We investigate highly efficient frequency-degenerate parametric generation through inverse four-wave-mixing (IFWM) in silicon nanowaveguides, which exhibits distinctly from traditional FWM phenomenon and manifests itself as a unique process producing signal and idler photon pairs with frequencies at the center of two pumps. The influences of dispersion, nonlinear coefficient and frequency detuning on the IFWM process are numerically analyzed in detail. On this basis, the optimal condition for high gain IFWM and the nanowaveguide with high nonlinearity and large normal dispersion are proposed. These results substantiate the feasibility of such frequency-degenerate parametric generation in CMOS-compatible integrated platforms, which could find important potential in signal-processing systems for photonics networks and entangled qubits generation for quantum optics.
We investigate highly efficient frequency-degenerate parametric generation through inverse four-wave-mixing (IFWM) in silicon nanowaveguides, which exhibits distinctly from traditional FWM phenomenon and manifests itself as a unique process producing signal and idler photon pairs with frequencies at the center of two pumps. The influences of dispersion, nonlinear coefficient and frequency detuning on the IFWM process are numerically analyzed in detail. On this basis, the optimal condition for high gain IFWM and the nanowaveguide with high nonlinearity and large normal dispersion are proposed. These results substantiate the feasibility of such frequency-degenerate parametric generation in CMOS-compatible integrated platforms, which could find important potential in signal-processing systems for photonics networks and entangled qubits generation for quantum optics.
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.
.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.
Correlated single photons provide a means to drive applications such as quantum computing and quantum communications. Correlated single photons can be generated via parametric down conversion in second–order nonlinear media or spontaneous four–wave mixing in third–order nonlinear media. In particular, complementary metal–oxide–semiconductor (CMOS) technology allows for seamless integration with electronics, providing the potential for a completely on-chip solution for quantum information processing. Ultra–silicon–rich nitride platform is a backend CMOS compatible platform, that has already been used to obtain high gain optical parametric amplification, wideband supercontinuum and enhanced nonlinearity in photonic crystal waveguides due to its large nonlinearity. In this work, we demonstrate correlated photon pair generation based on spontaneous four–wave mixing using ultra-silicon-rich nitride waveguides for the application in CMOS–based optical quantum technologies. A CW pump at a wavelength of 1555.747nm amplified using an EDFA is filtered through five wavelength division multiplexers (WDM) with a bandwidth of 1.2nm, providing 175dB suppression of EDFA induced pump sideband noise. The filtered quasi–TE pump, adjusted using a fiber polarization controller, is coupled into an ultra–silicon–rich nitride waveguide using a lensed fiber. A SiO2 cladded waveguide with a width of 550nm and height of 300nm possesses a high nonlinear parameter of 530W^-1/m with anomalous dispersion necessary for spontaneous four-wave mixing. The waveguide output is coupled into a lensed fiber and 7 cascaded WDMs are used to provide 245dB of residual pump filtration. The pump–suppressed output is spectrally separated into signal/idler part using WDMs. We refer to lower (higher) frequency photon as the signal (idler). The spontaneously generated signal and idler photons are filtered using cascaded tunable band pass filters (OTF) centered at 1571.24nm and cascaded WDMs centered at 1540.56nm, respectively. The bandwidth of the tunable OTF and WDM is 0.5nm and 1.2nm, therefore the correlated signal/idler photons are observed within the bandwidth window of 0.5nm induced by the OTF. The signal and idler photons are measured using InGaAs/InP avalanche photodetectors. The time correlation between signal and idler photons is obtained using a time interval analyzer with a detection efficiency of 20% and dead time of 15μs.The time bin is set to 81ps and the photon collection time is 240s. The coincidence peak is located ~11ns in the time–bin histogram due to the optical-path difference between the tunable OTF and WDM at respective signal and idler sides. The experimental raw coincidence counts (Hz), calculated by subtracting the accidental rate from the coincidence peak, show a quadratic increase with respect to coupled pump power. At the maximum coupled power of 5mW, the raw coincidence count is ~1Hz. We achieve a raw coincidence–to–accidental ratio (CAR) of up to 3. Therefore, we succeeded to observe correlated photon pair generation based on spontaneous four–wave mixing using the ultra–silicon–rich-nitride waveguide as a CMOS compatible platform, for future applications in quantum technologies.
