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We apply in simulation a reservoir computer based on evanescently coupled GaAs microrings for real-time compensation of a nonlinear distortion of a 50 Gbaud 16-QAM signal with the launch power up to 12 dBm in a standard single-mode optical fibre. We clearly evidence the crucial role of fast nonlinear response in enabling all-optical signal recovery in real time. With our system we are able to reduce the signal error rate below the forward error correction limit for a 20 km fibre and 12 dBm launch power., Comment: 13 pages, 5 figures

We consider theoretically a network of directly coupled optical microcavities to implement a space-multiplexed optical neural network in an integrated nanophotonic circuit. Nonlinear photonic network integrations based on direct coupling ensures a highly dense integration, reducing the chip footprint by several orders of magnitude compared to other implementations. Different nonlinear effects inherent to such microcavities are studied when used for realizing an all-optical autonomous computing substrate, here based on the reservoir computing concept. We provide an in-depth analysis of the impact of basic microcavity parameters on computational metrics of the system, namely, the dimensionality and the consistency. Importantly, we find that differences between frequencies and bandwidths of supermodes formed by the direct coupling is the determining factor of the reservoir's dimensionality and its scalability. The network's dimensionality can be improved with frequency-shifting nonlinear effects such as the Kerr effect, while two-photon absorption has an opposite effect. Finally, we demonstrate in simulation that the proposed reservoir is capable of solving the Mackey-Glass prediction and the optical signal recovery tasks at GHz timescale.

We introduce a numerical procedure which permits to drastically accelerate the design of multimode photonic crystal resonators. Specifically, we demonstrate that the optical response of an important class of such nanoscale structures is reproduced accurately by a simple, one-dimensional model, within the entire spectral range of interest. This model can describe a variety of tapered photonic crystal structures. Orders of magnitude faster to solve, our approach can be used to optimize certain properties of the nanoscale cavity. Here we consider the case of a nanobeam cavity, where the confinement results from the modulation of its width. The profile of the width is optimized, in order to flatten the resonator dispersion profile (so that all modes are equally spaced in frequency). This result is particularly relevant for miniaturizing parametric generators of non-classical light, optical nano-combs and mode-locked laser sources. Our method can be easily extended to complex geometries, described by multiple parameters.

Canonical Four-Wave-Mixing occurs in a resonator with only the required number of modes, thereby inhibiting competing parametric processes. The properties of the recently introduced photonic crystal parametric oscillator, Marty et al. Nat. Photonics, 15, 53 (2021), are discussed extensively. We compare the bichromatic design with other geometries of photonic crystal resonators. Based on a statistical study over more than 100 resonators and 10 parametric oscillators, robustness against fabrication tolerances is assessed, performances are evaluated in terms of average values and their dispersion, and the dependence on the main parameters is shown to follow the theoretical scaling. The lowest pump power at threshold is $\approx$ 40 $\mu$W and we show the existence of a minimum value of the cavity photon lifetime as a condition for parametric oscillation, which is related to three photon absorption., Comment: 14 pages, 12 figures

A new process to produce Orientation-Patterned Gallium Phosphide (OP-GaP) on GaAs with almost perfectly parallel domain boundaries is presented. Taking advantage of the chemical selectivity between phosphides and arsenides, OP-GaP is processed into suspended shallow-ridge waveguides. Efficient Second-Harmonic Generation from Telecom wavelengths is achieved in both Type-I and Type-II polarisation configurations. The highest observed conversion efficiency is \SI{200}{\percent\per\watt\per\centi\meter\squared}, with a bandwidth of \SI{2.67}{\nano\meter} in a \SI{1}{\milli\meter}-long waveguide. The variation of the conversion efficiency with wavelength closely follows a squared cardinal sine function, in excellent agreement with theory, confirming the good uniformity of the poling period over the entire length of the waveguide., Comment: 21 pages, 6 figures

We demonstrate a nonlinear photomodulation spectroscopy method to image the mode profile of a high-Q photonic crystal resonator (PhCR). This far-field imaging method is suitable for ultrahigh-Q cavities which we demonstrate on a Q = 619000 PhCR. We scan the PhCR surface with a 405 nm pump beam that modulates the refractive index by local thermal tuning, while probing the response of the resonance. We enhance resolution by probing at high power, using the thermo-optical nonlinearity of the PhCR. Spatial resolution of the thermo-optical effect is typically constrained by the broad thermal profile of the optical pump. Here we go beyond the thermal limit and show that we can approach the diffraction limit of the pump light. This is due to free carrier absorption that heats up the PhCR only when there is overlap between the optical pump spot and the optical mode profile. This is supported with a thermo-optical model that reproduces the high-resolution mode mapping. Results reveal that the observed enhanced resolution is reached for surprisingly low carrier density.

