## 1 Introduction  
Coherent detection is an effective method for its exceptional resolution, measurement accuracy, and signal-to-noise ratio [1]. It is widely used in various fields, including atmospheric optics, hyperfine wind structure detection, spacecraft pose measurement, and moving object identification [2, 3, 4, 5]. Lidars employing coherent detection rely on single-longitudinal mode (SLM) laser sources, which offer narrow linewidth and long coherence length, to enhance their detection range and resolution [6]. However, in a previous experiment, we observed that the frequency of the oscillating longitudinal mode in an SLM laser could drift spontaneously. This drift, likely caused by changes in the optical path length, can undermine the laser's performance. To address this issue, electro-optic (EO) crystals have been proposed as a solution. The refractive index of an EO crystal can be adjusted by applying an electric field, allowing for precise control of the optical path length and longitudinal mode spacing in a laser. This process, known as EO frequency modulation, has proven effective in stabilizing laser frequencies. In recent years, EO frequency modulation has been extensively studied for its ability to achieve rapid and precise frequency tuning in solid-state lasers. [PERSON] and [PERSON] demonstrated a frequency-modulated Nd:YAG laser using an LiTaO\({}_{3}\) electro-optic phase modulator, achieving a tuning range of 12 GHz with a sensitivity of 12 MHz/V and a frequency shift of 1.2 GHz in 0.6 ns [7]. [PERSON] et al. developed a diode-pumped Nd:YAG ring laser with an integrated electro-optic modulator, achieving a tuning coefficient of 0.75 MHz/V, a tuning range of 3 GHz, and an output power of 440 mW [8]. [PERSON] et al. reported a tunable single-frequency Nd:YLF laser at 526.5 nm using an LiTaO\({}_{3}\)-based Fabry-Perot etalon, achieving a tuning range of 12 GHz and a sensitivity of 12 MHz/V [9]. [PERSON] et al. demonstrated a linearly frequency-modulated Nd:YVO\({}_{4}\) laser using RbTiOPO\({}_{4}\) (RTP) crystals, achieving a tuning speed of 2.40 THz/s, a tuning range of 6 GHz, and a frequency deviation of less than 60 MHz during linear modulation [10]. Further advancements include a 14 GHz broadband frequency-tuned Nd:YVO\({}_{4}\) laser using an RTP etalon and piezoelectric transducer (PZT), enabling continuous tuning without mode hops and achieving terahertz-per-second tuning speeds [11]. Recent developments in EO spectral tuning have further expanded the capabilities of tunable lasers. Various EO tuning methods have been explored, leveraging the Pockels effect in materials like LiNbO\({}_{3}\) (LN) and KH\({}_{2}\)PO\({}_{4}\) (KDP). For instance, broadband tuning over 17.2 GHz with a response time of 10 ns has been demonstrated in a diode-pumped Nd:YVO\({}_{4}\) laser using LN crystals for coarse and fine tuning [12]. Similarly, LN-based microdisk lasers have achieved ultranarrow linewidths of 322 Hz with a tuning efficiency of 50 pm/100 V [13]. Additionally, LN-based grating-assisted directional couplers have shown high EO tuning efficiencies of up to 1.736 nm/V [14]. In another study, a Yb:GdCOB laser was tuned from 1024 to 1034 nm using a KDP-based Lyot filter, achieving a maximum output power of 3.21 W [15]. These advancements highlight the potential of EO tuning for applications requiring fast, precise, and broadband wavelength control in compact laser systems. Moreover, a nonperiodically poled LiNbO\({}_{3}\) (NPPLN) device was optimized for EO spectral tuning in a multi-wavelength optical parametric oscillator, achieving tuning rates of \(\sim\)0.5 nm/(kV/mm) for dual signals at 1540 and 1550 nm [16]. Building on these advancements, this study focuses on the application of EO crystals to stabilize the frequency of SLM lasers. We constructed a Nd:YVO\({}_{4}\) laser and achieved SLM oscillation by incorporating K9-glass Fabry-Perot (FP) etalons with different reflectivities into the oscillator.