Ultrafast Tilting of the Dispersion of a Photonic Crystal and Adiabatic Spectral Compression of Light Pulses

We demonstrate, by theory and experiment, the ultrafast tilting of the dispersion curve of a photonic-crystal waveguide following the absorption of a femtosecond pump pulse. By shaping the pump-beam cross section with a nanometric shadow mask, different waveguide eigenmodes acquire different spatial overlap with the perturbing pump, leading to a local flattening of the dispersion by up to 11%. We find that such partial mode perturbation can be used to adiabatically compress the spectrum of a light pulse traveling through the waveguide.

Figure 1

(a) Schematic of adiabatic light control. An input light pulse excites eigenmodes of a photonic crystal, whose dispersion ${\omega }_k$ is then blueshifted and flattened by an external perturbation. When no light is scattered between eigenmodes, the pulse undergoes an adiabatic spectral compression. (b) Experimental realization. While a probe pulse travels through a Si-based photonic-crystal waveguide, a pump pulse generates free charge carriers in the illuminated Si regions. The shadow mask causes a $k$-dependent spatial overlap between the waveguide mode and pump pattern.

Figure 2

Theoretical [(a)-(c)] and experimental [(d)-(f)] results for the waveguide dispersion changes. (a) Bottom panel: The shape of the unit cell of the photonic-crystal waveguide together with the shadow mask. Panels (i)–(xi): Profiles of electromagnetic energy density $u_k(\mathit{r})$ of selected waveguide eigenmodes with $k$ indicated in (b). Note the logarithmic color scale. (b) Dispersion ${\omega }_k$ of the waveguide eigenfrequencies. (c) Solid line: Calculated overlap $O_k$ between the eigenmode $k$ [see (a)] and the pump pattern $f(\mathit{r})$ given by the shadow mask (inset). Dashed line: $O_k$ for a spatially uniform change in the Si refractive index. (d) Measured real part of the Fourier-transformed output pulse $E_o(\omega ,\tau )$ versus $\omega$ at 40 ps before (red) and 1 ps after (blue) waveguide pumping. (e) Dispersion curves of unpumped and pumped waveguides as extracted from (d). (f) Dispersion shift $\Delta {\omega }_k$ at several delay times obtained by subtraction of the measured ${\omega }_k$ [see (e)]. Dashed gray line: Theoretical curve of Fig. 2c, repeated for comparison. Bar: Error estimated from signal variations at delays $\tau <-15\mathrm{ps}$.

Figure 3

Adiabatic spectral compression of a light pulse. (a) Output intensity spectra versus $\tau$ for a Fourier-limited input pulse of frequency 194.2 THz and duration of 1.9 ps. (b) Output intensity spectra at delays indicated by arrows in (a), that is, for the mode shift occurring long before, after, or while the probe is inside the waveguide. Spectra are normalized to the same height and shifted to have center frequency $\omega =0$.