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Abstract
Based on a single-beam injection distributed feedback semiconductor laser (DFB-SL) combining with optical heterodyne, a photonic scheme for generating dual-linear chirp microwave (dual-LCM) signal with identical or complementary chirp is proposed and experimentally demonstrated. For such a scheme, a continuous-wave (CW) light with a frequency of finj is split into two parts. One part is passing through a Mach-Zehnder modulator (MZM) driven by a modified sawtooth signal, and then its intensity varies with time as a sawtooth wave. Such a light is injected to a DFB-SL for generating a single linearly chirped microwave (single-LCM) signal. The other part of the CW light with frequency of finj is sent to a phase modulator (PM) driven by a sinusoidal signal, and one of higher-order sidebands is selected by a tunable optical filter and taken as the referenced light. Through heterodyning the referenced light with the single-LCM signal, a dual-LCM signal with identical (or complementary) chirp can be obtained. The experimental results demonstrate that, by adjusting the injection parameters and the frequency of the sinusoidal signal loaded on the PM, the central frequency of the generated dual-LCM signal can be widely tuned. For the period of the sawtooth signal at 10 µs, the bandwidth for each frequency band included in the generated dual-LCM signal is 19.36 GHz under identical chirp and 16.98 GHz under complementary chirp, respectively. Correspondingly, the time bandwidth product (TBWP) for each frequency band can reach 1.936 × 105 under identical chirp and 1.698 × 105 under complementary chirp, respectively.
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1. Introduction
Linear chirp microwave (LCM) signals have been widely used in optical communication, optical fiber wireless network and modern radar systems [1,2]. Particularly, high-quality LCM signals are urgently needed for high-resolution remote detection in radar systems [3]. LCM signals can be produced by using electronic circuit such as microwave oscillators [4], and direct digital synthesizers [5]. Due to the bandwidth limitation, the bandwidth of the LCM signals generated by electronic devices is relatively small. In order to generate LCM signals with large bandwidth, many photonic-based methods have been successively proposed such as frequency-to-time mapping [6–9], two coherent lights beating [10–14] and optical heterodyne beating [15–18]. In particular, the LCM photonic generation scheme based on a modulated optical injected semiconductor laser have attracted extensive attention since the generated LCM signals possess adjustable center frequency and large bandwidth [19–23]. The frequency of a LCM signal can continuously sweep within a region or two regions, and the according LCM signal is named as single-LCM or dual-LCM signal. Taking single-LCM signals as radar waveform, severe Doppler coupling due to its knife-edge ambiguity function might cause a poor two-dimensional united resolution of range and velocity. In order to cope with this problem, dual-LCM signals are utilized as radar waveform. Dual-LCM signals generally include two complementary or identical chirp signals. The complementary chirp dual-LCM waveform consists of two complementary chirped components within the same temporal period, i.e., one is up-chirped and the other is down-chirped. For the identical chirp dual-LCM signal, the waveform consists of two similar chirped components. In radar applications, the time increments induced by Doppler-frequency-shift of the up-chirped waveform and the down-chirped waveform are opposite. Therefore, the delay-Doppler coupling effect can be offset by analyzing the arrival times of two complementary waveforms in the same echo signal [24,25]. Taking the identical chirp dual-LCM signals as radar waveform, the target frequency responses measured by two radar signals in different frequency bands can be fused to obtain the target frequency response in a wider band. Using the wider-band target frequency response can not only improve the range resolution, but also obtain more accurate information such as scattering center type, which is extremely beneficial to radar target recognition [26–28]. The basic method for generating dual-LCM signal is to use a high-order modulator to re-modulate a single or dual-LCM baseband signal to achieve optical frequency doubling. Higher-order modulations commonly used a dual parallel Mach-Zehnder modulator [29–32] and a dual-polarization dual-parallel Mach-Zehnder modulator [33–35]. These methods can flexibly choose different carrier frequencies, but the tunability of bandwidth is a challenge.
