Abstract

Self-focusing has recently been used for fast saturable absorber mode locking and femtosecond pulse generation in Ti:Al2O3 lasers. We describe the operation, design, and optimization of self-focusing loss modulators for mode locking. A new formalism is developed that simplifies the treatment of self-focusing in thick nonlinear media by using a simple transform of the complex Gaussian beam parameter. Theoretical predictions are confirmed by experimental measurements.

© 1992 Optical Society of America

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    [CrossRef]
  19. T. Y. Chang, Opt. Eng. 20, 220 (1981).
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    [CrossRef]

1991

1990

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1987

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

1981

T. Y. Chang, Opt. Eng. 20, 220 (1981).

1975

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1975).
[CrossRef]

1971

E. L. Kerr, Phys. Rev. A 4, 1195 (1971).
[CrossRef]

1966

H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

1965

V. I. Talanov, Sov. Phys. JETP Lett. 2, 218 (1965).

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

1964

R. Y. Chiao, E. Garmine, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

Chang, T. Y.

T. Y. Chang, Opt. Eng. 20, 220 (1981).

Chen, S.

Chiao, R. Y.

R. Y. Chiao, E. Garmine, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Couillaud, B.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Diodati, F. P.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

Fujimoto, J. G.

Gabetta, G.

Garmine, E.

R. Y. Chiao, E. Garmine, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Goldblatt, N.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, W. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Huang, D.

Ippen, E. P.

Jacobson, J.

Kean, P. N.

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Kerr, E. L.

E. L. Kerr, Phys. Rev. A 4, 1195 (1971).
[CrossRef]

Khokhlov, R. V.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).

Lariontsev, E. G.

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1975).
[CrossRef]

Marconi, M. C.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

Martinez, O. E.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

Negus, D. K.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Piché, M.

Ramaswamy, M.

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, W. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Salin, F.

Serkin, V. N.

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1975).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, W. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sibbett, W.

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, W. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Spence, D.

Spinelli, L.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Squier, J.

Sukhorukov, A. P.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

Talanov, V. I.

V. I. Talanov, Sov. Phys. JETP Lett. 2, 218 (1965).

Townes, C. H.

R. Y. Chiao, E. Garmine, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Van Stryland, W. W.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, W. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Wang, J.

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Appl. Phys. Lett.

H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. C. Marconi, O. E. Martinez, F. P. Diodati, Opt. Commun. 63, 211 (1987).
[CrossRef]

M. Piché, Opt. Commun. 86, 156 (1991).
[CrossRef]

Opt. Eng.

T. Y. Chang, Opt. Eng. 20, 220 (1981).

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, W. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Opt. Lett.

Phys. Rev. A

E. L. Kerr, Phys. Rev. A 4, 1195 (1971).
[CrossRef]

Phys. Rev. Lett.

R. Y. Chiao, E. Garmine, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Sov. J. Quantum Electron.

E. G. Lariontsev, V. N. Serkin, Sov. J. Quantum Electron. 5, 796 (1975).
[CrossRef]

Sov. Phys. JETP Lett.

V. I. Talanov, Sov. Phys. JETP Lett. 2, 218 (1965).

Other

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

S. A. Akhmanov, R. V. Khokhlov, A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

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Figures (3)

Fig. 1
Fig. 1

Z-scan data (dotted curves) and theoretical prediction (solid curves) for two thicknesses of BK7 glass. For z = 0 the focal plane coincides with the center of the glass and z increases as the medium is moved toward the aperture, which was placed 10 cm after the focal plane. The parameters are λ = 625 nm, n0 = 1.51, n2 = 3.45 × 10−20 m2/W, a = 5.35, b = 0.44 mm, and normalized aperture d/2w = 0.68. For the thinner sample [curves labeled (a)], l = 3.175 mm and l/n0 = 4.76b0; for the thicker sample [curves labeled (b)], l = 6.35 mm and l/n0 = 9.53b0. The pulse energy was 11 nJ, and the peak power was P = 0.88 MW

Fig. 2
Fig. 2

Two self-focusing loss modulator designs that maximize saturable absorber action.

Fig. 3
Fig. 3

(a) Calculated linear transmission and (b) the nonlinear loss modulation versus normalized aperture size. Given the same parameters, the two modulators shown in Fig. 2 perform identically. The four curves in (b) are plotted with nonlinear medium thicknesses of 0.5n0b, 1n0b, 2n0b, and 4n0b. The normalized beam power is set to P/Pcr = 0.2, which is equivalent to the following parameters: λ = 800 nm, n0 = 1.51, n2 = 3.45 × 10−20 m2/W (BK7 glass), a = 5.35, Pcr = 2.62 MW, and P = 525 kW.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

n ( r ) = n 0 + 2 n 2 P π w 2 exp [ - 2 ( r / w ) 2 ] n 0 ( 1 - r 2 2 h sf 2 ) ,
h sf = w 2 2 π a n 0 2 n 2 P .
d q d z = 1 n 0 + q 2 n 0 h sf 2 .
E ( r ) = E 0 exp ( k p i r 2 2 - j k p r r 2 2 ) = E 0 exp ( - r 2 w 2 - j k r 2 2 R ) .
d p r d z = - p r 2 n 0 + ( ξ p i ) 2 n 0 ,
ξ d p i d z = - ξ p i 2 p r n 0 ,
ξ 1 - P P cr ,
P cr a λ 2 8 π n 0 n 2 ,
q = Ξ ^ - 1 M ^ Ξ ^ q ,
Ξ ^ q 1 Re ( 1 / q ) + j ξ Im ( 1 / q ) ,
Ξ ^ - 1 q 1 Re ( 1 / q ) + j ξ - 1 Im ( 1 / q ) ,

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