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Abstract
Based on the period-one (P1) dynamics of an optically injected semiconductor laser (SL), a photonic scheme enabling the generation of a tunable high-quality frequency-modulated continuous-wave (FMCW) signal is investigated experimentally. Under a modulated optical injection, the laser is driven into P1 oscillation with a modulated microwave frequency. In this work, optical feedback is also introduced to further reduce the microwave phase noise. The experimental results show that the central frequency of the generated FMCW signal can be widely tuned from 11.41 to 50.05 GHz by simply adjusting injection parameters while the frequency sweep range of the FMCW signal can be controlled by varying the modulation index. Under proper operating parameters, the sweep range and rate of the FMCW signal are 18.42 GHz (13.73 GHz- 32.15 GHz) and 1.14 GHz/ns, respectively. Further, by introducing an optical feedback loop, the frequency comb contrast of the FMCW signal is drastically increased by 27.15 dB when the reciprocal of the feedback delay time matches with the modulation frequency exactly due to the locking effect of the external cavity optical modes.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Frequency-modulated continuous-wave (FMCW) microwave signals in the form of a sinusoid with time-varying microwave frequencies can be widely utilized in ranging, imaging, and communication applications [1,2]. For example, in modern frequency domain radar systems, the FMCW microwave signal can be used to determine the round-trip propagation delay by measuring the frequency difference between the transmitted and received signals. Thus a FMCW signal with high central frequency, wide tunability, large sweep range, and fast sweep rate is highly desired to achieve long distance detection with high resolution [3]. Conventionally, a FMCW signal can be generated by two traditionally electrical approaches. One is based on a voltage-controlled oscillator (VCO) [4], and the other is based on a digital signal processing (DSP) technique [5]. Due to the limitation of electrical bandwidth, the central frequency of the FMCW signal generated by the two electrical approaches noted above is relatively low and the frequency sweep range (rate) is also relatively small (slow).
In recent years, numerous photonic techniques have been proposed [6–23] for acquiring FMCW signals with high central frequency, large sweep range and fast sweep rate, including frequency-to-time mapping (FTM), heterodyne-beating, beating of two coherent light sources, and a chip-based technique. For the FTM, the optical spectrum of an optical pulse train is first modified by a spectral shaper (e.g. a fiber Bragg grating, a Sagnac loop or a programmable optical filter) which maps this shaping into the time domain in a dispersive medium [6–8]. Although the central frequency of the generated FMCW signal can reach up to 30 GHz, its tunability is very poor because of the fixed response of the optical spectral shaper. The heterodyne-beating technique can generate high-frequency and widely tunable FMCW signals by heterodyning a continuous wave (CW) light source with a wavelength-swept light source or pre-chirped optical pulses [9–13], but the optical phase fluctuations from two individual lasers would degrade the signal quality after optical-to-electrical conversion. The technique of beating two coherent light sources with a quadratic phase difference can be implemented by a phase modulator [14], a polarization modulator [15,16], a mode-locked laser [17,18], or an optoelectronic oscillator [19,20]. The sweep range of the generated FMCW signal is limited by the modulation index of the electro-optical modulator and a high-speed microwave arbitrary waveform generator is required, which makes the system complicated and costly. Other schemes for generating FMCW have been reported based on a silicon photonic chip-based spectral shaper [21,22] or monolithic integrated amplified feedback laser [23]. While these approaches created systems with compact footprints, high coupling efficiencies, and the potential for use in modern radar applications, they suffer from poor tunability. Obviously, each of the techniques mentioned above has its respective advantages and some room for improvement.