Recently, on the basis of single light injection, through introducing an extra injection beam for forming dual-beam optical injection to a DFB-SL, an approach for generating the dual-LCM signals is proposed and demonstrated by the group of Pan [36,37]. The results show that, under proper injection conditions, the SL can operate in so-called Scenario B of dual-beam injection. Under this case, the nonlinear dynamic state excited by original injection beam is preserved, and meanwhile the extra injection beam is suppressed. The regenerated extra injection beam provides another reference light for heterodyning, and therefore a dual-LCM signal can be achieved. For such a scheme, by simply adjusting injection parameters, the frequency regions of dual-LCM signal can be tuned. However, as pointed out in Ref. [36], since there exist competitions between two single-beam injection dynamics, the introduction of extra injection beam will more or less change the dynamic state of the DFB-SL under original single optical injection through the charge carriers in the laser cavity. As a result, the strength and the frequency of the extra injection beam need be restricted within suitable ranges.
In this paper, inspired by the works reported in Refs. [36,37], we propose another photonic scheme for generating dual-LCM signals. For such a scheme, different from the scheme in Refs. [36,37], only a single-beam is injected into a DFB-SL, and the single-LCM signal output from the DFB-SL under single-beam injection is heterodyned with additional reference light for achieving dual-LCM signal. The additional reference light comes from one of high-order phase-modulated sidebands of the injection light, therefore excellent coherence with the injection light can be ensured. Moreover, since the dynamics of DFB-SL is independent of additional reference light, the frequency and strength of additional reference light can be set flexibly. The experimental results show that, the central frequency of the generated dual-LCM signal can be widely tuned by simply adjusting the injection parameters as well as the frequency of the sinusoidal signal loaded on the PM. The bandwidth for each frequency band included in the generated dual-LCM signal with identical chirp can reach 19.36 GHz, and the time bandwidth product (TBWP) reach 1.936 × 105. The bandwidth for each frequency band included in the generated dual-LCM signal with complementary chirp can reach 16.98 GHz and the TBWP reach 1.698 × 105.
2. Experimental setup
The schematic diagram of the experimental setup is displayed in Fig. 1. In this system, the injected laser is a commercial 1550 nm distributed feedback semiconductor laser (DFB-SL), whose bias current and temperature are monitored by a current-temperature controller (ILX-Lightwave, LDC-3908). A CW light with a frequency of finj provided by a tunable laser (TL, Santec TSL-710) is split into two parts by a 50:50 fiber coupler (FC1). One part is modulated by a Mach–Zehnder modulator (MZM, Fujitsu, 40 GHz) after passing through a polarization controller (PC1), and then injected into the DFB-SL after passing through another PC (PC2), an erbium-doped optical fiber amplifier (EDFA1), a variable attenuator (VA), an optical circulator (OC) and a 90:10 FC (FC2). The injection strength ξi (=Pinj/ PSL, Pinj is the power of the injected light and PSL is the power of free-running DFB-SL) is changed by adjusting VA. The frequency detuning fi (= finj- fSL, finj is the frequency of injected light and fSL is the free-running frequency) is adjusted by changing finj. An electrical signal generated by an arbitrary waveform generator (AWG, Tektronix, AWG70001A, 1.5 KSa/s - 50 GSa/s) is used for driving MZM. PC1 and PC2 are utilized to adjust the polarization of the injected light and MZM. The other part of the CW light is modulated by a phase modulator (PM, iXblue, 20 GHz) and then passed through a tunable optical filter (TOF, ExFOXTM-50) to obtain a lower sideband flsb (<fSL) or an upper sideband fusb(> fSL) as shown in Fig. 1. A sinusoidal electrical signal with a frequency of fp from a signal generator (SG, Anritsu MG3692C) is used for driving PM. The frequency difference fpl (=fSL - flsb) and fpu (=fusb - fSL) are adjusted by changing the frequency fp. PC3 and PC4 are utilized to calibrate the polarization of the injected light and PM. Finally, the optical signals of the two parts are combined and sent to the test system via by FC3. A schematic diagram of the optical spectrum at point D is illustrated in Fig. 1. The optical spectrum is measured by a spectrum analyzer (OSA, Aragon Photonics BOSA lite+, 20 MHz resolution), the power spectrum is measured with an electronic spectrum analyzer (ESA, R&S FSW, 67 GHz bandwidth) via by a photodetector (PD2, XPDV2120R, 50 GHz bandwidth). The time series is recorded by an oscilloscope (OSC, DSO-X91604A, 16 GHz) via by a photodetector (PD1, New Focus 1544B, 12 GHz bandwidth).
