Abstract

The work presents a theoretical analysis of quasi-phase-matched intracavity interaction in the constant-intensity approximation at frequencies summing with simultaneous regard for the losses and phases of interacting waves. An analytical expression for optimum correlation between interacting waves has been received. It is shown that, by the choice of optimum values of phase mismatch, pump intensity, and phase relationship, it is possible considerably to increase conversion efficiency in comparison with the noncavity case. The numerical estimation of expected conversion efficacy in conditions of an experiment is presented.

© 2012 Optical Society of America

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  1. G. D. Laptev and A. A. Novikov, “Intracavity quasi-phase matched frequency self conversion of optical radiation in Nd:Mg:LiNbO3 crystal with regular domain structures,” Quantum Electron. 31, 981–986 (2001).
    [CrossRef]
  2. N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
    [CrossRef]
  3. G. D. Laptev, A. A. Novikov, and A. S. Chirkin, “Interaction of light waves in active nonlinear and periodically poled nonlinear crystals,” JETP Lett. 78, 38–50 (2003).
    [CrossRef]
  4. M. Pierrou, F. Laurell, H. Karlsson, T. Kellner, C. Czeranowsky, and G. Huber, “Generation of 740 mW of blue light by intracavity frequency doubling with a first-order quasi-phase-matched KTiOPO4 crystal,” Opt. Lett. 24, 205–207 (1999).
    [CrossRef]
  5. Y. F. Chen, Y. S. Chen, and S. W. Tsai, “Diode-pumped Q-switched laser with intracavity sum frequency mixing in periodically poled KTP,” Appl. Phys. B 79, 207–210(2004).
    [CrossRef]
  6. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  7. T. Y. Fan, A. Gordova-Plaza, M. J. F. Digonnet, R. L. Byer, and H. J. Shaw, “Nd:MgO:LiNbO3 spectroscopy and laser devices,” J. Opt. Soc. Am. B 3, 140–148 (1986).
    [CrossRef]
  8. S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, P. De Natale, and M. Chiarini, “Investigation on reversed domain structures in lithium niobate crystals patterned by interference lithography,” Opt. Express 11, 392–405(2003).
    [CrossRef]
  9. O. Pfister, J. S. Wells, L. Hollberg, L. Zink, D. A. Van Baak, M. D. Levenson, and W. R. Bozenberg, “Continuous-wave frequency tripling and quadrupling by simultaneous three-wave mixings in periodically poled crystals: application to a two-step 1.19–10.71 μm frequency bridge,” Opt. Lett. 22, 1211–1214 (1997).
    [CrossRef]
  10. F. Brunner, E. Innerhofer, S. V. Marchese, T. Sudmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red–green–blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29, 1921–1923 (2004).
    [CrossRef]
  11. Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
    [CrossRef]
  12. Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
    [CrossRef]
  13. A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
    [CrossRef]
  14. C.-L. Wang, K.-H. Lin, T.-M. Hwang, Y.-F. Chen, S.-C. Wang, and C.-L. Pan, “Mode-locked diode-pumped self-frequency-doubling neodymium yttrium aluminum borate laser,” Appl. Opt. 37, 3282–3285 (1998).
    [CrossRef]
  15. D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
    [CrossRef]
  16. P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
    [CrossRef]
  17. Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Zh. Eksp. Teor. Fiz. 73, 1271–1282 (1977) [Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Sov. Phys. JETP 46, 669–680 (1977)].
  18. Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
    [CrossRef]
  19. R. J. Kasumova, “Quasi-phase-matched sum-frequency generation in layered structures,” J. Appl. Spectrosc. 78, 659–667 (2011).
    [CrossRef]
  20. R. J. Kasumova and A. A. Karimi, “Efficiency of sum frequency generation by regular domain structures,” J. Appl. Spectrosc. 77, 144–147 (2010).
    [CrossRef]

2011 (1)

R. J. Kasumova, “Quasi-phase-matched sum-frequency generation in layered structures,” J. Appl. Spectrosc. 78, 659–667 (2011).
[CrossRef]

