Abstract

Broadly tunable multiple high-harmonic conical beams have been generated by means of a multistep χ(2) cascade processes in a two dimensional nonlinear photonic crystal. The nonlinear structure consists of a square lattice of inverted hexagonal domains with diameters and distances between domains as low as 1 μm. The large number of reciprocal lattice vectors provided by both the square nonlinear structure and the hexagonal shaped domains, along with imperfections on the size and shape of the individual domains make possible the simultaneous generation of second up to fifth harmonic conical beams in a single nonlinear structure by using different types of phase matching geometries. The frequency response can be tuned in an extremely large spectral range, and continuous generation of nonlinear conical beams covering the whole visible spectral region can be achieved. Further, the same photon energy can be generated at different orders, so that concentrically emitted conical beams with angular dispersion as large as Δθ = 50° can be observed. The results highlight the significance of highly controlled engineered 2D nonlinear structures to generate advanced multi-photon devices with large spatial and spectral tunable response.

©2012 Optical Society of America

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2012 (3)

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

2011 (5)

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99(24), 241109 (2011).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36(16), 3266–3268 (2011).
[Crossref] [PubMed]

L. Mateos, P. Molina, L. E. Bausa, and M. O. Ramirez, “Second harmonic conical waves for symmetry studies in chi((2)) nonlinear photonic crystals,” Appl. Phys. Express 4(8), 082202 (2011).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98(16), 161113 (2011).
[Crossref]

2010 (4)

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

2009 (3)

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102(15), 153902 (2009).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

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]

2008 (4)

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18(5), 709–715 (2008).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

T. Ellenbogen, A. Ganany-Padowicz, and A. Arie, “Nonlinear photonic structures for all-optical deflection,” Opt. Express 16(5), 3077–3082 (2008).
[Crossref] [PubMed]

2007 (1)

C. Canalias and V. Pasiskevicius, “Mirrorles optical parametric oscillator,” Nat. Photonics 1(8), 459–462 (2007).
[Crossref]

2006 (1)

2005 (2)

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95(13), 133901 (2005).
[Crossref] [PubMed]

C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase matched second harmonic generation in sub-micrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005).
[Crossref]

2003 (1)

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

2002 (1)

1998 (1)

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

1997 (2)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[Crossref]

D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol. % magnesium oxide–doped lithium niobate,” J. Opt. Soc. Am. B 14(12), 3319–3322 (1997).
[Crossref]

1995 (1)

An, N.

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Arie, A.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36(16), 3266–3268 (2011).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

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]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

T. Ellenbogen, A. Ganany-Padowicz, and A. Arie, “Nonlinear photonic structures for all-optical deflection,” Opt. Express 16(5), 3077–3082 (2008).
[Crossref] [PubMed]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95(13), 133901 (2005).
[Crossref] [PubMed]

Assanto, G.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

Ayoub, M.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99(24), 241109 (2011).
[Crossref]

Bahabad, A.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95(13), 133901 (2005).
[Crossref] [PubMed]

Bao, X. H.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Bausa, L. E.

L. Mateos, P. Molina, L. E. Bausa, and M. O. Ramirez, “Second harmonic conical waves for symmetry studies in chi((2)) nonlinear photonic crystals,” Appl. Phys. Express 4(8), 082202 (2011).
[Crossref]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18(5), 709–715 (2008).
[Crossref]

Berger, V.

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

Best, A.

Bosenberg, W. R.

Bratfalean, R. T.

Broderick, N. G. R.

Busacca, A.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

Butt, H. J.

Byer, R. L.

Canalias, C.

C. Canalias and V. Pasiskevicius, “Mirrorles optical parametric oscillator,” Nat. Photonics 1(8), 459–462 (2007).
[Crossref]

C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase matched second harmonic generation in sub-micrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005).
[Crossref]

Carrasco, S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Chen, C. D.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

Chen, X.

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Chen, Y. A.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Chiuri, A.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102(15), 153902 (2009).
[Crossref] [PubMed]

Cui, W. N.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

De Martini, F.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102(15), 153902 (2009).
[Crossref] [PubMed]

de Sterke, C. M.

Deng, X.

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Denz, C.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99(24), 241109 (2011).
[Crossref]

Du, J.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

Eckardt, R. C.

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]

T. Ellenbogen, A. Ganany-Padowicz, and A. Arie, “Nonlinear photonic structures for all-optical deflection,” Opt. Express 16(5), 3077–3082 (2008).
[Crossref] [PubMed]

Fejer, M. M.

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Fokine, M.

C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase matched second harmonic generation in sub-micrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005).
[Crossref]

Gallo, K.

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98(16), 161113 (2011).
[Crossref]

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]

T. Ellenbogen, A. Ganany-Padowicz, and A. Arie, “Nonlinear photonic structures for all-optical deflection,” Opt. Express 16(5), 3077–3082 (2008).
[Crossref] [PubMed]

Garcia, B. J.