Fig. 1. Schematic of the experimental setup. TL: tunable laser; DFB-SL: distributed feedback semiconductor laser; PC: polarization controller; MZM: Mach-Zehnder modulator; AWG: arbitrary waveform generator; EDFA: erbium-doped fiber amplifier; VA: variable attenuator; OC: optical circulator; POM: power meter; FC: fiber coupler; PM: phase modulator; SG: signal generator; TOF: tunable optical filter; PD: photodetector; OSA: optical spectrum analyzer; OSC: oscilloscope; ESA: electrical spectrum analyzer; flsb: lower sideband frequency; fusb: upper sideband frequency; finj: tunable laser frequency; fc: the frequency of the DFB-SL.
During the experiment, MZM is biased at the quadrature point to achieve linear modulation, the bias current and temperature of DFB-SL is set at 40 mA and 20.0°C. Under this condition, the free-running frequency of the laser is 192.94 THz, and the output power is 4.82 mW.
3. Experimental results and discussion
3.1. Generation of dual-LCM signals by lower sideband frequency component
As verified by Refs. [36,37], for the dual-LCM signals generation scheme by a modulated optical injected DFB-SL, the oscillation performance of DFB-SL under CW optical injection directly determines the quality of the generated dual-LCM signal. Therefore, it is necessary to first investigate the performance of the DFB-SL under CW optical injection. Figure 2(a1) gives the optical spectrum of the DFB-SL under the injection parameters (ξi, fi) = (0.27, 10 GHz) (blue line) and the optical spectrum of the lower sideband with a frequency difference fpl = 10 GHz (red dotted line). The spectrum of the free-running DFB-SL (red solid line) is shown in Fig. 2(a1) for comparison. As can be seen from the diagram, after introducing optical injection, the cavity resonance of the DFB-SL is red-shifted from fSL to fc, and the injection light with the detuning frequency fi is regenerated in the laser as shown by the red arrow. Three highly dominant frequency components (finj, fc and flsb) are clearly observed in the optical spectrum. Therefore, two obvious peaks located at f1 (= finj - fc) =16.45 GHz and f2 (= fc - flsb) =3.55 GHz are observed in the power spectrum, as shown in Fig. 2(a2). Figure 2(a3) displays the variation of the frequency f1, f2 with the injection strength ξi under fi = 10 GHz and fpl = 10 GHz. Considering that too high injection power may damage the laser, the injection strength ξi does not exceed 2.31 in this work. As shown in Fig. 2(a3), when the injection strength ξi is increased from 0.09 to 2.31, the frequency f1 is increased from 14.33 to 31.85 GHz. Meanwhile, the frequency f2 is firstly decreased from 5.67 GHz, after arriving at 0 GHz, and then increased to 11.85 GHz. The reason is that, with the increase of ξi, the frequency fc of the DFB-SL moves towards the sideband frequency flsb, after passing through the frequency fc1, and then moves away from fc1 (as displayed in the inset). Figure 2(b1) gives the optical spectrum of the DFB-SL under the parameters (ξi, fi) = (0.27, 20 GHz) (blue line) and the optical spectrum of the lower sideband with a frequency difference fpl = 20 GHz (red dotted line). It can be clearly seen that there are three highly dominant frequency components as shown in Fig. 2(b1). Therefore, two obvious peaks located at f1 =22.53 GHz and f2 =17.47 GHz are observed in the power spectrum, as displayed in Fig. 2(b2). Figure 2(b3) shows the variation of the frequency f1, f2 with the injection strength ξi at fi=20 GHz and fpl=20 GHz. As seen from the diagram, when ξi increases from 0.09 to 2.31, the frequency f1 is increased from 20.94 to 36.15 GHz, and the frequency f2 is decreased from 19.06 to 3.85 GHz. For a given fi, the values of f1 and f2 are almost linearly changed with the increase of injection strength ξi. Therefore, by selecting an appropriate value of fi and scanning the range of ξi, a LCM signal with a desired scanning frequency can be generated.
