Frequency Stabilization of Pulsed Injection-Seeded OPO Based on Optical Heterodyne Technique

Xiao Chen(陈晓)$^{1,2}$, Xiao-Lei Zhu(朱小磊)$^{1\hyperlink{s}{**}}$, Shi-Guang Li(李世光)$^{1\hyperlink{s}{**}}$, Xiu-Hua Ma(马秀华)$^{1}$,\\ Wei Xie(谢伟)$^{1,2}$, Ji-Qiao Liu(刘继桥)$^{1}$, Wei-Biao Chen(陈卫标)$^{1}$, Ren Zhu(朱韧)$^{1}$

doi:10.1088/0256-307X/35/2/024201

⇦Chinese Physics Letters, 2018, Vol. 35, No. 2, Article code 024201⇨ Frequency Stabilization of Pulsed Injection-Seeded OPO Based on Optical Heterodyne Technique * Xiao Chen(陈晓)1,2, Xiao-Lei Zhu(朱小磊)1**, Shi-Guang Li(李世光)1**, Xiu-Hua Ma(马秀华)1, Wei Xie(谢伟)1,2, Ji-Qiao Liu(刘继桥)1, Wei-Biao Chen(陈卫标)1, Ren Zhu(朱韧)1 Affiliations 1Key Laboratory of Space Laser Communication and Detection Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 2University of Chinese Academy of Sciences, Beijing 100049 Received 10 November 2017 ^*Supported by the National Key Research and Development Program of China under Grant No 2016YFC1400902, the National Natural Science Foundation of China under Grant Nos 61505230 and 61475170, and the Shanghai Natural Science Foundation under Grant No 15ZR1445000.
^**Corresponding author. Email: xlzhu@siom.ac.cn; sgli@siom.ac.cn Citation Text: Chen X, Zhu X L, Li S G, Ma X H and Xie W et al 2018 Chin. Phys. Lett. 35 024201 Abstract A frequency stabilizing system for a pulsed injection seeded 1550 nm optical parametric oscillator (OPO) at 20 Hz repetition rate is demonstrated. The optical heterodyne method is used to measure the frequency difference between the seed laser and the OPO output. Using the frequency difference as the error signal, a proportional-integral controller in combination with a scanner is applied to stably match the OPO cavity length to the seed laser frequency. The root-mean-square (rms) error of the frequency discrimination method is $ < $0.07 MHz according to a 'frequency shifting-chopping-beat' evaluation. The frequency fluctuation of the frequency-stabilized OPO is 0.29 MHz (rms), and the Allan deviation is less than 20 kHz for averaging time of more than 3 s. DOI:10.1088/0256-307X/35/2/024201 PACS:42.60.Lh, 42.65.Yj, 42.60.By © 2018 Chinese Physics Society Article Text Space-borne integrated path differential absorption (IPDA) lidar is considered as an effective tool for global observation of carbon dioxide (CO$_{2}$).[1-3] This technique requires a tunable single-longitudinal mode (SLM) pulsed laser source which coincides with appropriate absorption line of CO$_{2}$ molecules (1572 nm).[2] In such applications, pulsed injection-seeded optical parametric oscillators (OPOs) appear favorable due to their unsurpassed tunability. To minimize the error contribution from the laser frequency and to ensure 1 ppm precision for CO$_{2}$ measurements, the frequency fluctuation of the laser source needs to be $ < $0.3 MHz (rms),[1,3] which is a challenging goal for the frequency stabilization of a pulsed injection-seeded OPO. In the injection seeding process, laser oscillation occurs at the axial mode nearest the seed frequency.[4,5] The frequency stability of OPO output is mainly determined by the stability of OPO cavity length when seed frequency is stabilized at a high level, which has already been achieved for cw seed laser at 1572 nm[3] and some other wavelengths.[6] Thus matching the OPO cavity length to the frequency of a stabilized seed laser is an effective and available strategy to generate frequency-stabilized laser pulses. Widely used cavity-length control methods such as ramp-and-fire[7] and Pound–Drever–Hall[8] suffer from the fact that the finesse of the OPO cavity with high output coupling is low compared with the stability requirement.[9] The buildup-time reduction method[10] is also hard to apply because the time reduction of concerned OPO is less than 1 ns. In 2009, Martin et al.[9] introduced a cavity-length control method based on the optical heterodyne technique, which uses the frequency difference between OPO output and the seed laser as the error signal to ensure stable injection seeding. In 2011, Andreas et al.[2] applied this method to a pulsed 1572 nm OPO at 100 Hz repetition rate and the frequency fluctuation of the developed OPO is less than 70 kHz (the Allan deviation for averaging time of more than 3 s). However, details about this method and its performance have not been reported yet, nor a pulsed injection-seeded OPO with frequency fluctuation of less than 0.3 MHz (rms). In this Letter, frequency stabilization based on the optical heterodyne technique is studied. A real-time optical heterodyne measurement is demonstrated to monitor the frequency difference between the seed laser and the output of a pulsed injection-seeded OPO at 1550 nm at 20 Hz repetition rate. Then the measured frequency difference serves as the error signal of a proportional-integral (PI) controller to control the cavity length of the OPO and to match the cavity to the seed laser. A scanner is used to search for an appropriate matching point for the PI controller. The performance of this system is analyzed and the frequency-stabilized OPO has a high-frequency stability of 0.29 MHz (rms) compared with the seed laser. Figure 1 shows the setup of the frequency-stabilized pulsed injection-seeded OPO. The pump laser is a self-developed single-frequency Nd:YAG laser at 20 Hz repetition rate at 1064 nm. The seed laser is a cw single-longitudinal mode semiconductor laser (Redfern Integrated Optics Inc). It has a narrower linewidth of less than 3 kHz at 1550 nm, low phase noise and a good short term frequency stability, thus it is able to provide a reliable reference. The power of the seed laser injected into the OPO is 1.5 mW, which is enough for successful injection seeding when the cavity length is matched to the seed frequency. Except for the seed and the pump laser, the remaining part can be divided into two units: the OPO cavity and the control unit.

