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Abstract
A regeneratively mode-locked optoelectronic oscillator is proposed to realize multi-mode phase locking in optoelectronic oscillators by coupling a modulating signal generation loop. To verify the feasibility of the scheme, a numerical simulation model is established. In addition, a proof-of-concept experiment is demonstrated in a single-loop optoelectronic oscillator with a 2.2 km polarization-maintaining single-mode fiber, using an electric amplitude modulator/Mach-Zehnder modulator as an active mode-locking device. The generated microwave pulse signal has a center frequency of 10 GHz and a repetition rate of 95 kHz. We believe this scheme can provide a new approach to overcome the problem of detuning between the modulating frequency and the mode spacing during long-term operation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The optoelectronic oscillator (OEO) utilizes long fibers with low loss as energy storage elements, which has the advantage of high Q values and can generate microwave signals with low phase noise [1,2]. However, the use of long fibers also leads to small oscillation mode spacing in the OEO cavity. In order to achieve stable single-mode oscillations, it is necessary to resolve the contradiction that the small mode spacing caused by long fibers and the microwave filter bandwidth can hardly be satisfied simultaneously. Thus, researchers have been working on suppressing multi-mode oscillations in the cavity for a long time. For this purpose, various schemes such as coupled OEO [3–5], multiloop OEO [6], injected OEO [7] and whispering gallery mode resonators [8] have been proposed. In addition, a new mode selection technique called Parity-Time symmetric OEO [9] is also proposed, making it possible to achieve stable single-mode oscillation without narrowband filters.
Recently, multimode oscillation in OEO also has started to attract the attention of researchers. In 2011, Levy et al. first implemented a passively mode-locked OEO to generate a single-cycle radio frequency (RF) pulse signal by employing a saturable RF amplifier [10]. In 2018, Hao et al. proposed a Fourier-domain mode-locked OEO [11], which can generate linearly chirped microwave waveforms with a large time-bandwidth product. Simultaneous oscillation of multiple modes in the OEO loop is achieved by frequency domain scanning, overcoming the time limitation of mode establishment in tunable OEO. Meanwhile, the active mode-locking technique has also been introduced into the OEO to generate ultrashort microwave pulse signals. In 2020, Yang et al. successfully achieved actively mode-locked OEO by periodically modulating the intracavity loss using an additional electro-optic intensity modulator [12]. In 2021, Zeng et al. implemented phase locking of adjacent modes in OEO by amplitude modulation in the microwave domain [13,14]. Subsequently, they also proposed a simpler structured active mode-locking scheme by modulating the bias port of the electro-optic modulator [15], which can achieve 100th-order harmonic active mode-locking. Lately, we also observed the rational harmonic mode-locking phenomenon in actively mode-locking OEOs [16]. In the above active mode-locking OEO schemes, the precise matching of the modulation frequency with the free spectral range is essential. Nevertheless, changes in the environment (temperature or mechanical vibration, etc.) will cause the fiber length to vary, making it difficult to achieve exact matching in long-time operation. When the detuning amount gradually increases and exceeds a certain range, the pulse amplitude will be seriously jittered or even loss of lock, which greatly affects the robustness of actively mode-locked OEOs.
In this paper, an actively mode-locked OEO scheme without an external modulation source is proposed. A portion of the output of the optoelectronic oscillation loop is converted into a modulating signal for mode-locking by means of a square-law detector, a narrow-band filter, and an electronic amplifier. Due to the frequency of the modulating signal generated by this scheme can change in real-time with the cavity length, it can achieve long-term accurate matching between the modulation frequency and the mode spacing. Since the scheme is similar to the regeneratively mode-locked laser [17], it is termed regeneratively mode-locked OEO. A numerical simulation model is established and used to verify the feasibility of the scheme in theory. Furthermore, a proof-of-concept experiment is demonstrated by feeding back to different modulators, which generates a microwave pulse signal with a center frequency of 10 GHz and a repetition rate of 95 kHz.
2. Methods
The schematic diagram of the regeneratively mode-locked OEO is illustrated in Fig. 1(a), which includes the actively mode-locked loop and the modulating signal generation loop. The actively mode-locked loop consists of a laser diode (LD), a variable optical attenuator (VOA), a Mach-Zehnder modulator (MZM) biased at the quadrature point, a long polarization-maintaining (PM) fiber, a photodetector (PD), a bandpass filter (BPF1), an electronic amplifier (EA1), an electrical power divider, and an amplitude modulator (AM). To achieve the mode-locking, a signal with a frequency equal to an integral multiple of the mode spacing is required to drive the AM. Different from other approaches using an external signal source, the modulating signal used here is obtained by a square-law detector and the corresponding bandpass filter in the second loop. The square-law detector is a key component to detect the envelope of signals, which is composed of nonlinear components and loads with low-pass filter characteristics. When two feedback loops are locked simultaneously, a microwave pulse signal can be generated. Alternatively, the mode-locking can also be realized by loading the modulating signal into the bias port of the MZM [16] shown in Fig. 1(b).
Fig. 1. Schematic diagram of a regeneratively mode-locked OEO (a) based on AM, (b) based on MZM. DC: direct current, AC: alternating current.
