Solitary Pulse Generation by Backward Raman Scattering in ${\mathbf{H}}_2$-Filled Photonic Crystal Fibers

Using a hydrogen-filled hollow-core photonic crystal fiber as a nonlinear optical gas cell, we study amplification of ns-laser pulses by backward rotational Raman scattering. We find that the amplification process has two characteristic stages. Initially, the pulse energy grows and its duration shortens due to gain saturation at the trailing edge of the pulse. This phase is followed by formation of a symmetric pulse with a duration significantly shorter than the phase relaxation time of the Raman transition. Stabilization of the Stokes pulse profile to a solitonlike hyperbolic secant shape occurs as a result of nonlinear amplification at its front edge and nonlinear absorption at its trailing edge (caused by energy conversion back to the pump field), leading to a reshaped pulse envelope that travels at superluminal velocity.

Figure 1

Schematic of the experimental setup for the study of pulse amplification by backward rotational SRS in a hydrogen-filled HC-PCF.

Figure 2

Temporal structure of amplified Stokes pulses measured after propagation along 1.5 m of HC-PCF filled with ${\mathrm{H}}_2$ at 3 bar for pump energies of 4, 8, 12, 16, and $20\mu \mathrm{J}$. The seed Stokes pulse is shown with a dashed line, magnified by a factor of 50. The inset shows a single shot measurement of the amplified Stokes pulse envelope at a pressure of 1.5 bar.

Figure 3

(a) Duration and temporal position of the peak of the amplified Stokes pulses as a function of pump energy (HC-PCF is filled with hydrogen at 3 bar). (b) Experimental output Stokes pulse shapes (see Fig. 2) normalized to their peak intensity for increasing values of pump energy from right to left: 8, 12, 16, 20, $24\mu \mathrm{J}$.

Figure 4

The intensity envelopes of the pump (shaded in gray) and Stokes (red line) pulses shown at different times in a reference frame moving at the Stokes velocity $v_s$. Temporal compression of the Stokes pulse ($t<3\mathrm{ns}$) is followed by the formation of a quasisoliton pulse traveling faster than the velocity of light $v_s$ (the vertical dashed line shows the position of Stokes light moving at exactly $v_s$). The inset shows the amplitudes of the pump and the quasisoliton pulse. Also shown is the long-lived Raman coherence at Doppler line center (slanted line fill).