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

He, J. L.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

Hu, X. P.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

Hum, D. S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Imbrock, J.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99(24), 241109 (2011).
[Crossref]

Jundt, D.

Kivshar, Y. S.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Kong, Y.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Koynov, K.

Krolikowski, W.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36(16), 3266–3268 (2011).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Kumar, S.

Langrock, C.

Laurell, F.

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98(16), 161113 (2011).
[Crossref]

C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase matched second harmonic generation in sub-micrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005).
[Crossref]

Levenius, M.

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98(16), 161113 (2011).
[Crossref]

Li, H. X.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

Liao, J.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95(13), 133901 (2005).
[Crossref] [PubMed]

Liu, H.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

Lu, C. Y.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Lu, H.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Mataloni, P.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102(15), 153902 (2009).
[Crossref] [PubMed]

Mateos, L.

L. Mateos, P. Molina, L. E. Bausa, and M. O. Ramirez, “Second harmonic conical waves for symmetry studies in chi((2)) nonlinear photonic crystals,” Appl. Phys. Express 4(8), 082202 (2011).
[Crossref]

McGeehan, J. E.

Ming, N. B.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[Crossref]

Molina, P.

L. Mateos, P. Molina, L. E. Bausa, and M. O. Ramirez, “Second harmonic conical waves for symmetry studies in chi((2)) nonlinear photonic crystals,” Appl. Phys. Express 4(8), 082202 (2011).
[Crossref]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18(5), 709–715 (2008).
[Crossref]

Monro, T. M.

Morandotti, R.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

Mu, S. Y.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

Myers, L. E.

Nasr, M. B.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Neshev, D. N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Pan, G. S.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Pan, J. W.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Pasiskevicius, V.

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98(16), 161113 (2011).
[Crossref]

C. Canalias and V. Pasiskevicius, “Mirrorles optical parametric oscillator,” Nat. Photonics 1(8), 459–462 (2007).
[Crossref]

C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase matched second harmonic generation in sub-micrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005).
[Crossref]

Pasquazi, A.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

Peng, C. Z.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Pierce, J. W.

Ramirez, M. O.

L. Mateos, P. Molina, L. E. Bausa, and M. O. Ramirez, “Second harmonic conical waves for symmetry studies in chi((2)) nonlinear photonic crystals,” Appl. Phys. Express 4(8), 082202 (2011).
[Crossref]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18(5), 709–715 (2008).
[Crossref]

Ren, H.

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Richardson, D. J.

Roedig, P.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99(24), 241109 (2011).
[Crossref]

Roppo, V.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36(16), 3266–3268 (2011).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Rossi, A.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102(15), 153902 (2009).
[Crossref] [PubMed]

Saleh, B. E. A.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Saltiel, S. M.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Sergienko, A. V.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Sheng, Y.

Shiloh, R.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36(16), 3266–3268 (2011).
[Crossref] [PubMed]

Small, D. L.

Stivala, S.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

Teich, M. C.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Torner, L.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Torres, J. P.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[Crossref] [PubMed]

Vallone, G.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102(15), 153902 (2009).
[Crossref] [PubMed]

Voloch-Bloch, N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

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]

Wang, H. T.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

Wang, T. X.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Wang, W.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36(16), 3266–3268 (2011).
[Crossref] [PubMed]

Willner, A. E.

Xu, F.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

Xu, P.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

Yao, X. C.

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
[Crossref]

Zelmon, D. E.

Zheng, Y.

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Zhong, M. L.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

Zhu, S. N.

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[Crossref]

Zhu, Y. Y.

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[Crossref]

Adv. Funct. Mater. (1)

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18(5), 709–715 (2008).
[Crossref]

Appl. Phys. Express (1)

L. Mateos, P. Molina, L. E. Bausa, and M. O. Ramirez, “Second harmonic conical waves for symmetry studies in chi((2)) nonlinear photonic crystals,” Appl. Phys. Express 4(8), 082202 (2011).
[Crossref]

Appl. Phys. Lett. (8)

N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

H. X. Li, S. Y. Mu, P. Xu, M. L. Zhong, C. D. Chen, X. P. Hu, W. N. Cui, and S. N. Zhu, “Multicolor Cerenkov conical beams generation by cascaded- chi((2)) processes in radially poled nonlinear photonic crystals,” Appl. Phys. Lett. 100(10), 101101 (2012).
[Crossref]

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99(24), 241109 (2011).
[Crossref]

J. L. He, J. Liao, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Simultaneous cw red, yellow, and green light generation, “traffic signal lights”, by frequency doubling and sum-frequency mixing in an aperiodically poled LiTaO3,” Appl. Phys. Lett. 83(2), 228–230 (2003).
[Crossref]