2010 (1)

R. J. Kasumova and A. A. Karimi, “Efficiency of sum frequency generation by regular domain structures,” J. Appl. Spectrosc. 77, 144–147 (2010).
[CrossRef]

2004 (2)

2003 (2)

2002 (2)

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
[CrossRef]

2001 (3)

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
[CrossRef]

G. D. Laptev and A. A. Novikov, “Intracavity quasi-phase matched frequency self conversion of optical radiation in Nd:Mg:LiNbO3 crystal with regular domain structures,” Quantum Electron. 31, 981–986 (2001).
[CrossRef]

1999 (3)

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

M. Pierrou, F. Laurell, H. Karlsson, T. Kellner, C. Czeranowsky, and G. Huber, “Generation of 740 mW of blue light by intracavity frequency doubling with a first-order quasi-phase-matched KTiOPO4 crystal,” Opt. Lett. 24, 205–207 (1999).
[CrossRef]

1998 (2)

C.-L. Wang, K.-H. Lin, T.-M. Hwang, Y.-F. Chen, S.-C. Wang, and C.-L. Pan, “Mode-locked diode-pumped self-frequency-doubling neodymium yttrium aluminum borate laser,” Appl. Opt. 37, 3282–3285 (1998).
[CrossRef]

Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
[CrossRef]

1997 (1)

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1986 (1)

1977 (1)

Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Zh. Eksp. Teor. Fiz. 73, 1271–1282 (1977) [Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Sov. Phys. JETP 46, 669–680 (1977)].

Arisholm, G.

Bagayev, S. N.

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Bozenberg, W. R.

Brunner, F.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

T. Y. Fan, A. Gordova-Plaza, M. J. F. Digonnet, R. L. Byer, and H. J. Shaw, “Nd:MgO:LiNbO3 spectroscopy and laser devices,” J. Opt. Soc. Am. B 3, 140–148 (1986).
[CrossRef]

Capmany, J.

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Chai, B. H. T.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Chen, Y. F.

Y. F. Chen, Y. S. Chen, and S. W. Tsai, “Diode-pumped Q-switched laser with intracavity sum frequency mixing in periodically poled KTP,” Appl. Phys. B 79, 207–210(2004).
[CrossRef]

Chen, Y. S.

Y. F. Chen, Y. S. Chen, and S. W. Tsai, “Diode-pumped Q-switched laser with intracavity sum frequency mixing in periodically poled KTP,” Appl. Phys. B 79, 207–210(2004).
[CrossRef]

Chen, Y.-F.

Chiarini, M.

Chin, A.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Chirkin, A. S.

G. D. Laptev, A. A. Novikov, and A. S. Chirkin, “Interaction of light waves in active nonlinear and periodically poled nonlinear crystals,” JETP Lett. 78, 38–50 (2003).
[CrossRef]

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Zh. Eksp. Teor. Fiz. 73, 1271–1282 (1977) [Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Sov. Phys. JETP 46, 669–680 (1977)].

Czeranowsky, C.

Dawes, J. M.

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

De Natale, P.

De Nicola, S.

Dekker, P.

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

Digonnet, M. J. F.

Eichenhold, J.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Fan, T. Y.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Ferraro, P.

Finizio, A.

Firsov, V. V.

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

Garsia, S. J.

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Gordova-Plaza, A.

Grilli, S.

Hammons, D.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Hollberg, L.

Huber, G.

Hwang, T.-M.

Innerhofer, E.

Ito, H.

Jaque, D.

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Karimi, A. A.

R. J. Kasumova and A. A. Karimi, “Efficiency of sum frequency generation by regular domain structures,” J. Appl. Spectrosc. 77, 144–147 (2010).
[CrossRef]

Karlsson, H.

Kasumova, R. J.

R. J. Kasumova, “Quasi-phase-matched sum-frequency generation in layered structures,” J. Appl. Spectrosc. 78, 659–667 (2011).
[CrossRef]

R. J. Kasumova and A. A. Karimi, “Efficiency of sum frequency generation by regular domain structures,” J. Appl. Spectrosc. 77, 144–147 (2010).
[CrossRef]

Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
[CrossRef]

Keller, U.