3. Simulation
A numerical simulation is carried out to investigate the principle of the regeneratively mode-locked OEO. The main algorithm flow chart in the simulation is shown in Fig. 2. Assuming that the optoelectronic oscillation loop has started to oscillate around 10 GHz, there are multiple longitudinal modes with equal mode spacing in the cavity at the same time. As a result, the oscillation signal ${V_0}(t)$ in the loop can be expressed as a superposition of multiple sinusoidal signals with a center frequency near 10 GHz and random phases, as shown in Eq. (1).
where n is the total number of longitudinal modes in the cavity, $A(i)$ and $\varphi (i)$ are the amplitude and phase of the $i$-th order longitudinal mode, respectively. $A(i)$ accords with Gaussian distribution and ${f_c}(i)$ presents the frequency of the $i$-th order longitudinal mode, where the spacing between adjacent modes is set to 95 kHz, i.e., $ f_c(i+1)-f_c(i)=95 \mathrm{kHz}.$The initial input signal ${V_0}(t)$ is firstly injected into the MZM and then is sent to PD. Since the dispersion and the loss of the fiber has a small effect on the simulation results, it is neglected here. The output signal ${V_{PD}}(t)$ of the PD can be written as follows
where ${\rho _{PD}}$ is the responsivity of the PD and is set to 0.8 A/W. R is the output impedance of the PD, which is set to 50 $\varOmega $. ${P_{t}}(t)$ is the output power of the MZM, which can be expressed asAfterward, ${V_{PD}}(t )$ is sent to the bandpass filter (BPF1), the output signal ${V_{f1}(t)}$ of the filter can be expressed as
where ${\ast} $ denotes convolution operation, ${h_1}(t)$ is the impulse response of the bandpass filter, In the simulation, the center frequency and the 3-dB bandwidth of the filter (BPF1) are set to 10 GHz and 10 MHz, respectively. A microwave amplifier (EA1) is used to compensate for the power loss. ${G_{A1}}$ is the gain coefficient of the amplifier, which is given by where ${g_1}$ represents the small-signal gain coefficient, which is set to 8. ${P_{in}}$ is the input power of the amplifier. ${P_{sat1}}$ is the saturation power, which is set to 1 W.Following this, the output signal ${V_{A1}}(t)$ is split into three parts equally. Among them, ${V_a}(t)$ is injected into the amplitude modulator and ${V_c}(t)$ is used for monitoring. ${V_b}(t)$ is converted into its envelope signal ${V_s}(t) = {[{V_b}(t)]^2}$ with the mode interval of 95 kHz and its harmonics through the square operation. Next, the envelope signal ${V_s}(t)$ is amplified to ${V_{A2}}(t)$ by a RF amplifier (EA2) with the gain coefficient ${G_{A2}}$. The expression of ${G_{A2}}$ can be written as
where ${g_2}$ is set to 2, and ${P_{sat2}}$ is set to 500 mW. Then, the modulating signal ${V_m}(t)$ is extracted by a narrowband filter (BPF2), which is calculated as where ${h_2}(t)$ is the impulse response of the filter (BPF2) with a center frequency of 95 kHz and a 3-dB bandwidth of 10 kHz. Afterward, ${V_m}(t)$ is injected into the amplitude modulator and its output signal denoted as ${V_a}(t) \cdot [1 + {V_m}(t)]$ is sent to the filter (BPF1) of the main loop to start the next cycle.Generally, the calculating time window is consistent with the OEO roundtrip time ${T_r}$, i.e., 10.5 µs. To improve the spectral resolution, the time window is extended to $N{T_r}$, where N is an integer. A pulse reaches the steady state after propagating around 400 cycles and the results of 200 impluses are stored to calculate the corresponding spectrum. Figure 3 and Fig. 4 shows the measurements of the input signal and output signal in the numerical simulation, respectively. It can be seen from Fig. 3(a) and Fig. 4(a) that the signal changes from a continuous signal to a pulsed signal, which is due to coherent superposition of longitudinal modes with constant phase. Figure 3(b) and Fig. 4(b) show the corresponding spectrum with a center frequency of 10 GHz and a mode spacing of 95 kHz, respectively. The simulation results confirm that the regeneratively mode-locked OEO scheme is feasible in principle.
Fig. 3. (a) Temporal waveform and (b) spectrum of the input signal ${V_0}(t )$ in numerical simulation.
Fig. 4. (a) Temporal waveform and (b) spectrum of the generated microwave pulse train by numerical simulation.
