Objective The optical frequency comb generation schemes mainly include mode-locked laser, electro-optic modulation comb, nonlinear Kerr micro-resonator comb, and nonlinear supercontinuum-based comb. For the nonlinear supercontinuum-based comb scheme, flat optical frequency comb generation has been extensively studied, which is based on self-phase modulation and optical wave breaking in silica-based high nonlinear fibers (HNLFs) with near-zero flattened normal dispersion. The dispersion of the silica-based HNLFs needs to be near zero in the normal dispersion regime to generate the flattened and broadened spectrum. Furthermore, several hundred meters long silica HNLFs are required because of their relatively low nonlinearity coefficients. However, such a long fiber causes dispersion variation along the fiber owing to the fabrication inaccuracy. Herein, high repetition rate flat optical frequency comb generation based on normal dispersion lithium niobate (LiNbO3) optical waveguides is proposed and numerically analyzed. The 3.6-m-long cavity-less nonlinear LiNbO3 optical waveguide with normal dispersion can be used to solve the dispersion variation problem in the HNLFs. The repetition rate of the proposed optical frequency comb can reach 10--50 GHz owing to the electro-optic modulator tunable optical pulse source, and the waveguide structure and parameters used in the simulation are achievable using current technologies. The proposed optical frequency comb has potential applications in astronomy, optical communication, and microwave photonics. The parameters influencing optical frequency comb performances, time-frequency evolution mechanism, and spectral coherence are also analyzed, which provides a detailed guideline for flat optical frequency comb generation.
Methods Firstly, the dispersion and nonlinear coefficient of the LiNbO3 waveguide are obtained using the finite element method mode solver. Then, the time-frequency evolution process of the pulse in the waveguide is simulated with the generalized nonlinear Schr?dinger equation. By simulating the pulse evolution process in time and frequency domains, a flat broadband optical frequency comb is obtained after a 3.6 m propagation length. Next, the time-frequency evolutions of a hyperbolic secant pulse, a Gaussian pulse, and a super-Gaussian pulse are simulated using the X-Frog technology. The pulse time-frequency evolution mechanism is analyzed. X-Frog spectrograms connect the time and frequency domains of the pulse, which clearly shows the change of pulse chirp during the propagation. In addition, the effects of several parameters, such as the second-order dispersion, initial peak power, initial pulse width, third-order dispersion, initial pulse chirp, loss, and initial pulse waveform, on the performance of the optical frequency comb are analyzed. Finally, the spectral coherence of the optical frequency comb is obtained by simulating 100 individual spectra, where the input chirp-free hyperbolic secant pulses are seeded with different random simulated quantum-limited shot noises. It is verified that the optical frequency comb has good spectral coherence in the whole bandwidth.
Results and Discussions Firstly, the LiNbO3 waveguide structure with optimized normal dispersion and nonlinear coefficient is obtained through dispersion engineering (Fig. 1). Figure 2 shows a schematic diagram of optical frequency comb generation. A flat optical frequency comb with a 3 dB bandwidth of about 32 nm is obtained with a suitable propagation length (Fig. 3). It is found that for an optical frequency comb with a repetition rate of 10--50 GHz, the pulse-overlapping effect for adjacent pulses can be ignored in a short propagation length (3.6 m herein), which verifies that studying the spectral envelope of single-shot pulse and spectral envelope of optical frequency comb has certain commonalities (Fig. 4). Second, based on the X-Frog technology, the mechanisms of spectral broadening and flattening due to normal dispersion, self-phase modulation, and optical wave breaking are analyzed. The time-frequency evolution processes of the hyperbolic secant and Gaussian pulses are identical. The optical wave breaking effect occurs during propagation. However, for the energy transfer from the central wavelength of the front edge (back edge) to the long wavelength (short wavelength), the Gaussian pulse is more effective than the hyperbolic secant pulse (Figs. 5 and 6). For the super-Gaussian pulse, there is almost no optical wave breaking during propagation. However, comparing with the hyperbolic secant pulse and Gaussian pulse, the super-Gaussian pulse can produce a flatter optical frequency comb (Fig. 7). Third, based on the empirical formula for the propagation length of optical wave breaking and flat bandwidth, the parameters influencing the performances of the optical frequency comb are analyzed (Fig. 8). Finally, it is verified that the proposed optical frequency comb exhibits good spectral coherence, beneficial for its applications (Fig. 9).
Conclusions Herein, a new generation scheme for high repetition rate flat optical frequency comb generation based on a normal dispersion LiNbO3 optical waveguide was proposed. By optimizing the LiNbO3 ridge waveguide structure and dispersion engineering, a flat optical frequency comb with a 3 dB bandwidth of about 32 nm was realized via simulation. The time-frequency evolution processes of hyperbolic secant, Gaussian, and super-Gaussian input pulses during propagation were analyzed. From the simulation results, a flat broadband optical frequency comb is generated in the normal dispersion LiNbO3 waveguide owing to the combined effects of normal dispersion, self-phase modulation, and optical wave breaking. In addition, the effects of several parameters, such as the second-order dispersion, initial peak power, initial pulse width, third-order dispersion, initial pulse chirp, loss, and initial pulse waveform, on the performance of the optical frequency comb were studied. The proposed optical frequency comb exhibits good spectral coherence in the whole spectral range. This study shows that the LiNbO3 waveguide has a potential benefit for the 1550-nm broadband flat optical frequency comb based on a normal dispersion integrated nonlinear optical waveguide.