Kellner, T.

Kerimova, N. V.

Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
[CrossRef]

Kitamura, K.

Kravtsov, N. I.

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

Kurimura, S.

Laptev, G. D.

G. D. Laptev, A. A. Novikov, and A. S. Chirkin, “Interaction of light waves in active nonlinear and periodically poled nonlinear crystals,” JETP Lett. 78, 38–50 (2003).
[CrossRef]

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

G. D. Laptev and A. A. Novikov, “Intracavity quasi-phase matched frequency self conversion of optical radiation in Nd:Mg:LiNbO3 crystal with regular domain structures,” Quantum Electron. 31, 981–986 (2001).
[CrossRef]

Laurell, F.

Levenson, M. D.

Li, D.-H.

D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
[CrossRef]

Li, P.-X.

D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
[CrossRef]

Lin, K.-H.

Liu, Y.

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

Lu, Y. L.

Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
[CrossRef]

Lu, Y. Q.

Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Marchese, S. V.

Ming, N. B.

Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
[CrossRef]

Naumov, I. I.

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

Novikov, A. A.

G. D. Laptev, A. A. Novikov, and A. S. Chirkin, “Interaction of light waves in active nonlinear and periodically poled nonlinear crystals,” JETP Lett. 78, 38–50 (2003).
[CrossRef]

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

G. D. Laptev and A. A. Novikov, “Intracavity quasi-phase matched frequency self conversion of optical radiation in Nd:Mg:LiNbO3 crystal with regular domain structures,” Quantum Electron. 31, 981–986 (2001).
[CrossRef]

Pan, C.-L.

Paschotta, R.

Peale, R.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Pfister, O.

Pierattini, G.

Pierrou, M.

Piper, J. A.

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

Richardson, M.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Salmanova, R. A.

Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
[CrossRef]

Shah, I.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Shaw, H. J.

Sudmeyer, T.

Tagiev, Z. H.

Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
[CrossRef]

Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Zh. Eksp. Teor. Fiz. 73, 1271–1282 (1977) [Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Sov. Phys. JETP 46, 669–680 (1977)].

Tsai, S. W.

Y. F. Chen, Y. S. Chen, and S. W. Tsai, “Diode-pumped Q-switched laser with intracavity sum frequency mixing in periodically poled KTP,” Appl. Phys. B 79, 207–210(2004).
[CrossRef]

Ueda, K.

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

Usami, T.

Van Baak, D. A.

Wang, C.-L.

Wang, J.

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

Wang, S.-C.

Wells, J. S.

Ye, Q.

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

Zhang, S.-W.

D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
[CrossRef]

Zhang, Z.-G.

D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
[CrossRef]

Zheng, J. J.

Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
[CrossRef]

Zink, L.

Appl. Opt. (1)

Appl. Phys. B (2)

Y. F. Chen, Y. S. Chen, and S. W. Tsai, “Diode-pumped Q-switched laser with intracavity sum frequency mixing in periodically poled KTP,” Appl. Phys. B 79, 207–210(2004).
[CrossRef]

Y. Q. Lu, J. J. Zheng, Y. L. Lu, and N. B. Ming, “Spectral properties and quasi-phase-matched second-harmonic generation in a new active medium: optical superlattice Nd:MgO:LiNbO3,” Appl. Phys. B 67, 29–32 (1998).
[CrossRef]

Chin. Phys. Lett. (1)

D.-H. Li, P.-X. Li, Z.-G. Zhang, and S.-W. Zhang, “Compact high-power blue light from a diode-pumped intracavity-doubled Nd:YAG laser,” Chin. Phys. Lett. 19, 1632–1634 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

J. Appl. Spectrosc. (2)

R. J. Kasumova, “Quasi-phase-matched sum-frequency generation in layered structures,” J. Appl. Spectrosc. 78, 659–667 (2011).
[CrossRef]