Time-correlated photon pairs are generated by triply-resonant Four-Wave-Mixing in a In$_{0.5}$Ga$_{0.5}$P Photonic Crystal cavitiy. Maximal efficiency is reached by actively compensating the residual spectral misalignment of the cavity modes. The generation rate reaches 5 MHz in cavities with Q-factor $\approx 4\times 10^4$, more than one order of magnitude larger than what is measured using ring resonators with similar Q factors fabricated on the same chip. The Photonic Crystal source is integrated on a Si photonic circuit, an important asset for applications in quantum technologies.

Stochastic computing allows a drastic reduction in hardware complexity using serial processing of bit streams. While the induced high computing latency can be overcome using integrated optics technology, the design of realistic optical stochastic computing architectures calls for energy efficient switching devices. Photonics Crystal (PhC) nanocavities are $\mu m^2$ scale devices offering 100fJ switching operation under picoseconds-scale switching speed. Fabrication process allows controlling the Quality factor of each nanocavity resonance, leading to opportunities to implement architectures involving cascaded gates and multi-wavelength signaling. In this report, we investigate the design of cascaded gates architecture using nanocavities in the context of stochastic computing. We propose a transmission model considering key nanocavity device parameters, such as Quality factors, resonance wavelength and switching efficiency. The model is calibrated with experimental measurements. We propose the design of XOR gate and multiplexer. We illustrate the use of the gates to design an edge detection filter. System-level exploration of laser power, bit-stream length and bit-error rate is carried out for the processing of gray-scale images. The results show that the proposed architecture leads to 8.5nJ/pixel energy consumption and 512ns/pixel processing time.

We theoretically and experimentally investigate type II second harmonic generation in III-V-on-insulator wire waveguides. We show that the propagation direction plays a crucial role and that longitudinal field components can be leveraged for robust and efficient conversion. We predict that the maximum theoretical conversion is larger than that of type I second harmonic generation for similar waveguide dimensions and reach an experimental conversion efficiency of 12 %/W, limited by the propagation loss.

Miniaturization of devices has been a primary objective in microelectronics and photonics for decades, aiming at denser integration, enhanced functionalities and drastic reduction of power consumption. Headway in nanophotonics is currently linked to the progress in concepts and technologies necessary for applications in information and communication, brain inspired computing, medicine and sensing and quantum information. Amongst all nanostructures, semiconductor photonic crystals (PhCs) occupy a prominent position as they enable the fabrication of quasi ultimate optical cavities. Low threshold laser diodes or Raman lasers , low power consuming optical memories , efficient single photon sources or single photon quantum gates are impressive examples of their capabilities. We report the demonstration of about 20 micron long PhC semiconductor optical parametric oscillator (OPO) at telecom wavelength exploiting nearly diffraction limited optical modes. The pump power threshold is measured below 0.2 mW. Parametric oscillation was reached through the drastic enhancement of Kerr optical Four Wave Mixing by thermally tuning the high Q modes of a nanocavity into a triply resonant configuration. Miniaturization of this paradigmatic source of coherent light paves the way for quantum optical circuits, dense integration of highly efficient nonlinear sources of squeezed light or entangled photons pairs., Comment: submitted manuscript

The different dynamical behaviors of the Hermite-Gaussian (HG) modes of mode-locked nanolasers based on a harmonic photonic cavity are investigated in detail using a model based on a modified Gross-Pitaevskii Equation. Such nanolasers are shown to exhibit mode-locking with a repetition rate independent of the cavity length, which is a strong asset for compactness.The differences with respect to conventional lasers are shown to originate from the peculiar gain competition between HG modes, which is investigated in details. In the presence of a saturable absorber, the different regimes, i. e. Q-switching, Q-switched mode-locking, and continuous-wave (cw) mode locking, are isolated in a phase diagram and separately described. Mode-locking is found to be robust against phase-intensity coupling and to be achievable in a scheme with spatially separated gain and absorber., Comment: to be published in Physical Review A

We design a focusing grating coupler by a simultaneous apodization of the filling factor and the period. In addition to in plane focusing to the input waveguide providing a total length of less than 70{\mu}m, a further apodization of the curvature allows out of plane focusing into a fiber set 150{\mu}m away from the grating surface. The design is proposed for novel semiconductor on insulator waveguides such as GaInP. The coupling efficiency is calculated from two dimensional simulation which is about 45%., Comment: 7 pages, 10 figures

