From classical four-wave mixing to parametric fluorescence in silicon microring resonators
Stefano Azzini, Davide Grassani, Mattéo Galli, Lucio Claudio Andreani, Marc Sorel, Michael John Strain, L. G. Helt, John E. Sipe, Marco Liscidini, Daniele Bajoni
Four-wave mixing (FWM) can be either stimulated or occur spontaneously. The first process is intrinsically much stronger and well understood through classical nonlinear optics. The latter, also known as parametric fluorescence, can be explained only in the framework of a quantum theory of light. We experimentally demonstrated that, in a microring resonator, there is a simple relation between the efficiencies of these two processes that is independent of the nonlinearity and ring size. In particular, we have shown the average power generated by parametric fluorescence can be immediately estimated from a classical FWM experiment. These results suggest that classical nonlinear characterization of a photonic integrated structure can provide accurate information on its nonlinear quantum properties.
Four-wave mixing (FWM) can be either stimulated or occur spontaneously. The first process is intrinsically much stronger and well understood through classical nonlinear optics. The latter, also known as parametric fluorescence, can be explained only in the framework of a quantum theory of light. We experimentally demonstrated that, in a microring resonator, there is a simple relation between the efficiencies of these two processes that is independent of the nonlinearity and ring size. In particular, we have shown the average power generated by parametric fluorescence can be immediately estimated from a classical FWM experiment. These results suggest that classical nonlinear characterization of a photonic integrated structure can provide accurate information on its nonlinear quantum properties.
Four-wave mixing can be stimulated or occur spontaneously: the latter effect, also known as parametric fluorescence, can be explained only in the framework of a quantum theory of light, and it is at the basis of many protocols to generate nonclassical states of the electromagnetic field. In this work we report on our experimental study of spontaneous four wave mixing in microring resonators and photonic crystal molecules integrated on a silicon on insulator platform. We find that both structures are able to generate signal and idler beams in the telecom band, at rates of millions of photons per second, under sub-mW pumping. By comparing the experiments on the two structures we find that the photonic molecule is an order of magnitude more efficient than the ring resonator, due to the reduced mode volume of the individual resonators.
Four-wave mixing (FWM) in silicon photonics offers promising applications in optical signal processing, wavelength conversion, and quantum photonics, necessitating a comprehensive understanding of its underlying physics and limitations. Stimulated four-wave mixing in silicon photonic wire waveguides has been investigated theoretically by considering two-photon absorption, free carrier absorption, and free carrier dispersion, etc., operating near λ∼1550 nm. It has been shown that these effects severely degrade the performance when operating at higher pump power levels. We present exact numerical calculations of idler wavelength conversion efficiency and bandwidth taking into account the abovementioned nonlinearities, to show the effects of various parameters within the waveguide structure. We extended to investigate silicon photonic microring resonators in terms of the four-wave mixing performance of high-Q-value microring resonators, which are very promising as photon sources (spontaneous four-wave mixing) for large-scale quantum photonic circuits. Our analysis illustrates the limitations of analytical models in describing FWM in ring resonator behavior at a moderate input power level, necessitating a rigorous numerical approach. Experimentally, we demonstrate stimulated FWM (1525 nm≤λp≤1575 nm) in a silicon photonic wire with a cross-section of 500 nm×220 nm and with a small waveguide length of 2 mm. The idler-to-signal conversion efficiency of about −35 dB has been measured for an approximate launched pump power of 30 mW. The conversion efficiency is improved further in the microring resonator as predicted by the simulation results.
Four Wave Mixing (FWM) is the main nonlinear interaction in integrated silicon devices, which finds diffuse use in all-optical signal processing and wavelength conversion. Despite the numerous works on coupled resonator devices, which showed record conversion efficiencies and broadband operation, the possibility to coherently control the strength of the stimulated FWM interaction on a chip has received very limited attention. Here, we demonstrate both theoretically and experimentally, the manipulation of FWM in a photonic molecule based on two side coupled silicon microring resonators. The active tuning of the inter-resonator phase and of their eigenfrequencies allows setting the molecule in a sub-radiant state, where FWM is enhanced with respect to the isolated resonators. On the other hand, we can reconfigure the state of the photonic molecule to have energy equipartition among the resonators, and suppress FWM by making the two Signal waves to interfere destructively in the side coupled waveguides. This work constitutes an experimental demonstration of the control of a nonlinear parametric interaction via coherent oscillation phenomena in an integrated optical device.