Fig. 2. (a1),(a2) Optical spectrum and power spectrum of merged signals in the two parts under (ξi, fi) = (0.27, 10 GHz) and fpl=10 GHz; (a3) variation of f1, f2 with ξi for fpl=10 GHz, fi = 10 GHz; (b1),(b2) optical spectrum and power spectrum of merged signals at (ξi, fi) = (0.27, 20 GHz) and fpl =20 GHz; (b3) variation of f1, f2 with ξi for fpl=20 GHz, fi = 20 GHz.
Next, we investigate the generation of dual-LCM signals. An electrical signal with an approximate sawtooth profile is loaded on MZM to modulate the injection intensity, and the modulation index and modulation frequency are represented by m and fm respectively. Under this case, the frequency of generated microwave is determined by the transmission function of the MZM and the injection strength. As demonstrated above, the frequency of the generated microwave is almost linearly changed with the increase of the injection strength ξi. However, as we know, the transmission function of the MZM is nonlinear. As a result, a modified sawtooth signal should be utilized as the modulation signal for compensating the nonlinear of MZM. Referring to Ref. [38], we adopt a sawtooth signal as the modulation signal to obtain the function relationship (G) between the microwave frequency and the sawtooth signal. In order to generate a desired dual-LCM signal, the modified sawtooth signal should take the form of G-1(sawtooth), where G-1 is the inverse function of G. In this work, fm is fixed at 100 kHz, m is equal to VRF/Vπ, where Vπ is the half-wave voltage and VRF is the driving voltage. Considering the bandwidth limitation of the oscilloscope used in this work (16 GHz), we only record the dual-LCM waveform with relatively small instantaneous frequency. For the dual-LCM waveform with higher bandwidth than 16 GHz, only the frequency range of the dual-LCM waveforms can be acquired through recording the optical spectrum and power spectrum.
By setting the modulation parameters with (m, fm) = (0.26, 100 kHz) and keeping the parameters at (ξi, fi) = (0.27, 10 GHz) and fpl =10 GHz, the results of the generated dual-LCM signals are displayed in Fig. 3 (a)-(d). Figure 3(a) displays the waveform of the generated dual-LCM signals within a temporal range of 50 µs, where the inset is the waveform of the sawtooth signal used for driving the MZM. Figure 3(b) shows the instantaneous frequency of the generated dual-LCM signals calculated by the short-time Fourier transform (STFT). As shown in Fig. 3(b), the generated waveform includes an up-chirp waveform (LCM1) and a down-chirp waveform (LCM2), forming a complementary chirp dual-LCM signal in the same 10 µs period. The instantaneous frequency of LCM1 varies linearly from 14.12 GHz to 16.45 GHz and the center frequency is 15.28 GHz. The instantaneous frequency of LCM2 varies linearly from 3.55 GHz to 5.88 GHz and the center frequency is 4.72 GHz. The TBWP (= Δf T) of the dual-LCM signals is 2.33 ×104. Figure 3(c) records the optical spectrum of the dual-LCM signals. As can be seen from this diagram, the frequency finj and flsb are located at the both sides of the frequency of the DFB-SL, therefore a dual-LCM signal with complementary chirp can be obtained in the power spectrum. Figure 3(d) shows the power spectrum of the dual-LCM signals with two equal bandwidths Δf 1,2 = 2.33 GHz. From this diagram, the frequency range of LCM1 is also from 14.12 to 16.45 GHz and the frequency range of LCM2 is also from 3.55 to 5.88 GHz, which is consistent with the result in Fig. 3(b).
Fig. 3. (a) Recorded waveform of dual-LCM signals, (b) acquired frequency-to-time relation, (c) optical spectrum and (d) power spectrum of the generated dual-LCM signals under (ξi, fi) = (0.27, 10 GHz) and (m, fm) = (0.26, 100 kHz) for fpl =10 GHz.
