TY - JOUR

T1 - Stability and collisions of moving semi-gap solitons in Bragg cross-gratings

AU - Mayteevarunyoo, T.

AU - Malomed, Boris A.

AU - Chu, P. L.

AU - Roeksabutr, A.

N1 - Funding Information:
This work of B.A.M. was supported, in a part, by the Israel Science Foundation through the grant No. 8006/03. T.M. and B.A.M. appreciate hospitality of the Department of Electronics Engineering at the City University of Hong Kong.

PY - 2004/11/15

Y1 - 2004/11/15

N2 - We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity; the same model applies to a fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on the case when the system's spectrum contains no true bandgap, but only semi-gaps (which are gaps only with respect to one branch of the dispersion relation), that nevertheless support soliton families. Solely zero-velocity solitons were previously studied in this system, while current experiments cannot generate solitons with the velocity smaller than half the maximum group velocity. We find the semi-gaps for the moving solitons in an analytical form, and demonstrated that they are completely filled with (numerically found) solitons. Stability of the moving solitons is identified in direct simulations. The stability region strongly depends on the frustration parameter, which controls the difference of the present system from the usual model for the single BG. A completely new situation is possible, when the interval of absolute values of the velocities for stable solitons is limited not only from above, but also from below. Collisions between stable solitons may be both elastic and strongly inelastic. Close to their instability border, the solitons collide elastically only if their velocities c1 and c2 are small; however, collisions between more robust solitons are elastic in a strip around c1 = -c2.

AB - We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity; the same model applies to a fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on the case when the system's spectrum contains no true bandgap, but only semi-gaps (which are gaps only with respect to one branch of the dispersion relation), that nevertheless support soliton families. Solely zero-velocity solitons were previously studied in this system, while current experiments cannot generate solitons with the velocity smaller than half the maximum group velocity. We find the semi-gaps for the moving solitons in an analytical form, and demonstrated that they are completely filled with (numerically found) solitons. Stability of the moving solitons is identified in direct simulations. The stability region strongly depends on the frustration parameter, which controls the difference of the present system from the usual model for the single BG. A completely new situation is possible, when the interval of absolute values of the velocities for stable solitons is limited not only from above, but also from below. Collisions between stable solitons may be both elastic and strongly inelastic. Close to their instability border, the solitons collide elastically only if their velocities c1 and c2 are small; however, collisions between more robust solitons are elastic in a strip around c1 = -c2.

UR - http://www.scopus.com/inward/record.url?scp=7044231559&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2004.08.063

DO - 10.1016/j.physleta.2004.08.063

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AN - SCOPUS:7044231559

SN - 0375-9601

VL - 332

SP - 220

EP - 229

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3-4

ER -