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## Second-harmonic emission in two-dimensional photonic crystals

Emmanuel Centeno and Didier Felbacq »View Author Affiliations

^{1}and Didier Felbacq

^{1}

^{1}Groupe d’Etude des Semiconducteurs UMR-CNRS 5650 Université Montpellier II, Place E. Bataillon, CC074, 34095 Montpellier, France

JOSA B, Vol. 23, Issue 10, pp. 2257-2264 (2006)

http://dx.doi.org/10.1364/JOSAB.23.002257

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### Abstract

A second-harmonic superprism effect in 2D photonic crystals is demonstrated numerically. A full control of the second-harmonic emission is achieved by tailoring the photonic dispersion curves. This effect is demonstrated by using a multiple scattering method generalized to the second-harmonic generation. We show that small angular variations or a wavelength tuning of the fundamental field induce large shifts of the second-harmonic emission

© 2006 Optical Society of America

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(290.4210) Scattering : Multiple scattering

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: December 2, 2005

Revised Manuscript: May 10, 2006

Manuscript Accepted: May 28, 2006

**Citation**

Emmanuel Centeno and Didier Felbacq, "Second-harmonic emission in two-dimensional photonic crystals," J. Opt. Soc. Am. B **23**, 2257-2264 (2006)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-10-2257

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### References

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- E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005). [CrossRef] [PubMed]

**Abare, A. C.**

- H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999). [CrossRef]

**Abram, I.**

- Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002). [CrossRef]

**Abramovitz, M.**

- M. Abramovitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1970).

**Adibi, B. A.**

- B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003). [CrossRef]

**Agio, M.**

- A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002). [CrossRef]

**Albert, J. P.**

- J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004). [CrossRef]

**Andreani, L. C.**

- A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003). [CrossRef]

**Antoine-Vincent, N.**

- N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003). [CrossRef]

**Aydin, K.**

- E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004). [CrossRef]

**Baba, T.**

**Berger, V.**

- V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998). [CrossRef]

**Bertolotti, M.**

- 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 chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001). [CrossRef]
- M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999). [CrossRef]

**Bloemer, M. J.**

- 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 chi(2) interactions," Phys. Rev. E 64, 016609-016618 (2001). [CrossRef]
- M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999). [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]

**Bouadma, N.**

- A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55μm," Appl. Phys. Lett. 80, 547-549 (2002). [CrossRef]

**Bowden, C. M.**

- 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]

**Bowers, J. E.**

- H. Schmidt, A. C. Abare, J. E. Bowers, S. P. Denbaars, and A. Imamoglu, "Large interband second-order susceptibilities in InxGa1−xN/GaN quantum wells," Appl. Phys. Lett. 75, 3611-3613 (1999). [CrossRef]

**Briot, O.**

- J. Torres, D. Coquillat, R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot, M. Le Vassor d'Yerville, E. Centeno, D. Cassagne, and J. P. Albert, "Giant second-harmonic generation in a one-dimensional GaN photonic crystal," Phys. Rev. B 69, 085105-085113 (2004). [CrossRef]

**Bulu, I.**

- E. Ozbay, I. Bulu, K. Aydin, H. Caglayan, and K. Guven, "Physics and applications of photonic crystals," Photonics Nanostruct. Fundam. Appl. 2, 87-95 (2004). [CrossRef]

**Businaro, L.**

- A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizetti, L. C. Andreani, F. Romanato, L. Businaro, E. DiFabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-161310 (2003). [CrossRef]

**Byrne, D.**

- N. Antoine-Vincent, N. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, "Determination of the refractive indices of AlN, GaN, and AlxGa1−xN grown on (111)Si substrates," J. Appl. Phys. 93, 5222-5226 (2003). [CrossRef]

**Cabuz, A. L.**

- A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004). [CrossRef]

**Caglayan, H.**

**Cassagne, D.**

- E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005). [CrossRef] [PubMed]
- A. L. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004). [CrossRef]

