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Dynamics of ultrashort pulse propagation through fiber gratings

Lawrence R. Chen, J. E Sipe, Seldon D. Benjamin, Howard Jung, and Peter W. E. Smith

Open Access Open Access

Abstract

By directly integrating the time-domain coupled-mode equations, we can explicitly obtain and examine the backward and forward propagating waves as a function of position and time within fiber grating structures. We apply this numerical procedure to calculate the temporal reflection and transmission response of fiber gratings subject to ultrashort pulse inputs. This allows us to study the dynamics of the ultrashort pulse-grating interaction.

©1997 Optical Society of America

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Supplementary Material (3)

Media 1: MOV (6649 KB)     
Media 2: MOV (5401 KB)     
Media 3: MOV (5737 KB)     

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Figures (3)
Fig. 1.
Fig. 1. A single frame from the movie illustrating the propagation of a 1-ps pulse through a weak uniform grating. The dotted lines indicate the grating boundaries. The backward propagating wave appears in red and the forward propagating wave in blue. The peak of the forward propagating pulse is off the scale since the scale has been expanded to retain as much detail as possible. To run the movie, click on the above figure. [Media 1]

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Fig. 2.
Fig. 2. A single frame from the movie illustrating the propagation of a 1-ps pulse through a weak uniform grating. The dotted lines indicate the grating boundaries. The backward propagating wave appears in red and the forward propagating wave in blue. The peak of the forward propagating pulse is off the scale since the scale has been expanded to retain as much detail as possible. To run the movie, click on the above figure. [Media 2]

Download Full Size | PDF

Fig. 3.
Fig. 3. A single frame from the movie illustrating the propagation of a 1-ps pulse through a very strong uniform grating. The dotted lines indicate the grating boundaries. The backward propagating wave appears in red and the forward propagating wave in blue. The peak of the forward propagating pulse is initially off the scale since the scale has been expanded to retain as much detail as possible. To run the movie, click on the above figure. [Media 3]

Download Full Size | PDF

Tables (1)

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Table 1. Characteristics of gratings used in the numerical simulations.

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Equations (4)

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n ( z ) = n 0 + σ ( z ) + 2 κ ( z ) cos [ 2 k 0 z + ϕ ( z ) ]
E z t = a + z t e − j ( ω 0 t + δt − k 0 z + ϕ ( z ) 2 ) + a − z t e − j ( ω 0 t + δt + k 0 z − ϕ ( z ) 2 )
j ( ∂ a + ζ t ∂ ζ + n 0 c k 0 ∂ a + ζ t ∂ ζ ) + ( σ ( ζ ) 2 n 0 2 + n 0 δ c k 0 − 1 2 ϕ ′ ( ζ ) ) a + ( ζ , t ) + κ ( ζ ) 2 n 0 2 a − ζ t = 0
− j ( ∂ a − ζ t ∂ ζ − n 0 c k 0 ∂ a − ζ t ∂ t ) + ( σ ( ζ ) 2 n 0 2 + n 0 δ c k 0 − 1 2 ϕ ′ ( ζ ) ) a − ζ t + κ ( ζ ) 2 n 0 2 a + ζ t = 0
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