We measure the dynamics of the thermo-optical nonlinearity of both a mode-gap nanocavity and a delocalized mode in a Ga$_{\mathrm{0.51}}$In$_{\mathrm{0.49}}$P photonic crystal membrane. We model these results in terms of heat transport and thermo-optical response in the material. By step-modulating the optical input power we push the nonlinear resonance to jump between stable branches of its response curve, causing bistable switching. An overshoot of the intensity followed by a relaxation tail is observed upon bistable switching. In this way, the thermal relaxation of both the localized resonance and the delocalized resonance is measured. Significant difference in decay time is observed and related to the optical mode profile of the resonance. We reproduce the observed transient behavior with our thermo-optical model, implementing a non-instantaneous nonlinearity, and taking into account the optical mode profile of the resonance, as experimentally measured.

Mode-locking is predicted in a nanolaser cavity forming an effective photonic harmonic potential. The cavity is substantially more compact than a Fabry-Perot resonator with comparable pulsing period, which is here controlled by the potential. In the limit of instantaneous gain and absorption saturation, mode-locking corresponds to a stable dissipative soliton, which it very well approximated by the coherent state of a quantum mechanical harmonic oscillator. This property is robust against non-instantaneous material response and non-zero phase-intensity coupling.

We investigate type I second harmonic generation in III-V semiconductor wire waveguides aligned with a crystallographic axis. In this direction, because of the single nonzero tensor element of III-V semiconductors, only frequency conversion by mixing with the longitudinal components of the optical fields is allowed. We experimentally study the impact of the propagation direction on the conversion efficiency and confirm the role played by the longitudinal components through the excitation of an antisymmetric second harmonic higher order mode.

A new tuning mechanism is introduced in high-Q multimode photonic crystal resonators allowing to harness the resonant enhancement of the parametric resonance systematically. As a consequence, ultra-efficient stimulated and spontaneous Four Wave Mixing at continuous microWatt pumping levels are observed, and the scaling with Q is demonstrated. Experimental results are in perfect agreement with an analytical model without fitting parameters., Comment: 6 pages, 5 figures

Oscillators in the GHz frequency range are key building blocks for telecommunication, timing and positioning applications. Operating directly in the GHz and compactness while keeping high frequency stability, is still an up-to-date challenge. Recently, optomechanical crystals, compact by nature, have demonstrated GHz frequency modes, thus gathering prerequisite features for using them as oscillators. Here we report on the demonstration, in ambient atmospheric conditions, of an optomechanical oscillator designed with an original concept based on bichromatic one-dimensional optomechanical crystal. Self sustained oscillations directly at 3 GHz are routinely achieved with a low optical power threshold of 40 $\mu W$ and short-term linewidth narrowed down to 100 Hz in agreement with phase noise measurements (-113 dBc/Hz at 1 MHz from the carrier) for free running optomechanical oscillators. This oscillator is made of InGaP, low loss and TPA-free piezoelectric material which makes it valuable for optomechanics., Comment: 11 pages, 5 figures

An effective harmonic potential for photons is achieved in a photonic crystal structure, owing to the balance of the background dispersion and a bichromatic potential. Consequently, ultra-compact resonators with several equi-spaced resonances and high loaded Q factors (0.7 million) are demonstrated. A detailed statistical analysis is carried out by exploiting the complex reflection spectra measured with Optical Coherent Tomography. The log-normal distribution of the intrinsic Q-factors peaks at 3 million. The device is made of $Ga_{0.5}In_{0.5}P$ in order to suppress the two photon absorption in the Telecom spectral range considered here. This is crucial to turn the strong localization of light into ultra-efficient parametric interactions.

Ga$_{0.51}$In$_{0.49}$P is a promising candidate for thermally tunable nanophotonic devices due to its low thermal conductivity. In this work we study its thermo-optical response. We obtain the linear thermo-optical coefficient $dn/dT=2.0\pm0.3\cdot 10^{-4}\,\rm{K}^{-1}$ by investigating the transmission properties of a single mode-gap photonic crystal nanocavity., Comment: 7 pages, 4 figures

We measure and analyze reflection spectra of directly coupled systems of waveguides and cavities. The observed Fano lines offer insight in the reflection and coupling processes. Very different from side-coupled systems, the observed Fano line shape is not caused by the termini of the waveguide, but the coupling process between the measurement device fiber and the waveguide. Our experimental results and analytical model show that the Fano parameter that describes the Fano line shape is very sensitive to the coupling condition. A movement of the fiber well below the Rayleigh range can lead to a drastic change of the Fano line shape.