It should be noted that, the waveform of the driving sawtooth signal (see Fig. 3(a)) has been preliminary modified for generating dual-LCM signal with good linearity. In order to illustrate the necessity for adopting modified sawtooth signal to drive the MZM, we calculate the linearity of the generated dual-LCM signals (R2) under the modified/unmodified sawtooth signal adopted, and the results are presented in Fig. 4. After linearly fitting the instantaneous frequency versus time curve with a linear regression method, R2 can be obtained [39]. The higher the calculated R2 value is, the better the linearity of the signal is. Here, ξi is increased from 0.06 to 0.36, and other parameters are the same as those used in Fig. 3. From this diagram, it can be seen that with the increase of the injection strength, the linearity of the dual-LCM signal generated under adopting the unmodified sawtooth signal increases from 0.876 to 0.914. Under adopting the modified sawtooth signal, the linearity of generated dual-LCM signal firstly increases from 0.927 to 0.997 quickly, and then maintains at a stable level. Obviously, the modification of the driving sawtooth signal is helpful for generating dual-LCM signal with higher linearity. It should be pointed out that, for ξi weaker than 0.18, the DFB-SL is operating at a transition state between four-wave mixing and P1 oscillation, therefore the linearity of the generated dual-LFM signal is poor even if a modified sawtooth signal is adopted.
In radar applications, the bandwidth of the dual-LCM signal is a crucial indicator to determine the ranging resolution. In the following, the effects of some operating parameters on the bandwidth will be revealed. Figure 5(a1) shows the variation of the bandwidth of the dual-LCM signals with injection strength ξi at (m, fm) = (0.6, 100 kHz). The frequency detuning fi is taken 10 GHz, and fpl is taken 10 GHz. The frequency scans over an area bounded by the maximum fct + Δf ∕2 and the minimum fct - Δf ∕2 denoted by solid and hollow symbols, respectively. Here, fct is the central frequency and Δf (= Max- Min) is the bandwidth. As shown in Fig. 5(a1), the bandwidth Δf and the central frequency fct of LCM1 increases gradually with the increase of ξi. At ξi = 2.31, the maximum bandwidth of the LCM1 can reach 12.84 GHz. Meanwhile, with the increase of ξi, the bandwidth of LCM2 also increases to 12.84 GHz, but the central frequency firstly decreases and then gradually increases. The reason may be explained as follows. With the increase of injection strength ξi, the frequency fc of the DFB-SL gradually moves towards the sideband flsb, as shown in Fig. 5(a2). As verified by Refs. [37], when finj and flsb locate at both sides of fc (point A), a dual-LCM signal with complementary chirp can be obtained. When finj and flsb are on the same sides of fc (point C), a dual-LCM signal with identical chirp can be obtained. Therefore, within the range of 0.09-0.51, LCM1 and LCM2 form a dual-LCM signal with complementary chirp. Within the range of 0.51-2.31, LCM1 and LCM2 form a dual-LCM signal with identical chirp. Figure 5(b1) gives the variation of the bandwidth with the injection strength ξi at (m, fm) = (0.6, 100 kHz), fi = 20 GHz and fpl = 20 GHz. As seen from this diagram, the bandwidth Δf and central frequency fct of LCM1 increases gradually with the increase of ξi. For ξi = 2.31, the maximum bandwidth can reach 12.79 GHz. With the increase of ξi, the bandwidth of LCM2 also increases gradually to 12.79 GHz, but the central frequency decreases gradually. Figure 5(b2) gives a schematic diagram explaining the evolution process of the bandwidth with the injection strength ξi. Within the range of 0.09-2.31, the LCM1 and LCM2 form a dual-LCM signal with complementary chirp.
Fig. 5. (a1),(b1) Bandwidth variation with ξi for different fi, fpl at (m, fm) = (0.6, 100 kHz), where the red line represents LCM1 and the blue line represents LCM2, and “max” and “min” are the maximum and minimum values of frequency; (a2),(b2) schematic diagram for illustrating the bandwidth variation with injection strength ξi.
