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Influence of precursor fields on ultrashort pulse autocorrelation measurements and pulse width evolution

Kurt E. Oughstun and Hong Xiao

Open Access Open Access

Abstract

The influence of the precursor fields of a double resonance Lorentz model dielectric on ultrashort pulse autocorrelation measurements and the resultant dynamical pulse width evolution is presented.

©2001 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Angular frequency dependence of the real and imaginary parts of the complex index of refraction for a double resonance Lorentz model dielectric (solid curves) and the spectral amplitudes for 1cycle, 5 cycle, and 10 cycle Van Bladel envelope pulses (shaded regions).

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Fig. 2.
Fig. 2. Numerically determined propagated field (upper diagram) and the corresponding second-order interferometric autocorrelation (lower diagram) using the exact dispersion model (solid curves) and the cubic dispersion approximation (dotted curves) of the complex wavenumber at 3 absorption depths into the double resonance Lorentz model dielectric.

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Fig. 3.
Fig. 3. Same as in figure 2, but at 5 absorption depths into the dispersive, lossy medium.

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Fig. 4.
Fig. 4. Same as in figure 2, but at 7 absorption depths into the dispersive, lossy medium.

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Fig. 5.
Fig. 5. Same as in figure 2, but at 10 absorption depths into the dispersive, lossy medium.

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Fig. 6.
Fig. 6. Numerically measured relative pulse width as a function of propagation distance (relative to the absorption depth) in a double resonance Lorentz model dielectric for several initial pulse widths.

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Equations (8)

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n ( ω ) = ( 1 − b 2 0 ω 2 − ω 0 2 + 2 i δ 0 ω − b 2 2 ω 2 − ω 2 2 + 2 i δ 2 ω ) 1 2 .
A ( z , t ) = 1 2 π ℜ { i ∫ ia − ∞ ia + ∞ u ˜ ( ω − ω c ) exp [ i ( k ˜ ( ω ) z − ω t ) ] dω }
k ˜ ( ω ) = ∑ j = 0 ∞ 1 j ! k ˜ ( j ) ( ω c ) ( ω − ω c ) j ,
k ˜ ( ω ) ≈ k ˜ ( ω c ) + k ˜ ( 1 ) ( ω c ) ( ω − ω c ) + k ˜ ( 3 ) ( ω c ) 2 ! ( ω − ω c ) 2 + k ˜ ( 3 ) ( ω c ) 3 ! ( ω − ω c ) 3 .
A ( z , t ) = 1 2 π ℜ { i ∫ ia − ∞ ia + ∞ u ~ ( ω − ω c ) exp [ ( z / c ) ϕ ( ω , θ ) ] dω } ,
A ( z , t ) ∼ A S ( z , t ) + A m ( z , t ) + A B ( z , t )
A j ( z , t ) = a j ( c 2 πz ) 1 2 ℜ { i u ˜ ( ω j − ω c ) [ − ϕ ( ω j , θ ) ] 1 2 exp [ z c ϕ ( ω j , θ ) ] }
I A ( z , τ ) = { ∫ − ∞ ∞ ∣ { A ( z , t ) + A ( z , t − τ ) } 2 ∣ 2 dt } ⁄ { 16 ∫ − ∞ ∞ A 4 ( z , t ) dt } ,
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