**Cassan, E.**

**Centeno, E.**

- E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005). [CrossRef] [PubMed]
- E. Centeno, "Second-harmonic superprism effect in photonic crystals," Opt. Lett. 30, 1054-1056 (2005). [CrossRef] [PubMed]
- E. Centeno and D. Felbacq, "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals," J. Opt. Soc. Am. A 17, 320-327 (2000). [CrossRef]
- E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000). [CrossRef]

**Centini, M.**

**Chen, J. C.**

- 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]

**Chen, Y.**

**Cheng, C.**

- F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004). [CrossRef]

**Chow, E.**

**Coquillat, D.**

**Corbolan, R.**

- J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997). [CrossRef]

**Cordobàn, R.**

**Cowan, A. R**

- A. R Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. B 65, 85106-85112 (2002). [CrossRef]

**D'Aguanno, G.**

**Denbaars, S. P.**

**DiFabrizio, E.**

**Disseix, P.**

**Dowling, J. P.**

**Dumeige, Y.**

- Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 43901-43904 (2002). [CrossRef]

**Fan, S.**

- S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998). [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]

**Fedeli, J. M.**

**Felbacq, D.**

- E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000). [CrossRef]
- E. Centeno and D. Felbacq, "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals," J. Opt. Soc. Am. A 17, 320-327 (2000). [CrossRef]
- D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2533 (1994). [CrossRef]

**Fujita, S.**

**Gouezigou, L. Le**

**Guizetti, G.**

**Guven, K.**

**Haus, J. W.**

**Hauss, H. A.**

- S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Hauss, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998). [CrossRef]

**Hirao, K.**

- F. Ren, R. Li, C. Cheng, H. Wang, J. Qiu, J. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109-245113 (2004). [CrossRef]

**Imamoglu, A.**

**Jiang, Z. M.**

- B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, "A two-dimensional nonlinear photonic crystal for strong second-harmonic generation," J. Appl. Phys. 91, 6769-6771 (2002). [CrossRef]

**Joannopoulos, J.**

**Joannopoulos, J. D.**

- S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, "Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength," Opt. Lett. 25, 1297-1299 (2000). [CrossRef]
- J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

**John, S.**

- S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]

**Johnson, S.**

**Johnson, S. G.**

**Kafesaki, M.**

**Kawakami, S.**

- H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999). [CrossRef]
- H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998). [CrossRef]

**Kawashima, T.**

- H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999). [CrossRef]
- H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystal," Phys. Rev. B 58, R10096-R10099 (1998). [CrossRef]

**Kohler, S.**

**Kosaka, H.**

**Kurland, I.**

**Lascaray, J. P.**

**Laval, S.**

**Legros, R.**

**Levenson, A.**

**Levenson, J. A.**

**Leymarie, J.**

**Li, L.-M.**

- L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic bandgap materials," Phys. Rev. B 58, 9587-9590 (1998). [CrossRef]

**Li, R.**

**Lin, S. Y.**

**Lupu, A.**

**Lyan, P.**

**Malvezzi, A. M.**

**Manka, A. S.**

**Martorell, J.**

- J. Martorell, R. Vilaseca, and R. Corbolan, "Second-harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997). [CrossRef]
- J. Trull, R. Vilaseca, J. Martorell, and R. Cordobàn "Second-harmonic generation in local modes of a truncated periodic structure," Opt. Lett. 20, 1746-1750 (1995). [CrossRef] [PubMed]

**Massies, J.**

**Matsumoto, T.**

**Maystre, D.**

**Meade, R.**

- J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

**Mekis, A.**

**Melhaoui, L. El.**

**Méndez, E. R.**

**Mendoza, B. S.**

**Mériadec, C.**

**Mihailovic, M.**

**Ming, N. B.**

- S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997). [CrossRef]

**Momeni, B.**

- B. Momeni and B. A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003). [CrossRef]

**Monnier, P.**

**Nada, N.**

- M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1993). [CrossRef]

**Natali, N.**

**Nefedov, I.**

**Noda, S.**

- S. Noda, "Three-dimensional photonic crystals operating at optical wavelength region," Physica B 279, 142-149 (2000). [CrossRef]

**Notomi, M.**

**Ozbay, E.**

**Passaseo, A.**

**Patrini, M.**

**Peyrade, D.**

**Qiu, J.**

**Ren, F.**

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