R. J. Kasumova and A. A. Karimi, “Efficiency of sum frequency generation by regular domain structures,” J. Appl. Spectrosc. 77, 144–147 (2010).
[CrossRef]

J. Opt. B (1)

Z. H. Tagiev, R. J. Kasumova, R. A. Salmanova, and N. V. Kerimova, “Constant-intensity approximation in a nonlinear wave theory,” J. Opt. B 3, 84–87 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

G. D. Laptev, A. A. Novikov, and A. S. Chirkin, “Interaction of light waves in active nonlinear and periodically poled nonlinear crystals,” JETP Lett. 78, 38–50 (2003).
[CrossRef]

Opt. Commun. (2)

Q. Ye, I. Shah, J. Eichenhold, D. Hammons, R. Peale, M. Richardson, A. Chin, and B. H. T. Chai, “Investigation of diode-pumped, self-frequency doubled RGB lasers from Nd:YCOB crystals,” Opt. Commun. 164, 33–37 (1999).
[CrossRef]

P. Dekker, J. M. Dawes, J. A. Piper, Y. Liu, and J. Wang, “Self-frequency-doubling ytterbium lasers,” Opt. Commun. 195, 431–436 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Quantum Electron. (3)

A. A. Kaminskii, D. Jaque, S. N. Bagayev, K. Ueda, S. J. Garsia, and J. Capmany, “New nonlinear-laser properties of ferroelectric Nd3+:Ba2NaNb5O15  cw stimulated emission (F3/24−I11/24 and F3/24−I13/24), collinear and diffuse self-frequency doubling and summation,” Quantum Electron. 29, 95–97 (1999).
[CrossRef]

G. D. Laptev and A. A. Novikov, “Intracavity quasi-phase matched frequency self conversion of optical radiation in Nd:Mg:LiNbO3 crystal with regular domain structures,” Quantum Electron. 31, 981–986 (2001).
[CrossRef]

N. I. Kravtsov, G. D. Laptev, I. I. Naumov, A. A. Novikov, V. V. Firsov, and A. S. Chirkin, “Intracavity quasi-phase matched frequency summing in a laser based on a periodically poled active nonlinear Nd:Mg:LiNbO3 crystal,” Quantum Electron. 32, 923–924 (2002).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Zh. Eksp. Teor. Fiz. 73, 1271–1282 (1977) [Z. H. Tagiev and A. S. Chirkin, “Fixed intensity approximation in the theory of nonlinear waves,” Sov. Phys. JETP 46, 669–680 (1977)].

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Figures (4)

Fig. 1.
Fig. 1.

Active-nonlinear RDS crystal inside a cavity. M1 and M2 are the cavity mirrors, Λ is the RDS period, lj is the length of jth domain, and χ(2) is the coefficient of quadratic nonlinear susceptibility; A1,2,3± are the complex amplitudes of generated laser wave, pump wave, and wave of summary frequency at frequencies ω1,2,3, respectively, in the direction of axis z (plus sign) and in the direction opposite to axis z (minus sign).

Fig. 2.
Fig. 2.

Dependences of intracavity conversion efficiency of radiation energy of pump wave to energy of wave of sum frequency η3(lj) on reduced lengths of layers Γ2lj, j=1/6, calculated in the constant-intensity approximation for λjlj,opt=π/2(j=1/4), δ1,2,3=0, Δ/2Γ2=3.5. η3(l1) on Γ2l1 is curve 1. η3(l2) on Γ2l2 (at Γ2l1,opt) is curve 2. η3(l3) on Γ2l3 (at Γ2l1,opt, Γ2l2,opt) is curve 3. η3(l4) on Γ2l4 (at Γ2l1,opt, Γ2l2,opt, Γ2l3,opt) is curve 4. η3(l5) on Γ2l5 (at Γ2l1,opt, Γ2l2,opt, Γ2l3,opt, Γ2l4,opt) are solid and dotted curves 5. η3(l6) on Γ2l6 (at Γ2l1,opt, Γ2l2,opt, Γ2l3,opt, Γ2l4,opt=Γ2l5,opt) is curve 6. Here Ψ=Ψopt (solid curve 5), 0 (dashed curve 5).