C. Canalias, V. Pasiskevicius, M. Fokine, and F. Laurell, “Backward quasi-phase matched second harmonic generation in sub-micrometer periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 86(18), 181105 (2005).
[Crossref]

K. Gallo, M. Levenius, F. Laurell, and V. Pasiskevicius, “Twin-beam optical parametric generation in χ(2) nonlinear photonic crystals,” Appl. Phys. Lett. 98(16), 161113 (2011).
[Crossref]

IEEE J. Quantum Electron. (1)

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

IEEE Photon. J. (1)

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photon. J. 2(1), 18–28 (2010).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Nat. Photonics (3)

C. Canalias and V. Pasiskevicius, “Mirrorles optical parametric oscillator,” Nat. Photonics 1(8), 459–462 (2007).
[Crossref]

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]

X. C. Yao, T. X. Wang, P. Xu, H. Lu, G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, and J. W. Pan, “Observation of eight photon entanglement,” Nat. Photonics 6(4), 225–228 (2012).
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Figures (5)

Fig. 1
Fig. 1

(a). Optical picture of a square lattice of inverted ferroelectric domains in LiNbO3. The period of the structure is Λ~2 μm. (b) Schematic of the experimental set-up for conical high harmonic generation process for an incident fundamental beam along the z axis of the crystal. (c-f) Experimental images of multiple high-harmonic conical beams recorded in the far field when the fundamental wavelength was fixed at 1450, 1900, 2100 and 2300nm, respectively.

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Fig. 2
Fig. 2

(a). Schematic diagram showing the longitudinal phase matching condition of the multistep cascaded χ(2) –Cerenkov harmonic generation via Type I and Type II processes for the different harmonics observed in this work. (b) Multicolor ring-shaped Cerenkov multiple high harmonic generation recorded in the far field when the fundamental beam was tuned at 2100 nm. Red, green and blue conical emissions are simultaneously obtained via multistep frequency tripling, quadrupling and quintupling of the fundamental wave. (c) Angular dependence of the generated harmonic beams as a function of the fundamental wavelength. Theoretical calculations and experimental points are represented by solid lines and dots respectively.

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Fig. 3
Fig. 3

(a). Schematic diagram showing the transverse phase matching condition of the multistep cascaded χ(2)-nonlinear Raman Nath diffraction for the different harmonic generation processes observed in this work: Second Harmonic Generation (SHG), Third Harmonic Generation (THG), Fourth Harmonic Generation (FHG) and Fifth Harmonic Generation (FiHG). (b,c) Far field nonlinear patterns recorded when the fundamental beam was fixed at 1900nm and 2300nm, respectively. The inner rings have been labelled as α i (a,b) where “i” correspond to the harmonic order (i = 2,...5) and (a,b) is the order of the NLRN process involved. (d) Angular dependence of the generated conical NLRN patterns as a function of the fundamental wavelength. Theoretical fittings (solid lines), experimental data (coloured dots). Blue, orange and green lines correspond to 3th, 4th and 5th harmonics, respectively.

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Fig. 4
Fig. 4

Experimentally obtained external conical angles for a frequency converted wavelength of 500 nm by different types of phase matching geometries. Solid dots: Cerenkov type high harmonic generation. Open circles: Nonlinear Raman Nath diffraction processes.

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Fig. 5
Fig. 5

Effect of the polarization of the fundamental beam on the generated nonlinear patterns.(a-d) Third and fourth Cerenkov harmonic waves for different linear polarization angles. From left to right: γ = 0°, 45°, 90° and 135°, respectively. (e-f) Far field nonlinear patterns obtained for linearly polarized fundamental beams with polarization states parallel to x (γ = 0°) and y axis (γ = 90°) of the crystal. Fourth and fifth Cerenkov rings along with a set of inner rings arising from NLRN diffraction processes can be distinguished.

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Equations (6)

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Type I k (i+1)ω cos θ (i+1) I = k iω cos θ i + k ω =(i+1)⋅ k ω
Type II k (i+1)ω cos θ (i+1) II = k iω + k ω
cos θ (i+1) I = (i+1)⋅ k ω k (i+1)ω = n ω n (i+1)ω
cos θ (i+1) II = k iω + k ω k (i+1)ω = i⋅ n iω + n ω (i+1)⋅ n (i+1)ω
k 3ω sin α 3 ( a,b ) =| G → m 1 , m 2 + G → n 1 , n 2 |= ( m 1 + n 1 ) 2 + ( m 2 + n 2 ) 2 G o
k iω sin α i ( a i , b i ) =| G ⇀ m 1 , m 2 + G → n 1 , n 2 +... |= ( m 1 + n 1 +... ) 2 + ( m 2 + n 2 +... ) 2 G o

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