In this work, we report the modeling and the experimental demonstration of intermodal spontaneous as well as stimulated four-wave mixing (FWM) in silicon waveguides.In intermodal FWM, the phase-matching condition is achieved by exploiting the different dispersion profiles of the optical modes in a multimode waveguide.Since both the energy and the wave vectors have to be conserved in the FWM process, this leads to a wide tunability of the generated photon wavelength, allowing us to achieve a large spectral conversion.We measured several waveguides that differ by their widths and demonstrate large signal generation spanning from the pump wavelength (1550 nm) down to 1202 nm.A suited setup evidences that the different waves propagated indeed on different order modes, which supports the modeling.Despite observing a reduced efficiency with respect to intramodal FWM due to the decreased modal overlap, we were able to show a maximum spectral distance between the signal and idler of 979.6 nm with a 1550 nm pump.Our measurements suggest the intermodal FWM is a viable means for large wavelength conversion and heralded photon sources.
In this work, we report the modeling and the experimental demonstration of intermodal spontaneous as well as stimulated four-wave mixing (FWM) in silicon waveguides.In intermodal FWM, the phase-matching condition is achieved by exploiting the different dispersion profiles of the optical modes in a multimode waveguide.Since both the energy and the wave vectors have to be conserved in the FWM process, this leads to a wide tunability of the generated photon wavelength, allowing us to achieve a large spectral conversion.We measured several waveguides that differ by their widths and demonstrate large signal generation spanning from the pump wavelength (1550 nm) down to 1202 nm.A suited setup evidences that the different waves propagated indeed on different order modes, which supports the modeling.Despite observing a reduced efficiency with respect to intramodal FWM due to the decreased modal overlap, we were able to show a maximum spectral distance between the signal and idler of 979.6 nm with a 1550 nm pump.Our measurements suggest the intermodal FWM is a viable means for large wavelength conversion and heralded photon sources.
The possibility to perform broad wavelength generation and conversion is of great interest in classical and quantum optics. With the introduction of integrated nonlinear silicon photonics, these tasks have been made even more viable thanks to the combination of the high nonlinear refractive index of silicon with the high confinement provided by the photonic waveguides. Exploiting this platform, several solutions for wavelength conversion have been investigated, for both optical processing [1] and applications in the Mid Infrared (MIR) [2]. The possibility to perform broad and controllable wavelength generation can be exploited also for creating integrated sources of quantum states of light based on single photons [3] or correlated photon pairs [4]. Both the generation and conversion can be accomplished by means of Four Wave Mixing (FWM). FWM is a nonlinear optical process in which two pump photons at frequency are converted into signal and idler photons at frequencies and ω/ respectively (with ωI/ωS). In the particular case of wavelength conversion, FWM is stimulated by a seed wave at the same wavelength of the signal (idler) that will be converted to the wavelength of the idler (signal). FWM has to satisfy the energy conservation, according to which the relation ωP+ ωP= ωS+ ωIholds, and its efficiency is ruled by the phase matching condition. This latter condition is related to the phase mismatch among the waves involved in the FWM process, that is evaluated as Δk = kp+ kp−kS−kI, where kP, kS, kIare the wavevectors for the pump, the signal and the idler, respectively. When Δk = 0, the phase matching condition is fulfilled and the efficiency of FWM is maximized. What is important for wavelength generation and conversion is the spectral position of the phase matching condition, which determines the wavelength at which the maximum efficiency of the conversion or generation process is achieved. Because of this, techniques for the control of the phase matching condition have been developed, focusing on the possibility to tailor the Group Velocity Dispersion (GVD) through a proper engineering of the waveguide geometry [5]. While these techniques consider only the first order waveguide mode, here we propose to exploit the higher order modes propagating inside a multimode waveguide. The dispersion of the higher order modes can be used to tune the spectral position of the phase matching condition for the FWM process, achieving controllable and large spectral translation in both Stimulated Four Wave Mixing (sFWM) and Spontaneous Four Wave Mixing (SFWM).
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.
On-chip heralded single photon sources are of key importance in the development of chip-scale devices exploiting the quantum properties of light. Single photon states can be produced as single photons heralded from correlated photon pairs generated through spontaneous four wave mixing. On-chip heralded single photon sources based on spontaneous four wave mixing have been already demonstrated. However, the heralded and herald photons are usually generated with wavelengths very close to the pump one, limiting the pump rejection efficiency and the application to the mid infrared. Moreover, the common sources of heralded photons based on spontaneous four wave mixing require spectral post filtering to achieve high purity, limiting the brightness and the integration of these sources. A solution to these problems can be provided by intermodal four wave mixing. In this work, we demonstrate the generation of photon pairs through intermodal four wave mixing in silicon waveguides, measuring the coincidences between the idler at 1.281 μm and the signal at 1.952 μm. We then discuss the application of intermodal four wave mixing to on-chip heralded single photon sources.
A detailed analysis of four-wave mixing (FWM) and its required phase-matching conditions in graded-index multimode optical fibers is presented. The analysis is relevant mainly for spontaneous frequency conversion and photon pair generation via FWM, when the fiber length is of the order of a meter or shorter, and the signal and idler are generated at large frequency separations from the pump. An analytic expression for calculating the phase mismatch occurring as a result of the waveguide dispersion among the pump, signal, and idler beams is derived, and it agrees well with independent numerical analysis. This expression simplifies calculations considerably, as it allows the prediction of the wavelengths of the signal and idler by using only the mode group number of the spatial modes involved in the FWM process and the refractive index profile of the fiber. The scaling of the signal–pump–idler frequency separations with the mode group numbers is explored. The abundance of the configuration degeneracies of the FWM process in graded-index multimode fibers indicates that nearly identical signal and idler frequencies can be obtained for many different pump, signal, and idler spatial mode profile combinations.
.We experimentally study the generation of correlated pairs of photons through four-wave mixing (FWM) in embedded silicon waveguides. The waveguides, which are designed to exhibit anomalous group-velocity dispersion at wavelengths near 1555 nm, allow phase matched FWM and thus efficient pair-wise generation of non-degenerate signal and idler photons. Photon counting measurements yield a coincidence-to-accidental ratio (CAR) of around 25 for a signal (idler) photon production rate of about 0.05 per pulse. We characterize the variation in CAR as a function of pump power and pump-to-sideband wavelength detuning. These measurements represent a first step towards the development of tools for quantum information processing which are based on CMOS-compatible, silicon-on-insulator technology.
Single photon sources by heralding time correlated photons are described. By intermodal four wave mixing (FWM) in a silicon photon circuit, we generate a herald photon at 1260 nm and the heralded one beyond 2 um, with a coincidence to accidental ratio larger than 50 and a single photon purity of 0.75. The discrete band intermodal phase matching does not require further filtering to improve the purity of the single photon. Moreover, the intermodal FWM exhibits high controllability of the signal/idler wavelengths, that can be generated far from the Raman and pump noise, with improved noise filtering.