Abstract

We have constructed a blue laser source consisting of an amplified, grating tuned diode laser that is frequency doubled by a KNbO3 crystal in a compact standing wave cavity and produces as much as 200 mW of internal second-harmonic power. We have analyzed the unusual characteristics of this standing wave cavity to clarify the advantages and disadvantages of this configuration as an alternative to a ring cavity for second-harmonic generation. We emphasize its efficiency and stability and the fact that it has an inherent walk-off compensation, similar to twin crystal configurations. We demonstrate its utility for laser cooling and trapping of earth alkalis by stabilizing the laser to the 461-nm transition of strontium, using a heat pipe, and then forming a magneto-optic trap of strontium from a Zeeman-slowed atomic beam.

© 2004 Optical Society of America

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  3. Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
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  8. T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  38. J. Zimmermann, J. Struckmeier, M. R. Hofmann, J.-P. Meyn, “Tunable blue laser based on intracavity frequency doubling with a fan-structured periodically poled LiTaO3 crystal,” Opt. Lett. 27, 604–606 (2002).
    [CrossRef]
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2003 (4)

H. Katori, M. Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
[CrossRef] [PubMed]

X. Xu, T. H. Loftus, J. L. Hall, A. Gallagher, J. Ye, “Cooling and trapping of atomic strontium,” J. Opt. Soc. Am. B 20, 968–976 (2003).
[CrossRef]

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

C. Batchelor, W. J. Chung, S. Shen, A. Jha, “Enhanced room-temperature emission in Cr4+ ions containing alumino-silicate glasses,” Appl. Phys. Lett. 82, 4035–4037 (2003).
[CrossRef]

2002 (2)

J. Zimmermann, J. Struckmeier, M. R. Hofmann, J.-P. Meyn, “Tunable blue laser based on intracavity frequency doubling with a fan-structured periodically poled LiTaO3 crystal,” Opt. Lett. 27, 604–606 (2002).
[CrossRef]

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

2001 (2)

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

I. Jovanovic, B. J. Comaskey, D. M. Pennington, “Angular effects and beam quality in optical parametric amplification,” J. Appl. Phys. 90, 4328–4337 (2001).
[CrossRef]

1999 (4)

I. Juwiler, A. Arie, A. Skliar, G. Rosenman, “Efficient quasi-phase-matched frequency doubling with phase compensation by a wedged crystal in a standing-wave external cavity,” Opt. Lett. 24, 1236–1238 (1999).
[CrossRef]

H. Katori, T. Ido, Y. Isoya, M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

1997 (3)

1995 (2)

L. Shiv, J. L. Sørensen, E. S. Polzik, “Inhibited light-induced absorption in KNbO3,” Opt. Lett. 20, 2270–2272 (1995).
[CrossRef] [PubMed]

J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for cw 10.2 μm SHG,” Opt. Commun. 119, 320–326 (1995).
[CrossRef]

1994 (3)

1993 (1)

U. Sterr, K. Sengstock, J.-H. Müller, W. Ertmer, “High-resolution isotope shift measurement of the MgI 1S0–3P1 intercombination transition,” Appl. Phys. B 56, 62–64 (1993).
[CrossRef]

1992 (3)

1991 (2)

E. S. Polzik, H. J. Kimble, “Frequency doubling with KNbO3 in an external cavity,” Opt. Lett. 16, 1400–1402 (1991).
[CrossRef] [PubMed]

S. K. Wong, G. Fournier, P. Mathieu, P. Pace, “Beam divergence effects on nonlinear frequency mixing,” J. Appl. Phys. 71, 1091–1101 (1991).
[CrossRef]

1990 (1)

L. K. Samanta, T. Yanagawa, Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

1988 (1)

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

1979 (1)

V. D. Volosov, A. G. Kalintsev, V. N. Krylov, “Phase effects in a double-pass frequency doubler,” Sov. Tech. Phys. Lett. 5, 5–7 (1979).

1977 (1)

M. H. Dunn, A. I. Ferguson, “Coma compensation in off-axis laser resonators,” Opt. Commun. 20, 214–218 (1977).
[CrossRef]

1976 (1)

V. D. Volosov, A. G. Kalintsev, “Optimum optical second-harmonic generation in tandem crystals,” Sov. Tech. Phys. Lett. 2, 373–375 (1976).

