Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays

doi:10.1364/OE.19.023188

Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays

Frank Setzpfandt, Andrey A. Sukhorukov, Dragomir N. Neshev, Roland Schiek, Alexander S. Solntsev, Raimund Ricken, Yoohong Min, Wolfgang Sohler, Yuri S. Kivshar, and Thomas Pertsch »View Author Affiliations

Optics Express, Vol. 19, Issue 23, pp. 23188-23201 (2011)
http://dx.doi.org/10.1364/OE.19.023188

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Abstract

We study experimentally and numerically the dynamics of a recently found topological phase transition for discrete quadratic solitons with linearly coupled SH waves. We find that, although no stationary states are excited in the experimental situation, the generic feature of the phase transition of the SH is preserved. By utilizing simulations of the coupled mode equations we identify the complex processes leading to the phase transition involving spatial focusing and the generation of new frequency components. These distinct signatures of the dynamic phase transition are also demonstrated experimentally.

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics

ToC Category:
Waveguide Arrays

History
Original Manuscript: September 7, 2011
Revised Manuscript: October 16, 2011
Manuscript Accepted: October 20, 2011
Published: November 1, 2011

Virtual Issues
Nonlinear Optics (2011) Optical Materials Express

Citation
Frank Setzpfandt, Andrey A. Sukhorukov, Dragomir N. Neshev, Roland Schiek, Alexander S. Solntsev, Raimund Ricken, Yoohong Min, Wolfgang Sohler, Yuri S. Kivshar, and Thomas Pertsch, "Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays," Opt. Express 19, 23188-23201 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23188

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References

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003). [CrossRef] [PubMed]
A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B43, 163001 (2010). [CrossRef]
H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett.85, 1863–1866 (2000). [CrossRef] [PubMed]
T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett.88, 093901 (2002). [CrossRef] [PubMed]
S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009). [CrossRef]
C. Denz, S. Flach, and Y. S. Kivshar, eds., Nonlinearities in Periodic Structures and Metamaterials (Springer, 2010).
A. B. Aceves, C. D. Angelis, S. Trillo, and S. Wabnitz, “Storage and steering of self-trapped discrete solitons in nonlinear waveguide arrays,” Opt. Lett.19, 332–334 (1994). [CrossRef] [PubMed]
O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett.21, 1105–1107 (1996). [CrossRef] [PubMed]
R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Controlled switching of discrete solitons in waveguide arrays,” Opt. Lett.28, 1942–1944 (2003). [CrossRef] [PubMed]
T. Pertsch, R. Iwanow, R. Schiek, G. I. Stegeman, U. Peschel, F. Lederer, Y. H. Min, and W. Sohler, “Spatial ultrafast switching and frequency conversion in lithium niobate waveguide arrays,” Opt. Lett.30, 177–179 (2005). [CrossRef] [PubMed]
F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008). [CrossRef]
H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998). [CrossRef]
A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica,” Opt. Express14, 6055–6062 (2006). [CrossRef] [PubMed]
J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003). [CrossRef] [PubMed]
R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett.93, 113902 (2004). [CrossRef] [PubMed]
G. I. Stegeman, M. Sheik-Bahae, E. V. Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett.18, 13–15 (1993). [CrossRef] [PubMed]
R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B15, 2255–2268 (1998). [CrossRef]
F. Setzpfandt, A. A. Sukhorukov, D. N. Neshev, R. Schiek, Y. S. Kivshar, and T. Pertsch, “Phase transitions of nonlinear waves in quadratic waveguide arrays,” Phys. Rev. Lett.105, 233905 (2010). [CrossRef]
S. Droulias, K. Hizanidis, J. Meier, and D. Christodoulides, “X - waves in nonlinear normally dispersive waveguide arrays,” Opt. Express13, 1827–1832 (2005). [CrossRef] [PubMed]
Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, “Discrete x-wave formation in nonlinear waveguide arrays,” Phys. Rev. Lett.98, 023901 (2007). [CrossRef] [PubMed]
M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett.103, 113903 (2009). [CrossRef] [PubMed]
S. Carrasco, J. P. Torres, D. Artigas, and L. Torner, “Generation of multicolor spatial solitons with pulsed light,” Opt. Commun.192, 347–355 (2001). [CrossRef]
F. Baronio, A. Barthelemy, S. Carrasco, V. Couderc, C. D. Angelis, L. Lefort, Y. Min, P. H. Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B: Quantum Semiclassical Opt.6, S182–S189 (2004). [CrossRef]
C. Conti and S. Trillo, “X waves generated at the second harmonic,” Opt. Lett.28, 1251–1253 (2003). [CrossRef] [PubMed]
O. Jedrkiewicz, J. Trull, G. Valiulis, A. Piskarskas, C. Conti, S. Trillo, and P. Di Trapani, “Nonlinear x waves in second-harmonic generation: Experimental results,” Phys. Rev. E68, 026610 (2003). [CrossRef]
G. Valiulis, V. Jukna, O. Jedrkiewicz, M. Clerici, E. Rubino, and P. DiTrapani, “Propagation dynamics and x-pulse formation in phase-mismatched second-harmonic generation,” Phys. Rev. A83, 043834 (2011). [CrossRef]
R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Highly localized discrete quadratic solitons,” Opt. Lett.30, 1033–1035 (2005). [CrossRef] [PubMed]
W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, “Integrated optical devices in lithium niobate,” Opt. Photon. News19, 24–31 (2008). [CrossRef]
C. G. Trevino-Palacios, G. I. Stegeman, M. P. D. Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Intensity dependent mode competition in second harmonic generation in multimode waveguides,” Appl. Phys. Lett.67, 170–172 (1995). [CrossRef]
F. Setzpfandt, D. N. Neshev, R. Schiek, F. Lederer, A. Tünnermann, and T. Pertsch, “Competing nonlinearities in quadratic nonlinear waveguide arrays,” Opt. Lett.34, 3589–3591 (2009). [CrossRef] [PubMed]
F. Setzpfandt, A. Sukhorukov, and T. Pertsch, “Discrete quadratic solitons with competing second-harmonic components” (submitted to Phys. Rev. A).
T. Peschel, U. Peschel, and F. Lederer, “Discrete bright solitary waves in quadratically nonlinear media,” Phys. Rev. E57, 1127–1133 (1998). [CrossRef]
A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, “Parametric localized modes in quadratic nonlinear photonic structures,” Phys. Rev. E63, 016615 (2000). [CrossRef]
W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992).
M. Bache, O. Bang, B. B. Zhou, J. Moses, and F. W. Wise, “Optical cherenkov radiation in ultrafast cascaded second-harmonic generation,” Phys. Rev. A82, 063806 (2010). [CrossRef]
J. T. Manassah, “Effects of velocity dispersion on a generated second harmonic signal,” Appl. Opt.27, 4365–4367 (1988). [CrossRef] [PubMed]
L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. van Linden van den Heuvell, “Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects,” Opt. Lett.15, 1464–1466 (1990). [CrossRef] [PubMed]
R. Schiek, R. Iwanow, T. Pertsch, G. I. Stegeman, G. Schreiber, and W. Sohler, “One-dimensional spatial soliton families in optimallyengineered quasi-phase-matched lithium niobate waveguides,” Opt. Lett.29, 596–598 (2004). [CrossRef] [PubMed]
S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001). [CrossRef] [PubMed]
F. Setzpfandt, D. N. Neshev, A. A. Sukhorukov, R. Schiek, R. Ricken, Y. Min, Y. S. Kivshar, W. Sohler, F. Lederer, A. Tünnermann, and T. Pertsch, “Nonlinear dynamics with higher-order modes in lithium niobate waveguide arrays,” Appl. Phys. B: Lasers Opt.104, 487–493 (2011). [CrossRef]
C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett.78, 4749–4752 (1997). [CrossRef]
A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, “Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media,” Opt. Lett.23, 506–508 (1998). [CrossRef]

