We report on the demonstration of an effective, nonlinearity-induced non-reciprocal behavior in a single non-magnetic multi-mode Taiji resonator. Non-reciprocity is achieved by a combination of an intensity-dependent refractive index and of a broken spatial reflection symmetry. Continuous wave power dependent transmission experiments show non-reciprocity and a direction-dependent optical bistability loop. These can be explained in terms of the unidirectional mode coupling that causes an asymmetric power enhancement in the resonator. The observations are quantitatively reproduced by a numerical finite-element theory and physically explained by an analytical coupled-mode theory. This nonlinear Taiji resonator has the potential of being the building block of large arrays where to study topological and/or non-Hermitian physics. This represents an important step towards the miniaturization of nonreciprocal elements for photonic integrated networks.

Non-Hermitian physics has found a fertile ground in optics. Recently, the study of mode coalescence, i.e., exceptional points, has led to the discovery of intriguing and counterintuitive phenomena. Degeneracies are typically modeled through the coupled mode theory to determine the behavior of eigenstates and eigenvalues. However, the complex nature of the eigenvalues makes their characterization from the response spectrum difficult. Here, we demonstrate that a coherent interferometric excitation allows estimation of both the real and imaginary parts of the eigenvalues. We study the clockwise and counter-clockwise modes in optical microresonators both in the case of Hermitian and non-Hermitian intermodal coupling. We show the conditions by which a resonant doublet, due to the dissipative coupling of counter-propagating modes caused by surface roughness backscattering, merges to a single Lorentzian. This permits us to estimate the optimal quality factor of the microresonator in the absence of modal coupling caused by backscattering. Furthermore, we demonstrate that a taiji microresonator working at an exceptional point shows a degeneracy splitting only in one propagation direction and not in the other. This follows from the strongly non-Hermitian intermodal coupling caused by the inner S-shaped waveguide.

Electric-field-induced second-harmonic generation is demonstrated in silicon waveguides with reverse biased lateral p-i-n junctions. Phase matching is achieved by periodically poling the applied electric field. Two different poling configurations are compared: in the first, the p- and n-type doped regions of the junctions are on different sides of the waveguide (simple configuration), while in the second, they are alternated periodically across the waveguide sides (interdigitated configuration). Both simulations and experiments show that the generation efficiency is increased by 10 times comparing the interdigitated and simple configurations. The effective second-order susceptibility modulation obtained at a reverse bias voltage of 3.5 V is Δ χ e f f , S ( 2 ) ≃ 0.14 p m / V for the simple configuration and Δ χ e f f , I ( 2 ) ≃ 0.64 p m / V for the interdigitated one.

Local heating is widely used to trim or tune photonic components in integrated optics. Typically, it is achieved through the power dissipation of metal microwires driven by a current and placed nearby the photonic component. Then, via the thermo-optic effect, both the amplitude and the phase of the complex optical field propagating in the component can be controlled. In the last decade, optical integrated circuits with a cascade of more than 60 thermo-optical phase shifters were demonstrated for quantum simulators or optical neural networks. In this work, we demonstrate a simple two layers feed-forward neural network based on cascaded of thermally controlled Mach-Zehnder interferometers and microring resonators. We show that the dynamics of a high quality factor microresonator integrated into a Silicon On Insulator (SOI) platform is strongly affected by the current flowing in metal heaters where these last generate both local as well as global heating on the integrated photonic circuit. Interestingly, microheaters, even when they are at distances of a few millimetres from the optical component, influence all the microresonators and the Mach-Zehnder interferometers in the photonic circuit. We model the heat flux they generate and modify accordingly the non-linear equations of a system formed by a microresonator coupled to a bus waveguide. Furthermore, we show experimentally that the use of microheaters can be a limiting factor for the feed-forward neural network where three microresonators are used as non-linear nodes. Here, the information encoding, as well as the signal processing, occurs within the photonic circuit via metal heaters. Specifically, the network reproduces a given non-linear surjective function based on a domain of at most two inputs and a co-domain of just one output. As a result, its training aims to determine the values of the currents to apply to the heaters in the hidden layers, which allows replicating a certain shape. We demonstrate how the network exploits mainly the heat flow generated by the information encoding to reproduce a target avoiding the use of all the hidden layer heaters. This work shows that in large thermally actuated integrated photonic circuit, the thermal cross talk is an issue.

No abstract