Lasers with high-frequency stability^[1] play an indispensable role in many precision measurements such as gravitational wave (GW) detection^[2,3], optical frequency standards^[4,5], and test of Lorentz invariance^[6]. The past two decades have witnessed significant improvements in ultrastable continuous-wave (CW) lasers in terms of portability^[7], footprint, and control automation^[8–12]. In recent years, automatic laser frequency locking has progressively evolved from analog modules to analog–digital hybrid systems^[8–10], and then to all-digital controllers^[11,12] based on a field-programmable gate array (FPGA). The FPGA-based frequency-locked system has the advantages of high speed and great adaptability. Nevertheless, their noise properties at Fourier frequencies down to 1 mHz or even lower need to be quantitively examined for many applications relying on effective control of low-frequency noises. Meanwhile, replacing the free-space optical components with their optical-fiber counterparts in frequency-locked optics is another development trend to lower the weight and enhance the reliability. Being a key component in the all-fiber frequency-locked optics, a waveguide electro-optic modulator (EOM) generates unwanted amplitude modulation^[13] whose impact and suppression should be further investigated.

With the technological advance of space-based gravitational wave (GW) detection, there is an increasing demand for spaceborne ultrastable lasers. Known for their exceptionally low noise, 1064 nm neodymium-doped yttrium aluminum garnet (Nd:YAG) lasers built upon nonplanar ring oscillators (NPROs) are primary laser sources in planned LISA-like GW detectors. Nevertheless, in these detectors with unmatched baselines of millions of kilometers, the frequency noise of a free-running laser, if untreated, results in a background that overwhelms the GW signal by approximately 11–12 orders of magnitude. To reach the targeted detection sensitivities, two measures are taken jointly to cope with the laser frequency noise. First, prestabilizing the laser onboard the spacecraft is done to suppress its frequency noise to 30Hz/√Hz (1 mHz–1 Hz)^[14–17]. Subsequently, the influence of the residual frequency noise is further reduced by 7–8 orders of magnitude by adopting time-delayed interferometry (TDI)^[18–22]. Effective suppression of laser frequency noise during the prestabilization phase is one of the major technological challenges for LISA-like space programs of GW detection.

In response to the demand for ultrastable lasers suitable for GW detection in space, we are developing a spaceborne 1064 nm ultrastable laser. One of the crucial steps in this task is to verify the noise performance of the control unit adopting the FPGA architecture. We developed two independently operated laser stabilization systems, each of which consists of an FPGA-based control unit and a spaceborne 1064 nm NPRO Nd:YAG laser^[23]. The Nd:YAG laser is frequency-locked to a laboratory-operated 20-cm ultrastable reference cavity^[24] using the Pound–Drever–Hall (PDH) method^[25]. To adapt to space applications, optical fibers and fibered components are introduced to the PDH locked optics. The current configuration allows a rigorous evaluation of the FPGA approach to a frequency-locked system with ultralow noise suitable for space GW detection. Two major noise sources, the laser intensity fluctuation and residual amplitude modulation (RAM) generated by the waveguide EOM, are suppressed by implementing additional feedback control loops, and their individual contributions to the frequency noise are measured. The laser frequency stability up to a few thousand seconds is evaluated using the optical heterodyne beat of the two locked NPRO Nd:YAG lasers.

The experimental setup for laser frequency stabilization is shown in Fig. 1. Two nearly identical systems, referred to as West and East hereinafter, are built and are independently operated, allowing performance verification via beat frequency measurement. In each system, a spaceborne Nd:YAG laser^[23] is locked to an ultrastable optical reference cavity^[24] with a length of 20 cm and a finesse on the order of 400,000, using the PDH frequency stabilization technique. The spacer and two mirrors of the cavity are made of Corning ultralow expansion glass (ULE) and fused silica (FS), respectively. The input mirror of the cavity is flat and the other one is concave [radius of curvature (ROC), 1 m]. Except for a polarization beam splitter (PBS) and a quarter-wave plate, fibered optical components are used, including an electronic variable optical attenuator (VOA), a beam splitter, and a waveguide EOM (iXblue NIR-MPX-LN-0.1), which are interconnected by polarization-maintaining (PM) single-mode fiber-optic patch cables. The laser beam first passes the VOA for optical intensity stabilization and then is divided into two beams; one beam is used to beat against the second laser, and the other is phase-modulated and subsequently coupled into the reference cavity through an optical fiber collimator (OFC). The reflected light from the cavity is guided to a photodetector (PD1) whose output is sent to the FPGA control unit for frequency demodulation.

The FPGA (Xilinx, Virtex-5) board provides a total of 5 digital-to-analog converters (DACs) and 11 analog-to-digital converters (ADCs). All DACs are 14-bit and run at a sampling rate of 100 Msps. Among the 11 ADCs, there are two high-speed ones of 16 bit, 130 Msps and 14 bit, 40 Msps that are used for sampling radio frequency (RF) signals; the rest are low-speed ones consisting of two subsets of 14 bit, 3 Msps and 12 bit, 1 Msps. Circuits realizing the functional blocks shown in Fig. 1 are laid out on the FPGA board based on a control program written in Verilog hardware description language. Emulating a payload controller, a separate board based on a microprocessor (STM32) is used to perform control and monitoring functions through serial communications with the FPGA board.

