By Govind Agrawal
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Extra resources for Applications of Nonlinear Fiber Optics, Second Edition (Optics and Photonics Series)
9). 6 because they are stationary in the local reference frame of a moving dynamic grating. Physically, each such gap soliton represents a superposition of two pulses of different frequencies (ω0 ± Ω) that would travel at different speeds in the absence of the grating. Indeed, numerical solutions of Eqs. 7) with κ = 0 show that the two pulses separate rapidly . 5 THz and ψ = π/ 2. When a dynamic grating is present, the two pulses form a gap soliton that is trapped by the grating and appears stationary in the frame of the input pulse.
In a phase-sampled grating –, the magnitude of κ remains ﬁxed but its phase varies periodically along the grating. In all cases, κ(z) Chapter 1. 5-mm superstructure grating with d = 1 mm. (After Ref. ) becomes a periodic function of z. It is this periodicity that modiﬁes the stop band of a uniform grating. The period d of κ(z) is typically ∼1 mm. If the average index n¯ also changes with the same period d, both δ and κ become periodic in the nonlinear coupled-mode equations. 6 for a uniform grating.
In the case of CW beams, the set of four coupled equations was solved numerically in 1994 and several birefringence-related nonlinear effects were identiﬁed . 3 of Ref. . The critical power at which this instability occurs is reduced considerably in the presence of a Bragg grating . Nonlinear birefringence also affects Bragg solitons. In the NLS limit (γP0 κ), the four equations reduce a pair of coupled NLS equations. 11) where Δβ ≡ β0 x − β0 y is related to the beat length LB as Δβ = 2π/ LB .