It is worth noting that a photonic generation technique of FMCW signals based on the period-one (P1) nonlinear dynamics of an optically injected semiconductor laser (SL) has been proposed and investigated theoretically and experimentally [24–27]. The P1 oscillation is a form of nonlinear dynamics in a single-mode semiconductor laser subject to an optical injection. For a given frequency detuning, with the increase of the injection strength, the laser undergoes a Hopf bifurcation and then traces a limit-cycle trajectory, which yields a sustained intensity oscillation at a single-tone microwave frequency. According to the dependence of the P1 frequency on the injection power [28,29] under a certain detuning frequency, an FMCW signal centered at the P1 frequency can be yielded by modulating the strength of the injection light. Under this case, the power spectrum distribution of the generated FMCW signal is a frequency comb whose comb space is equal to the modulation frequency. In 2015, Zhuang et al. numerically investigated the photonic generation of a FMCW signal based on the P1 oscillation, and the result shows that the sweep range and rate of the generated FMCW signal can be tuned by adjusting the modulation index and the modulation frequency [24]. In 2016, Zhou et al. experimentally demonstrated the FMCW signal generation by the P1 oscillation [25], and the generated FMCW signal has a sweep range of 12 GHz and a time-bandwidth product of 1.2 × 105. In 2017, N. G. Usechak et al. demonstrated a high-speed wideband voltage-controlled oscillator based on an optically injected semiconductor laser [26], and obtained a FMCW signal with a tuning range of 6-16 GHz and a tuning rate of 1 GHz/ns. Although such a technique has many advantages such as wide tunability of central frequency, optical controllability and structural simplicity, the generated FMCW signal inherently contains the phase noise due to the intrinsic spontaneous emission noise of the laser, which needs to be suppressed for some particular scenarios. In 2016, Zhuang et al. utilized an optoelectronic feedback loop to stabilize the FMCW signal, and an FMCW signal with a sweep range of 7.7 GHz and a sweep rate of 0.42 GHz/ns is obtained. Moreover, the frequency comb contrast is improved by 30 dB [27]. However, a photodetector is required in the feedback loop, which increases the complexity and cost of the system.
In this paper, through adopting an optical feedback loop to suppress the phase noise, a scheme for acquiring a high-quality FMCW signal is proposed based on an optical injection SL operating at P1 oscillation. Different from an optoelectronic feedback loop, there is no high-frequency electronic devices included in the optical feedback loop, and therefore the optical feedback scheme is simple and low-cost. The experimental results demonstrate that the central frequency of the generated FMCW signal can be tuned within a wide range from 11.41 to 50.05 GHz, and the sweep range and the sweep rate can reach 18.42 GHz (13.73 GHz-32.15 GHz) and 1.14 GHz/ns, respectively. After further introducing the optical feedback loop, the frequency comb contrast of the FMCW signal can be improved by 27.15 dB (from 10.38 dB to 37.53 dB) under optimized operating parameters. Additionally, the influences of the modulation frequency and the feedback power on the frequency comb contrast are also verified.
2. Experimental setup
The schematic diagram of the experimental setup is shown in Fig. 1. A commercial 1550 nm single-mode distributed feedback semiconductor laser (DFB-SL) serves as the injected laser. The bias current and temperature of the DFB-SL are controlled by a high accuracy and low-noise current-temperature controller (ILX-Lightwave, LDC-3724C). The light output from a tunable laser (TL, Santec TSL-710, 1480 nm-1640 nm) is injected into the DFB-SL after passing through a polarization controller 1 (PC 1), Mach–Zehnder modulator (MZM) (10-GHz bandwidth), PC 2, erbium-doped fiber amplifier (EDFA), variable attenuator (VA 1), 80:20 fiber coupler 1 (FC 1), optical circulator (OC) and FC 2 successively. The injection power Pinj can be adjusted by controlling VA 1, and it is monitored by an optical power meter (PM) through the 10% path of the FC 2. The detuning frequency fi ( = finj- fSL, finj is the frequency of the injection light, and fSL is the frequency of the free-running DFB-SL) can be controlled by adjusting the frequency of the injection light. The MZM, driven by an external electrical signal generated by a signal generator (SG, Agilent E8257C), is utilized to modulate the intensity of the injection light. PC 1 and PC 2 are used to control and match the polarizations of the injection light, MZM, and DFB-SL. The output of the DFB-SL is divided into two parts by FC 3 after passing through OC. The 20% part is sent to the measurement system after passing through FC 4 and FC 5. A photodetector (PD 1, New Focus 1544B, 12-GHz bandwidth) and a digital oscilloscope (OSC, Agilent DSO-X91604A, 16-GHz bandwidth) are used to record the time series of the DFB-SL output. A high-speed photodetector (PD 2, U2T- XPDV2120R, 50-GHz bandwidth) and an electronic spectrum analyzer (ESA, R&S FSW, 67-GHz bandwidth) are utilized to measure the electrical spectrum of the generated microwave signal, and an optical spectrum analyzer (OSA, Aragon Photonics BOSA lite + , 20-MHz resolution) is used to analyze the optical spectrum distribution. The 80% output from FC 3 is sent to VA 2, PC 3, FC 1, OC, FC 2 successively and then fed back into the DFB-SL to stabilize the frequency of the P1 oscillation.