The FPGA circuit is configured to perform three major tasks, which are laser driving, frequency locking, and stabilization of laser intensity and RAM. The laser driving module stabilizes the temperature of the NPRO and controls the current of two 808-nm laser diodes pumping the NPRO. In the frequency-locked module, direct digital synthesis (DDS) is adopted to facilitate the modulation, demodulation, and frequency sweep. A sinusoidal signal (2.5 and 2.4 MHz in West and East systems, respectively) is generated by DDS and sent to EOM for phase modulation; its phase-adjustable replica serves as a local. The alternating current (AC) output of PD1 is sampled by the 16-bit ADC, which runs at a slightly reduced sampling rate of 100 Msps. The real-time data from ADC are multiplied by the digital local and then digitally filtered, resulting in frequency discrimination as the input of a digital loop filter for gain compensation. The analog actuation signal is delivered by the 14-bit DAC and applied to a piezoelectric transducer (PZT) attached to the NPRO. Parallel to the fast PZT channel, there is a slow one that works by adjusting the set point to which the temperature of NPRO is stabilized, enabling a much larger frequency tuning range. A low-frequency (2 Hz) sawtooth signal can be superimposed on the frequency actuation signal or act alone on the PZT, allowing the search of the cavity resonance or diagnosis of the PDH error signal.

Additional feedback control loops are implemented to suppress the laser intensity noise and RAM. The intensity of the laser is measured by PD2 whose direct current (DC) output is digitized by an ADC (14 bit, 3 Msps) and compared with a preset value. The resulting error signal is processed by a digital proportional-integral-derivative (PID) controller and then converted to an analog signal that drives the VOA to actively stabilize the laser intensity. For RAM suppression, instead of using two channels that control both the bias voltage and the temperature of the EOM^[13], here only the bias voltage is actively adjusted in the feedback control loop. The EOM-generated RAM is measured by PD2, whose AC output is sampled by the 14-bit, 40 Msps ADC; the downstream RAM-suppressing hardwire on the FPGA board follows the same design for the frequency locking. The feedback loop is formed by adding a DC bias voltage to the modulating signal through a bias tee, canceling the RF fundamental component emerging from the AC output of PD2. Before closing this control loop, the DC bias is set to a value at which a local maximum of the discrimination slope is reached. Meanwhile, the RAM is maximized by varying the phase of the local. This initialization process allows a long-term uninterrupted feedback control of RAM.

The frequency search is realized by a combination of temperature and voltage scans. First, the FPGA board initiates a bidirectional search by varying the temperature of the NPRO, which exhibits a frequency-temperature dependence of 3.1 GHz/°C and a time constant of ∼1s. The temperature scan consists of large and small steps corresponding to frequency changes of 12 and 1.5 MHz, respectively, covering a frequency range of ∼6GHz or equivalently 8 free spectral ranges (FSRs) of the 20-cm cavity. The cavity transmission, detected by PD3, is used to determine whether a resonance of TEM00 mode is encountered during the temperature scan. The temperature is scanned by first using the large step; if a cavity resonance occurs, the scanning step is switched to the small one. Once the resonance is within the capture range of the PZT, the temperature scan stops, and the PZT voltage scan takes over to locate the center of the resonance and prepare for a lock.

Figure 2 shows representative signals recorded during the PZT voltage scan, frequency locking, and locked state. At a rate of 2 Hz and with an actuation coefficient of 1 MHz/V, the PZT repeatedly actuates frequency sweeps of 20 MHz (peak to peak) during which the cavity transmission is continuously monitored by PD3. The resonance is confirmed when an increase in the cavity transmission occurs in four consecutive sweeps, and the frequency sweep is reduced to 2.5 MHz. Otherwise, the NPRO temperature is fine-tuned with a step size corresponding to a frequency change of 300 kHz, relocating the transmission peak to the middle of the PZT voltage scan. The voltage scan continues until the transmission signal reaches a preset value (here, 100 mV), and the PZT feedback control loop is closed. The gain of the control loop is compensated by the digital loop filter adopting an incremental PID algorithm; the bandwidth of the control loop is ∼10kHz.

In the locked state, the voltage applied to PZT will eventually saturate due to the long-term drifts of NPRO and cavity. Every 3 s, this voltage is queried, and if the voltage exceeds ±5V, then it is pulled back by fine-tuning the NPRO temperature, thus preventing the PZT from being overburdened. The NPRO has a mode-hop-free temperature tuning range of about 15 GHz, which is large enough for uninterrupted long-term locking. An anti-jamming mechanism^[26] is added to the locked state in which if a glitch appears in the error signal, the loop filter enters a 100-ms holding mode in which the input is disconnected and the output is latched on to the value at the sight of the interference. This approach allows a fast recovery from strong perturbations, and in Fig. 2 its effectiveness is demonstrated by the signals around 5.8 s.

