Bridging the gap between ultrafast optics and resonant photonics via omni-resonance

Abstract

High-finesse planar Fabry-P{é}rot (FP) cavities spectrally filter the incident field at discrete resonances, and thus cannot be utilized to resonantly enhance the field of ultrashort pulses. Introducing judicious angular dispersion into a pulse can give rise to `omni-resonance', whereby the entire bandwidth of a spatiotemporally structured ultrafast pulse couples to a single longitudinal cavity resonance, even when the pulse bandwidth far exceeds the resonant linewidth. Here we show that omni-resonance increases the intra-cavity peak intensity above that of a pulse having equal energy and bandwidth when tightly focused in free space -- maintained across its entire bandwidth and along a cavity longer than the Rayleigh length of the focused pulse. This paves the way towards broadband resonant enhancement of nonlinear optical effects, thereby bridging the gap between ultrafast optics and resonant photonics.

Figures (7)

• Figure 1: (a) Coupling a plane-wave pulse to a planar FP cavity. The temporal profile and spectrum before and after the cavity are plotted on the left and right, respectively. In the middle we depict the FP cavity and the transfer function $T_{\mathrm{FP}}(0,\omega)$. (b) Coupling a focused Gaussian pulse to the FP cavity. The panels are similar to (a), but spatiotemporal profiles here replace the purely temporal counterparts. (c-f) Omni-resonance. (c) The spatiotemporal profile and spectrum for a plane-wave pulse. (d) Setup to pre-condition the plane-wave pulse for omni-resonance. (e) Spectral support for the omni-resonant field on the free-space and cavity light-cones, along with the spectral projection onto the $(k_{x},\tfrac{\omega}{c})$-plane. (f) Same as (b) for the omni-resonant configuration.
• Figure 2: (a) Energy fraction coupled to the cavity from a focused Gaussian pulse $\Delta\mathcal{E}_{\mathrm{G}}$ and (b) an omni-resonant STWP $\Delta\mathcal{E}_{\mathrm{ST}}$. (c) Cavity enhancement $\eta_{\mathrm{ST}}$ for the omni-resonant STWP with respect to free space. The inset shows the STWP free-space peak intensity while varying $\delta\lambda_{\mathrm{ST}}$. (d) The spatiotemporal spectrum $|\widetilde{\psi}(k_{x},\omega)|^{2}$ and intensity profile $I(x,z=0;t)$ for two omni-resonant STWPs with $\delta\lambda_{\mathrm{ST}}=40$ pm and 200 pm, corresponding to the points in the inset in (c).
• Figure 3: Field resonant enhancement $\eta_{\mathrm{G}}$ for a focused Gaussian pulse with respect to its free-space counterpart. The columns correspond to different bandwidths $\Delta\lambda$, and the rows to different cavity lengths $d$. Two color palettes distinguish the regimes $\eta_{\mathrm{G}}<1$ (blue) and $\eta_{\mathrm{G}}>1$ (red).
• Figure 4: Cavity enhancement $\eta_{\mathrm{ST,G}}$ for an omni-resonant STWP with respect to a free-space focused Gaussian pulse (holding $\mathcal{E}$ and $\Delta x$ fixed). The columns correspond to bandwidths $\Delta\lambda$, and the rows to cavity lengths $d$. Two color palettes distinguish the regimes $\eta_{\mathrm{ST,G}}<1$ (blue) and $\eta_{\mathrm{ST,G}}>1$ (red).
• Figure 5: Energy fraction $\Delta\mathcal{E}_{\mathrm{G}}$ of a focused Gaussian pulse coupled to a planar FP cavity. Each column corresponds to a fixed temporal bandwidth $\Delta\lambda=3.35,6.7$, and 13.4 nm, and each row corresponds to a different cavity length $d=2,5$, and 10 $\upmu$m. In each panel we vary the spectral uncertainty $\delta\lambda_{\mathrm{ST}}$ and the cavity finesse $\mathcal{F}$. The central panel corresponds to Fig. 2(a) in the main text. The initial energy is held constant throughout.