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Moving and stationary spatial-temporal solitons in a resonantly absorbing Bragg reflector

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Abstract

Spatial-temporal characteristics of ultrashort optical pulses in a resonantly absorbing Bragg reflector are numerically evaluated. The moving and stationary spatial-temporal gap solitons are shown to exist in the photonic structure for a finite spatially-distributed light field in a finite thickness sample. A practical method of trapping light pulses in the photonic structure is presented.

©2005 Optical Society of America

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Supplementary Material (3)

Media 1: GIF (710 KB)     
Media 2: GIF (693 KB)     
Media 3: GIF (836 KB)     

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Figures (4)

Fig. 1.
Fig. 1. Animation of the pulse evolution through an RPC with detuning χ = 0. The amplitude of the initial pulse is Ω0 = 0.5. The top panel is the forward-propagating pulse and the bottom panel is the back ward propagating pulse. The numbers in brackets denote the maximum value of the intensity in that plot (727 KB gif animation).
Fig. 2.
Fig. 2. Animation of Gaussian pulse evolution through the RPC. Parameters are the same as Fig. 1 except for χ =1.4 and Ω0 = 5.5 (710 KB gif animation).
Fig. 3.
Fig. 3. Full width of the half maximum of the forward pulse. Solid line: FWHM in the longitude direction; dotted line: FWHM in the transverse direction; space bracketed by the dash line: RPC structure.
Fig. 4.
Fig. 4. The evolution of hyperbolic secant pulse through an RABR with detuning χ = -0.15 and initial amplitude Ω0 = 3.5 (856 KB gif animation).

Equations (9)

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Ω + t = Ω z + i η Ω + P + i F 2 Ω +
Ω t = + Ω + z + i η Ω + + P + i F 2 Ω
P t = i δ P + ( Ω + + Ω ) w
w t = Re ( ( Ω + + Ω ) P * )
Ω + ( x , z , t = 0 ) = Ω 0 exp ( ( z z 0 ) 2 σ z 2 + i χ ( z z 0 ) ) exp ( x 2 σ x 2 )
Ω ( x , z , t = 0 ) = 0
P ( x , z , t = 0 ) = 0
w ( x , z , t = 0 ) = 1
Ω + ( x , z , t = 0 ) = Ω 0 sec h ( ( z z 0 ) σ z ) exp ( i χ ( z z 0 ) ) exp ( x 2 σ x 2 )
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