Abstract

We experimentally study polarization dependent linear and nonlinear dynamics in waveguide arrays. We found that in certain arrays, the band structure and the modal shapes of the array modes are markedly different for the two polarizations, in a manner that cannot be simply explained using the effective index approximation. Specifically, one of the gaps was found to be missing for the TM polarization. In the nonlinear regime, we observe mixed-polarization nonlinear localizations in high bands, such as Band-2 Floquet-Bloch vector solitons. The band structure anomaly enabled the excitation of a multiband moving breather.

© 2005 Optical Society of America

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References

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App. Phys. Lett. (1)

J. S. Aitchison, Jin. U. Kang, G. I. Stegeman, �??Signal Gain due to a polarization coupling in an AlGaAs Channnel Waveguide,�?? App. Phys. Lett 67, 2456 (1995).
[CrossRef]

Appl. Phys. B. (1)

P. St. J. Russell, �??Optics of Floquet-Bloch waves in dielectric gratings,�?? Appl. Phys. B 39, 231 (1986).
[CrossRef]

Appl. Phys. Lett. (2)

A Villeneuve, J.U. Kang, J.S. Aitchison , and G.I. Stegeman, �??Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs multiple quantum well waveguides at half the band gap,�?? Appl. Phys. Lett. 67, 760 (1995)
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho and M. Segev, �??Incoherently coupled soliton pairs in biased photorefractive crystals,�?? Appl. Phys. Lett 68, 1763 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, �??The nonlinear optical properties of AlGaAs at the half band gap,�?? IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

JOSA B (1)

A. Schauer, I. V. Melnikov and J. S. Aitchison, �??Collisions of orthogonally polarized spatial solitons in AlGaAs slab waveguides,�?? JOSA B 21, 57 (2004).
[CrossRef]

Nature (2)

D. N. Christodoulides, F. Lederer and Y. Silberberg, �??Discretizing light behavior in linear and nonlinear waveguide lattices,�?? Nature 424, 817 (2003).
[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,�?? Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rep. (1)

S. Flach and C. R. Willis, �??Discrete Breathers,�?? Phys. Rep. 295, 181 (1998)
[CrossRef]

Phys. Rev. Let. (1)

A. A. Sukhorukov and Yu. S. Kivshar, �??Multigap discrete vector solitons,�?? Phys. Rev. Lett. 91, 113902-4 (2003)
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Ahkmediev, �??Observation of Manakov soliton in AlGaAs planar waveguides,�?? Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. E. Fleischer, M. Segev, and D. N. Christodoulides, �??Multi-band vector lattice solitons,�?? Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. Eisenberg, Y. Silberberg, R. Morandotti and J.S. Aitchison �??Observation of mutually trapped multiband optical breathers in waveguide arrays,�?? Phys. Rev. Lett. 90, 253902 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays,�?? Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

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 (1998).
[CrossRef]

D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti and J.S. Aitchison, �??Band Structure of Waveguide Arrays and Excitation of Floquet-Bloch Solitons,�?? Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

D. Mandelik, R. Morandotti, J.S. Aitchison and Y. Silberberg, �??Gap solitons in waveguide arrays,�?? Phys. Rev. Lett. 92, 93904 (2004)
[CrossRef]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Yu. S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,�?? Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Science (1)

G. I. Stegeman and M. Segev, �??Optical spatial solitons and their interactions: universality and diversity,�?? Science 286, 1518 (1999).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

V.E. Zakharov, A.B. Shabat, �??Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,�?? Sov. Phys. JETP 34, 62 (1972)

S. V. Manakov, �??On the theory of two-dimensional stationary self-focusing of electromagnetic waves,�?? Sov. Phys. JETP 38, 248 (1974).

Supplementary Material (2)

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Figures (10)

Fig. 1.
Fig. 1.

Band gap structure of a waveguide array and measured Floquet-Bloch modes of each band: Calculated band gap structure for the waveguide array (left) reveals the allowed bands and the gaps. Light coupled to forbidden ß is reflected back from the array, while light coupled to allowed ß is coupled to a band specific Floquet-Bloch mode (right) (following ref. [5]).

