Abstract

A new scheme for nondestructive characterization of quasi-phase-matching grating structures and temperature gradients through inverse Fourier theory using second-harmonic-generation experiments is proposed. By inserting a mirror to reflect the signals back through the sample, we show how it is possible to retrieve the relevant information by measuring only the generated second-harmonic power, avoiding more complicated phase measurements. The potential of the scheme is emphasized through theoretical and numerical investigations in the case of periodically poled lithium niobate bulk crystals.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, and D. B. Ostrowsky, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197–3203 (1997).
    [CrossRef]
  5. P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
    [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. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
    [CrossRef]
  8. K. Mizuuchi and K. Yamamoto, “Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts,” Opt. Lett. 23, 1880–1882 (1998).
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  9. S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
    [CrossRef]
  10. P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
    [CrossRef]
  14. L. Torner, C. B. Clausen, and M. M. Fejer, “Adiabatic shaping of quadratic solitons,” Opt. Lett. 23, 903–905 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. G. Imeshev, M. Proctor, and M. M. Fejer, “Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings,” Opt. Lett. 23, 673–675 (1998).
    [CrossRef]
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    [CrossRef]
  22. R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
    [CrossRef] [PubMed]
  23. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  24. For extraordinary polarized electric fields leading to the use of d33: a1=5.35583, a2=0.100473, a3=0.20692, a4= 100, a5=11.34927, a6=1.5334×10−2, b1=4.629× 10−7, b2=3.862×10−8, b3=−0.89×10−8, and b4= 2.657×10−5.
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  26. J. A. Armstrong, N. Bloembergen, and P. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  27. P. St. J. Russel, “Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms,” IEEE J. Quantum Electron. 27, 830–835 (1991).
    [CrossRef]
  28. Y. J. Ding, “Second-harmonic generation based on quasi-phase matching: a novel configuration,” Opt. Lett. 21, 1445–1447 (1996).
    [CrossRef] [PubMed]
  29. X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181, 153–159 (2000).
    [CrossRef]

2002

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[CrossRef]

2001

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

2000

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

S. Carrasco, J. P. Torres, L. Torner, and R. Schiek, “Engineerable generation of quadratic solitons in synthetic phase matching,” Opt. Lett. 25, 1273–1275 (2000).
[CrossRef]

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181, 153–159 (2000).
[CrossRef]

1999

1998

1997

1996

1995

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

1994

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
[CrossRef] [PubMed]

1992

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]

1991

P. St. J. Russel, “Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms,” IEEE J. Quantum Electron. 27, 830–835 (1991).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, and P. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Arbore, M. A.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, and P. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Aschieri, P.

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, and D. B. Ostrowsky, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197–3203 (1997).
[CrossRef]

Aschiéri, P.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Baek, Y.

Baldi, P.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, and D. B. Ostrowsky, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197–3203 (1997).
[CrossRef]

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

Bamford, D. J.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

Bang, O.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[CrossRef]

Barr, J. R. M.

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Bisson, S. E.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, and P. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Byer, R. L.

R. L. Byer, “Quasi-phase matched nonlinear interactions and devices,” J. Nonlinear Opt. Phys. 6, 549–592 (1997).
[CrossRef]

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]

Carrasco, S.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[CrossRef]

S. Carrasco, J. P. Torres, L. Torner, and R. Schiek, “Engineerable generation of quadratic solitons in synthetic phase matching,” Opt. Lett. 25, 1273–1275 (2000).
[CrossRef]

Cha, M.

Chanvillard, L.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

Chou, M. H.

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
[CrossRef]

Cino, A. C.

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

Clausen, C. B.

de Micheli, M.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

De Micheli, M. P.

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, and D. B. Ostrowsky, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197–3203 (1997).
[CrossRef]

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

Delacourt, D.

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

Ding, Y. J.

X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181, 153–159 (2000).
[CrossRef]

Y. J. Ding, “Second-harmonic generation based on quasi-phase matching: a novel configuration,” Opt. Lett. 21, 1445–1447 (1996).
[CrossRef] [PubMed]

El Hadi, K.