1968 (1)

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

Alford, W. J.

Arie, A.

Arimondo, E.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Armstrong, D. J.

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

Batchelor, C.

C. Batchelor, W. J. Chung, S. Shen, A. Jha, “Enhanced room-temperature emission in Cr4+ ions containing alumino-silicate glasses,” Appl. Phys. Lett. 82, 4035–4037 (2003).
[CrossRef]

Bergquist, J. C.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Bernard, J. C.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Biaggio, I.

Bidel, Y.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Bode, M.

M. Bode, I. Freitag, A. Tünnermann, H. Welling, “Frequency-tunable 500-mW continuous-wave all-solid-state single-frequency source in the blue spectral region,” Opt. Lett. 22, 1220–1222 (1997).
[CrossRef] [PubMed]

M. Bode, “Abstimmbare Einfrequenz-Strahlquellen honer Stabilität im infraroten, sichtbaren und ultravioletten Spektralbereich,” Ph.D. dissertation (Universität Hannover, Hannover, Germany, 1999).

Bonnenberger, R.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Boulanger, B.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Boyd, G. D.

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1993).

Busse, L. E.

L. E. Busse, L. Goldberg, M. R. Surette, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

Byer, R. L.

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

Cabirol, X.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Chen, Y. C.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Chung, W. J.

C. Batchelor, W. J. Chung, S. Shen, A. Jha, “Enhanced room-temperature emission in Cr4+ ions containing alumino-silicate glasses,” Appl. Phys. Lett. 82, 4035–4037 (2003).
[CrossRef]

Comaskey, B. J.

I. Jovanovic, B. J. Comaskey, D. M. Pennington, “Angular effects and beam quality in optical parametric amplification,” J. Appl. Phys. 90, 4328–4337 (2001).
[CrossRef]

Curtis, E. A.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Delande, D.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Diddams, S. A.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Dinneen, T. P.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Drullinger, R. E.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Dunn, M. H.

M. H. Dunn, A. I. Ferguson, “Coma compensation in off-axis laser resonators,” Opt. Commun. 20, 214–218 (1977).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

Ertmer, W.

U. Sterr, K. Sengstock, J.-H. Müller, W. Ertmer, “High-resolution isotope shift measurement of the MgI 1S0–3P1 intercombination transition,” Appl. Phys. B 56, 62–64 (1993).
[CrossRef]

Ferguson, A. I.

M. H. Dunn, A. I. Ferguson, “Coma compensation in off-axis laser resonators,” Opt. Commun. 20, 214–218 (1977).
[CrossRef]

Fève, J. P.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Fournier, G.

S. K. Wong, G. Fournier, P. Mathieu, P. Pace, “Beam divergence effects on nonlinear frequency mixing,” J. Appl. Phys. 71, 1091–1101 (1991).
[CrossRef]

Freitag, I.

Gallagher, A.

X. Xu, T. H. Loftus, J. L. Hall, A. Gallagher, J. Ye, “Cooling and trapping of atomic strontium,” J. Opt. Soc. Am. B 20, 968–976 (2003).
[CrossRef]

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Goldberg, L.

L. E. Busse, L. Goldberg, M. R. Surette, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

Günter, P.

Gupta, P.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Hall, J. L.

X. Xu, T. H. Loftus, J. L. Hall, A. Gallagher, J. Ye, “Cooling and trapping of atomic strontium,” J. Opt. Soc. Am. B 20, 968–976 (2003).
[CrossRef]

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Henking, R.

Hofmann, M. R.

Hollberg, L.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Honda, K.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Ido, T.

H. Katori, T. Ido, Y. Isoya, M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Isoya, Y.

H. Katori, T. Ido, Y. Isoya, M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Itano, W. M.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Jha, A.

C. Batchelor, W. J. Chung, S. Shen, A. Jha, “Enhanced room-temperature emission in Cr4+ ions containing alumino-silicate glasses,” Appl. Phys. Lett. 82, 4035–4037 (2003).
[CrossRef]

Jovanovic, I.

