Various methods have been proposed for generating optical frequency combs, including mode-locked lasers, electro-optic modulation combs, nonlinear supercontinuum combs, and nonlinear Kerr microresonator combs schemes. Compared with other methods, cascaded electro-optic modulator combs and cavity-less supercontinuum combs schemes can enable continuous tuning of comb spacing, providing greater flexibility for applications that require frequency spacing tuning. Optical frequency combs with good flatness are essential for many applications. By leveraging techniques such as pulse compression, self-phase modulation, and parametric mixing in near-zero normal dispersion highly nonlinear fibers (HNLFs) over hundreds of meters, a relatively flat broadband optical frequency comb can be achieved. However, during fiber fabrication, random fluctuations in the core radius cause irregular alternations between normal and anomalous dispersion, leading to non-uniformity and reduced bandwidth of the optical frequency comb. This issue can be mitigated by using small-core multicomponent glass fibers or integrated optical waveguides with high nonlinear refractive index coefficients while minimizing the nonlinear fiber/waveguide length.

Compared with fibers, integrated optical waveguides offer a higher index contrast between the core and cladding, resulting in a high confinement factor and greater flexibility in dispersion engineering. Various integrated nonlinear optical materials have been explored for generating optical frequency combs. Silicon nitride (Si₃N₄) is widely used in nonlinear optical applications due to its broad transparency window and absence of two-photon absorption in the 1550 nm band. Additionally, Si₃N₄ waveguides can withstand continuous laser power of up to 10 W. Currently, a low-loss, high-confinement Si₃N₄ nonlinear integrated waveguide fabrication process with a thickness exceeding 600 nm is under development. Researchers have employed multimode-wide waveguides to reduce optical scattering loss at the core-cladding interface, achieving a waveguide loss of 1 dB/m.

Regarding pumping light sources, some researchers have used electro-optically modulated pulses to pump Si₃N₄ optical waveguides for optical frequency comb generation. However, electro-optic modulated pulse source devices tend to be bulky, whereas phase-locked dual-frequency lasers offer a more compact alternative as wide-pulse sources and can be miniaturized using distributed feedback (DFB) lasers. Therefore, we focus on optimizing a phase-locked dual-frequency laser-pumped cavity-less Si₃N₄ nonlinear optical waveguide for optical frequency comb generation in the 1550 nm band. The resulting optical frequency combs have broad applications in optical communications, microwave photonics, and other related fields.

An optical frequency comb was generated using the TE₀ fundamental mode. First, dispersion engineering of the TE₀ mode in the Si₃N₄ optical waveguide at 1550 nm was performed to achieve suitable dispersion and nonlinear coefficient. The second-order and third-order dispersions (β₂ and β₃) at 1550 nm were determined to be 51.16 ps²/km and 0.16 ps³/km, respectively. The effective area A_eff was calculated as 1.61 μm², and the nonlinear coefficient (γ) as 0.63 W^-1‧m^-1. Since optical frequency comb generation via nonlinear effects requires high peak pulse power, a phase-locked dual-frequency laser was employed as a wide-pulse source. To enhance the peak pulse power, a two-stage pulse compression technique was used. This process involved chirped pulse compression in normal dispersion nonlinear fibers (HNLFs) and standard single-mode fibers (SSMFs), followed by pulse shaping using a programmable pulse shaper to enable spectrum broadening in the Si₃N₄ nonlinear optical waveguide. The optical frequency comb was generated through the combined effects of normal dispersion, self-phase modulation, and optical wave breaking in the Si₃N₄ optical waveguide. The time-frequency evolution of the pulse was simulated using the Generalized Nonlinear Schrödinger Equation (GNLSE) with a split-step Fourier algorithm. Additionally, the effects of power ratio and frequency spacing of the phase-locked dual-frequency laser on optical frequency comb generation were analyzed.

A Si₃N₄ optical waveguide structure with optimized normal dispersion and nonlinear coefficient was achieved through dispersion engineering (Fig. 1). A schematic diagram illustrating optical frequency comb generation using a phase-locked dual-frequency laser with two-stage pulse compression and a cavity-less normal-dispersion Si₃N₄ optical waveguide is shown in Fig. 2. A phase-locked dual-frequency laser with 1 W total power (power ratio x = 1) was initially used without pulse compression to directly pump a 3 m long cavity-less normal-dispersion Si₃N₄ optical waveguide with 1 dB/m waveguide loss. This resulted in a spectral bandwidth of approximately 10 nm (Fig. 3). In contrast, incorporating two-stage pulse compression significantly broadened the optical frequency comb spectrum due to the combined effects of normal dispersion, self-phase modulation, and optical wave breaking in the Si₃N₄ waveguide, achieving a 20 dB bandwidth of approximately 100 nm (Fig. 4). Considering a 3 dB/m Si₃N₄ optical waveguide loss, a slight reduction in both temporal pulse power and spectral bandwidth was observed. Additionally, when accounting for a 1 dB coupling loss between the fiber and the Si₃N₄ waveguide, the 20 dB bandwidth of the optical frequency comb decreased to approximately 80 nm. Due to the large pedestal and tail of the two-stage compressed pulse waveform, significant power fluctuations were observed in the central spectrum, which is unfavorable for practical applications such as multi-wavelength light sources in optical communications. To address this, a pulse shaper was used to enhance the spectral flatness. When the compressed pulse was shaped into a hyperbolic secant pulse, a 10 dB bandwidth of approximately 90 nm was achieved for a central flat optical frequency comb. When the pulse was shaped into a Gaussian profile, a 10 dB bandwidth of approximately 90 nm and a 3 dB bandwidth of approximately 57 nm were obtained. When the pulse was shaped into a third-order super-Gaussian pulse, a 3 dB bandwidth of approximately 90 nm was achieved for a central flat optical frequency comb (Fig. 5). The impact of an unequal power ratio in the phase-locked dual-frequency laser on optical frequency comb generation was also investigated. With a power ratio of x=0.1, the optical frequency comb exhibited a reduced 20 dB bandwidth of approximately 45 nm (Fig. 6). The power ratio of the dual-frequency laser significantly influenced the 3 dB bandwidth, with optimal optical frequency comb generation achieved at x=1 (Fig. 7). Finally, the effect of the frequency spacing (ν_m) of the phase-locked dual-frequency laser on the temporal and spectral characteristics of the optical frequency comb was examined. A frequency spacing of ν_m=200 GHz resulted in an optical frequency comb with a 20 dB bandwidth of approximately 100 nm (Fig. 8). However, changes in the frequency spacing had minimal impact on the 3 dB bandwidth of the optical frequency comb (Fig. 9).

We proposes a scheme for generating an optical frequency comb in cavity-less Si₃N₄ nonlinear optical waveguides pumped by a phase-locked dual-frequency laser. By employing two-stage pulse compression and leveraging the combined effects of normal dispersion, self-phase modulation, and optical wave breaking in a 3 m long normal-dispersion Si₃N₄ optical waveguide, an optical frequency comb with a 20 dB bandwidth of approximately 100 nm is achieved. When the compressed pulse is shaped into a Gaussian pulse, the central flatness of the optical frequency comb is improved, resulting in a 3 dB bandwidth of approximately 57 nm. Finally, the effects of power ratio and frequency spacing of the phase-locked dual-frequency laser on optical frequency comb generation are analyzed. This study demonstrates the feasibility of generating a broadband optical frequency comb in meter-length normal-dispersion Si₃N₄ integrated nonlinear optical waveguides, which will contribute to the advancement of cavity-less tunable broadband optical frequency comb research.