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

G. Imeshev, M. Proctor, and M. M. Fejer, “Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings,” Opt. Lett. 23, 673–675 (1998).
[CrossRef]

L. Torner, C. B. Clausen, and M. M. Fejer, “Adiabatic shaping of quadratic solitons,” Opt. Lett. 23, 903–905 (1998).
[CrossRef]

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
[CrossRef]

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]

Fujimura, M.

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Galvanauskas, A.

Ge, C.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Hadi, K. E.

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

Hanna, D. C.

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Harter, D.

Huang, L.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

Imeshev, G.

Johansen, S. K.

S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[CrossRef]

Jundt, D. H.

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
[CrossRef]

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]

Kim, D. Y.

Kulp, T. J.

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]

Ming, N.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Mizuuchi, K.

Mu, X.

X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181, 153–159 (2000).
[CrossRef]

Nouh, S.

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

Ostrowsky, D. B.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, and D. B. Ostrowsky, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197–3203 (1997).
[CrossRef]

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

Papuchon, M.

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

Pershan, P.

J. A. Armstrong, N. Bloembergen, and P. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Powers, P. E.

Proctor, M.

Pruneri, V.

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Qin, Y.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Risk, W. P.

X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181, 153–159 (2000).
[CrossRef]

Russel, P.

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Russel, P. St. J.

P. St. J. Russel, “Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms,” IEEE J. Quantum Electron. 27, 830–835 (1991).
[CrossRef]

Schiek, R.

Seibert, H.

Sohler, W.

Stegeman, G. I.

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
[CrossRef] [PubMed]

Sundheimer, M.

Sundheimer, M. L.

Torner, L.

Torres, J. P.

Treviño-Palacios, C. G.

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

Wang, H.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Webjörn, J.

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

Yamamoto, K.

Zhu, S.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Zhu, Y.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Zotova, I. B.

X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, “Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide,” Opt. Commun. 181, 153–159 (2000).
[CrossRef]

Appl. Phys. Lett.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. de Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” Appl. Phys. Lett. 76, 1089–1091 (2000).
[CrossRef]

Electron. Lett.

P. Baldi, C. G. Treviño-Palacios, G. I. Stegeman, M. P. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Simultaneous generation of red, green and blue light in room temperature periodically poled lithium niobate waveguides using single source,” Electron. Lett. 31, 1350–1351 (1995).
[CrossRef]

J. Webjörn, V. Pruneri, P. Russel, J. R. M. Barr, and D. C. Hanna, “Quasi-phase-matched blue light generation with lithium niobate, electrically poled via liquid electrodes,” Electron. Lett. 30, 894–895 (1994).
[CrossRef]

IEEE J. Quantum Electron.

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]

P. St. J. Russel, “Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms,” IEEE J. Quantum Electron. 27, 830–835 (1991).
[CrossRef]

IEEE Photon. Technol. Lett.

K. R. Parameswaran, M. Fujimura, M. H. Chou, and M. M. Fejer, “Low-power all-optical gate based on sum frequencymixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
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S. K. Johansen, S. Carrasco, L. Torner, and O. Bang, “Engineering of spatial solitons in two-period QPM structures,” Opt. Commun. 203, 393–402 (2002).
[CrossRef]

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P. Baldi, M. P. De Micheli, K. E. Hadi, S. Nouh, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[CrossRef]

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M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
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G. Imeshev, M. Proctor, and M. M. Fejer, “Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings,” Opt. Lett. 23, 673–675 (1998).
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[CrossRef]

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[CrossRef]

Other

M. M. Fejer, in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1998), pp. 375–406.

For extraordinary polarized electric fields leading to the use of d33: a1=5.35583, a2=0.100473, a3=0.20692, a4= 100, a5=11.34927, a6=1.5334×10−2, b1=4.629× 10−7, b2=3.862×10−8, b3=−0.89×10−8, and b4= 2.657×10−5.

R. Schiek, H. Fang, and C. G. Treviño-Palacios, “Measurement of the non-uniformity of the wave-vector mismatch in waveguides for second-harmonic generation,” in Digest on Topical Meeting on Nonlinear Guided Waves and Their Applications (Optical Society of America, Washington D.C., 1998), pp. 256–258.

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Figures (8)

Fig. 1
Fig. 1

Illustration of how to generate an even grating function with the help of a mirror.