I. Jovanovic, B. J. Comaskey, D. M. Pennington, “Angular effects and beam quality in optical parametric amplification,” J. Appl. Phys. 90, 4328–4337 (2001).
[CrossRef]

Juwiler, I.

Kaiser, R.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Kalintsev, A. G.

V. D. Volosov, A. G. Kalintsev, V. N. Krylov, “Phase effects in a double-pass frequency doubler,” Sov. Tech. Phys. Lett. 5, 5–7 (1979).

V. D. Volosov, A. G. Kalintsev, “Optimum optical second-harmonic generation in tandem crystals,” Sov. Tech. Phys. Lett. 2, 373–375 (1976).

Katori, H.

H. Katori, M. Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
[CrossRef] [PubMed]

H. Katori, T. Ido, Y. Isoya, M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Kerkoc, P.

Killian, T. C.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Kimble, H. J.

Klappauf, B.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Kleinman, D. A.

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Komori, K.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Kozlovsky, W. J.

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

Krylov, V. N.

V. D. Volosov, A. G. Kalintsev, V. N. Krylov, “Phase effects in a double-pass frequency doubler,” Sov. Tech. Phys. Lett. 5, 5–7 (1979).

Kumakura, M.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Kurosu, T.

T. Kurosu, F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys. 31, 908–912 (1992).
[CrossRef]

Kürz, P.

Kuwata-Gonokami, M.

H. Katori, T. Ido, Y. Isoya, M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Labeyrie, G.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Laha, S.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Lee, W. D.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Lodahl, P.

P. Lodahl, J. L. Sørensen, E. S. Polzik, “High efficiency second harmonic generation with a low power diode laser,” Appl. Phys. B 64, 383–386 (1997).
[CrossRef]

Loftus, T. H.

Mabuchi, H.

Maki, K.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Marnier, G.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Martinez, Y. N.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Mathieu, P.

S. K. Wong, G. Fournier, P. Mathieu, P. Pace, “Beam divergence effects on nonlinear frequency mixing,” J. Appl. Phys. 71, 1091–1101 (1991).
[CrossRef]

Ménaert, B.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Meyn, J.-P.

Mickelson, P. G.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Miniatura, C.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Mlynek, J.

Müller, J.-H.

U. Sterr, K. Sengstock, J.-H. Müller, W. Ertmer, “High-resolution isotope shift measurement of the MgI 1S0–3P1 intercombination transition,” Appl. Phys. B 56, 62–64 (1993).
[CrossRef]

Nabors, C. D.

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

Nagel, S. B.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Oates, C. W.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Ovsiannikov, V. D.

H. Katori, M. Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
[CrossRef] [PubMed]

Pace, P.

S. K. Wong, G. Fournier, P. Mathieu, P. Pace, “Beam divergence effects on nonlinear frequency mixing,” J. Appl. Phys. 71, 1091–1101 (1991).
[CrossRef]

Pal’chikov, V. G.

H. Katori, M. Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
[CrossRef] [PubMed]

Paschotta, R.

R. Paschotta, P. Kürz, R. Henking, S. Schiller, J. Mlynek, “82% Efficient continuous-wave frequency doubling of 1.06 μm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[CrossRef] [PubMed]

R. Paschotta, “Einfach und doppeltresonante monolithische, Frequenzverdoppler für Experimente, in der Quantenoptik,” Ph.D. dissertation (Universität Konstanz, Konstanz, Germany, 1994).

Pennington, D. M.

I. Jovanovic, B. J. Comaskey, D. M. Pennington, “Angular effects and beam quality in optical parametric amplification,” J. Appl. Phys. 90, 4328–4337 (2001).
[CrossRef]

Polzik, E. S.

Raymond, T. D.

Rosenman, G.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Samanta, L. K.

L. K. Samanta, T. Yanagawa, Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

Schiller, S.

Sengstock, K.

U. Sterr, K. Sengstock, J.-H. Müller, W. Ertmer, “High-resolution isotope shift measurement of the MgI 1S0–3P1 intercombination transition,” Appl. Phys. B 56, 62–64 (1993).
[CrossRef]

Shen, S.