Weakly coupled high-Q nanophotonic cavities are building blocks of slow-light waveguides and other nanophotonic devices. Their functionality critically depends on tuning as resonance frequencies should stay within the bandwidth of the device. Unavoidable disorder leads to random frequency shifts which cause localization of the light in single cavities. We present a new method to finely tune individual resonances of light in a system of coupled nanocavities. We use holographic laser-induced heating and address thermal crosstalk between nanocavities using a response matrix approach. As a main result we observe a simultaneous anticrossing of 3 nanophotonic resonances, which were initially split by disorder., Comment: 11 pages

We report phase sensitive amplification in a 1.5mm long, $Ga_{0.5}In_{0.5}P$ dispersion engineered photonic crystal waveguide which has a flattened dispersion profile. A signal degenerate configuration with pulsed pumps whose total peak power is only 0.5W yields a phase sensitive extinction ratio of 10dB., Comment: 4 pages, 7 figures

We demonstrate a nanophotonic parametric light source with a record high normalized conversion efficiency of $3\times 10^6\, W^{-2}$, owing to resonantly enhanced four wave mixing in coupled high-Q photonic crystal resonators. The rate of spontaneously emitted photons reaches 14 MHz., Comment: 3 pages 3 figures 1 table

We integrate about 100 single Cadmium Selenide semiconductor nanowires in self-standing Silicon Nitride photonic crystal cavities in a single processing run. Room temperature measurements reveal a single narrow emission linewidth, corresponding to a Q-factor as large as 5000. By varying the structural parameters of the photonic crystal, the peak wavelength is tuned, thereby covering the entire emission spectral range of the active material. A very large spectral range could be covered by heterogeneous integration of different active materials.

The dispersion of a CROW made of photonic crystal mode-gap cavities is pronouncedly asymmetric. This asymmetry cannot be explained by the standard tight binding model. We show that the fundamental cause of the asymmetric dispersion is the fact that the cavity mode profile itself is dispersive, i.e., the mode wave function depends on the driving frequency, not the eigenfrequency. This occurs because the photonic crystal cavity resonances do not form a complete set. By taking into account the dispersive mode profile, we formulate a mode coupling model that accurately describes the asymmetric dispersion without introducing any new free parameters., Comment: 4 pages, 4 figures

The carrier lifetime of a photonic crystal all-optical switch is optimized by controlling the surface of GaAs by Atomic Layer Deposition. We demonstrate an all optical modulation capability up to 100GHz at Telecom wavelengths, with a contrast as high as 7dB. Wavelength conversion has also been demonstrated at a repetition rate of 2.5GHz with average pump power of about 0.5mW, Comment: 6 pages, 8 figures

We demonstrated a two-fold acceleration of the fast time constant characterising the recovery of a P-doped Indium-Phosphide Photonic Crystal all-optical gate. Time-resolved spectral analysis is compared with a three-dimensional drift-diffusion model for the carrier dynamics, demonstrating the transition from the ambipolar to the faster minority carrier dominated diffusion regime. This open the perspective for faster yet efficient nanophotonic all-optical gates., Comment: 4 pages, 4 figures

A compact (15{\mu}m${\times}${\mu}m) and highly-optimized 2${\times}$2 optical switch is demonstrated on a CMOS-compatible photonic crystal technology. On-chip insertion loss are below 1dB, static and dynamic contrast are 40dB and >20dB respectively. Owing to efficient thermo-optic design, the power consumption is below 3 mW while the switching time is 1 {\mu}s., Comment: 8 pages, 6 figures

We perform spatially dependent tuning of a GaInP photonic crystal cavity using a continuous wave violet laser. Local tuning is obtained by laser heating of the photonic crystal membrane. The cavity resonance shift is measured for different pump positions and for two ambient gases: helium and nitrogen. We find that the width of the temperature profile induced in the membrane depends strongly on the thermal conductivity of the ambient gas. For He gas a narrow spatial width of the temperature profile of 2.8 um is predicted and verified in experiment., Comment: 4 pages, 5 figures

Single photons are of paramount importance to future quantum technologies, including quantum communication and computation. Nonlinear photonic devices using parametric processes offer a straightforward route to generating photons, however additional nonlinear processes may come into play and interfere with these sources. Here we analyse these sources in the presence of multi-photon processes for the first time. We conduct experiments in silicon and gallium indium phosphide photonic crystal waveguides which display inherently different nonlinear absorption processes, namely two-photon (TPA) and three-photon absorption (ThPA), respectively. We develop a novel model capturing these diverse effects which is in excellent quantitative agreement with measurements of brightness, coincidence-to-accidental ratio (CAR) and second-order correlation function g(2)(0), showing that TPA imposes an intrinsic limit on heralded single photon sources. We devise a new figure of merit, the quantum utility (QMU), enabling direct comparison and optimisation of single photon sources., Comment: 6 figures, 12 pages

