Abstract

A versatile and accurate approach that combines a numerical iteration technique and a transfer-matrix method (TMM) is developed to solve the general problem of second harmonic generation (SHG) with pump depletion in quasi-phase-matched (QPM) nonlinear optical structures. We derive the iterative formulae from the nonlinear coupled wave equations and obtain the intensity distribution of fundamental wave and second harmonic wave by TMM. The approach shows quick numerical convergence of iteration and maintains perfect conservation of total energy. The simulation results show that the model coincides with the one under undepleted pump approximation very well when the SHG efficiency is small (well below 15%) and agrees very well with the effective nonlinear susceptibility model in handling general SHG problems even when the conversion efficiency is high up to 100%. Our method is applicable to general nonlinear optical structures, such as periodic, quasi-periodic, and aperiodic QPM structures, photonic crystals, and micro-cavities that might involve complicated modulation on the linear and nonlinear susceptibility.

© 2010 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. B. Ma, T. Wang, Y. Sheng, P. Ni, Y. Wang, B. Cheng, and D. Zhang, “Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice,” Appl. Phys. Lett. 87(25), 251103 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[CrossRef]

J. Yuan, “Computing for second harmonic generation in one-dimensional nonlinear photonic crystals,” Opt. Commun. 282(13), 2628–2633 (2009).
[CrossRef]

J. Xia, “Enhancement of second harmonic generation in one-dimensional nonlinear photonic-crystal microcavities,” Opt. Express 17(22), 20069–20077 (2009).
[CrossRef]

M. L. Ren and Z. Y. Li, “Giant enhancement of second harmonic generation in nonlinear photonic crystals with distributed Bragg reflector mirrors,” Opt. Express 17(17), 14502–14510 (2009).
[CrossRef]

2008

J. J. Li, Z. Y. Li, and D. Z. Zhang, “Nonlinear frequency conversion in two-dimensional nonlinear photonic crystals solved by a plane-wave-based transfer-matrix method,” Phys. Rev. B 77(19), 195127 (2008).
[CrossRef]

Y. Q. Qin, Ch. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef]

2007

J. J. Li, Z. Y. Li, and D. Z. Zhang, “Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef]

J. J. Li, Z. Y. Li, Y. Sheng, and D. Z. Zhang, “Giant enhancement of second harmonic generation in poled ferroelectric crystals,” Appl. Phys. Lett. 91(2), 022903 (2007).
[CrossRef]

2005

P. Xu, S. N. Zhu, X. Q. Yu, S. H. Ji, Z. D. Gao, G. Zhao, Y. Y. Zhu, and N. B. Ming, “Experimental studies of enhanced Raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72(6), 064307 (2005).
[CrossRef]

B. Ma, T. Wang, Y. Sheng, P. Ni, Y. Wang, B. Cheng, and D. Zhang, “Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice,” Appl. Phys. Lett. 87(25), 251103 (2005).
[CrossRef]

2004

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef]

M. J. A. de Dood, W. T. M. Irvine, and D. Bouwmeester, “Nonlinear photonic crystals as a source of entangled photons,” Phys. Rev. Lett. 93(4), 040504 (2004).
[CrossRef]

2003

P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003).
[CrossRef]

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046607 (2003).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94(2), 811–821 (2003).
[CrossRef]

2002

2001

X. H. Wang and B. Y. Gu, “Nonlinear frequency conversion in 2D χ(2) photonic crystals and novel nonlinear double-circle construction,” Eur. Phys. J. B 24(3), 323–326 (2001).
[CrossRef]

1999

Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35(2), 162–178 (1999).
[CrossRef]

1998

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[CrossRef]

1997

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22(24), 1834–1836 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, Ch. Zh. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO3,” Phys. Rev. Lett. 78(14), 2752–2755 (1997).
[CrossRef]

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78(25), 4749–4752 (1997).
[CrossRef]

1995

H. M. Masoudi and J. M. Arnold, “Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method,” IEEE J. Quantum Electron. 31(12), 2107–2113 (1995).
[CrossRef]

1994

G. Bao and D. C. Dobson, “Second harmonic generation in nonlinear optical films,” J. Math. Phys. 35(4), 1622–1633 (1994).
[CrossRef]

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(11), 2631–2654 (1992).
[CrossRef]

1989

1984

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

1982

K. C. Rustagi, S. C. Mehendale, and S. Meenakshi, “Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals,” IEEE J. Quantum Electron. 18(6), 1029–1041 (1982).
[CrossRef]

1975

J. D. McMullen, “Optical parametric interactions in isotropic materials using a phase-corrected stack of nonlinear dielectric plates,” J. Appl. Phys. 46(7), 3076–3081 (1975).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Arnold, J. M.