C. Batchelor, W. J. Chung, S. Shen, A. Jha, “Enhanced room-temperature emission in Cr4+ ions containing alumino-silicate glasses,” Appl. Phys. Lett. 82, 4035–4037 (2003).
[CrossRef]

Shimizu, F.

T. Kurosu, F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys. 31, 908–912 (1992).
[CrossRef]

Shiv, L.

Simien, C. E.

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

Skliar, A.

Smith, A. V.

Sørensen, J. L.

P. Lodahl, J. L. Sørensen, E. S. Polzik, “High efficiency second harmonic generation with a low power diode laser,” Appl. Phys. B 64, 383–386 (1997).
[CrossRef]

L. Shiv, J. L. Sørensen, E. S. Polzik, “Inhibited light-induced absorption in KNbO3,” Opt. Lett. 20, 2270–2272 (1995).
[CrossRef] [PubMed]

Sterr, U.

U. Sterr, K. Sengstock, J.-H. Müller, W. Ertmer, “High-resolution isotope shift measurement of the MgI 1S0–3P1 intercombination transition,” Appl. Phys. B 56, 62–64 (1993).
[CrossRef]

Struckmeier, J.

Surette, M. R.

L. E. Busse, L. Goldberg, M. R. Surette, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

Takahashi, Y.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Takamoto, M.

H. Katori, M. Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
[CrossRef] [PubMed]

Takano, T.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Takasu, Y.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Tünnermann, A.

Udem, Th.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Vogel, K. R.

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

K. R. Vogel, “Laser cooling on a narrow atomic transition and measurement of the two-body cold collision loss rate in a strontium magneto-optical trap,” Ph.D dissertation (University of Colorado, Boulder, Colo., 1999).

Volosov, V. D.

V. D. Volosov, A. G. Kalintsev, V. N. Krylov, “Phase effects in a double-pass frequency doubler,” Sov. Tech. Phys. Lett. 5, 5–7 (1979).

V. D. Volosov, A. G. Kalintsev, “Optimum optical second-harmonic generation in tandem crystals,” Sov. Tech. Phys. Lett. 2, 373–375 (1976).

Welling, H.

Wilkowski, D.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Wong, S. K.

S. K. Wong, G. Fournier, P. Mathieu, P. Pace, “Beam divergence effects on nonlinear frequency mixing,” J. Appl. Phys. 71, 1091–1101 (1991).
[CrossRef]

Wu, L.-S.

Xu, X.

Yabuzaki, T.

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

Yamamoto, Y.

L. K. Samanta, T. Yanagawa, Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

Yanagawa, T.

L. K. Samanta, T. Yanagawa, Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

Ye, J.

Zimmermann, J.

Zondy, J. J.

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Zondy, J.-J.

J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for cw 10.2 μm SHG,” Opt. Commun. 119, 320–326 (1995).
[CrossRef]

Zysset, B.

Appl. Phys. B (2)

U. Sterr, K. Sengstock, J.-H. Müller, W. Ertmer, “High-resolution isotope shift measurement of the MgI 1S0–3P1 intercombination transition,” Appl. Phys. B 56, 62–64 (1993).
[CrossRef]

P. Lodahl, J. L. Sørensen, E. S. Polzik, “High efficiency second harmonic generation with a low power diode laser,” Appl. Phys. B 64, 383–386 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

C. Batchelor, W. J. Chung, S. Shen, A. Jha, “Enhanced room-temperature emission in Cr4+ ions containing alumino-silicate glasses,” Appl. Phys. Lett. 82, 4035–4037 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

J. Appl. Phys. (4)

I. Jovanovic, B. J. Comaskey, D. M. Pennington, “Angular effects and beam quality in optical parametric amplification,” J. Appl. Phys. 90, 4328–4337 (2001).
[CrossRef]

S. K. Wong, G. Fournier, P. Mathieu, P. Pace, “Beam divergence effects on nonlinear frequency mixing,” J. Appl. Phys. 71, 1091–1101 (1991).
[CrossRef]

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

L. E. Busse, L. Goldberg, M. R. Surette, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

T. Kurosu, F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys. 31, 908–912 (1992).
[CrossRef]

Opt. Commun. (4)

