Abstract

The exact expressions of the electromagnetic field pertinent to Gaussian and flattened Gaussian linearly polarized boundary distributions have been derived in closed-form terms for any point lying on the axis. The obtained results allow the fields to be predicted for an arbitrary transverse beam size. Numerical results showing the differences between the exact results and those obtained within the paraxial framework are also presented.

© 2002 Optical Society of America

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2001 (3)

2000 (2)

1999 (3)

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

H.-C. Kim, Y. H. Lee, “Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

M. Santarsiero, R. Borghi, “Correspondence between super-Gaussian and flattened Gaussian beams,” J. Opt. Soc. Am. A 16, 188–190 (1999).
[CrossRef]

1998 (3)

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

S. R. Seshadri, “Electromagnetic Gaussian beams,” J. Opt. Soc. Am. A 15, 2712–2792 (1998).
[CrossRef]

H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
[CrossRef]

1997 (1)

1996 (3)

1994 (2)

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

1988 (1)

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

1985 (1)

1975 (1)

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

1973 (1)

1972 (1)

1961 (1)

Ambrosini, D.

Bagini, V.

Borghi, R.

Bosch, S.

Carnicer, A.

Carter, W. H.

Ciattoni, A.

Crosignani, B.

De Silvestri, S.

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Di Porto, P.

Enoch, S.

Felsen, L.

Friberg, A. T.

Fukumitsu, O.

Gori, F.

Gradshtein, I. S.

I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

Gralak, B.

Hall, D. G.

Heurtley, J. C.

Heyman, H.

Joannopoulos, J.

J. Joannopoulos, R. Meade, J. Winn, Photonic Crystals (Princeton, U. Press, Princeton, N.J., 1995).

Kettunen, V.

Kim, H.-C.

H.-C. Kim, Y. H. Lee, “Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

Kuittinen, M.

Laabs, H.

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
[CrossRef]

Laporta, P.

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Lee, Y. H.

H.-C. Kim, Y. H. Lee, “Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

Magni, V.

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Marti´nez-Herrero, R.

Maystre, D.

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Meade, R.

J. Joannopoulos, R. Meade, J. Winn, Photonic Crystals (Princeton, U. Press, Princeton, N.J., 1995).

Meji´as, P. M.

Ostenberg, H.

Pacileo, A. M.

Ryzhik, I. M.

I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

Santarsiero, M.

Savchencko, A. Yu.

Schirripa Spagnolo, G.

Seshadri, S. R.

Sheppard, C. J. R.

Smith, L. W.

Svelto, O.

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Takenaka, T.

Tayeb, G.

Torok, P.

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

Turunen, J.

Vahimaa, P.

Varga, P.

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

Winn, J.

J. Joannopoulos, R. Meade, J. Winn, Photonic Crystals (Princeton, U. Press, Princeton, N.J., 1995).

Yariv, A.

Yokota, M.

Zel’dovich, B. Ya.

IEEE J. Quantum Electron. (2)

H. Laabs, A. T. Friberg, “Nonparaxial eigenmodes of stable resonators,” IEEE J. Quantum Electron. 35, 198–207 (1999).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (9)

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

Opt. Commun. (4)

H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
[CrossRef]

H.-C. Kim, Y. H. Lee, “Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

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

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Pure Appl. Opt. (1)

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

Other (4)

J. Joannopoulos, R. Meade, J. Winn, Photonic Crystals (Princeton, U. Press, Princeton, N.J., 1995).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972).

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