Fig. 1 Schematic of the experimental setup. TL: tunable laser; DFB-SL: distributed feedback semiconductor laser; PC: polarization controller; MZM: Mach-Zehnder modulator; SG: signal generator; EDFA: erbium-doped fiber amplifier; VA: variable attenuator; OC: optical circulator; FC: fiber coupler; PM: power meter; PD: photodiode; ESA: electrical spectrum analyzer; OSA: optical spectrum analyzer; OSC: oscilloscope.
During the experiment, a voltage of 4.80 V is added to the bias electrode of MZM to make the MZM operate at its quadrature point. The DFB-SL is biased at 4.57 times its threshold current (10.70 mA) and temperature-stabilized at 20.55°C. Under this condition, the lasing wavelength and the output optical power of the DFB-SL are 1553.57 nm (corresponding frequency fSL = 193.10 THz) and 6.22 mW, respectively, and the relaxation resonance frequency of the DFB-SL is 8.15 GHz.
3. Experimental results and discussion
3.1 Tunability of the central frequency of FMCW
We first analyze the tunability of the central frequency of FMCW signal, which is standardized by the frequency of P1 oscillation. For this case, the RF signal loaded on the MZM is cut off while the 20% port of FC 1 is disconnected in Fig. 1. In other words, the DFB-SL is only subject to CW optical injection. Under suitable injection parameters (Pinj, fi), the optically injected DFB-SL can be rendered into the P1 state, and its frequency can be adjusted by changing the injection parameters (Pinj, fi). Figure 2(a) shows the output optical spectrum of the DFB-SL when the injection parameters are set at (Pinj, fi) = (6.0 mW, 4.0 GHz), where the red solid curve and blue dashed curve denote the optical spectrum of DFB-SL with and without optical injection, respectively. As shown in this diagram, with optical injection, the cavity resonance of the DFB-SL red-shifts from fSL to fc and two dominant optical frequency components with equal amplitudes separated by the P1 oscillation frequency f0 = 26.09 GHz are observed in the optical spectrum. Figure 2(b) gives the P1 oscillation frequencies as a function of the injection power at different detuning frequencies. From this diagram, it can be seen that the oscillation frequency of P1 can be widely tuned from 11.41 to 50.05 GHz by simply adjusting the injection power and/or the detuning frequency. For a fixed detuning frequency, the FMCW central frequency increases almost linearly with the injection power Pinj over a large range.
Fig. 2 (a) Optical spectrum output from the DFB-SL subject to CW optical injection; (b) measured output P1 frequency f0 as a function of the injection power Pinj at different detuning frequency fi.
3.2 Sweep range of the FMCW signal
Next, we discuss the sweep range of the FMCW signal. By connecting the electrode of the MZM and the SG, the injected light can be modulated by the sinusoidal signal generated by the SG. The MZM is modulated by a time-varying voltage which is described by mVπcos(2πfmt), where m is the modulation index and fm is the modulation frequency. In this work, the round-trip delay time (τ) of the optical feedback loop is 51 ns, and the corresponding frequency (1/τ) is about 19.66 MHz. In the following discussion, the value of fm is fixed at 1/τ (19.66 MHz) except when analyzing the impact of the deviation of fm from 1/τ. After being modulated by the sinusoidal signal, the injection strength is modulated. As a result, the P1 oscillation frequency is also modulated, and then a photonic FMCW microwave signal can be generated. Figure 3 shows the measured FMCW signal when the injection and modulation parameters are set at (Pinj, fi) = (0.5 mW, 4.0 GHz) and (m, fm) = (0.01, 19.66 MHz), respectively. The output time series of the DFB-SL in a time window of 240 ns is recorded by the OSC as shown in Fig. 3(a), and the zoom-in waveform from 125 ns to 177 ns is shown in Fig. 3(b). The two insets in Fig. 3(b) show the waveforms in two smaller time windows of 125-126 ns and 151-152 ns, in which the time intervals between