L. K. Samanta, T. Yanagawa, Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for cw 10.2 μm SHG,” Opt. Commun. 119, 320–326 (1995).
[CrossRef]

M. H. Dunn, A. I. Ferguson, “Coma compensation in off-axis laser resonators,” Opt. Commun. 20, 214–218 (1977).
[CrossRef]

J. P. Fève, J. J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, “Optimized blue light generation in optically contacted walk-off compensated RbTiOAsO4 and KTiOP1-yAsyO4,” Opt. Commun. 161, 359–369 (1999).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (1)

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Phys. Rev. Lett. (5)

Th. Udem, S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, L. Hollberg, “Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser,” Phys. Rev. Lett. 86, 4996–4999 (2001).
[CrossRef] [PubMed]

Y. Takasu, K. Maki, K. Komori, T. Takano, K. Honda, M. Kumakura, T. Yabuzaki, Y. Takahashi, “Spin-singlet Bose-Einstein condensation of two-electron atoms,” Phys. Rev. Lett. 91, 040404 (2003).
[CrossRef] [PubMed]

H. Katori, T. Ido, Y. Isoya, M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

H. Katori, M. Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
[CrossRef] [PubMed]

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, R. Kaiser, “Coherent light transport in a cold strontium cloud,” Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef] [PubMed]

Sov. Tech. Phys. Lett. (2)

V. D. Volosov, A. G. Kalintsev, “Optimum optical second-harmonic generation in tandem crystals,” Sov. Tech. Phys. Lett. 2, 373–375 (1976).

V. D. Volosov, A. G. Kalintsev, V. N. Krylov, “Phase effects in a double-pass frequency doubler,” Sov. Tech. Phys. Lett. 5, 5–7 (1979).

Other (7)

M. Bode, “Abstimmbare Einfrequenz-Strahlquellen honer Stabilität im infraroten, sichtbaren und ultravioletten Spektralbereich,” Ph.D. dissertation (Universität Hannover, Hannover, Germany, 1999).

R. Paschotta, “Einfach und doppeltresonante monolithische, Frequenzverdoppler für Experimente, in der Quantenoptik,” Ph.D. dissertation (Universität Konstanz, Konstanz, Germany, 1994).

C. E. Simien, Y. C. Chen, P. Gupta, S. Laha, Y. N. Martinez, P. G. Mickelson, S. B. Nagel, T. C. Killian, “Using absorption imaging to study ion dynamics in an ultracold neutral plasma,” http://arxiv.org/abs/physics/0310017 , accessed 20December, 2003.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1993).

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

K. R. Vogel, “Laser cooling on a narrow atomic transition and measurement of the two-body cold collision loss rate in a strontium magneto-optical trap,” Ph.D dissertation (University of Colorado, Boulder, Colo., 1999).

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Schematic of singly resonant cavity design, showing the path of the fundamental and the SH waves. Surfaces are S1, dichroic beam splitter; S2, spherical mirror input coupler; S3, AR surface coated for both wavelengths; S4, HR surface coated for both wavelengths.

Fig. 2
Fig. 2

Typical on-resonance reflection coefficients, R versus γP in for ℒ = 0.5% and input couplers R c = 96.5% (dashed curves), 97.5% (dotted curve), and 98.5% (solid curve). (a) Dependence of overall conversion efficiency η = P /P in on input coupler reflectivity for γP in = 0.522 × 10-3 and ℒ = 0.5% (dashed-dotted curve) and ℒ = 1.0% (dashed-double-dotted curve).

Fig. 3
Fig. 3

(a) Beam radii at the crystal face and at the input coupler scaled to confocal value w cf at the crystal face as a function of scaled cavity length H. (b) Corresponding confocal waist versus ℛ.

Fig. 4
Fig. 4

(a) Comparison of overall efficiency (rising curves, left scale) and optimum input coupler reflectivity (descending curves, right scale) versus power-conversion factor for various parasitic loss values: ℒ = 0.25% (dotted curves), 0.5% (dashed-dotted curves), 1.0% (dashed curves), and 2% (solid curves). (b) Ratio s of efficiency versus loss to conversion [from Eq. (6)].