According to the results in Fig. 5, we analyze the effects of the modulation index m on the bandwidth of the dual-LCM signals under ξi = 2.31, and the results are shown in Fig. 6. Here, Figs. 6(a), (b) correspond to fi = 10 GHz, fpl = 10 GHz and fi = 20 GHz, fpl = 20 GHz, respectively. Considering the bearing capacity of the device, the maximum value of m is 0.7. The frequency scans in a shaded region bounded by the maximum fct + Δf ∕2 and the minimum fct - Δf ∕2 indicated by solid and hollow circle symbols, respectively. Obviously, for different fi and fpl, the change trends of the bandwidth with the modulation index m are similar. As shown in Fig. 6(a), with the increase of m, the bandwidths of both LCM signals gradually increase, and the maximum bandwidth reaches 14.82 at m = 0.7. Similarly, as shown in Fig. 6(b), the bandwidths of both LCM signals also increase gradually with the increase of m, and the maximum bandwidth reaches 16.98 GHz at m = 0.7.
Fig. 6. (a),(b) Variation of the bandwidth with m at different fi and fpl under ξi = 2.31, where the solid and hollow circle symbols indicate the maximum and minimum frequencies.
3.2. Generation of dual-LCM signals by upper sideband frequency component
In the following, we will analyze the dual-LCM signals generated by beating the time-varying frequency component of the output of DFB-SL with the upper sideband frequency fusb. The DFB-SL is driven into P1 oscillation under injection parameters (ξi, fi) = (0.27, 10 GHz). An upper sideband with a frequency fusb (>fSL) is filtered out through a TOF. Figure 7(a) displays the optical spectrum of the two parts combined under the parameters (ξi, fi) = (0.27, 10 GHz) and fpu = 20 GHz. It can be seen that the frequency of the DFB-SL has a red shift due to introducing the injection light. Many optical sidebands are generated by the P1 dynamic state. The upper sideband fusb is shown in Fig. 7(a) with a red dotted line. By beating the optical signals of two parts combined, two obvious peaks located at f1 = 16.52 GHz and f2 = 26.52 GHz can be observed in the power spectrum, as shown in Fig. 7(b). Figure 7(c) gives the variation of the frequency f1, f2 with the injection strength ξi. From this diagram, when ξi increases from 0.09 to 2.31, the frequency f1 is increased from 15.20 to 34.53 GHz, and the frequency f2 is increased from 25.20 to 44.53 GHz.
Fig. 7. (a) Optical spectrum and (b) power spectrum of merged signals under (ξi, fi) = (0.27, 10 GHz) and fpu =20 GHz; (c) variation of frequency f1 and f2 with ξi at different fpu and fi. The red solid line in Fig. 7(a) is the optical spectrum of the free-running DFB-SL.
Based on the results in Fig. 7, by setting the modulation parameters at (m, fm) = (0.12, 100 kHz) and keeping the parameters at (ξi, fi) = (0.27, 10 GHz) and fpu =20 GHz, Fig. 8(a) displays optical spectrum of the dual-LCM signals. From this diagram, it can be seen that the frequency finj and flsb are on the same sides of the frequency of the DFB-SL, therefore a dual-LCM signal with identical chirp can be obtained in the power spectrum. Figure 8(b) shows the power spectrum of dual-LCM signals with two equal bandwidths Δf 1,2 = 2.70 GHz. The frequency range of LCM1 is from 14.53 to 17.23 GHz and the center frequency is 15.88 GHz. The frequency range of LCM2 is from 24.53 to 27.23 GHz and the center frequency is 25.88 GHz. Figure 8(c) depicts the variation of the dual-LCM signal bandwidth with the injection strength ξi under (m, fm) = (0.6, 100 kHz) and fi =10 GHz, fpu =20 GHz. It can be seen from this diagram, when ξi increases, the bandwidths of LCM1 and LCM2 gradually increase. For ξi =2.31, the bandwidth reaches the maximum value of 16.2 GHz. Moreover, we analyze the effect of the modulation index m on the dual-LCM signals bandwidth, as shown in Fig. 8(d), where the injection parameters (ξi, fi) are fixed at (0.27, 10 GHz) and fpu is taken 20 GHz. With the increase of m, the bandwidth Δf increases gradually. For m = 0.7, the maximum bandwidth can reach 19.36 GHz. As a result, the bandwidth of the generated dual-LCM signal is depended on the injection strength ξi and the modulation index m.
