Soliton-number analysis of soliton-effect pulse compression to single-cycle pulse widths

We demonstrate that the soliton-effect compression to few- and single-cycle pulse widths in a highly nonlinear fiber can be optimized by properly choosing the input soliton number. Soliton compression to a $2\text{−}\mathrm{fs}$ pulse width with a compression ratio up to 50 is demonstrated for light pulses with an initial central wavelength of $1070\mathrm{nm}$ by solving the generalized nonlinear Schrödinger equation for a dispersion profile typical of a small-core photonic-crystal fiber.

Figure 1

(Color online) (a) Compression ratio $\Phi$ as a function of the input soliton number $N$ calculated using the NSE [Eq. (1)] (dashed line) and the GNSE [Eq. (2)] for transform-limited $(\alpha =0)$ hyperbolic-secant light pulses with an input pulse width of $30\mathrm{fs}$ (rectangles), $45\mathrm{fs}$ (open circles), and $60\mathrm{fs}$ (filled circles). (b) The wavelength dependences of the nonlinearity coefficient $\gamma$ (dotted line) and the group-velocity dispersion (solid line) of the fiber used in simulations. Also shown are the series-expansion approximations of the dispersion profile including ${\beta }_k$ terms up to the third ($k=3$, dashed line), fifth ($k=5$, dashed-dotted line), and seventh ($k=7$, open circles) order.

Figure 2

(Color online) Temporal evolution of a transform-limited hyperbolic-secant light pulse with ${\tau }_0=30\mathrm{fs}$ and an input energy of (a) $1.6\mathrm{nJ}$ $(N\approx 3.4)$ and (b) $9\mathrm{nJ}$ $(N\approx 8.1)$ in a fiber with spectral profiles of GVD and $\gamma$ shown in Fig. 1b.

Figure 3

(Color online) Optimal soliton number $N_c$ (filled circles and filled rectangles) and compression quality factor $Q$ (open circles and open rectangles) as functions of the input pulse width for a fiber dispersion profile shown in the inset to Fig. 1 (circles) and a polynomial approximation of the same dispersion profile including dispersion effects up to the third order through ${\beta }_k$ terms with $k⩽3$ (rectangles). The pulse width at $z=z_c$ is $2\mathrm{fs}$ (circles) and $3\mathrm{fs}$ (rectangles).

Figure 4

(Color online) Temporal evolution of a hyperbolic-secant light pulse with ${\tau }_0=30\mathrm{fs}$, $\alpha =-0.05{\mathrm{ps}}^2$, and an initial energy of $6.4\mathrm{nJ}$ in a fiber with spectral profiles of ${\beta }_2$ and $\gamma$ shown in the inset to Fig. 1.

Figure 5

(Color online) The length of optimal compression $z_c$ (circles) and compression quality factor $Q$ (rectangles) as functions of the input pulse width of a linearly chirped hyperbolic-secant pulse with ${\tau }_0=30\mathrm{fs}$, which is compressed to a pulse width of $2\mathrm{fs}$ in a fiber with spectral profiles of ${\beta }_2$ and $\gamma$ shown in the inset to Fig. 1.