Fig. 5
Fig. 5

Effective propagation path for the circulating fundamental and the SH in the unfolded cavity with relative phase shift ϕ r , fundamental walk-off angle ρ, and crystal cut angle Φ. A 1 is the approximately constant, vertically polarized fundamental (slanted, barred lines). A 2(y, x) are horizontally polarized SH (solid lines with filled circles) fields at various points in the propagation as referred to in the text. The output SH field at x = 2L c is the coherent sum of the contribution produced in each half. Axes show relative orientations of crystal’s principal axes for each half.

Fig. 6
Fig. 6

Comparison of relative SH conversion factor γ calculated by the semianalytic result (solid curves) with that of the heuristic equation (dotted curves) for a single pass through length L c of the crystal for (a) case I with β = 0.1, (b) case II with β = 2, and (c) case III with β = 1. The vertical scale is arbitrary and serves only to show the change in form because for a given β, L c and ρ can be chosen to make all three cases visible in the same figure.

Fig. 7
Fig. 7

Comparison of SH conversion double-pass tuning curves (solid curves) for case I (β = 0.1) and case II (β = 5) for three reflection phase shifts (ϕ r = 0, π/2, π). Each figure is normalized to the single-pass case of length L c (dashed curve) and shown with the single-pass case of length 2L c (dotted curve).

Fig. 8
Fig. 8

Ratio of maximum double-pass SHG conversion to the single pass versus relative phase mismatch ϕ r caused by the HR crystal coating for β = 2.

Fig. 9
Fig. 9

Typical cavity scan of a slightly nondegenerate cavity, showing two TEM00 modes with the higher-order modes separated by roughly FSR/4.

Fig. 10
Fig. 10

Effect of thermal lensing on (a) the waist in the crystal, (b) the beam radius at the input coupler, and (c) the fraction of the cold-cavity mode that will still couple to the thermally altered modes versus scaled cavity length for various thermal index gradients . Solid curves, the cold cavity ( = 0) case shown in Fig. 3. Dashed (dotted) curves, positive (negative) thermal index gradients of values = +(-)0.1, +(-)0.2, and +(-)0.25 cm-2 moving out from the solid curves.

Fig. 11
Fig. 11

Example of CCD images of the SH far-field intensity profile along with curves that show the y axis cut through the center for ΔkL c /2π ∼ 1.72 (right) and for the maximum at ΔkL c /2π ∼ 0.47 (left).

Fig. 12
Fig. 12

Comparison of temperature-tuning curve Pk(T)L c ] for the adjusted experimental data (diamonds), the analytic equation (solid curve), and the nearly indistinguishable numerical integration (dashed curve). Upper and lower axes, measured temperature and associated phase mismatch, respectively, as related in Appendix A. Data are multiplied by 6 to permit a qualitative comparison with the calculations.

Fig. 13
Fig. 13

Comparison of (a) the y-axis modulation of SH intensity profiles measured by a CCD camera in the far field with the profiles predicted by (b) Eq. (14) and by (c) numerical integration of Eqs. (11) and (12) as we vary Δk. The camera image plane is ∼90 cm from the waist in the crystal, and profiles in (b) and (c) were obtained from the Fourier transform of the near-field calculations.

Fig. 14
Fig. 14

Experimental data (diamonds) for (a) conversion efficiency η = P /P in versus mode-matched power P in and (b) the experimental reflected power ratio (on resonance to off resonance) versus total power in P in/∊. Shown for comparison are curves calculated with (solid curves, see text) and without (dotted curves) BLIIRA.

Fig. 15
Fig. 15

Depiction of axis definition for relating crystallographic axes (a, b, c) to lab axes (x, y, z) defined by the chosen polarization (y) and propagation (x) directions. This example is appropriate for KNbO3 of type I (e + e = o) phase matching described in the text. Here Φ is the phase-matching angle in the ab plane, ρ is the walk-off angle, S is the Poynting vector, k is the wave vector, D is the displacement vector, and E ω and E are the fundamental and the SH electric field vectors, respectively. All vectors are in the ab plane, except for E , which lies along the -z axis.