Fig. 8. (a) Optical spectrum and (b) power spectrum of the generated dual-LCM signals under (ξi, fi) = (0.27, 10 GHz) and (m, fm) = (0.12, 100 kHz) at fpu =20 GHz; (c) bandwidth variation with the injection strength ξi, and (d) bandwidth variation with the modulation index m at fi = 10 GHz and fpu=20 GHz.
From above discussions, a large ξi is beneficial to generate large bandwidth dual-LCM signals. Finally, we set ξi at 2.31 and further explore the optimal value of m to generate large bandwidth dual-LCM signals. Since the bandwidths of two different frequency bands of the dual-LCM signals are equal, the bandwidth discussed below refers to the bandwidth of a single frequency band in dual-LCM signals. Figure 9(a) gives a schematic diagram of the sideband in order to better explain the problem discussed. Figures 9(b)-(d) describes the variation of the bandwidth with fi, fpl and fpu under ξi = 2.31 and m taking its optimal value m0. For given values of fi, fpl or fpu, m0 can be determined by continuously changing m and inspecting the bandwidth of the generated dual-LCM signals. When the bandwidth reaches the maximum value, the corresponding m value is m0. Figure 9(b) describes the variation of the bandwidth with fi under fpl =10 GHz and m taken the optimal value m0. As shown in Fig. 9(b), with the increase of fi, the bandwidth of the generated dual-LCM signals firstly increases from 11.29 GHz, after reaching the maximum value of 15.20 GHz and then gradually decreases to 4.51 GHz. Figure 9(c) describes the variation of the bandwidth with fpl under fi =10 GHz and m taken the optimal value m0. With the increase of fpl, Δf firstly increases to the maximum value of 16.95 GHz, after gradually decreases to 7.84 GHz, and then rises to 15.84 GHz. Figure 9(d) shows the bandwidth variation with fpu under fi =10 GHz and m taken the optimal value m0. With the increase of fpu, the bandwidth shows an oscillation trend. For fpu = 20 GHz, the maximum bandwidth can reach 19.36 GHz.
Fig. 9. (a) A schematic diagram of the sideband, (b) bandwidth varied with frequency detuning fi, (c) and with fpl, (d) and with fpu under ξi = 2.31 and m taken its optimized value. The optimized values of the modulation index m0 are shown in red lines in Figs. 9 (b)-(d).
By the way, it should be pointed out that although high sampled rate of AWG is utilized in this work, our experiments show that the performances of the generated dual-LCM signal is not degraded obviously under low sampled rate of AWG. Additionally, since the proposed system is similar to those reported in Refs. [21–23] in principle, the relevant methods in Refs. [21–23] can also be adopted for improving the purity and stability of the generated dual-LCM signal.
4. Conclusion
In conclusion, we have proposed and experimentally demonstrated a photonic scheme to generate dual-LCM signals with identical or complementary chirp by using single-beam injection to a DFB-SL and optical heterodyne technique. For this scheme, a CW light from a TL is split into two parts. One part is sent to a MZM driven by an approximate sawtooth signal for generating an optical signal with time-dependent intensity, which is injected into a DFB-SL for generating a single-LCM signal. The other part is sent to a PM driven by a sinusoidal signal, and one of modulated higher-order sidebands is selected by a TOF for providing a reference light. Through optically heterodyning the reference light with the single-LCM signal output from the single-beam injection DFB-SL, a dual-LCM signal with identical or complementary chirp can be obtained. The experimental results indicate that, by simply adjusting the injection parameters as well as the frequency of the sinusoidal signal loaded on the PM, the central frequency of the generated dual-LCM signals can be widely tuned. In a period of 10 µs, the bandwidth for each frequency band included in the generated dual-LCM signals with identical chirp can reach 19.36 GHz and the corresponding TBWP can reach 1.936 × 105, the bandwidth of the generated dual-LCM signals with complementary chirp can reach 16.98 GHz and the corresponding TBWP can reach 1.698 × 105. Moreover, the effects of operation parameters on the bandwidth of the generated dual-LCM signals have also been analyzed.
Funding
Fundamental Research Funds for the Central Universities (XDJK2019B069); National Natural Science Foundation of China (61875167).
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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