Abstract

A computational study on the efficient second-harmonic generation (SHG) in one-dimensional nonlinear photonic crystals (PhCs) is presented. The design requirements are specified in terms of the corresponding fundamental wavelength of the incident wave, at which the maximum conversion efficiency of SHG occurs. The computational approach has developed a Newton-type local optimization method to optimize the fill factor and the period of a PhC. An optimal structure can be determined by controlling the band structure such that the frequencies of the fundamental and second-harmonic waves are precisely located at the lower edges of photonic bandgaps. The results of our numerical experiments show the optimal design problem can be solved efficiently based on crucial initial data given by some useful engineering intuitions. The SHG with high conversion efficiency is achieved by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure of the PhC precisely.

© 2012 Optical Society of America

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2011 (2)

G. Bao, Z. Xu, and J. Yuan, “Continuation finite element simulation of second harmonic generation in photonic crystals,” Commun. Comput. Phys. 10, 57–69 (2011).
[CrossRef]

M. Luo and Q. H. Liu, “Enhancement of second-harmonic generation in an air-bridge photonic crystal slab: simulation by spectral element method,” J. Opt. Soc. Am. B 28, 2879–2887 (2011).
[CrossRef]

2010 (3)

M. L. Ren and Z. Y. Li, “Exact iterative solution of second harmonic generation in quasi-phase-matched structures,” Opt. Express 18, 7288–7299 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, J. Trull, and K. Staliunas, “Broad angle phase matching in sub-diffractive photonic crystals,” Opt. Commun. 283, 3533–3535 (2010).
[CrossRef]

2009 (3)

2008 (3)

S. Zhou and X. Wang, “Method of enhancing second-harmonic generation of antiferromagnetic film,” J. Opt. Soc. Am. B 25, 1639–1644 (2008).
[CrossRef]

L. Zhao, B. Gu, and Y. Zhou, “A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals,” Opt. Commun. 281, 2954–2958 (2008).
[CrossRef]

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

2007 (2)

2006 (1)

M. Bertolotti, “Wave interactions in photonic band structures: an overview,” J. Opt. A 8, S9–S32 (2006).
[CrossRef]

2005 (1)

M. Roussey, M. P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101(2005).
[CrossRef]

2004 (2)

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[CrossRef]

F. Ren, R. Li, C. Cheng, and H. Wang, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B 70, 245109 (2004).
[CrossRef]

2002 (2)

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structure,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[CrossRef]

2000 (1)

1999 (1)

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, “A numerical study of optical second-harmonic generation in a one-dimensional photonic structure,” Appl. Phys. Lett. 75, 1676–1678 (1999).
[CrossRef]

1998 (1)

1997 (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

1977 (1)

Afonso, C. N.

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

Akhouayri, H.

Baida, F. I.

M. Roussey, M. P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101(2005).
[CrossRef]

Bao, G.

G. Bao, Z. Xu, and J. Yuan, “Continuation finite element simulation of second harmonic generation in photonic crystals,” Commun. Comput. Phys. 10, 57–69 (2011).
[CrossRef]

Bermel, P.

Bernal, M. P.

M. Roussey, M. P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101(2005).
[CrossRef]

Bertolott, M.

M. Bertolott, C. M. Bowden, and C. Sibilia, Nanoscale Linear and Nonlinear Optics (American Institute of Physics, 2001).

Bertolotti, M.

Bloemer, M. J.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structure,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Bourgeade, A.

Bowden, C. M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structure,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

M. Bertolott, C. M. Bowden, and C. Sibilia, Nanoscale Linear and Nonlinear Optics (American Institute of Physics, 2001).

Bravo-Abad, J.

Centini, M.

Chaos, J. A.

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

Cheng, C.

F. Ren, R. Li, C. Cheng, and H. Wang, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Cojocaru, C.

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, J. Trull, and K. Staliunas, “Broad angle phase matching in sub-diffractive photonic crystals,” Opt. Commun. 283, 3533–3535 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

K. Staliunas, Y. Loiko, R. Herrero, C. Cojocaru, and J. Trull, “Efficient parametric amplification of narrow beams in photonic crystals,” Opt. Lett. 32, 1992–1994 (2007).
[CrossRef]

Courjal, N.

M. Roussey, M. P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101(2005).
[CrossRef]

D’Aguanno, G.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Edier, M.

R. Waynant and M. Edier, Electro-Optics Handbook(McGraw-Hill, 1994).

Enoch, S.

Freysz, E.

Gonzalo, J.

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

Gu, B.

L. Zhao, B. Gu, and Y. Zhou, “A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals,” Opt. Commun. 281, 2954–2958 (2008).
[CrossRef]

Haus, J. W.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Herrero, R.

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

K. Staliunas, Y. Loiko, R. Herrero, C. Cojocaru, and J. Trull, “Efficient parametric amplification of narrow beams in photonic crystals,” Opt. Lett. 32, 1992–1994 (2007).
[CrossRef]

Hong, C. S.

Joannopoulos, J. D.