Fig. 2.
Fig. 2.

The experimental setup. Inset: schematic drawing of the sample and the light coupling geometry

Fig. 3.
Fig. 3.

Measured band gap structure of a waveguide array in TE and TM polarizations: Cross sections of the measured intensity distribution at the sample output as a function of the input beam angle for (a) TE polarization and (b) TM polarization. For angles that match the band gaps the beam is reflected from the array interface, back into the continuum region. Between the gaps, the beam excites pure FB modes. For the TM polarization the gap between band 2 and band 3 is missing.

Fig. 4.
Fig. 4.

Band 2 to Band 3 transition in TE and TM (movies): These movies show a magnified image of the beam at the array output, with input beam angle scanned around the transition between bands 2 and 3 for TE (top) and TM (bottom) polarization. The characteristic modal shapes for bands 2 and 3 are clearly observed. In the TE polarization there is a significant reduction in the transmission intensity at angles corresponding to the transition between bands 2 and 3 due to the gap reflection, and the transition seems discontinuous. In the TM polarization the transition is smoother — the reduction of transmitted intensity in the transition angles caused by the gap reflection seems to be much lower, and the evolution of the 2nd band modal shape into the 3rd is smooth and clearly seen. [Media 1] [Media 2]

Fig. 5.
Fig. 5.

Photographs taken at the array output, for a mixed input beam at an angle of 43 mrad, in which the TE component (top panel) is coupled mainly the second band, while the TM component (bottom panel) is coupled mostly the third, as can be clearly seen from the different modal shapes.

Fig. 6.
Fig. 6.

Different TE and TM modal shapes in the second band: A magnified view showing the different modal shapes of the second band for TE (top) and TM (bottom) polarizations.

Fig. 7.
Fig. 7.

Formation of Floquet-Bloch solitons for TE (a) and TM (b) beams (top — low power, bottom — high power), coupled to band 2. Both polarizations exhibit self focusing and soliton formation, while keeping their characteristic modal shapes, being different for TE and TM polarizations, as in the linear case.

Fig. 8.
Fig. 8.

Formation of a band-2 FB vector solitons: A beam with nearly equal TE and TM components was launched into the waveguide array in a side coupling geometry, such that a pure band-2 is exited in the array, as can be clearly seen from the characteristic modal shape. (a) At low power the mixed input beam diffracts strongly. (b) At high peak power of 1100 W the beam focuses to its input width, implying that a band-2 FB vector soliton has formed. At this state, the beam constitutes a TE component with a peak power of 540 W (c) and a TM component with a peak power of 560 W (d). When launching each component separately into the array, at a power which equals that of the corresponding component constituting the mixed beam, the TE (e) and TM (f) components do not localize (although focusing somewhat). This proves that indeed, a jointly-trapped vector soliton has been excited in the array.

Fig. 9.
Fig. 9.

Guiding of a weak Floquet-Bloch mode by a bright, orthogonally polarized Floquet-Bloch soliton: A beam which consists of a low peak power (170 W) TE component and a high peak power (1380 W) TM component is launched into band 2. When both components are present they exhibit focusing. (a) Shows both components, (b) shows the TM component and (c) the TE component. (d) Shows the TE beam at the same peak power (170 W) without the TM component being present. The presence of a high power TM beam has induced focusing of the weak TE component as well.

Fig. 10.
Fig. 10.

A multiband moving breather formation and breakup: (a) A view of the array’s output facet with the input beam tilted to an angle in which a moving breather is formed at low output power (top), medium (middle) and high power (bottom). The beam is composed of two different bands at all powers, as can be easily seen from the different characteristic modal shapes of the 2nd and 3rd band on the left and on the right. (b) Normalized output intensity distribution at the output facet as a function of output power. Clear focusing of the beam is observed, and then the beam breaks up into two components, each component residing in a different band. (c) Photograph of the waveguide array as seen from above, showing the multiphoton florescence emitted by beam, exhibiting a clear beating pattern.

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