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Four-wave mixing in one-dimensional photonic crystals: inhomogeneous-wave excitation
Anatoli V. Andreev, Alexei V. Balakin, Alexander B. Kozlov, Ilya A. Ozheredov, Ilya R. Prudnikov, Alexander P. Shkurinov, Pascal Masselin, and Gael Mouret »View Author Affiliations
^{1}Department of Physics and International Laser Center, M. V. Lomonosov Moscow State University, Moscow 119899, Russia
^{2}Laboratoire de Physico Chimie de l’Atmosphère, Centre National de la Recherche Scientifique Unité Mixte de Recherche 8101, Université du Littoral, 145 Avenue Maurice Schumann, 59140 Dunkerque, France
Corresponding author: masselin@univ-littoral.fr
JOSA B, Vol. 19, Issue 8, pp. 1865-1872 (2002)
http://dx.doi.org/10.1364/JOSAB.19.001865
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Abstract
We present what is to our knowledge the first study of nonlinear four-wave mixing in one-dimensional photonic crystals. The possibility of inhomogeneous-wave excitation at the four-wave mixing frequency
© 2002 Optical Society of America
OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
Citation
Anatoli V. Andreev, Alexei V. Balakin, Alexander B. Kozlov, Ilya A. Ozheredov, Ilya R. Prudnikov, Alexander P. Shkurinov, Pascal Masselin, and Gael Mouret, "Four-wave mixing in one-dimensional photonic crystals: inhomogeneous-wave excitation," J. Opt. Soc. Am. B 19, 1865-1872 (2002)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-8-1865
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References
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- A. V. Balakin, D. Boucher, E. Fertein, P. Masselin, A. V. Pakulev, A. Yu. Resniansky, A. P. Shkurinov, and N. I. Koroteev, “Experimental observation of the interference of three- and five-wave mixing processes into the signal of second harmonic generation in bacteriorhodopsine solution,” Opt. Commun. 141, 343–352 (1997). [CrossRef]
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- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Berto-lotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Disper-sive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
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- J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]
- G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ^{(2)} interactions,” Phys. Rev. E 64, 016609–1-9 (2001).
- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Berto-lotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Disper-sive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
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- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
- A. V. Balakin, D. Boucher, E. Fertein, P. Masselin, A. V. Pakulev, A. Yu. Resniansky, A. P. Shkurinov, and N. I. Koroteev, “Experimental observation of the interference of three- and five-wave mixing processes into the signal of second harmonic generation in bacteriorhodopsine solution,” Opt. Commun. 141, 343–352 (1997). [CrossRef]
- G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ^{(2)} interactions,” Phys. Rev. E 64, 016609–1-9 (2001).
- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Berto-lotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Disper-sive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
- I. S. Fogel, J. M. Bendickson, M. D. Tocci, M. J. Bloemer, M. Scalora, C. M. Bowden, and J. P. Dowling, “Spontaneous emission and nonlinear effects in photonic bandgap materials,” Pure Appl. Opt. 7, 393–407 (1998). [CrossRef]
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
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- N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasi-phase matching conditions,” Phys. Rev. E 63, 046609–1-10 (2001). [CrossRef]
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
- G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ^{(2)} interactions,” Phys. Rev. E 64, 016609–1-9 (2001).
- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Berto-lotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Disper-sive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
- A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]
- G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ^{(2)} interactions,” Phys. Rev. E 64, 016609–1-9 (2001).
- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Berto-lotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Disper-sive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant third harmonic in porous silicon photonic crystals and microcavities,” JETP Lett. 75, 15–19 (2002). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, G. Marovskii, G. Mattei, D. Schumacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic in microcavities based on porous silicon photonic crystals,” JETP Lett. 73, 6–9 (2001). [CrossRef]
- I. S. Fogel, J. M. Bendickson, M. D. Tocci, M. J. Bloemer, M. Scalora, C. M. Bowden, and J. P. Dowling, “Spontaneous emission and nonlinear effects in photonic bandgap materials,” Pure Appl. Opt. 7, 393–407 (1998). [CrossRef]
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
- J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]
- G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ^{(2)} interactions,” Phys. Rev. E 64, 016609–1-9 (2001).
- A. Fainstein and B. Jusserand, “Raman scattering enhancement by optical confinement in a semiconductor planar microcavity,” Phys. Rev. Lett. 75, 3764–3767 (1995). [CrossRef] [PubMed]
- A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant third harmonic in porous silicon photonic crystals and microcavities,” JETP Lett. 75, 15–19 (2002). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, G. Marovskii, G. Mattei, D. Schumacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic in microcavities based on porous silicon photonic crystals,” JETP Lett. 73, 6–9 (2001). [CrossRef]
- A. V. Balakin, D. Boucher, E. Fertein, P. Masselin, A. V. Pakulev, A. Yu. Resniansky, A. P. Shkurinov, and N. I. Koroteev, “Experimental observation of the interference of three- and five-wave mixing processes into the signal of second harmonic generation in bacteriorhodopsine solution,” Opt. Commun. 141, 343–352 (1997). [CrossRef]
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
- I. S. Fogel, J. M. Bendickson, M. D. Tocci, M. J. Bloemer, M. Scalora, C. M. Bowden, and J. P. Dowling, “Spontaneous emission and nonlinear effects in photonic bandgap materials,” Pure Appl. Opt. 7, 393–407 (1998). [CrossRef]
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
- N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed]
- G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ^{(2)} interactions,” Phys. Rev. E 64, 016609–1-9 (2001).