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[1] D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003). [CrossRef] [PubMed]

[2] A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B43, 163001 (2010). [CrossRef]

[3] H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett.85, 1863–1866 (2000). [CrossRef] [PubMed]

[4] T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett.88, 093901 (2002). [CrossRef] [PubMed]

[5] S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009). [CrossRef]

[6] C. Denz, S. Flach, and Y. S. Kivshar, eds., Nonlinearities in Periodic Structures and Metamaterials (Springer, 2010).

[7] A. B. Aceves, C. D. Angelis, S. Trillo, and S. Wabnitz, “Storage and steering of self-trapped discrete solitons in nonlinear waveguide arrays,” Opt. Lett.19, 332–334 (1994). [CrossRef] [PubMed]

[8] O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett.21, 1105–1107 (1996). [CrossRef] [PubMed]

[9] R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Controlled switching of discrete solitons in waveguide arrays,” Opt. Lett.28, 1942–1944 (2003). [CrossRef] [PubMed]

[10] T. Pertsch, R. Iwanow, R. Schiek, G. I. Stegeman, U. Peschel, F. Lederer, Y. H. Min, and W. Sohler, “Spatial ultrafast switching and frequency conversion in lithium niobate waveguide arrays,” Opt. Lett.30, 177–179 (2005). [CrossRef] [PubMed]

[11] F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008). [CrossRef]

[12] H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett.81, 3383–3386 (1998). [CrossRef]

[13] A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica,” Opt. Express14, 6055–6062 (2006). [CrossRef] [PubMed]

[14] J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003). [CrossRef] [PubMed]

[15] R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett.93, 113902 (2004). [CrossRef] [PubMed]

[16] G. I. Stegeman, M. Sheik-Bahae, E. V. Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett.18, 13–15 (1993). [CrossRef] [PubMed]

[17] R. Schiek, Y. Baek, and G. I. Stegeman, “Second-harmonic generation and cascaded nonlinearity in titanium-indiffused lithium niobate channel waveguides,” J. Opt. Soc. Am. B15, 2255–2268 (1998). [CrossRef]

[18] F. Setzpfandt, A. A. Sukhorukov, D. N. Neshev, R. Schiek, Y. S. Kivshar, and T. Pertsch, “Phase transitions of nonlinear waves in quadratic waveguide arrays,” Phys. Rev. Lett.105, 233905 (2010). [CrossRef]

