TY - GEN

T1 - Transformations of gap solitons in linearly coupled Bragg gratings with a mismatch

AU - Tsofe, Yossi J.

AU - Malomed, Boris A.

PY - 2007

Y1 - 2007

N2 - An optical model based on two linearly coupled Bragg gratings, with equal periodicities and a phase shift 9 between them (mismatch) is considered. For θ = 0, the symmetry-breaking bifurcation of gap solitons (GSs) in this model was investigated before. The objective of the present work is to study an effect of the mismatch on families of symmetric and asymmetric GSs, and bifurcation between them. It is found that the system's bandgap is always completely filled with solitons. The largest velocity of moving solitons, c max, is found as a function of θ and coupling constant. The mismatch transforms symmetric GSs into quasi-symmetric (QS) ones, in which the two components are not identical, but their peak powers and energies are equal. The QS solitons are stable against symmetry-breaking perturbations as long as asymmetric (AS) solutions do not exist. In addition, the mismatch breaks the spatial symmetry of the GSs, separating peaks in the two components of the soliton, and giving rise to side hump(s) in them. If θ is small, stable AS solitons emerge from their QS counterparts through a supercritical bifurcation. However, for a larger mismatch, the bifurcation may become subcritical. A condition for the stability against oscillatory perturbations is essentially the same as in the ordinary grating: both QS and AS solitons are stable, in this sense, if their intrinsic frequency is positive, i.e., they are stable in a half of the bandgap.

AB - An optical model based on two linearly coupled Bragg gratings, with equal periodicities and a phase shift 9 between them (mismatch) is considered. For θ = 0, the symmetry-breaking bifurcation of gap solitons (GSs) in this model was investigated before. The objective of the present work is to study an effect of the mismatch on families of symmetric and asymmetric GSs, and bifurcation between them. It is found that the system's bandgap is always completely filled with solitons. The largest velocity of moving solitons, c max, is found as a function of θ and coupling constant. The mismatch transforms symmetric GSs into quasi-symmetric (QS) ones, in which the two components are not identical, but their peak powers and energies are equal. The QS solitons are stable against symmetry-breaking perturbations as long as asymmetric (AS) solutions do not exist. In addition, the mismatch breaks the spatial symmetry of the GSs, separating peaks in the two components of the soliton, and giving rise to side hump(s) in them. If θ is small, stable AS solitons emerge from their QS counterparts through a supercritical bifurcation. However, for a larger mismatch, the bifurcation may become subcritical. A condition for the stability against oscillatory perturbations is essentially the same as in the ordinary grating: both QS and AS solitons are stable, in this sense, if their intrinsic frequency is positive, i.e., they are stable in a half of the bandgap.

KW - Bandgap

KW - Subcritical bifurcation

KW - Supercritical bifurcation

KW - Symmetry breaking

UR - http://www.scopus.com/inward/record.url?scp=34249006009&partnerID=8YFLogxK

U2 - 10.1117/12.726974

DO - 10.1117/12.726974

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AN - SCOPUS:34249006009

SN - 0819467421

SN - 9780819467423

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - 14th International School on Quantum Electronics

T2 - 14th International School on Quantum Electronics: Laser Physics and Applications

Y2 - 18 September 2006 through 22 September 2006

ER -