With the success of ground-based gravitational wave detection, space-based gravitational wave detection has attracted wide attention from many research institutions around the world. The missions such as Laser Interferometer Space Antenna (LISA) initiated by NASA and ESA, New Gravitational Wave Observatory (NGO) initiated by ESA, and Tianqin program and Taiji program proposed by China, have high demands on the laser frequency noise at low Fourier frequencies between 0.1 mHz and 1 Hz. In order to fully meet the demands of those missions, the development of ultra-stable lasers with higher frequency stability and coherence has never been suspended. Currently, the most popular way to achieve ultra-stable lasers is to stabilize the laser frequency onto a high-finesse Fabry-Perot (F-P) cavity by using the Pound-Drever-Hall (PDH) method. However, it requires fine alignment of free-space optical components and precise spatial mode matching, which dramatically increases the complexity and bulk of the system and is easily disturbed by the external environment. Therefore, it is difficult to meet the requirements in the transportable applications of ultra-stable laser systems. In this article, an alternative approach is proposed, which uses an optical fiber-delay-line (FDL) as a frequency discriminator to stabilize the laser frequency. This approach has the advantages of high compactness, high reliability, small volume, and light weight, which make it a viable candidate for future laser-based gravitational wave detection missions.

The frequency stabilization of lasers is realized by using an unequal arm heterodyne Michelson fiber interferometer composed of an optical fiber delay line of 500 m. In order to reduce the influence of vibration noises on frequency-stabilized lasers, the optical fiber delay line of 500 m is precisely coiled on a low vibration sensitivity fiber spool. Then, the entire interferometer is placed in a small vacuum chamber, where all components such as an optical delay line of 500 m, single mode broadband coupler module (SMCM), and acoustic-optic modulator (AOM) are installed in a structurally stable thermal shielding system (Fig. 3). In addition, a two-stage active thermal controller is used to reduce the temperate fluctuation on the optical fiber interferometer. The first stage temperature stabilization is applied on the vacuum chamber with a temperature fluctuation of less than 5 mK over a 24 h period. The second stage temperature stabilization is applied on the fifth-layer thermal shield using thermoelectric coolers (TECs) mounted between the shield and the vacuum chamber, and the temperature fluctuation can be further minimized within 0.2 mK. Finally, by comparing with an independent ultra-stable laser of 1550 nm with better frequency stability via an optical frequency comb, the performance of the laser is measured.

The thermal time constant of the thermal shielding system is 6 h, and the temperature fluctuation of the inner fiber caused by the outermost thermal shielding can be suppressed to the original 4×10^-7. For a temperature perturbation of 0.2 mK, the induced frequency instability of stabilized laser is 9×10^-16. By comparing with another ultra-stable laser, the measured frequency noise power spectral density is lower than 30 Hz/Hz^1/2 at Fourier frequencies from 30 mHz to 1 Hz (Fig. 6), in comparison with the pre-stabilization requirement for the LISA mission. The Allan variance of the beat note is also analyzed. As demonstrated in Fig. 7, the fractional frequency instability of 1.2×10^-14 at averaging time of 1 s and that of 3×10^-13 at averaging time of 1000 s are achieved. However, the result is more than two orders of magnitude higher than the calculated thermal effect. One of the possible reasons may come from the fluctuation of optical power and radio frequency (RF) power, both of which fluctuate under the influence of ambient temperature fluctuations and will produce additional temperature fluctuations for the optical fiber interferometer, thus introducing additional noises. Another possibility may come from the RF modulation and demodulation links. The phase of RF signals will vary with temperature due to the thermal-delay effect of the RF links. This phase variation also causes excess frequency noises of the stabilized laser.

This paper reports a laser-frequency-stabilization system of 1064 nm based on an optical fiber Michelson interferometer for future inter-satellite laser interferometer missions. This system, constructed by all fiber devices, is featured with compact structure, small volume, and high reliability. The achieved performances satisfy the laser frequency stabilization requirements of the LISA mission (≤300 Hz/Hz^1/2 at frequencies from 1 mHz to 1 Hz), and this technique is expected to be used in future space-based gravitational wave detection missions.