[19] S. Droulias, K. Hizanidis, J. Meier, and D. Christodoulides, “X - waves in nonlinear normally dispersive waveguide arrays,” Opt. Express13, 1827–1832 (2005). [CrossRef] [PubMed]

[20] Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, “Discrete x-wave formation in nonlinear waveguide arrays,” Phys. Rev. Lett.98, 023901 (2007). [CrossRef] [PubMed]

[21] M. Heinrich, A. Szameit, F. Dreisow, R. Keil, S. Minardi, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Observation of three-dimensional discrete-continuous x waves in photonic lattices,” Phys. Rev. Lett.103, 113903 (2009). [CrossRef] [PubMed]

[22] S. Carrasco, J. P. Torres, D. Artigas, and L. Torner, “Generation of multicolor spatial solitons with pulsed light,” Opt. Commun.192, 347–355 (2001). [CrossRef]

[23] F. Baronio, A. Barthelemy, S. Carrasco, V. Couderc, C. D. Angelis, L. Lefort, Y. Min, P. H. Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B: Quantum Semiclassical Opt.6, S182–S189 (2004). [CrossRef]

[24] C. Conti and S. Trillo, “X waves generated at the second harmonic,” Opt. Lett.28, 1251–1253 (2003). [CrossRef] [PubMed]

[25] O. Jedrkiewicz, J. Trull, G. Valiulis, A. Piskarskas, C. Conti, S. Trillo, and P. Di Trapani, “Nonlinear x waves in second-harmonic generation: Experimental results,” Phys. Rev. E68, 026610 (2003). [CrossRef]

[26] G. Valiulis, V. Jukna, O. Jedrkiewicz, M. Clerici, E. Rubino, and P. DiTrapani, “Propagation dynamics and x-pulse formation in phase-mismatched second-harmonic generation,” Phys. Rev. A83, 043834 (2011). [CrossRef]

[27] R. Iwanow, G. I. Stegeman, R. Schiek, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Highly localized discrete quadratic solitons,” Opt. Lett.30, 1033–1035 (2005). [CrossRef] [PubMed]

[28] W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, “Integrated optical devices in lithium niobate,” Opt. Photon. News19, 24–31 (2008). [CrossRef]

[29] C. G. Trevino-Palacios, G. I. Stegeman, M. P. D. Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Intensity dependent mode competition in second harmonic generation in multimode waveguides,” Appl. Phys. Lett.67, 170–172 (1995). [CrossRef]

[30] F. Setzpfandt, D. N. Neshev, R. Schiek, F. Lederer, A. Tünnermann, and T. Pertsch, “Competing nonlinearities in quadratic nonlinear waveguide arrays,” Opt. Lett.34, 3589–3591 (2009). [CrossRef] [PubMed]

[31] F. Setzpfandt, A. Sukhorukov, and T. Pertsch, “Discrete quadratic solitons with competing second-harmonic components” (submitted to Phys. Rev. A).

[32] T. Peschel, U. Peschel, and F. Lederer, “Discrete bright solitary waves in quadratically nonlinear media,” Phys. Rev. E57, 1127–1133 (1998). [CrossRef]

[33] A. A. Sukhorukov, Y. S. Kivshar, O. Bang, and C. M. Soukoulis, “Parametric localized modes in quadratic nonlinear photonic structures,” Phys. Rev. E63, 016615 (2000). [CrossRef]

[34] W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992).

[35] M. Bache, O. Bang, B. B. Zhou, J. Moses, and F. W. Wise, “Optical cherenkov radiation in ultrafast cascaded second-harmonic generation,” Phys. Rev. A82, 063806 (2010). [CrossRef]

[36] J. T. Manassah, “Effects of velocity dispersion on a generated second harmonic signal,” Appl. Opt.27, 4365–4367 (1988). [CrossRef] [PubMed]

[37] L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. van Linden van den Heuvell, “Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects,” Opt. Lett.15, 1464–1466 (1990). [CrossRef] [PubMed]

[38] R. Schiek, R. Iwanow, T. Pertsch, G. I. Stegeman, G. Schreiber, and W. Sohler, “One-dimensional spatial soliton families in optimallyengineered quasi-phase-matched lithium niobate waveguides,” Opt. Lett.29, 596–598 (2004). [CrossRef] [PubMed]

[39] S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express8, 173–190 (2001). [CrossRef] [PubMed]

[40] F. Setzpfandt, D. N. Neshev, A. A. Sukhorukov, R. Schiek, R. Ricken, Y. Min, Y. S. Kivshar, W. Sohler, F. Lederer, A. Tünnermann, and T. Pertsch, “Nonlinear dynamics with higher-order modes in lithium niobate waveguide arrays,” Appl. Phys. B: Lasers Opt.104, 487–493 (2011). [CrossRef]

[41] C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced kerr effects in quasi-phase-matched quadratic media,” Phys. Rev. Lett.78, 4749–4752 (1997). [CrossRef]

[42] A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, “Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media,” Opt. Lett.23, 506–508 (1998). [CrossRef]

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Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays