Four Wave Mixing control in a photonic molecule made by silicon microring resonators

www.nature.com/scientificreports OPEN Received: 26 June 2018 Accepted: 25 November 2018 Published: xx xx xxxx Four Wave Mixing control in a photonic molecule made by silicon microring resonators Massimo Borghi1,2, Alessandro Trenti1,3 & Lorenzo Pavesi 1 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. Stimulated Four Wave Mixing (FWM), that is the all-optical, coherent energy transfer of a Signal wave into an Idler wave by means of two auxiliary Pump waves1, has been extensively studied for all-optical signal processing2,3, wavelength conversion4,5, frequency comb generation6,7, parametric oscillation and amplification8,9. To overcome the intrinsic weak χ(3) nonlinearity of silicon and silicon based materials1, and/or to decrease the optical power required for efficient FWM, several strategies have been adopted. Slow light waveguides enhance the effective Kerr nonlinearity by a factor S4 (here S denotes the slowing factor) with respect to a bare waveguide10. Typically, these are realized with line-defect Photonic Crystals (PhC) waveguides, where the reduced group velocity, combined with the extremely small mode area, increases the nonlinear coefficient11–15. Another method exploits the internal Field Enhancement (FE) of optical resonators. Indeed, with respect to a waveguide, these systems have a FWM efficiency which scales as FE8 16. Slow light waveguides, based on a cascade of N optical resonators, have been also demonstrated10. These have a FWM efficiency which scales as N2 with respect to a single cavity. Enhanced FWM through Coupled Resonators Optical Waveguides (CROW) has been shown with directly coupled microrings17,18 and PhC nanocavities19,20. Typically, these structures are treated as a whole, with tens or hundreds of repeating units. Long-range periodicity is deliberately sought to tailor the frequency-wavevector band diagram, in order to increase the group index while keeping the group velocity dispersion reasonably low21. However, dealing with a large number of unit cells inherently precludes the study of the impact on FWM of the inter-resonator phase and resonator eigenfrequencies relative detuning. Furthermore, these works are all focused on the enhancing of the parametric interaction, while little attention has been paid to explore the plenty of FWM regimes enabled by the structural complexity. In some works, photonic molecules22,23, constituted by two or three coupled resonators, have been analyzed in terms of their inter-cavity distance or their eigenfrequency separation, for the dynamical tuning of the Electromagnetic Induced Transparency (EIT) effect24–28, as well as for the onset of coherent collective phenomena like super or sub-radiance29. These studies were principally limited to a linear analysis, since their goal was mainly focused to slow-light or routing applications. Nonlinearities have been induced in these structures for light stopping30, storage31, cavity QED32, and spontaneous mirror-symmetry breaking33. The engineering of the field distribution inside photonic molecules has been exploited for FWM 1 Nanoscience Laboratory, Department of Physics, University of Trento, I-38123, Povo, Italy. 2Present address: Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol, BS8 1FD, UK. 3Present address: Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria. Correspondence and requests for materials should be addressed to M.B. (email: ) SCientifiC RePorTs | (2019) 9:408 | DOI:10.1038/s41598-018-36694-5 1 www.nature.com/scientificreports/ Figure 1. Sketch of the device under test. Two ring resonators, labelled 1 and 2, are separated by a distance L (center to center), and are both coupled to two side bus waveguides through a narrow coupling gap. The field decay rate γe in the waveguide is related to the extrinsic photon lifetime τe by γe = 1/τe. Similarly, the field decay rate γi associated to intrinsic losses of the material is related to the intrinsic photon lifetime τi by γi = 1/τi. Metallic microheaters (sketched in yellow) are placed on the top of each ring. The Pump (Pp) and the Idler (Pi) fields are injected into the In port, and are collected, together with the generated Signal (Ps) by stimulated FWM, at the output of the Drop port. among orthogonal supermodes34 and for the dynamical tuning of the evanescent coupling between two different cavities35,36. In this work, we investigate FWM in a system made by two silicon microring resonators (photonic dimer) which are side coupled by means of two waveguides. We aim at studying the coherent control of FWM and not to demonstrate record conversion efficiencies. We independently thermally tune the inter-resonator phase φ, and resonator eigenfrequency difference δ. We experimentally and theoretically demonstrate that, in the parameter space (φ,δ), the efficiency of FWM can be enhanced, left unchanged or completely suppressed with respect to the one of a single isolated resonator. These regimes cannot be easily resolved and accomplished in large structures, where the structural periodicity makes slow light effects to overwhelm any other side effect. Here, a FWM enhancement of (7.0 ± 0.2) dB with respect to each single constituent of the molecule is demonstrated. This efficiency increase is attributed to a sharp raise of the internal field enhancement of one of the resonator, caused by the presence of the other. We theoretically prove that this phenomenon is linked to the excitation of a sub-radiant mode of the photonic molecule. On the other hand, FWM suppression arises from the coherent destructive interference between the Signal waves which are generated in the two resonators and, then, c (...truncated)