Fig. 1. Overview of the Voigt optical frequency standard. (a) Three-dimensional diagram of the Voigt optical frequency standard. EOM, electro-optic modulator; ISO, isolator; PD, photon detector; PBS (polarizing beam splitter) and HW (half-wave plate) are, respectively, the glass cube and rotatable glass plate in the figure, used for adjusting laser polarization and laser power, which are not labeled with text in the figure. The output of Voigt optical frequency standard beats with the Nth tooth of a frequency-doubled erbium-doped optical frequency comb, which has undergone frequency doubling through a second harmonic generation (SHG) crystal, to estimate the frequency instability of the optical frequency standard with the beat-note signal fb. The initial frequency f0 and repetition frequency fr were locked to a hydrogen maser, whose frequency stability was 3.5×10−13/τ. (b) The short-term frequency instability (red dots) is obtained by conducting two system beat frequency tests, and its results are consistent with the equivalent frequency instability calculated from the measured frequency noise (green squares). The black dashed line represents the linear fit result of the beat frequency. The long-term frequency instability (black triangles) is determined through optical comb testing; however, within 100 s, it is primarily constrained by the limited instability of the optical comb (cyan pentagrams), while data beyond 100 s accurately reflect the long-term frequency instability of Voigt optical frequency standards.

Fig. 2. Experimental setup of the Voigt laser. The upper inset shows the transmission spectrum and atomic transition lines. The VADOF consists of two orthogonal PBSs and an Rb85 atomic vapor cell placed in a 3700 G magnetic field.

Fig. 3. (a) 52S1/2,F=3→52P3/2 transition lines of Rb85. (b) Voigt laser wavelength versus diode current. (c) Voigt laser wavelength versus diode temperature. (d) The temperature of the diode increases by 2.5°C every 120 s, with a waiting period of 60 s for the diode to warm up. Afterwards, the Voigt optical frequency standard is automatically locked to the atomic transition line and runs for 60 s.

Fig. 4. SAS signal (black) and MTS signal (red). The baseline noise around the frequency region (dashed line) far-detuned from the zero-crossing point of the MTS.

Fig. 5. (a) Equivalent instability versus reference cell temperature. (b) Equivalent instability versus probe power at different pump power. (c) Modified short-term instability and its linear fit.

Fig. 6. (a) Beat frequency of the Voigt optical frequency standard and optical comb at different EOM temperature. (b) Beat frequency of the Voigt optical frequency standard and optical comb at different probe power. (c) Allan deviation of the Voigt optical frequency standard without EOM temperature control (red), with EOM temperature control (black), and long-term instability at optimal power point (green).

Fig. 7. Allan deviation of the Voigt optical frequency standard, together with contribution of each parameter to frequency instability. The long-term instability results (black squares) within the integration time of 10 s are primarily influenced by the comb teeth instability (cyan dots), which masks the inherent instability of the Voigt optical frequency standard. Additionally, contributions to the final instability also arise from variations in reference gas cell temperature (red triangles), laser power (green diamonds), EOM temperature (blue pentagrams), and residual error noise in PID circuitry (purple pentagons).

Fig. 8. Experimental setup of the Voigt optical frequency standard. PBS, polarizing beam splitter; M, mirror; PD, photodetector; HW, half-wave plate; EOM, electro-optic modulator; BS, beam splitter; LPF, low-pass filter; Mixer, phase detector; SG, signal generator; AMP, amplifier.

Fig. 9. Voigt laser power versus laser diode current.

Fig. 10. VADOF transmission spectrum at a temperature range from 70°C to 90°C.

Fig. 11. VADOF transmission spectrum at a laser intensity range from 25 to 350  mW/mm2.