Third-order nonlinear processes require phase matching between the interacting fields to achieve high efficiencies. Typically in guided-wave χ(3) platforms this is achieved by engineering the dispersion of the modes through the transverse profile of the device. However, this limits the flexibility of the phase matching that can be achieved. Instead, we analyze four-wave mixing in a pair of asymmetric waveguides and show that phasematching may be achieved in any χ(3) waveguide by coupling of a nondegenerate pump from an adjacent waveguide. We demonstrate the additional flexibility that this approach yields in the case of photon-pair generation by spontaneous FWM, where the supermode dispersion may be modified to produce pure heralded single photons -- a critical capability required for example by silicon platforms for chip-scale quantum photonics.
Summary form only given. Generation of correlated photon pairs by spontaneous parametric four-wave mixing (FWM) in photonic crystal fibres (PCF) opens the way for many applications, particularly for fibre-based quantum communication devices. In degenerate FWM, two pump photons at frequency ωρare annihilated to produce simultaneously a signal photon at ωsand an idler photon at ωi, such as ωs+ ωi= 2ωp(energy conservation). This process occurs with high efficiency only if the phase-matching condition (i.e. momentum conservation) is satisfied [1].The group-velocity dispersion (GVD) of the silica-core PCF used in our experiments (fig.1.a, inset) has been experimentally determined by a time-of-flight measurement for wavelengths from 740 nm to 930 nm. The result is consistent with the analytical calculation provided by Saitoh and Koshiba [2]. Particularly, we estimate the zero-dispersion wavelength of the PCF: λZDW = 834 nm. From this GVD measurement, we deduce the phasematching curve given in fig.1.a, on which we note that there is a vertical asymptote at λp - 832 nm. Thus, FWM should not be observed if the pump wavelength λp is lower than this limit value. Our experimental observations are very different from this prediction. Indeed, by injecting inside the fundamental mode of a 1.3-m-long PCF hyperbolic secant picosecond pulses (with an intensity-FWHM duration of about 2 ps) at λinj = 815 nm with a 80-MHz repetition rate, we actually observe a spontaneous parametric FWM phenomenon (with sidebands generated around 925 nm and 745 nm), and moreover with a clear frequency dissymmetry with respect to the injected pulse frequency (ωinj = 2ππc/λinj) (fig.1.b): generated signal and idler frequencies ωs and ωi do not satisfy ωs + ωi = 2ωinj.A systematic study of this frequency-dissymmetric phenomenon shows that it occurs only when the injected pulse peak power (Pinj) is higher than a threshold value Pth, and that Pth increases when λinj decreases from λZDW. This variation of Pth as a function of λinj can be understood by considering the key role played by self-phase modulation (SPM) in the observed phenomenon. Indeed, the frequency-dissymmetric signal and idler waves are generated only when the spectral broadening (due to SPM) of the injected pulses is sufficient to reach a threshold wavelength λth (i.e. a threshold frequency ωth) of the order of 832 nm. This value corresponds to the position of the vertical asymptote in the phase-matching curve. Finally, we observe that ωs + ωi - 2ωth when Pinj Pth. All these observations highlight the fact that, when the injected pulse peak power Pinj is high enough, spectral broadening by SPM is sufficient to get a part of the injected pulse spectrum higher than the threshold value λth, and thus this part of the spectrum can play the role of pump in an efficient FWM process (i.e. with the phasematching condition satisfied). It is important to note that this phenomenon advantageously presents an extension of the spectral range on which an efficient FWM process can occur: instead of being restricted to injected pulse wavelengths higher than the zero-dispersion wavelength λZDW of the fibre (or at least, higher than a threshold wavelength λth of the order of λZDW), experimenters can work with lower wavelengths, providing the availability of a high enough peak power and/or interaction length to sufficiently broaden (by SPM) the injected pulse spectrum.