Fig. 1. Setup of the frequency-stabilized pulsed injection-seeded OPO.

The OPO resonator is a four-mirror ring cavity with potassium titanyl arsenate (KTA) in critical phase matching cut for wavelengths around 1550 nm.[2,11] It consists of two concave mirrors (M1 and M2), two flat mirrors (M3 and M4) and two identical crystals with compensated configuration to partially prevent the walk-off effect.[2] M1 serves as both the input window and output window with a transmittance of 30% at 1550 nm. M3 is mounted on a piezo-electric transducer (PZT), which can change the position of M3 to match the cavity to the seed wavelength. A sensitive photodiode (PD1) is set behind M4 to monitor the multiple-beam interference of the seed laser through the cavity. The optical length of the cavity is around 260 mm, resulting in a longitudinal-mode separation of 1.2 GHz. The energy of the laser pulse from the OPO is around 1.5 mJ and the pulse width is 22 ns (full width at half maximum, FWHM). For an injection-seeded OPO, frequency detuning between the seed laser and the closest axial mode of the cavity leads to linear frequency difference between the OPO output and the seed laser.[12] The resonance frequency $\nu$ is determined by the OPO cavity length $L$ and their relationship is expressed as $$\begin{align} L=\,&\frac{mc}{v},~~ \tag {1} \end{align} $$ $$\begin{align} \delta L=\,&\frac{m}{v^2}\cdot \delta v,~~ \tag {2} \end{align} $$ where $m$ is the interference order corresponding to the axial mode nearest the frequency of the seed laser, $\delta L$ is a small drift in cavity length $L$, $\delta v$ is the result shift in $\nu$, and $\delta v$ is approximately linearly related to $\delta L$ due to the fact that $\delta v$ is much less than $\nu$ at the concerned wavelength (1550 nm). Thus drifts in the cavity length will lead to linear frequency shifts in the OPO output. This relationship makes it possible to achieve frequency control in an injection-seeded OPO by changing the cavity length according to the frequency difference between the OPO output and the seed laser, which is just the frequency stabilization strategy introduced in this study. The control unit consists of a fiber pigtailed acoustic-optic modulator (AOM, IPF-400-40-1550-2FP, Brimrose), a single-mode polarization-maintaining fiber combiner, a high-speed photodetector (PD2, 5 GHz-bandwidth InGaAs PIN), an analog-digital converter (DAQ1, PCI-5154, 2 GS/s sampling rate, NI), an industrial personal computer (IPC), a digital-to-analog converter (DAQ2, PCI-6221, NI), and an amplifier. It controls the voltage on the PZT to compensate for the frequency detuning between the seed laser and the cavity. The controlling progress has two steps. The first step is measuring the frequency difference between the OPO output and the seed laser in real time by optical heterodyne method.[10,13] Part of the two beams are combined by the fiber combiner and the peak power of the pulsed optical signal is set to a level comparable to the cw laser. The electric field from the seed laser is frequency shifted by 400 MHz from the AOM, which is intended to minimize the overlap between the intensity envelope of the optical pulse and the optical heterodyne beat signal.[13] The intensity of the combined laser is detected by PD2, recorded by DAQ1 and then analyzed in the IPC. A fast-Fourier-transform (FFT) algorithm using the Hamming window type provides the spectral intensity of the seeded laser pulse. The frequency difference between the two beams is given by the frequency value corresponding to the maximum of the beat spectrum. To examine the reliability of this method, a frequency shifting-chopping-beat strategy is applied to evaluate the value of measurement error. As shown in Fig. 2, the seed laser is split into two beams by a single-mode polarization-maintaining fiber splitter. The AOM is pulse-modulated to chop one of the beams into pulsed laser while providing a frequency shift of around 400 MHz. The frequency difference between the chopped pulse and the other beam has good stability because the frequency fluctuation of the AOM is less than 6 kHz (rms). The fluctuation of the frequency difference measured by this system may be larger than 6 kHz due to the existence of error. The measurement error can be represented by the measured frequency fluctuation if it is much larger than 6 kHz.

