.

Appl. Opt. (2)

IEEE Photonics Technol. Lett. (1)

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photonics Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

P. Varga, P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

Optik (Stuttgart) (1)

L. Frank, “The properties of the Sommerfeld diffraction integral for a large aperture converging beam,” Optik (Stuttgart) 43, 149–157 (1975).

Phys. Rev. A (1)

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

Other (9)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1974).

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).

E. Shekel, A. Fiengold, Z. Fradkin, A. Geron, J. Levy, G. Matmon, D. Majer, E. Rafaeli, M. Rudman, G. Tidhar, J. Vecht, S. Ruschin, “64×64fast optical switching module,” in Optical Fiber Communication Conference, Vol. 1 of 2002 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 27–29.

Y. M. Engelberg, S. Ruschin, “Coma aberration in diffraction from a narrow slit,” in Optical Modeling and Performance Predictions, M. A. Kahan, ed., Proc. SPIE5178, 112–123 (2003).

G. N. Lawrence, “Optical modeling,” in Applied Optics and Optical Engineering Series, R. R. Shanon, J. C. Wyant, eds. (Academic, San Diego, Calif., 1992), Vol. XI, pp. 125–200.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Zemax User’s Manual, http://www.zemax.com/updates/index.html ; download file: ZEMAX̲Manual̲2003-02-04.exe.

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