H. M. Masoudi and J. M. Arnold, “Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method,” IEEE J. Quantum Electron. 31(12), 2107–2113 (1995).
[CrossRef]

Bang, O.

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78(25), 4749–4752 (1997).
[CrossRef]

Bao, G.

G. Bao and D. C. Dobson, “Second harmonic generation in nonlinear optical films,” J. Math. Phys. 35(4), 1622–1633 (1994).
[CrossRef]

Batchko, R. G.

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[CrossRef]

Bethune, D. S.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bouwmeester, D.

M. J. A. de Dood, W. T. M. Irvine, and D. Bouwmeester, “Nonlinear photonic crystals as a source of entangled photons,” Phys. Rev. Lett. 93(4), 040504 (2004).
[CrossRef]

Byer, R. L.

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22(24), 1834–1836 (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(11), 2631–2654 (1992).
[CrossRef]

Cheng, B.

B. Ma, T. Wang, Y. Sheng, P. Ni, Y. Wang, B. Cheng, and D. Zhang, “Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice,” Appl. Phys. Lett. 87(25), 251103 (2005).
[CrossRef]

P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003).
[CrossRef]

Clausen, C. B.

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78(25), 4749–4752 (1997).
[CrossRef]

de Dood, M. J. A.

M. J. A. de Dood, W. T. M. Irvine, and D. Bouwmeester, “Nonlinear photonic crystals as a source of entangled photons,” Phys. Rev. Lett. 93(4), 040504 (2004).
[CrossRef]

Dobson, D. C.

G. Bao and D. C. Dobson, “Second harmonic generation in nonlinear optical films,” J. Math. Phys. 35(4), 1622–1633 (1994).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[CrossRef]

Fejer, M. M.

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[CrossRef]

Gao, Z. D.

P. Xu, S. N. Zhu, X. Q. Yu, S. H. Ji, Z. D. Gao, G. Zhao, Y. Y. Zhu, and N. B. Ming, “Experimental studies of enhanced Raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72(6), 064307 (2005).
[CrossRef]

Ge, Ch. Zh.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, Ch. Zh. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO3,” Phys. Rev. Lett. 78(14), 2752–2755 (1997).
[CrossRef]

Gu, B. Y.

X. H. Wang and B. Y. Gu, “Nonlinear frequency conversion in 2D χ(2) photonic crystals and novel nonlinear double-circle construction,” Eur. Phys. J. B 24(3), 323–326 (2001).
[CrossRef]

He, J. L.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef]

Ho, K. M.

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94(2), 811–821 (2003).
[CrossRef]

Hu, X. P.

Y. Q. Qin, Ch. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef]

Imeshev, G.

Irvine, W. T. M.

M. J. A. de Dood, W. T. M. Irvine, and D. Bouwmeester, “Nonlinear photonic crystals as a source of entangled photons,” Phys. Rev. Lett. 93(4), 040504 (2004).
[CrossRef]

Jeong, Y.

Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35(2), 162–178 (1999).
[CrossRef]

Ji, S. H.

P. Xu, S. N. Zhu, X. Q. Yu, S. H. Ji, Z. D. Gao, G. Zhao, Y. Y. Zhu, and N. B. Ming, “Experimental studies of enhanced Raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72(6), 064307 (2005).
[CrossRef]

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[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(11), 2631–2654 (1992).
[CrossRef]

Kivshar, Y. S.

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. 78(25), 4749–4752 (1997).
[CrossRef]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Lee, B.

Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35(2), 162–178 (1999).
[CrossRef]

Li, J. J.

J. J. Li, Z. Y. Li, and D. Z. Zhang, “Nonlinear frequency conversion in two-dimensional nonlinear photonic crystals solved by a plane-wave-based transfer-matrix method,” Phys. Rev. B 77(19), 195127 (2008).
[CrossRef]

J. J. Li, Z. Y. Li, and D. Z. Zhang, “Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef]

J. J. Li, Z. Y. Li, Y. Sheng, and D. Z. Zhang, “Giant enhancement of second harmonic generation in poled ferroelectric crystals,” Appl. Phys. Lett. 91(2), 022903 (2007).
[CrossRef]

Li, Z. Y.