two adjacent peaks are 82.5 ps and 106.6 ps, respectively, and the corresponding instantaneous microwave frequencies are 12.12 GHz and 9.38 GHz, respectively. For ease of demonstration, the variation of the instantaneous microwave frequency is presented in Fig. 3(b) by the yellow circles, while a sinusoidal fitting curve is plotted by the red dashed curve. Obviously, the instantaneous microwave frequency continuously sweeps between 12.12 GHz and 9.38 GHz within a time period of 1/ fm. This result can also be demonstrated by the time-frequency analysis of the time series at the OSC by using the short-time Fourier transform (STFT) analysis, which is given in Fig. 3(c). Similarly, the instantaneous frequency of the FMCW signal is time-varying in the form of the sinusoid and sweeps between f0 ± ∆f / 2 in each period of 1/ fm. Accordingly, the sweep rate of the instantaneous frequency under this condition is π∆f fm = 0.17 GHz/ns. Figure 3(d) gives the corresponding power spectrum recorded by the ESA. It should be noted that the ESA’s LO sweep rate is in milliseconds while the FMCW is swept on a nanosecond time scale, and therefore the power spectrum in Fig. 3(d) corresponds to the times series within a wider time window than that used for calculating the spectrograms of the FMCW as shown in Fig. 3(c). From Fig. 3(d), one can observe that the frequency of the generated FMCW signal is within the range of 9.38 −12.12 GHz around the central frequency of f0 = 10.75 GHz. From the zoom-in power spectrum, it can be seen the power spectrum behaves periodicity in fm with a small comb contrast, and the spectral peaks have wide linewidths. Such a frequency structure is due to the noisy phase fluctuations of the P1 oscillation [27]. The ideal power spectrum presented by the ESA should be a frequency comb with components separated by fm. The reason is as follows: since the injection power is varied with a period of 1/ fm in this system, the output time series should be repeated with a period of 1/fm. As a result, the power spectrum should be composed of many discrete frequency components separated by fm. Through reducing the phase fluctuations of the P1 oscillation, the comb contrast can be increased, which means that a FMCW with better repeatability can be generated.
Fig. 3 (a) Measured time series of the generated FMCW signal; (b) zoom-in waveform of (a) (insets: zoom-in views in a time window of 1 ns); (c) variation of the instantaneous frequency with time obtained by short-time Fourier transform analysis; (d) recorded power spectrum of the generated FMCW signal.
In order to understand the influences of operating parameters on the sweep range ∆f, the mapping of ∆f as a function of Pinj and m is displayed in Fig. 4, where fi and fm are fixed at 4.0 GHz and 19.66 MHz, respectively. The injection power varies from 0.8 to 11.6 mW and the modulation index ranges from 0.01 to 0.10. It should be pointed out that the region with ∆f = 0 means that the DFB-SL operates at the other dynamical states except the P1 state. From this diagram, it can be seen that, for a fixed injection power Pinj, the sweep range ∆f increases rapidly with the increase of the modulation index m. On the contrary, for a fixed m, the sweep range ∆f varies slowly with Pinj. The reason is as follows: the instantaneous frequency of the FMCW is linearly dependent on the injection power, but the frequency sweep range of the FMCW is determined by the varied range of the injection power. With the increase of m, the peak-to-valley value of the injection power consequently increases, and therefore the sweep range of the FMCW signal increases. However, for a fixed value of m, the peak-to-valley value of the injection power is fixed. As a result, the sweep range of the FMCW signal is almost unvaried even if the mean power is varied. In this work, the sweep range ∆f reaches the maximum value of 18.42 GHz (13.73 GHz- 32.15 GHz) at m = 0.074 and Pinj = 7.2 mW, and the corresponding sweep rate is π∆f fm = 1.14 GHz/ns.
