An optical-frequency comb (OFC) is a comb-like structure with equal-frequency intervals in the frequency domain. Owing to their comb-like characteristics, OFCs have become the ideal light sources for precision spectral measurements. Compared with conventional mode-locked laser optical-frequency combs, which exhibit a carrier-envelope offset phase owing to differences between the phase and group velocities induced by dispersion, electro-optic frequency combs (EOFCs) are more advantageous as their repetition frequency is only determined by radio-frequency (RF) signal sources, which provide modulation signals. Consequently, the cavity length need not be adjusted to change the repetition frequency, and the carrier-envelope offset phase does not affect the EOFC owing to electro-optic modulation. Meanwhile, dual-comb spectroscopy (DCS) technology utilizes two OFCs with minimal repetition-frequency differences for optical-frequency multiheterodyne beat frequency detection. DCS offers high coherence and sensitivity, is not affected by the mechanical scanning rate, and can improve the speed of spectral measurements. An electro-optic DCS system based on electro-optic frequency combs combines the advantages of EOFCs and DCS technology. As it enables the repetition rate to be adjusted conveniently, it can easily generate low-repetition-frequency EOFCs, which are necessary for precise spectral measurements.

In this study, we used a multifrequency small-sinusoidal-signal method to generate a low-repetition-frequency EOFC with a repetition rate of 10 MHz. Considering that the modulation of multifrequency sinusoidal signals results in a modulation voltage and an initial phase to each comb tooth of the EOFC, the coefficients of each sideband of the EOFC are related to the two parameters above. Additionally, the Bessel-function value cannot be directly calculated numerically, which is not conducive to the energy control of each comb tooth and cannot guarantee the flatness of the EOFC. Hence, we propose a small-signal modulation method that uses a sufficiently low modulation voltage to generate mainly the first sideband per modulation signal and controls the modulation voltage of each frequency component of the modulation signal to be equal, thus yielding a flat electro-optic comb structure, except when the original center frequency is used. We used an arbitrary waveform generator (AWG) to output a small multifrequency sinusoidal modulation signal with 400 frequency components from 10 MHz to 4 GHz, and the phase of the modulation signal was set to random phases. We set the repetition-frequency difference between the two electro-optic combs to 500 Hz. The repetition frequencies of EOFC1 and EOFC2 are 10.0005 and 10 MHz, respectively, which implies that the repetition frequency of the interference signal from the electro-optic DCS is 500 Hz. To prevent spectrum aliasing, to ensure that the down conversion of the comb teeth corresponding to the two EOFCs is a one-to-one correspondence, and to eliminate the effect of low-frequency noise on the experimental results, the modulation frequency difference between the two acousto-optic modulators (AOMs) was set to 2.5 MHz, which implies the center frequency of the interference signal is 2.5 MHz. Based on a repetition rate of 10 MHz, we selected a 5 MHz-bandwidth low-pass filter to perform low-pass filtering on the interference signal from the electro-optic DCS.

The experimental data indicate that the frequency domain of the interference signal from the electro-optic DCS is consistent with the theoretically derived multifrequency small-sinusoidal-signal electro-optic phase modulation (Fig. 5). The flatness of the interference signal from the electro-optic DCS is approximately 5 dB, which implies that the method used to generate a flat EOFC without a center frequency is feasible (Fig. 6). We performed the Fourier transform on the measurement and reference DCS systems and then processed their intensity spectra to obtain the P9 and P10 absorption peaks of H¹³C¹⁴N gas. We fitted the experimental data using the Voigt function. The curve-fitting R² values of^{the P9 and P10 absorption peaks are 0.98928 (Fig. 7) and 0.99423 (Fig. 8), respectively, thus indicating favorable fitting results. The standard deviation of the fitting-curve residuals and measurement results of the P9 absorption peak is 1.191% (Fig.7), whereas that of the P10 absorption peak is 0.876%. This implies that we can apply the DCS system achieved via multifrequency small-sinusoidal-signal phase modulation to precision spectral measurements. Using the Lorentzian linewidths of the P9 and P10 absorption peaks, we calculated the pressure of the H13C14N gas cell to be approximately 11 Torr, which is consistent with the manufacturer's data.}

We proposed a method for realizing a DCS system based on multifrequency small-sinusoidal-signal electro-optic phase modulation. A multifrequency small-sinusoidal-signal was used to modulate the phase of a single-frequency continuous laser, which generated a 10-MHz EOFC with a low repetition resolution. The electro-optic DCS achieved was successfully used to measure the P10 absorption peak of H¹³C¹⁴N gas, which confirmed its feasibility for generating EOFCs. The generation of a single EOFC using a single electro-optic phase modulator significantly reduces the complexity of the experimental setup compared with the generation of EOFCs using cascaded electro-optic modulators, thus rendering the experimental setup more practical. Subsequent studies shall focus on achieving higher spectral resolutions, optimizing OFC flatness, and improving the comb output power to further improve precision spectral measurements.