Fig. 16
Fig. 16

Temperature dependencies of (top) the phase mismatch (1/2π)∂Δk/∂T and (bottom) the effective index of refraction ∂n y /∂T on wavelength for five temperatures, T = 0°, 27°, 50°, 100°, 150 °C (left to right). Each point was calculated for the phase-matching angle for that temperature and wavelength.

Tables (1)

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Table 1 Sellmeier Coefficients for KNbO3 a

Equations (47)

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R=1--C1/2 expi2k0Lp-Rc1/21-RcRm1--C1/2 expi2k0Lp2,
T=1-RcTm1--C1/21/21-Rc1--C1/2 expi2k0Lp2,
C1-RcRm1--C1/22=γPin1-Rc,
wc=λπH1-H1/21/2,
wm=λπH1-H1/21/2,
η=s2+11/2-s)2,
ηC+CC 11+s.
Em=Am2expikmx-mωt+c.c.  m=1, 2,
Δk=2k1-k2,
Im=0nmc2 |Am|2.
A1rx=i2k1t2A1r+i2k1ρ A1ry+ik1n12 dA1*rA2rexp-iΔkx,
A2rx=i2k2 t2A2r+ik22n22 dA1r2 expiΔkx,
A1r=E0 exp-z2w02-y-ρx+ρL/22w02
A2y, z, 2Lc=A2y, z, Lc+expiΔkLc+ϕrA2-y, z, Lc.
yω0y, zω0z, xLcx.
β=ρLc21/2w0,
r=81/2βx-y21/2β-12,
p=ΔkLc81/2β,
Kz=κLc81/2βexp-2z2, κ=iE02k1dn12.
A2y, z, Lc=Kzexpi ΔkLc2+i2yp×r-r+dr exp-r22expipr,
r±=±21/2β-2y.
Fy, Δk=-drΘr, β, yexp-r22expipr,
Θr, β, y=1|r+2y|21/2β0otherwise.
Fy, Δk=exp-2y2exp-i2yp2 sin21/2βpp=81/2β exp-2y2exp-i2ypsincΔkLc2,
A2y, z, Lc=κLc exp-2y2+z2×expi ΔkLc2sincΔkLc2.
Fy, Δk=2π1/2 exp-p22=2π1/2 exp-ΔkLc4β2,
A2y, z, Lc=2π1/2Kzexpi ΔkLc2+i2ypexp-ΔkLc4β2,
PIΔkLc=P0Isinc2ΔkLc221+cosΔkLc+ϕr,
PIIΔkLc=P0II exp-ΔkLc2β221+sincΔkLc×cosΔkLc+ϕr,
=ww02¯=z0Lc0Lc/z0dx1+x2=z0LcarctanLc/z0=z0Lc ϕf,
Pabs=αωPc+α2ωP2ω+αbI2ωPc2Lc.
Tr-Ta=ΔT1-TrTa, Tr=γE+lnr˜+r˜exp-ttdt
=-t=1-r˜tt!tr˜,
r˜2rw02,
ΔTT0-Ta=PabsTa4πLckth,
nr=na+n˙TTr-Ta
=na+n˙TΔT-2n˙TΔTΓaw02 r2
=n0-nˆ2 r2,
n˙=4n˙TΔTTaw02.
njλ, Ti2=S1ijλ2λ1ij2/λ2-λ1ij2+S2iλ2λ2ij2/λ2-λ2ij2-Dijλ2+1
njλ, T=C0jλ+C1jλT+C2jλT2.
D=0n2E-0n2kˆ·Ekˆ.
ρ=arctanñbñatanΘ-Θ.
ny2 sin2Θña2+ny2 cos2Θñb2=1.
âmidijkAmjAmk=âmidijkAmâmjAmâmk=AmAm[dijkâmiâmjâmk]AmAmdeff.
dijkλ, T=0δijkni2ω2-1njω2-1×nkω2-1.
δijk=ijk=δm2/C311-3.0 × 10-2322-3.2 × 10-2333-6.6 × 10-2223, 232-2.9 × 10-2113, 131-3.0 × 10-2.

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