3.3 Frequency comb contrast of the FMCW signal
As mentioned above, the comb contrast of the FMCW signal is relatively small due to the phase noise fluctuations of the P1 oscillation, while high repeatability of the FMCW signal is desirable in many applications. In order to obtain a high-quality FMCW signal, it is necessary to improve the comb contrast of FMCW signal. In this work, by connecting the 20% port of FC 1 in Fig. 1, an optical feedback loop is introduced to reduce the phase fluctuations of the microwave signal. Figure 5 displays the power spectra of the FMCW signal without and with optical feedback, where the injection parameters are set at (Pinj, fi) = (1.2 mW, 10.0 GHz) and the optical feedback parameters (feedback power Pf and round-trip delay time τ) are set at (Pf, τ) = (6 μW, 51 ns), respectively. Similar with the optoelectronic feedback case [27], the stabilization by optical feedback can be realized by a form of Fourier domain mode-locking [30]. When 1/τ exactly matches with the fm, the optical feedback loop will support the microwave modes separated by 1/τ, and then the microwave sidebands generated by the modulated injection can effectively lock the external cavity optical modes. In order to acquire the optimum effect, we set the modulation frequency at fm = 19.66 MHz in accordance with 1/τ and the modulation index at m = 0.047. Figure 5 gives the power spectra of the generated FMCW without and with optical feedback. When the optical feedback is not adopted as shown in Fig. 5(a), the frequency comb contrast is as low as R = 10.38 dB while the purity of the microwave is poor. However, after introducing an optical feedback, the linewidth of the microwave signal is greatly reduced and the frequency comb contrast is drastically enhanced. As shown in the inset of Fig. 5(b), the frequency comb contrast is significantly increased to R = 37.53 dB. As a result, the comb contrast R is improved by 27.15 dB through introducing optical feedback, which means that the repeatability of the FMCW signal has improved. Additionally, higher harmonics are not observed in this experiment.
Fig. 5 Power spectra of the generated FMCW based on the P1 oscillation in a DFB-SL subject to modulated optical injection without optical feedback (a) and with optical feedback (b). The injection, modulation and feedback parameters are set at (Pinj, fi) = (1.2 mW, 10.0 GHz), (m, fm) = (0.047, 19.66 MHz), and (Pf, τ) = (6 μW, 51 ns), respectively. RBW: 3MHz
The above results are obtained under the case of fm = 1/τ. In the following, we will analyze the case that there exists a deviation between fm and 1/τ. Figure 6 gives the frequency comb contrast R of the generated FMCW signal as a function of fm under different fi. Here, the injection power, the modulation index and the feedback power are fixed at Pinj = 1.2 mW, m = 0.047 and Pf = 6 μW, respectively, and fm is tuned from 19.16 to 20.11 MHz. As shown in this diagram, R always reaches the maximum value when fm is exactly equal to 1/τ. Once fm deviates from the 1/τ ( = 19.66 MHz), R drops immediately due to the destruction of the mode-locking, and the largest declined amplitude of R is over 30 dB.
Finally, Fig. 7 presents the influence of the optical feedback power Pf on the frequency comb contrast R is investigated under Pinj = 1.2 mW and (m, fm) = (0.047, 19.66 MHz) for different fi. Since the nonlinear dynamics of the injected DFB-SL is very sensitive to the feedback strength, the feedback power is required to be weak [29]. In this experiment, when the feedback power exceeds 7.5 μW, the output of DFB-SL includes other nonlinear dynamical states. For fi = 20 GHz and Pf = 7.5 μW, R reaches the maximum of 39.7 dB.
4. Conclusion
By utilizing the optical feedback stabilization, we have proposed and demonstrated a scheme for the photonic generation of a high-quality FMCW microwave signal based on the P1 oscillation of an optically injected DFB-SL. The results show that, by simply adjusting the injection parameters, the central frequency of the generated FMCW signal can be widely tuned beyond the relaxation resonance frequency in the range from 11.41 to 50.05 GHz, while the frequency sweep range of the generated FMCW signal can be controlled through adjusting the modulation index. Under proper operating parameters, the sweep range can reach up to 18.42 GHz (13.73 GHz-32.15 GHz), and the sweep rate is 1.14 GHz/ns correspondingly. Furthermore, the generated FMCW signal can be taken as a high-quality frequency comb after introducing an optical feedback loop for suppressing the phase noise. Due to the locking effect of the external cavity optical modes, the frequency comb contrast can be significantly increased by 27.15 dB.
Funding
National Natural Science Foundation of China (NSFC) (61475127, 61575163, 61775184, 61875167, 11704316); Natural Science Foundation of Chongqing City (CSTC2016jcyjA0575, CSTC2016jcyjA0082); Fundamental Research Funds for the Central Universities of China (XDJK2017B047, XDJK2018C079).
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