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Physical Review A

Coupled-mode phase matching on a silicon chip

Chao Wu, Pingyu Zhu, Miaomiao Yu, Weihong Luo, Qilin Zheng, Kaikai Zhang, Yingwen Liu, Ping Xu

Published Mar 6, 2025• 2 citations
Publisher

Abstract

Phase matching lies at the heart of the classical nonlinear process for frequency conversion and all-optical processing, as well as the spontaneous parametric process for the quantum light sources generation. In this work, we experimentally demonstrate the coupled-mode phase-matching (CMPM) engineered by the two-paralleled-coupled waveguides on a silicon-on-insulator (SOI) chip, extending the converted beam and entangled photons to the S band and L band. We measure the spectrum and efficiency of wavelength conversion, which successfully validates the designed CMPM scheme. We further measure the pairs generation rate of the biphoton based on the spontaneous four-wave mixing, which features a narrow bandwidth consistent well with the theoretical simulations. Multiple CMPM conditions can be achieved by exploiting the combinations of even and odd supermodes of the coupled system and tuned by designing a proper coupling gap between the two waveguides. The CMPM can extend the FWM nonlinear process ranging from the O band to the U band and even the midinfrared, enriching the working wavelength to a large extent. In addition, the CMPM features a discrete-band narrow bandwidth, which will greatly enhance the encoding density of frequency and the spectral purity of generated photon. In addition, our methods can be easily extended to a wide range of materials such as silicon nitride, dispensing with the dispersion engineering for phase matching.

DOI
10.1103/physreva.111.033504

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Phase matching lies at the heart of the classical nonlinear process for frequency conversion and all-optical processing, as well as the spontaneous parametric process for the quantum light sources generation. In this work, we experimentally demonstrate the coupled-mode phase-matching (CMPM) engineered by the two-paralleled-coupled waveguides on a silicon-on-insulator (SOI) chip, extending the converted beam and entangled photons to the S band and L band. We measure the spectrum and efficiency of wavelength conversion, which successfully validates the designed CMPM scheme. We further measure the pairs generation rate of the biphoton based on the spontaneous four-wave mixing, which features a narrow bandwidth consistent well with the theoretical simulations. Multiple CMPM conditions can be achieved by exploiting the combinations of even and odd supermodes of the coupled system and tuned by designing a proper coupling gap between the two waveguides. The CMPM can extend the FWM nonlinear process ranging from the O band to the U band and even the midinfrared, enriching the working wavelength to a large extent. In addition, the CMPM features a discrete-band narrow bandwidth, which will greatly enhance the encoding density of frequency and the spectral purity of generated photon. In addition, our methods can be easily extended to a wide range of materials such as silicon nitride, dispensing with the dispersion engineering for phase matching.
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).
Third-order nonlinear processes require phase matching between the interacting fields to achieve high efficiencies. Typically in guided-wave χ(3)χ^{(3)}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)χ^{(3)}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.
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.
Frequency entangled photon sources are in high demand in a variety of optical quantum technologies, including quantum key distribution, cluster state quantum computation and quantum metrology. In the recent decade, chip-scale entangled photon sources have been developed using silicon platforms, offering robustness, large scalability and CMOS technology compatibility. Here, we report the generation of frequency correlated photon pairs using a 150-GHz silicon nitride ring cavity. First, the device is characterized for studying the phase matching condition during spontaneous four-wave mixing. Next, we evaluate the joint spectrum intensity of the generated photons and confirm the photon pair generation in a total of 42 correlated frequency mode pairs, corresponding to a bandwidth of 51.25 nm. Finally, the experimental results are analyzed and the joint spectral intensity is quantified in terms of the phase matching condition.
Hybrid photonic circuits, harnessing the complementary strengths of multiple materials, represent a key resource to enable compact, scalable platforms for quantum technologies. In particular, the availability of bright sources of tunable biphoton states is eagerly awaited to meet the variety of applications currently under development. In this work we demonstrate a heterogeneously integrated device that merges biphoton generation and on-chip quantum state engineering, combining an AlGaAs photon-pair source with a CMOS-compatible silicon-on-insulator (SOI) circuit. Photon pairs are generated in the C telecom band via spontaneous parametric down-conversion and transferred to the SOI chip through a multimode evanescent coupling scheme. This design achieves a pair generation rate above 106^{6}6 s−1^{-1}−1mW−1^{-1}−1 and a coincidence-to-accidental ratio up to 600. Crucially, the coupling design induces strong and predictable transformations of the biphoton joint spectral amplitude, enabling complex quantum state engineering entirely on-chip in a compact device compliant with electrical pumping.
Hybrid photonic circuits, harnessing the complementary strengths of multiple materials, represent a key resource to enable compact, scalable platforms for quantum technologies. In particular, the availability of bright sources of tunable biphoton states is eagerly awaited to meet the variety of applications currently under development. In this work we demonstrate a heterogeneously integrated device working at room temperature that merges biphoton generation and on-chip quantum state engineering, combining an AlGaAs photon-pair source with a CMOS-compatible silicon-on-insulator (SOI) circuit. Photon pairs are generated in the C telecom band via spontaneous parametric down-conversion and transferred to the SOI chip through a multimodal evanescent coupling scheme. This design achieves a pair generation rate above 10 6 s −1 mW −1 and a coincidence-to-accidental ratio up to 600. Crucially, the coupling design induces strong and predictable transformations of the biphoton joint spectral amplitude, enabling complex quantum state engineering entirely on-chip in a compact device compliant with electrical pumping.