M. L. Ren and Z. Y. Li, “Giant enhancement of second harmonic generation in nonlinear photonic crystals with distributed Bragg reflector mirrors,” Opt. Express 17(17), 14502–14510 (2009).
[CrossRef]

J. J. Li, Z. Y. Li, and D. Z. Zhang, “Nonlinear frequency conversion in two-dimensional nonlinear photonic crystals solved by a plane-wave-based transfer-matrix method,” Phys. Rev. B 77(19), 195127 (2008).
[CrossRef]

J. J. Li, Z. Y. Li, Y. Sheng, and D. Z. Zhang, “Giant enhancement of second harmonic generation in poled ferroelectric crystals,” Appl. Phys. Lett. 91(2), 022903 (2007).
[CrossRef]

J. J. Li, Z. Y. Li, and D. Z. Zhang, “Second harmonic generation in one-dimensional nonlinear photonic crystals solved by the transfer matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 056606 (2007).
[CrossRef]

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046607 (2003).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94(2), 811–821 (2003).
[CrossRef]

Lin, L. L.

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94(2), 811–821 (2003).
[CrossRef]

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046607 (2003).
[CrossRef]

Ma, B.

B. Ma, T. Wang, Y. Sheng, P. Ni, Y. Wang, B. Cheng, and D. Zhang, “Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice,” Appl. Phys. Lett. 87(25), 251103 (2005).
[CrossRef]

P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003).
[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(11), 2631–2654 (1992).
[CrossRef]

Masoudi, H. M.

H. M. Masoudi and J. M. Arnold, “Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method,” IEEE J. Quantum Electron. 31(12), 2107–2113 (1995).
[CrossRef]

McMullen, J. D.

J. D. McMullen, “Optical parametric interactions in isotropic materials using a phase-corrected stack of nonlinear dielectric plates,” J. Appl. Phys. 46(7), 3076–3081 (1975).
[CrossRef]

Meenakshi, S.

K. C. Rustagi, S. C. Mehendale, and S. Meenakshi, “Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals,” IEEE J. Quantum Electron. 18(6), 1029–1041 (1982).
[CrossRef]

Mehendale, S. C.

K. C. Rustagi, S. C. Mehendale, and S. Meenakshi, “Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals,” IEEE J. Quantum Electron. 18(6), 1029–1041 (1982).
[CrossRef]

Miller, G. D.

Ming, N. B.

P. Xu, S. N. Zhu, X. Q. Yu, S. H. Ji, Z. D. Gao, G. Zhao, Y. Y. Zhu, and N. B. Ming, “Experimental studies of enhanced Raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72(6), 064307 (2005).
[CrossRef]

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, Ch. Zh. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO3,” Phys. Rev. Lett. 78(14), 2752–2755 (1997).
[CrossRef]

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[CrossRef]

P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003).
[CrossRef]

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[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, Ch. Zh. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO3,” Phys. Rev. Lett. 78(14), 2752–2755 (1997).
[CrossRef]

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[CrossRef]

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[CrossRef]

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P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef]

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B. Ma, T. Wang, Y. Sheng, P. Ni, Y. Wang, B. Cheng, and D. Zhang, “Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice,” Appl. Phys. Lett. 87(25), 251103 (2005).
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P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003).
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B. Ma, T. Wang, Y. Sheng, P. Ni, Y. Wang, B. Cheng, and D. Zhang, “Quasiphase matched harmonic generation in a two-dimensional octagonal photonic superlattice,” Appl. Phys. Lett. 87(25), 251103 (2005).
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P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
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P. Xu, S. N. Zhu, X. Q. Yu, S. H. Ji, Z. D. Gao, G. Zhao, Y. Y. Zhu, and N. B. Ming, “Experimental studies of enhanced Raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72(6), 064307 (2005).
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Y. Q. Qin, Ch. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
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P. Xu, S. N. Zhu, X. Q. Yu, S. H. Ji, Z. D. Gao, G. Zhao, Y. Y. Zhu, and N. B. Ming, “Experimental studies of enhanced Raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72(6), 064307 (2005).
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S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, Ch. Zh. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO3,” Phys. Rev. Lett. 78(14), 2752–2755 (1997).
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Y. Q. Qin, Ch. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
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J. J. Li, Z. Y. Li, and D. Z. Zhang, “Nonlinear frequency conversion in two-dimensional nonlinear photonic crystals solved by a plane-wave-based transfer-matrix method,” Phys. Rev. B 77(19), 195127 (2008).
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