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Photonic integrated circuits with second-order (χ⁽²⁾) nonlinearities are rapidly scaling to remarkably low powers. At this time, state-of-the-art devices achieve saturated nonlinear interactions with thousands of photons when driven by continuous-wave lasers, and further reductions in these energy requirements enabled by the use of ultrafast pulses may soon push nonlinear optics into the realm of single-photon nonlinearities. This tutorial reviews these recent developments in ultrafast nonlinear photonics, discusses design strategies for realizing few-photon nonlinear interactions, and presents a unified treatment of ultrafast quantum nonlinear optics using a framework that smoothly interpolates from classical behaviors to the few-photon scale. These emerging platforms for quantum optics fundamentally differ from typical realizations in cavity quantum electrodynamics due to the large number of coupled optical modes. Classically, multimode behaviors have been well studied in nonlinear optics, with famous examples including soliton formation and supercontinuum generation. In contrast, multimode quantum systems exhibit a far greater variety of behaviors, and yet closed-form solutions are even sparser than their classical counterparts. In developing a framework for ultrafast quantum optics, we identify what behaviors carry over from classical to quantum devices, what intuition must be abandoned, and what new opportunities exist at the intersection of ultrafast and quantum nonlinear optics. Although this article focuses on establishing connections between the classical and quantum behaviors of devices withχ⁽²⁾nonlinearities, the frameworks developed here are general and are readily extended to the description of dynamical processes based on third-orderχ⁽³⁾nonlinearities.

 

We propose a new approach to supercontinuum generation and carrier-envelope-offset detection based on saturated second-order nonlinear interactions in dispersion-engineered nanowaveguides. The technique developed here broadens the interacting harmonics by forming stable bifurcations of the pulse envelopes due to an interplay between phase-mismatch and pump depletion. We first present an intuitive heuristic model for spectral broadening by second-harmonic generation of femtosecond pulses and show that this model agrees well with experiments. Then, having established strong agreement between theory and experiment, we develop scaling laws that determine the energy required to generate an octave of bandwidth as a function of input pulse duration, device length, and input pulse chirp. These scaling laws suggest that future realization based on this approach could enable supercontinuum generation with orders of magnitude less energy than current state-of-the-art devices.

 

The sensitivity of gravitational-wave detectors is limited by the mechanical loss associated with the amorphous coatings of the detectors’ mirrors. Amorphous silicon has higher refraction index and lower mechanical loss than current high-index coatings, but its optical absorption at the wavelength used for the detectors is at present large. The addition of hydrogen to the amorphous silicon network reduces both optical absorption and mechanical loss for films prepared under a range of conditions at all measured wavelengths and temperatures, with a particularly large effect on films grown at room temperature. The uptake of hydrogen is greatest in the films grown at room temperature, but still below 1.5 at.% H, which show an ultralow optical absorption (below 10 ppm) measured at 2000 nm for 500-nm-thick films. These results show that hydrogenation is a promising strategy to reduce both optical absorption and mechanical loss in amorphous silicon, and may enable fabrication of mirror coatings for gravitational-wave detectors with improved sensitivity. 

This article reviews recent progress in quasi-phasematched${\chi }^{(2)}$nonlinear nanophotonics, with a particular focus on dispersion-engineered nonlinear interactions. Throughout this article, we establish design rules for the bandwidth and interaction lengths of various nonlinear processes, and provide examples for how these processes can be engineered in nanophotonic devices. In particular, we apply these rules towards the design of sources of non-classical light and show that dispersion-engineered devices can outperform their conventional counterparts. Examples include ultra-broadband optical parametric amplification as a resource for measurement-based quantum computation, dispersion-engineered spontaneous parametric downconversion as a source of separable biphotons, and synchronously pumped nonlinear resonators as a potential route towards single-photon nonlinearities.

 

We establish a model for supercontinuum generation in dispersion-engineered χ(2) nanowaveguides based on saturated second-harmonic generation, and show that this process exhibits favorable scaling laws when compared to approaches based on χ(3) nonlinearities. 

Abstract We report on the development and extensive characterization of co-sputtered tantala–zirconia (Ta 2 O 5 -ZrO 2 ) thin films, with the goal to decrease coating Brownian noise in present and future gravitational-wave detectors. We tested a variety of sputtering processes of different energies and deposition rates, and we considered the effect of different values of cation ratio η = Zr/(Zr + Ta) and of post-deposition heat treatment temperature T a on the optical and mechanical properties of the films. Co-sputtered zirconia proved to be an efficient way to frustrate crystallization in tantala thin films, allowing for a substantial increase of the maximum annealing temperature and hence for a decrease of coating mechanical loss φ c . The lowest average coating loss was observed for an ion-beam sputtered sample with η = 0.485 ± 0.004 annealed at 800 °C, yielding φ ¯ c = 1.8 × 1 0 − 4 rad. All coating samples showed cracks after annealing. Although in principle our measurements are sensitive to such defects, we found no evidence that our results were affected. The issue could be solved, at least for ion-beam sputtered coatings, by decreasing heating and cooling rates down to 7 °C h −1 . While we observed as little optical absorption as in the coatings of current gravitational-wave interferometers (0.5 parts per million), further development will be needed to decrease light scattering and avoid the formation of defects upon annealing.