Physical Factors Limiting the Spectral Extent and Band Gap Dependence of Supercontinuum Generation

Based on simulations of femtosecond pulse propagation in water we elucidate the physical factors that limit the attainable spectral extent of supercontinuum generation in bulk media. In contrast to the standard scenario, where arrest of self-focusing collapse by multiphoton absorption and plasma defocusing are viewed as imposing a limit to supercontinuum broadening, we show that linear chromatic dispersion also plays a major role. This insight provides an intuitive explanation of the observed band gap dependence of the attainable supercontinuum generation in condensed media.

Figure 1

Simulated wide-angle integrated SC spectra in water for a range of input pulse energies and $\xi =8.03\mathrm{c}\mathrm{m}$. Except for small absorption in the far infrared region, the spectra do not further evolve with increasing propagation distance.

Figure 2

On-axis electron densities and pulse intensities for both water and the artificial medium for an input pulse energy of $6\mu \mathrm{J}$.

Figure 3

On-axis variation of the real part of the local change in optical susceptibility $\mathrm{R}\mathrm{e}[\Delta \chi (0,\xi ,\tau )]$ for both water and the artificial medium at distances $\xi =7.78\mathrm{c}\mathrm{m}$ and $\xi =8.03\mathrm{c}\mathrm{m}$, and a pulse energy of $6\mu \mathrm{J}$. The curves for water (full lines) and the artificial medium (dashed lines) are barely discernible.

Figure 4

SC spectra for both water and the artificial medium, for a pulse energy of $6\mu \mathrm{J}$ and $\xi =8.03\mathrm{c}\mathrm{m}$. To correlate the changes in the spectra with the model susceptibilities, the real part of susceptibility is shown for both media.

Figure 5

Contour of the phase-matching boundaries (4) determined for water by the time scale ${\tau }_{\mathrm{s}\mathrm{c}\mathrm{l}}$ for an “incident” wave vector $\overrightarrow{v}=2\pi /\lambda \overrightarrow{z}$, corresponding to the pulse central wavelength $\lambda$ equal to 400 and 800 nm (indicated by labels). The full lines limit the region of allowed scattered wave vectors $\overrightarrow{v}+\overrightarrow{l}$ that satisfy the relaxed phase-matching condition (4) with ${\tau }_{\mathrm{s}\mathrm{c}\mathrm{l}}={10}^{-12}\mathrm{s}$. Dotted lines serve as a dual coordinate system showing the wavelength and the propagation angle.