Being a key component on a photonic chip, the microring usually specializes in a certain nonlinear optical process and can not simultaneously meet different working conditions for different processes. Here, we theoretically and experimentally investigate a reconfigurable silicon microring resonator to act as a optimization strategy for both classical four-wave mixing and quantum light sources. Experimental results show that the four-wave mixing efficiency with continuous wave and pulsed pump can be both optimized to a high value well matching numerical analysis. A variety of quantum light sources - including the heralded single-photon source, two-photon source and multi-photon source - are demonstrated to present a high performance and their key parameters including the pair generation rates (PGR), the heralding efficiency (HE) and the coincidence-to-accidental ratio (CAR) are controllable and optimizable. Such tunable nonlinear converter is immune to fabrication variations and can be popularized to other nonlinear optical materials, providing a simple and compact post-fabrication trimming strategy for on-chip all-optical signal processing and photonic quantum technologies.
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function.\n\nIn the limit of a low probability of pair production, photon pair production fficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical “seed” field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless enerated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption\nor free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis.\n\nBiphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This further allows estimation of the suitability of their associated photon pairs for various quantum information processing applications. As an alternative to dispersion engineering a channel waveguide photon pair source, it is calculated that microring resonators can very naturally produce nearly spectrally uncorrelated photon pairs, which behave very much like idealized single-mode photons and are thus useful for applications involving the interference of photons from multiple sources.
A common strategy for increasing the efficiency of Stimulated and Spontaneous FourWave Mixing (SFWM) in integrated optical devices, is to enhance the intensity of the propagating optical field through nanoscale geometrical engineering. Typically, this is accomplished by confining light into microresonators or into sequences of mutually coupled cavities. Usually these structures are treated as a whole, with tens or hundreds of repeating units. In these structures, long grange periodicity is deliberately sought to tailor the frequency wavevector band diagram, in order to increase the group index while keeping the group velocity dispersion as low as possible. Having to deal with a large number of unit cells inherently precludes the study of the impact of the internal degree of freedom on FWM. The implementation of complex and extended structures precludes the observation of FWM regimes which are in general hidden, or overhung, by the long range periodicity, and that can emerge only by acting at the single resonator level. In this work, we study SFWM in a system made by two Silicon microring resonators (photonic dimer) of radius 7 um, quality factor Q = 10000 and separation 53.1 um, which are indirectly coupled by means of two waveguides with a coupling gap of 160 nm. We independently change the inter-cavity phase f, and the resonator eigenfrequency detuning d, by respectively implementing a Peltier cell and micro-heaters placed on the top of the resonators. We experimentally and theoretically demonstrate that, in the parameter space spanned by (f, d), the efficiency of SFWM can be enhanced, left unchanged or being completely suppressed with the respect to a single uncoupled resonator. This plethora of regimes can not be easily resolved and accomplished in large structures, where the structural periodicity makes slow light to overwhelm any other side effect. Here, a FWM enhancement of 7 dB with respect to each single constituent of the molecule is demonstrated, and attributed to the increase of internal field enhancement of one of the resonator induced by the presence of the other. We theoretically prove that this phenomenon is linked to the excitation of a sub-radiant mode in the structure. FWM suppression arises from the coherent destructive interference between the signal waves generated in the two resonators which are scattered into a common waveguide channel. We find that in the region where SFWM is enhanced, also the efficiency of Spontaneous Four Wave Mixing, the quantum counterpart of the stimulated process, is increased. This opens a plenty of possibilities for the implementation of this device for the generation of correlated photon pairs. We suggest that pairs could be deterministically bunched into a single scattering channel with a brightness that overcomes the one of a critically coupled resonator. This could beat the effective 50% of losses which suffer All-Pass and Add-Drop resonators, and could show superior brightness with respect to asymmetric microrings or dual Mach-Zehnder-microrings devices, whose maximum achievable field enhancement is inherently limited by the level attained at critical coupling.