- A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]
- A. P. Shkurinov, N. I. Koroteev, G. Jonusauskas, and C. Rulliere, “Subpicosecond anisotropic CARS studies of vibrational mode-selective photoexcitation and relaxation of trans-stilbene: first few picoseconds,” Chem. Phys. Lett. 223, 573–580 (1994). [CrossRef]
- A. Fainstein and B. Jusserand, “Raman scattering enhancement by optical confinement in a semiconductor planar microcavity,” Phys. Rev. Lett. 75, 3764–3767 (1995). [CrossRef] [PubMed]
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
- A. V. Balakin, D. Boucher, E. Fertein, P. Masselin, A. V. Pakulev, A. Yu. Resniansky, A. P. Shkurinov, and N. I. Koroteev, “Experimental observation of the interference of three- and five-wave mixing processes into the signal of second harmonic generation in bacteriorhodopsine solution,” Opt. Commun. 141, 343–352 (1997). [CrossRef]
- A. P. Shkurinov, N. I. Koroteev, G. Jonusauskas, and C. Rulliere, “Subpicosecond anisotropic CARS studies of vibrational mode-selective photoexcitation and relaxation of trans-stilbene: first few picoseconds,” Chem. Phys. Lett. 223, 573–580 (1994). [CrossRef]
- A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996). [CrossRef]
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- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant third harmonic in porous silicon photonic crystals and microcavities,” JETP Lett. 75, 15–19 (2002). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, G. Marovskii, G. Mattei, D. Schumacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic in microcavities based on porous silicon photonic crystals,” JETP Lett. 73, 6–9 (2001). [CrossRef]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasi-phase matching conditions,” Phys. Rev. E 63, 046609–1-10 (2001). [CrossRef]
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, G. Marovskii, G. Mattei, D. Schumacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic in microcavities based on porous silicon photonic crystals,” JETP Lett. 73, 6–9 (2001). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant third harmonic in porous silicon photonic crystals and microcavities,” JETP Lett. 75, 15–19 (2002). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, G. Marovskii, G. Mattei, D. Schumacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic in microcavities based on porous silicon photonic crystals,” JETP Lett. 73, 6–9 (2001). [CrossRef]
- A. V. Andreev, A. V. Balakin, I. A. Ozheredov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602–1-9 (2001).
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasi-phase matching conditions,” Phys. Rev. E 63, 046609–1-10 (2001). [CrossRef]
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
- A. V. Balakin, D. Boucher, E. Fertein, P. Masselin, A. V. Pakulev, A. Yu. Resniansky, A. P. Shkurinov, and N. I. Koroteev, “Experimental observation of the interference of three- and five-wave mixing processes into the signal of second harmonic generation in bacteriorhodopsine solution,” Opt. Commun. 141, 343–352 (1997). [CrossRef]
- T. V. Dolgova, A. I. Maidykovskii, M. G. Martemyanov, G. Marovskii, G. Mattei, D. Schumacher, V. A. Yakovlev, A. A. Fedyanin, and O. A. Aktsipetrov, “Giant second harmonic in microcavities based on porous silicon photonic crystals,” JETP Lett. 73, 6–9 (2001). [CrossRef]
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- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasi-phase matching conditions,” Phys. Rev. E 63, 046609–1-10 (2001). [CrossRef]
- A. V. Andreev, A. V. Balakin, I. A. Ozheredov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602–1-9 (2001).
- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Berto-lotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Disper-sive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
- R. L. Nelson and R. W. Boyd, “Enhanced third-order nonlinear optical response of photonic bandgap materials,” J. Mod. Opt. 46, 1061–1069 (1999). [CrossRef]
- N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed]
- A. V. Andreev, A. V. Balakin, I. A. Ozheredov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602–1-9 (2001).
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
- A. V. Balakin, D. Boucher, E. Fertein, P. Masselin, A. V. Pakulev, A. Yu. Resniansky, A. P. Shkurinov, and N. I. Koroteev, “Experimental observation of the interference of three- and five-wave mixing processes into the signal of second harmonic generation in bacteriorhodopsine solution,” Opt. Commun. 141, 343–352 (1997). [CrossRef]
- L. G. Parratt, “Surface studies of solids by total reflection of x-rays,” Phys. Rev. 95, 359–369 (1954). [CrossRef]
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- N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed]
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Phys. Rev. E
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