Fig. 2
Fig. 2

SHG tuning curve for perfectly periodic QPM crystal of length L=1 cm and with domain length Λ=10 µm. The reflection-amplitude coefficients of r1=0.95 and r2=0.75 are given. The curve is in fact discrete, which is indicated with dots in the enlarged part of the curve shown in the inset.

Fig. 3
Fig. 3

Reconstructed grating function from the SHG tuning curve in Fig. 2. The entire grating function is shown to the left. Two enlarged parts of the grating are shown to the right: the middle part in the top, and the part around the end of the crystal in the bottom.

Fig. 4
Fig. 4

SHG tuning curve for periodic QPM crystal with duty cycle D=0.7. The other parameters are the same as for Fig. 2.

Fig. 5
Fig. 5

Determination of duty cycle D and domain length Λ in the presence of duty-cycle errors. The full curve shows the maximum relative SH output power p=P2,max/P2,max(D=0.5) as a function of D. The dashed line shows Λ, also as function of D, determined through Eq. (16). See text for explanation of the letters A, B, C, and D.

Fig. 6
Fig. 6

QPM crystal in mirror setup illustrating the even mirror-expanded temperature profile, t(z).

Fig. 7
Fig. 7

SHG tuning curve for periodic QPM crystal with a temperature profile varying according to Eq. (19). The parameters are L=5 cm, t0=1000 °C/m, D=0.5, r1=0.95, r2=0.75, Λ=10 µm, and λp=1.6 µm. The dashed vertical line indicates the location of the maximum with B(z)=0.

Fig. 8
Fig. 8

Retrieved temperature profiles for two different t0: (A) t0=1000 °C/m and (B) t0=500 °C/m. The full curves are the retrieved profiles, and the dashed curves are the actual profiles used in the numerical experiments.

Equations (20)

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i E1z+d(z)E1*E2 exp-i0zβ(z)dz=0,
i E2z+d(z)E12 expi0zβ(z)dz=0.
n2=a1+b1f+a2+b2fλ2-(a3+b3f)2+a4+b4fλ2-a52-a6λ2,
f=(T-24.5 °C)(T+570.82 °C).
P1=ηA|E1|2,P2=2ηA|E2|2,
|E2(β, L)|2=|E12(0)|2F{d˜(z)}F*{d˜(z)},
Ej(z=0+)=rj exp(imj)Ej(z=0-),j=1,2,
E2(L)=r2 exp(im2)E2(-L)+i[r12 exp(i2m1)+r2 exp(im2)]E1(-L)20Ld(z)[cos B cos(β0z)-sin B sin(β0z)]dz-[r12 exp(i2m1)-r2 exp(im2)]E1(-L)20Ld(z)[cos B sin(β0z)+sin B cos(β0z)]dz.
|E2(β0, L)|2(r12+r2)2E1(-L)4f2(β0),
d˜(z)cos B=2FIM-1{E2(L)}(r12+r2)E1(-L)2,
d˜(z)sin B=2FRE-1{E2(L)}(r12+r2)E1(-L)2,
d˜(z)=Fs-1{E2(L)}(r12+r2)E1(-L)=A2(r12+r2)P1,I Fs-1{ηP2,O}.
d(z)=1,0<z<Λ-1,Λ<z<2Λ=4π n=1,3,5, sin(nzπ/Λ)n.
P28π2 (r12+r2)2L2AηP12 sinc2πΛ+β0L,
d(z)=1,0<z<2DΛ-1,2DΛ<z<2Λ=-212-D+4π n=1,3, sin(nπ/2)sin(nDπ)n×sinn πΛz+nπ12-D+4π n=2,4, sin[(n+1)π/2]sin(nDπ)n×sinn πΛz+nπ12-D.
P28π2 (r12+r2)2L2AηP12 sin2(Dπ)×cos(q-πD)-cos(πD)q2,
q=sinq2sinq2-πDsin(q-πD).
f(β0)=n 2nπ 0Lcosn πΛz-β0z-B-cosn πΛz+β0z+Bdz,n=1,3,.
B(z)=ArctanFRE-1{ηP2,O}FIM-1{ηP2,O},
t(z)=t0z,z[00.5cm]0.5cm×t0,z[0.5cm4cm]-t0(5cm-z)/2,z[4cm5cm].

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