Negative-Frequency Resonant Radiation

Optical solitons or solitonlike states shed light to blueshifted frequencies through a resonant emission process. We predict a mechanism by which a second propagating mode is generated. This mode, called negative resonant radiation, originates from the coupling of the soliton mode to the negative-frequency branch of the dispersion relation. Measurements in both bulk media and photonic-crystal fibers confirm our predictions.

Figure 1

Typical dispersion relation $k=k(\omega )$, e.g., for fused silica glass with second- and third-order dispersion, (a) in the laboratory reference frame and (b) in the reference frame comoving at the soliton velocity. (c) The dispersion $D=D(\omega )$, as described in the text. Dashed curves indicate the (laboratory frame) negative frequency branches of the dispersion relation. For simplicity, we take $K_{\mathrm{NL}}=0$.

Figure 2

Experimental results for negative RR generation in bulk ${\mathrm{CaF}}_2$. (a) Measured spectra for increasing input energies (indicated next to each curve). The spectra are vertically displaced to increase visibility. The inset shows a sample spectrum ($16\mu \mathrm{J}$ input energy) corrected for the filter response. (b) ${\mathrm{CaF}}_2$ dispersion relation in the comoving frequency versus laboratory-frame wavelength coordinates, $\lambda =2\pi c/|\omega |$. Positions of the predicted RR and negative RR spectral peaks are indicated. The inset is a $20\times$ enlargement of the curve around the ${\lambda }_{\mathrm{RR}}$ wavelength.

Figure 3

Experimental results for negative RR generation in a photonic-crystal fiber. (a)–(b) Measured spectra in the visible and UV regions for three different input energies: 246 pJ (dotted line), 324 pJ (dashed line), and 366 pJ (solid line). (c) Full fiber dispersion relation: positions of the predicted RR and negative RR spectral peaks are indicated. The inset is a $25\times$ enlargement of the curve around the ${\lambda }_{\mathrm{RR}}$ wavelength.