Fig. 2. Evaluation scheme for the optical heterodyne method.

The width of the chopped pulses is set around 22 ns because the pulse width of the OPO output is around 22 ns. The insets in Fig. 2 are a typical heterodyne beat signal and its spectrum. Here 36000 of such signals are analyzed to calculate the frequency fluctuation. Figure 3(a) shows the result and Fig. 3(b) is the corresponding chart of the frequency distribution. The measured frequency fluctuation of these signals is 0.07 MHz (rms), which can represent the rms error of this measurement since it is much larger than 6 kHz. The results exhibit the high frequency discrimination precision of the optical heterodyne measurement. The histogram of the error fits well to a Gaussian distribution demonstrating that the error fluctuates independently. The frequency distribution is not centered at 400 MHz due to the pulse modulation on the AOM.

Fig. 3. Results of the evaluation scheme. (a) Central frequency of 36000 beat signals, and (b) chart of frequency distribution.

Fig. 4. The algorithmic flow to determine the needed voltage on the PZT.

The second step of the controlling progress is to determine the needed voltage on the PZT. The algorithmic flow is shown in Fig. 4. If the OPO is successfully injection-seeded at the beginning, the spectral peak of the signal from DAQ1 will be strong and can represent the actual spectra of the OPO output. In this case, the needed voltage can be calculated by a PI controller with the central frequency as error signal and the cavity will be stably matched to the seed laser. Otherwise, a scan of the cavity length will be needed to search an appropriate point to ensure successful injection seeding progress and to help starting the PI controller. The scanner can also ensure normal work of the PI controller even if a large disturbance occurs. It should be noted that the range of the output voltage must be large enough for the scanner to find at least one matching point. The PI controller and the scanner are both achieved in the IPC based on Labview,[14] making it easy to debug the parameters of this system. Figure 5(a) shows the variation of the voltage on the PZT while the control unit starts working and Fig. 5(b) is the variation of the frequency value corresponding to the maximum of the beat spectrum. The OPO cavity is not well matched to the seed laser at the beginning, thus the scanner is turned on to search for an appropriate matching point. The slope in the voltage variation before $t_1$ represents the searching progress. Once the point is found, the PI controller will replace the scanner and soon will match the cavity to the seed laser. The PI controller is able to keep working normally when small disturbance occurs on the cavity, but fails if the disturbance is too large or the calculated needed voltage is beyond the output range of the amplifier. When the PI controller fails to work, the scanner will be put into use and searches for a matching point again. The combination of the scanner and the PI controller increases the reliability of the frequency stabilization system.

Fig. 5. Variation of the voltage and the frequency when the control unit starts. (a) Variation of the voltage on the PZT. (b) Variation of the frequency value corresponding to the maximum of the beat spectrum.