Figure 3(a) shows the in-loop noises of the PDH frequency locking in West and East systems, together with the electronic noise and shot noise. The noises are measured at the demodulation output and then converted to frequency noises using the discrimination coefficients, which are 4.7×10−5V/Hz and 6.9×10−5V/Hz in West and East systems, respectively. At ∼100Hz and towards higher Fourier frequencies, the in-loop noise bumps up (servo bump), resulting in an elevated noise in the error signal when the frequency control loop is closed [Fig. 2(c)].

Due to the photothermal effect, the fluctuation of the intracavity optical power induces changes in the cavity length, thereby influencing the frequency stability of the locked laser. The optical power entering the cavity is 150 µW, and the frequency-power dependences of the West and East cavities are measured to be 2.2 and 3.8 Hz/µW, respectively. While PD2 is used for intensity stabilization, the DC output of PD1 is recorded for out-of-loop evaluation of the relative intensity noise (RIN). With intensity stabilization, the RIN measured by PD1 is reduced to 8×10−3/√Hz(100μHz)−4.0×10−4/√Hz(0.5Hz) in the West system, and a similar result is obtained in the other system. Figure 3(b) shows the resulting frequency noises in the two systems, estimated by the power sensitivities mentioned above. At 1 mHz, RIN contributes a frequency noise of 1Hz/√Hz, which is below the thermal noise originating from the optical cavity.

The RAM generated by the EOM is also one of the main sources of frequency noise in the PDH frequency locking. Although the waveguide of EOM is prepared with a proton exchange process to only allow extraordinary light to propagate^[27], we observe a nonzero amplitude modulation on the level of 50 ppm. This RAM is found to vary with the temperature and the DC bias voltage applied to the electrodes of EOM, a phenomenon that matches the signature of birefringence interference that has been thoroughly investigated^[28]. Figure 3(b) shows the RAM-induced frequency noises measured in the two systems when the feedback control of RAM is implemented. PD1 is used for RAM detection when the cavity is off-resonant, and the demodulated signals are converted to frequency noises using the corresponding PDH discrimination coefficients. Thanks to the flexibility of adding extra digital feedback control loops realized by the FPGA approach, the RAM-induced frequency noise has been reduced to be well below the cavity thermal noise in a wide spectral range from 100 µHz to 0.5 Hz.

To measure the frequency noise of the system, each Nd:YAG laser is locked to its own 20-cm optical cavity. The heterodyne beat between two locked lasers is downconverted and then measured by a frequency counter. The noise spectrum of the beat is given in Fig. 3(b). At 1 mHz, the frequency noise is 3.5Hz/√Hz, and in the measured frequency range of 100 µHz–0.5 Hz, it is below 20Hz/√Hz, which is higher than the thermal noise by factors of 2 to 5.

Figure 4(a) shows a 12-h time series of the beat note with a linear drift of 0.016 Hz/s removed. The Allan deviations computed from this time series at average time from 0.8 to 6000 s are shown in Fig. 4(b). The frequency instability of the heterodyne beat is reduced to 3.0×10−16 (2.1×10−16, a single laser) around 1 s, and it remains below 5.0×10−16 (3.5×10−16, a single laser) at an average time of up to 6000 s.

Finally, we note that the frequency drift of the cavity should be further investigated for space applications, especially for those in which long-term frequency stability is crucial. Although the relative drift rate of our two 20-cm ultrastable cavities gradually settled down since their first operation, in a zero-g environment, the drift rate can be different from its ground value even if enough relaxation time is allowed. One possible laboratory test is to check for a potential change in the steady-state drift rate after the cavity orientation is deliberately altered from horizontal to vertical.

As an important step toward an ultrastable laser for space-based GW detection, an FPGA-based laser frequency-locked system is developed and tested. To evaluate its performance, the system is employed to lock a spaceborne 1064 nm NPRO Nd:YAG laser to a laboratory-operated 20-cm ultrastable cavity. The optical power of the laser in front of the cavity is actively stabilized, and the RIN measured in front of the cavity is reduced to 8.0×10−3/√Hz(100μHz)−4.0×10−4/√Hz (0.5 Hz). Feedback control of RAM originating in the waveguide EOM is also adopted, reducing its contribution to levels below thermal noise limit. The heterodyne beat between two independently operated systems shows that the frequency noise is 3.5Hz/√Hz at 1 mHz, and the corresponding frequency stability is 3.0×10−16 (2.1×10−16, a single laser) around 1 s and stays at the level of 10−16 for 6000 s, demonstrating the potential of the FPGA-based locked system to achieve a 10−16 level of frequency stability. Currently, we are developing a space-version reference cavity that adopts ULE mirrors (one flat and one concave with an ROC of 0.5 m) and has a reduced length of 7.5 cm due to constraints on volume and weight. This cavity shows a higher level of thermal noise (∼10Hz/√Hz at 1 mHz) compared with the 20-cm cavity^[29]. To suppress low-frequency noises, precision temperature stabilization and thermal shields will be adopted. This reference cavity, together with the developed NPRO Nd:YAG laser and FPGA-based control unit, will realize an ultrastable laser whose frequency noise is below 30Hz/√Hz (1 mHz–1 Hz), satisfying the requirement of the space GW detection.