Cavity quantum electrodynamics advances the coherent control of a single quantum emitter with a quantized radiation field mode, typically piecewise engineered for the highest finesse and confinement in the cavity field. This enables the possibility of strong coupling for chip-scale quantum processing, but till now is limited to few research groups that can achieve the precision and deterministic requirements for these polariton states. Here we observe for the first time coherent polariton states of strong coupled single quantum dot excitons in inherently disordered one-dimensional localized modes in slow-light photonic crystals. Large vacuum Rabi splittings up to 311 {\mu}eV are observed, one of the largest avoided crossings in the solid-state. Our tight-binding models with quantum impurities detail these strong localized polaritons, spanning different disorder strengths, complementary to model-extracted pure dephasing and incoherent pumping rates. Such disorder-induced slow-light polaritons provide a platform towards coherent control, collective interactions, and quantum information processing., Comment: 17 pages, 5 figures and supplementary information

Solitary waves have consistently captured the imagination of scientists, ranging from fundamental breakthroughs in spectroscopy and metrology enabled by supercontinuum light, to gap solitons for dispersionless slow-light, and discrete spatial solitons in lattices, amongst others. Recent progress in strong-field atomic physics include impressive demonstrations of attosecond pulses and high-harmonic generation via photoionization of free-electrons in gases at extreme intensities of 1014 Wcm2. Here we report the first phase-resolved observations of femtosecond optical solitons in a semiconductor microchip, with multiphoton ionization at picojoule energies and 1010 Wcm2 intensities. The dramatic nonlinearity leads to picojoule observations of free-electron-induced blue-shift at 1016 cm3 carrier densities and self-chirped femtosecond soliton acceleration. Furthermore, we evidence the time-gated dynamics of soliton splitting on-chip, and the suppression of soliton recurrence due to fast free-electron dynamics. These observations in the highly dispersive slow-light media reveal a rich set of physics governing ultralow-power nonlinear photon-plasma dynamics., Comment: 14 pages (main body and supplement), 11 figures - earlier draft; http://www.nature.com/srep/2013/130122/srep01100/full/srep01100.html

We demonstrate dispersion tailoring by coupling the even and the odd modes in a line-defect photonic crystal waveguide. Coupling is determined ab-initio using group theory analysis, rather than by trial and error optimisation of the design parameters. A family of dispersion curves is generated by controlling a single geometrical parameter. This concept is demonstrated experimentally on 1.5mm-long waveguides with very good agreement with theory.

We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.

We investigate the nonlinear response of photonic crystal waveguides with suppressed two-photon absorption. A moderate decrease of the group velocity (~ c/6 to c/15, a factor of 2.5) results in a dramatic (30x) enhancement of three-photon absorption well beyond the expected scaling, proportional to 1/(vg)^3. This non-trivial scaling of the effective nonlinear coefficients results from pulse compression, which further enhances the optical field beyond that of purely slow-group velocity interactions. These observations are enabled in mm-long slow-light photonic crystal waveguides owing to the strong anomalous group-velocity dispersion and positive chirp. Our numerical physical model matches measurements remarkably., Comment: 10 pages, 4 figures

We investigate the nonlinear response of GaAs-based photonic crystal cavities at time scales which are much faster than the typical thermal relaxation rate in photonic devices. We demonstrate a strong interplay between thermal and carrier induced nonlinear effects. We have introduced a dynamical model entailing two thermal relaxation constants which is in very good agreement with experiments. These results will be very important for Photonic Crystal-based nonlinear devices intended to deal with practical high repetition rate optical signals., Comment: 10 pages, 8 figures, Phys Rev A (accepted)

We have realized and measured a GaAs nanocavity in a slab photonic crystal based on the design by Kuramochi et al. [Appl. Phys.Lett., \textbf{88}, 041112, (2006)]. We measure a quality factor Q=700,000, which proves that ultra-high Q nanocavities are also feasible in GaAs. We show that, due to larger two-photon absorption (TPA) in GaAs, nonlinearities appear at the microwatt-level and will be more functional in gallium arsenide than in silicon nanocavities., Comment: 3 pages, 2 figures, accepted for publication in Optics Letters