A detailed variation of the cavity and the voltage on the PZT is shown in Fig. 6. The red line is the intensity of multiple-beam interference of the seed laser through the cavity, which is generated by PD1 and can represent the variation of the cavity length. The steps that occur at intervals of 50 ms reflect the thermal effect of the KTA crystal from pump laser, and the slow drift comes from the heat dissipation progress. The blue line is the voltage on the PZT, which is attenuated to a suitable level for detecting. The steps of the voltage lag by around 9 ms behind the steps of the cavity length, demonstrating that the processing time for a single OPO pulse is around 9 ms. The processing time can be further reduced by replacing the IPC with a suitable field programmable gate array (FPGA). Variation of the cavity length caused by the voltage steps is smaller compared with the influence of thermal effect and the heat dissipation progress in the KTA crystal. However, fortunately, the influence is approximately stable because the stability of pump energy is pretty good ($ < $1%). Thus the voltage control on the PZT is still effective for frequency stabilization.

Fig. 6. Detailed variation of the cavity and the voltage on the PZT. Red line: variation of the intensity of multiple-beam interference of the seed laser though the cavity. Blue line: variation of the voltage on the PZT (attenuated to a suitable level for detecting).

Fig. 7. The frequency stability of the OPO stabilized by the heterodyne technique. (a) Drift of the frequency differences between the OPO output and the seed laser. (b) The Allan deviation generated from the frequency drift.

A disadvantage of this stabilization scheme is that it is not possible to react to vibrations with frequencies exceeding the repetition rate of the OPO.[2] However, the OPO cavity is a small ring milled from a monolithic steel block and has a rather good short-term stability. The resulting frequency stability of the OPO is shown in Fig. 7. The fluctuation of the frequency difference between the OPO output and the seed laser is 0.29 MHz (rms, 36000 pulses, 30 min), and the Allan deviation is less than 20 kHz for averaging time of more than 3 s. The difference of performance between this heterodyne method and widely used ramp-hold-fire (RHF)[15] frequency stabilization technique, which uses the cavity as the frequency discriminator, is also studied. When the RHF technique is used on the OPO described above, the frequency fluctuation becomes 1.15 MHz (rms, 36000 pulses, 30 min) and the Allan deviation is more than 0.3 MHz for averaging time of 3 s, as is shown in Fig. 8. The comparison exhibits the superiority of the frequency stabilization based on the optical heterodyne technique, which comes from the fact that the heterodyne method has higher precision of frequency discrimination than the concern OPO cavity.

Fig. 8. The result frequency stability of the OPO stabilized by the RHF technique. (a) Drift of the frequency differences between the OPO output and the seed laser. (b) The Allan deviation generated from the frequency drift.

In summary, a frequency stabilizing system for a pulsed injection seeded 1550 nm OPO at 20 Hz repetition rate has been demonstrated, which is expected to provide technical support for the application of CO$_{2}$ IPDA lidar. Optical heterodyne technique is used to monitor the frequency difference between the outgoing pulse and the seed laser with an rms error of less than 0.07 MHz. A scanner and a PI controller are applied to control the OPO cavity length according to the measured frequency difference, and their combination will ensure normal work of this system even if large disturbance occurs. The frequency fluctuation of the OPO pulses compared with the seed laser is 0.29 MHz (rms). The Allan deviation is less than 20 kHz for averaging time of more than 3 s. The described frequency stabilization exhibits superiority over the widely used RHF technique due to its high precision of frequency discrimination. References Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysisSPIE ProceedingsFrequency-stabilized laser system at 1572 nm for space-borne CO2 detection LIDARSingle axial mode operation of aQ-switched Nd:YAG oscillator by injection seedingLocking the cavity of a pulsed periodically poled lithium niobate optical parametric oscillator to the wavelength of a continuous-wave injection seeder by an “intensity-dip” methodImprovement of Laser Frequency Stabilization for the Optical Pumping Cesium Beam StandardFast resonance-detection technique for single-frequency operation of injection-seeded Nd:YAG lasersInjection seeded frequency stabilized Nd:YAG ring oscillator following a Pound-Drever-Hall schemeThe airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performanceFrequency jitter and spectral width of an injection-seeded Q-switched Nd:YAG laser for a Doppler wind lidarHigh-efficiency nanosecond optical parametric oscillator with the stable ring configurationFrequency shifts in injection-seeded optical parametric oscillators with phase mismatchControl of frequency chirp in nanosecond-pulsed laser spectroscopy 1 Optical-heterodyne chirp analysis techniquesArbitrary frequency stabilization of a diode laser based on visual Labview PID VI and sound card outputGeneration of Fourier-transform-limited 35-ns pulses with a ramp-hold-fire seeding technique in a Ti:sapphire laser

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