With the rapid advancement of quantum technology, broadband entangled photon sources have emerged as promising tools for a variety of applications, including quantum communications, precision measurements, spectroscopy, and quantum computation. However, current methods for generating broadband entangled photons face challenges, particularly in achieving frequencies over 100 THz. To address these limitations, this study proposes a coupled waveguide system based on a silicon on insulator (SOI) platform that utilizes evanescent-wave coupling phase matching (ECPM) to generate a flat ultra-wideband spectrum covering 114 THz and produces photons with a photon flux density of up to 1.11 ns^-1·THz^-1 when pumped with a power of 100 mW. Furthermore, the analysis results of the dual photon wave function and entanglement entropy confirm that the generated photon pairs exhibit high-quality continuous frequency entanglement characteristics. This study aims to provide an efficient and cost-effective solution for broadband entangled photon sources in applications such as wavelength-division multiplexing (WDM) systems, quantum optical coherence tomography, spectroscopic measurements, and quantum communications.

The study uses theoretical analysis and numerical calculation methods. Initially, the research focuses on observing the ultra-broadband phase matching phenomenon in a coupled waveguide system via the calculation of the phase matching function. Subsequently, investigations are conducted on four-wave mixing (FWM) with different mode combinations to select an appropriate mode combination. The study then quantifies the bandwidth of phase matching and optimizes the structural parameters of the waveguide in a three-dimensional solution space by using a simulated annealing algorithm. Finally, numerical calculations are performed to determine the photon flux density, two-photon wave function, and entanglement entropy of the photons generated by the designed waveguide. The results confirm that the designed structure efficiently and uniformly generates ultra-wideband continuously entangled photons.

After optimization, the ultra-broadband continuous entanglement source achieves a bandwidth exceeding 100 THz (Fig. 4). Specifically, with a pump power of 100 mW and propagation distance of 3 mm, the FWM exhibits a maximum efficiency of -40.8 dB, which corresponds to a frequency bandwidth of 114 THz at 5 dB (Fig. 5). The results of a sensitivity analysis indicate that maintaining an equivalent bandwidth above 700 nm is feasible by varying the coupling gap within the range of 370 nm to 390 nm, waveguide width within 764 nm to 756 nm, and waveguide height within 327 nm to 334 nm. It is further shown that the designed broadband entangled photon source can achieve a bandwidth exceeding 700 nm within an allowable error range (Fig. 6). Numerical calculations demonstrate that the generated photons exhibit high-quality continuous frequency entanglement and frequency dependence with an entanglement entropy of 7.211 for broadband entangled photons and that the maximum photon flux density reaches 1.11 ns^-1·THz^-1 at a pump power of 100 mW (Fig. 7). Overall, the results indicate that the proposed structure not only enables the generation of ultra-broadband entangled photons but also achieves high conversion efficiency (Table 1).

This study proposes a method by which to generate broadband entangled photons in a coupled waveguide system using ECPM. Compared with previous work, we generate entangled photons with a wider bandwidth and maintain a high generation efficiency by optimizing the structure of the coupled waveguide. The simple structure of the device significantly reduces the processing difficulty. First, we discover the mechanism of ultra-broadband phase matching in the coupled waveguide. Second, we quantify the contribution of phase matching to the bandwidth of FWM generation and optimize the waveguide geometry by using a simulated annealing algorithm to achieve ultra-broadband phase matching. Compared with that observed before the optimization, the phase matching bandwidth of the designed waveguide structure is expanded by 5.45 times. In addition, the results of this study demonstrate that the generated photons have a high level of continuous-frequency entanglement properties via the calculation of the two-photon wave function and entanglement entropy. The waveguide system designed and optimized in this study can generate broadband entangled photons spanning the O, E, S, C, L, and U bands in the wavelength range of 1184 nm to 2158 nm with a bandwidth as high as 114 THz. In addition, the structure produces photons with a photon flux density of up to 1.11 ns^-1·THz^-1 at a pump power of 100 mW while guaranteeing the bandwidth and spectral flatness. Finally, the scheme proposed in this study for the generation of broadband entangled photons is also applicable to waveguide systems of other materials. Hence, these findings broaden the application range of the ECPM in the field of future broadband entangled photon sources.