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express 15, 16161–16176 (2007).
[CrossRef]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Johnson, S. G.

Karle, T. J.

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

Ketterson, J. B.

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, “A numerical study of optical second-harmonic generation in a one-dimensional photonic structure,” Appl. Phys. Lett. 75, 1676–1678 (1999).
[CrossRef]

Kiehne, G. T.

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, “A numerical study of optical second-harmonic generation in a one-dimensional photonic structure,” Appl. Phys. Lett. 75, 1676–1678 (1999).
[CrossRef]

Kim, K.

Kim, S.

Kryukov, A. E.

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, “A numerical study of optical second-harmonic generation in a one-dimensional photonic structure,” Appl. Phys. Lett. 75, 1676–1678 (1999).
[CrossRef]

Li, R.

F. Ren, R. Li, C. Cheng, and H. Wang, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Li, Z. Y.

Lim, H.

Liu, Q. H.

Loiko, Y.

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

K. Staliunas, Y. Loiko, R. Herrero, C. Cojocaru, and J. Trull, “Efficient parametric amplification of narrow beams in photonic crystals,” Opt. Lett. 32, 1992–1994 (2007).
[CrossRef]

Lu, Y. Y.

Luo, M.

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Nayfeh, A. H.

A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, 1993).

Nistor, C.

C. Nistor, C. Cojocaru, J. Trull, and K. Staliunas, “Broad angle phase matching in sub-diffractive photonic crystals,” Opt. Commun. 283, 3533–3535 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

Pruneri, V.

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

Raineri, F.

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

Raj, R.

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

Ren, F.

F. Ren, R. Li, C. Cheng, and H. Wang, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Ren, M. L.

Rodriguez, A.

Rotermund, F.

Roussey, M.

M. Roussey, M. P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101(2005).
[CrossRef]

Scalora, M.

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structure,” J. Opt. Soc. Am. B 19, 2111–2121 (2002).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Sibilia, C.

Soljacic, M.

Staliunas, K.

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, J. Trull, and K. Staliunas, “Broad angle phase matching in sub-diffractive photonic crystals,” Opt. Commun. 283, 3533–3535 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

K. Staliunas, Y. Loiko, R. Herrero, C. Cojocaru, and J. Trull, “Efficient parametric amplification of narrow beams in photonic crystals,” Opt. Lett. 32, 1992–1994 (2007).
[CrossRef]

Surez-Garca, A.

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

Trull, J.

C. Nistor, C. Cojocaru, J. Trull, and K. Staliunas, “Broad angle phase matching in sub-diffractive photonic crystals,” Opt. Commun. 283, 3533–3535 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, T. J. Karle, F. Raineri, J. Trull, R. Raj, and K. Staliunas, “Lossless backward second-harmonic generation of extremely narrow sub-diffractive beams in two-dimensional photonic crystals,” Phys. Rev. A 82, 033805 (2010).
[CrossRef]

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, and K. Staliunas, “Second-harmonic generation of narrow beams in subdiffractive photonic crystals,” Phys. Rev. A 78, 053818 (2008).
[CrossRef]

K. Staliunas, Y. Loiko, R. Herrero, C. Cojocaru, and J. Trull, “Efficient parametric amplification of narrow beams in photonic crystals,” Opt. Lett. 32, 1992–1994 (2007).
[CrossRef]

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Wang, H.

F. Ren, R. Li, C. Cheng, and H. Wang, “Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes,” Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Wang, X.

Waynant, R.

R. Waynant and M. Edier, Electro-Optics Handbook(McGraw-Hill, 1994).

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Xu, Z.

G. Bao, Z. Xu, and J. Yuan, “Continuation finite element simulation of second harmonic generation in photonic crystals,” Commun. Comput. Phys. 10, 57–69 (2011).
[CrossRef]

Yariv, A.

Yeh, P.

Yuan, J.

G. Bao, Z. Xu, and J. Yuan, “Continuation finite element simulation of second harmonic generation in photonic crystals,” Commun. Comput. Phys. 10, 57–69 (2011).
[CrossRef]

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

Yuan, L.

Zhao, L.

L. Zhao, B. Gu, and Y. Zhou, “A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals,” Opt. Commun. 281, 2954–2958 (2008).
[CrossRef]

Zhou, S.

Zhou, Y.

L. Zhao, B. Gu, and Y. Zhou, “A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals,” Opt. Commun. 281, 2954–2958 (2008).
[CrossRef]

Appl. Phys. Lett. (3)

G. T. Kiehne, A. E. Kryukov, and J. B. Ketterson, “A numerical study of optical second-harmonic generation in a one-dimensional photonic structure,” Appl. Phys. Lett. 75, 1676–1678 (1999).
[CrossRef]

J. Gonzalo, J. A. Chaos, A. Surez-Garca, C. N. Afonso, and V. Pruneri, “Enhanced second-order nonlinear optical response of LiNbO3 films upon Er doping,” Appl. Phys. Lett. 81, 2532–2534 (2002).
[CrossRef]

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