Fig. 3.
Fig. 3.

Dependences of intracavity conversion efficiency η3(l5) on a number of domains n for Ψ=Ψopt, λjlj,opt=π/2 (j=1/4), δ3=0, Δ/2Γ2=3.5 (curve 1) and 3.7 (curves 2 and 3) calculated in the constant-intensity approximation (curves 1 and 2) and in the constant-field approximation (curve 3).

Fig. 4.
Fig. 4.

Dependences of intracavity conversion efficiency η3(l5) in the fifth domain on phase ratio Ψ for λjlj,opt=π/2 (j=1/4) at Δ/2Γ2=3.5, δ3=δ1+δ2, δ3/Γ2=0 (curve 2) and 0.1 (curve 1).

Equations (19)

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dA1±dz±δ1A1±=iγ1A3±(A2±)*exp(±iΔz),dA2±dz±δ2A2±=iγ2A3±(A1±)*exp(±iΔz),dA3±dz±δ3A3±=iγ3A1±A2±exp(iΔz),
A1,n(z=0)=A1,n1outexp(iφ1,n),A2,n(z=0)=A2,n1outexp(iφ2,n),A3,n(z=0)=A3,n1outexp(iφ3,n).
A1,1(z=0)=A1,0exp(iφ10),A2,1(z=0)=A20exp(iφ20),A3,1(z=0)=0.
A3(ln)=A3(ln1){cosλnln+[iγ3A1(ln1)A2(ln1)A3(ln1)+δ1+δ2δ3+iΔ2]sinλnlnλn}×exp(δ1+δ2+δ3+iΔ2ln),
λn2=Γ12+Γ22(δ3δ1δ2iΔ)2/4,Γ12=γ2γ3I1(n1),Γ22=γ1γ3I2(n1).
A3(l4)=A3(l3){cosλ4l4+[iγ3A1(l3)A2(l3)A3(l3)+δ1+δ2δ3+iΔ2]sinλ4l4λn}×exp(δ1+δ2+δ3+iΔ2l4),
λ42=Γ12+Γ22(δ3δ1δ2iΔ)2/4,Γ12=γ2γ3I1(3),Γ22=γ1γ3I2(3).
A1(z=0)=A1(l4)exp(iφr,1),A2(z=0)=A2(l4)exp(iφr,2),A3(z=0)=A3(l4)exp(iφr,3),
A3(l5)=A3(l4){cosλ5l5+i[iγ3A1(l4)A2(l4)A3(l4)+Δ2]sinλ5l5λ5}exp(δ3l5iΔ2l5+iφr,3).
λjj,opt=π/2(j=1/4),
A3(l5)=A3(l4){cosλ5l5i[(Δ2λ42Δλ32Δλ22Δ)exp(iΨ)Δ2]sinλ5l5λ5}×exp(δ3l5iΔ2l5+iφr,3),
λj2=2Γj2+Δ2/4,Γj2=γ1γ2I1(j1).
η3(l5)=η3(l4)exp(2δ3l5)×{(cosλ5l5+bsinΨsinλ5l5λ5)2+(Δ2bcosΨ)2sinλ5l5λ52},
b=(Δ2λ42Δλ32Δλ22Δ).
A3(l6)=A3(l5){cosλ6l6+i[γ3A1(l5)A2(l5)A3(l5)+Δ2]sinλ6l6λ6}exp(δ3l6iΔ2l6+iφr,3).
η3(l6)=η3(l5)exp(2δ3l6)×[cos2λ6l6+(Δ1Δ2+b)2sin2λ6l6λ62].
Ψ+atan(2λ5/Δtan(λ5l5))=πm,m=1,2,.
η3(l5)=η3(l4)exp(2δ3l5){cos2λ5l5+[(Δ2λ42Δλ32Δλ22Δ)Δ2]2sin2λ5l5λ52}.
η3max(l5)=η3(l4)exp(2δ3l5)(Δλ4Δλ32Δλ22Δ)2/λ52.

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