4. Experimental results
A proof-of-concept experiment based on the setup in Fig. 1(a) is performed. In the experiment, a continuous-wave light with a power of 20 dBm at 1550 nm is generated by a narrow linewidth laser (EM650, Gooch & Housego) and is sent to a MZM (MXAN-LN-20, iXblue) biased at its quadrature point after being attenuated by a VOA (VOA 50PM-APC, Thorlabs). Then, the intensity-modulated light passes through a spool of PM single-mode fiber (PM1550-XP, Thorlabs) with a length of 2.2 km and is converted into the microwave signal by a 20 Gb/s PD (DSC50S, Discovery Semiconductors) based on InGaAs PIN Photodiode. After being amplified by a microwave amplifier with a gain of 25 dB, the signal is filtered by a home-made bandpass filter with a center frequency of 10 GHz and a 3-dB bandwidth of 20 MHz. In the modulating signal generation loop, the signal power is detected by the detector (HP 08672-60129, Agilent Keysight) with an operating frequency range of 0.01 GHz to 18 GHz. A home-made bandpass filter is employed for selecting the required signal frequency. To finely control the loop power, a variable RF amplifier (SIM910 JFET Preamp, SRS) with a gain range from 0 to 20 dB is used.
Firstly, the main loop is equivalent to an actively mode-locked OEO when the modulating signal regeneration loop is open. Fundamental mode-locking is successfully achieved through loading a sinusoidal signal with a frequency of 95 kHz generated by a function generator (RIGOL DG 3101A) into the microwave AM. Figure 5(a) presents the temporal waveform measured by a high-speed real-time oscilloscope (Tektronix DPO75902SX, 200 GS/s, 59 GHz) of the output microwave pulse train. The pulse period is about 10. 5 µs, which matches with the fiber length of 2.2 km. Figure 5(b) shows the spectrum measured by a spectrum analyzer (R&S FSWP50, 1 MHz-50 GHz), where the mode interval is 95.3 kHz.
Fig. 5. (a) Temporal waveform and (b) spectrum of the pulse train generated by the AM-based actively mode-locked OEO with external modulation, (c) temporal waveform and (d) spectrum of the signal detected by the square-law detector.
Next, to realize regenerative mode-locking, it is vital to obtain the frequency signal of the mode interval. Here, it is achieved through an envelope signal detected by a square-law detector. The temporal waveform of the detected signal is shown in Fig. 5(c). We can see that the envelope is a non-negative pulse train, which characterizes the power information of the pulse signal in Fig. 5(a). What’s more, for a single pulse, there is no fine structure compared with Fig. 5(a). The corresponding spectrum shown in Fig. 5(d) does not include the carrier frequency and only consists of 95 kHz as well as its harmonic components, which is the key step for achieving the regeneratively mode-locked OEO.
Subsequently, we remove the external modulation source and then close the modulating signal generation loop. By tuning the VOA and the variable amplifier carefully, the phase-locking of the intracavity longitudinal modes is achieved. Figure 6 (a) shows the temporal waveform of the microwave pulse train with a spacing of 10.5 µs. We found that there is saturation at the pulse peak, which is restricted by the gain requirement of two loops. The corresponding spectrum measured at the resolution bandwidth (RBW) of 200 Hz is displayed in Fig. 6(b). Compared with the spectrum under the free-running state, the number of modes is significantly increased and mode power becomes balanced. Moreover, without the mode-competition effect, the spectrum is more stable and eliminates mode hopping.
Fig. 6. (a) temporal waveform and (b) spectrum of the pulse train generated by the AM-based regeneratively mode-locked OEO.
Additionally, we also have an attempt to realize the mode-locking by modulating the loop loss through the DC port of the MZM. As expected, a stable microwave pulse signal is generated after finely adjusting the gain of loop. The temporal waveform and the spectrum of the signal shown in Fig. 7 indicate that the mode-locking is also realized successfully. However, the generated signal has a higher bottom noise compared with the AM-based scheme, which may be attributed to the fact that the loop loss is more sensitive to the bias voltage of the MZM.
Fig. 7. (a) temporal waveform and (b) spectrum of the pulse train generated by the MZM-based regeneratively mode-locked OEO.
In our experiment, only the fundamental frequency mode-locking is demonstrated to verify the effectiveness of the regeneratively mode-locked scheme. It should be pointed out that the scheme can also be easily extended to the harmonic region to further increase the repetition rate. Furthermore, a regeneratively mode-locked OEO with tunable carrier frequency can be realized if the filter (BPF1) is replaced with a microwave photonic filter. At last, the regeneratively mode-locked principle may also be applicable in the Fourier-domain mode-locked OEO by using nonlinear microwave devices to extract the scanning frequency.
5. Conclusion
In summary, we have proposed a regeneratively mode-locked OEO scheme and built a numerical simulation model to validate the theoretical feasibility of the scheme. In addition, we performed a proof-of-concept experiment in a single-loop OEO by feeding back the modulating signal to the AM/MZM. The resulting pulse train has a center frequency of 10 GHz and a repetition rate of 95 kHz. Compared with traditional actively mode-locked OEOs, the scheme proposed here can achieve mode-locking without an external modulation source and real-time precise matching of the modulation frequency with the mode spacing, which improves the performance of the robustness and adaptability to the dynamic mode spacing. For application, evaluating phase noise and improving stability are also very valuable directions for subsequent research in the future. We believe that this scheme has great potential for applications such as pulsed Doppler radar, sensing, and multi-carrier communication [12–14].
Funding
National Natural Science Foundation of China (11803023); State Administration for Science, Technology and Industry for National Defense (HTKJ2020KL504004); National Key Laboratory Foundation of China (6142411186408).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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