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Abstract
We present a novel scheme for the accurate ranging for the multi-region in the rectangular-shape target using numbers of the chaotic x polarization components in the multiple parallel optically pumped spin-VCSELs with optical injection, where these chaotic x polarization components possess the attractive features of the uncorrelation in time and space under different optical injection strengths, and fast dynamic with femtosecond magnitude. Utilizing these features, the accurate ranging to the position vectors of the multi-region targets can be achieved by correlating the multi beams of the time-delay reflected chaotic polarization radar probe waveforms with their corresponding reference waveforms. The further investigations show that the ranging to the multi-region targets possesses very low relative error, which is less than 0.28%. Their range resolutions can be achieved as high as 0.9mm, and exhibit excellent strong anti-noise performance by the optimization of some key parameters such as the injection strength, the amplitude of external light, linear birefringence, spin relaxation rate. The precise ranging to the multi-region targets based on the multiple parallel optically pumped spin-VCSEL with optical injection offers interesting perspectives for the potential applications in quality detection of the multi-region surfaces.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the rapid development of artificial intelligence, lidar is playing an important role in automatic driving, unmanned aerial vehicle, robot vision and target tracking measurement and other fields [1–3]. By sensing the surrounding environment, lidar is expected to achieve the following functions: target precision ranging, high quality 3D imaging, target tracking and recognition, automatic positioning and mapping. At present, most of lidar ranging schemes used pulse lasers and CW lasers as light sources to obtain better signal-to noise ratio and measurement range [4–6]. However, the radar ranging based on pulse lasers and CW lasers has many shortcomings such as low resolution, high probability of intercept, weak anti-interference ability, high cost. The ranging based on the chaotic lidar (CLR) generated by using the nonlinear dynamic of semiconductor with optical feedback or optical injection exhibits many advantages over the ranging using pulse lasers and CW lasers, such as low probability of intercept, strong anti-interference ability and low cost [7–11]. Moreover, it has high resolution, benefiting from the broad bandwidth of the optical chaos. Finally, chaotic lidar is easily be generated and controlled due to its sensitivity to laser parameters.
Many previously reported works on CLR ranging have focused its realization by the cross correlation between the time-delayed reflected return signal and the replica of the transmitted chaotic signal [12–18]. The CLR ranging based on the cross-correlation theory has made some progresses in the recently reported works by using different devices. For example, Zhang and his coworkers proposed and demonstrated experimentally an ultra-wideband radar system for remote ranging based on microwave-photonic chaotic signal generation and optical-fiber distribution in 2014 [18]. Wang et al. investigated the performance of chaotic radar system for target detection and ranging through lossy media in 2015 [17]. In the same year, Yao et al. demonstrated a distributed multiple-input and multiple-output chaotic radar based on wavelength-division multiplexing technology [19]. In 2017, Wang et al. theoretically explored a radar system in which ranging resolution and anti-jamming capability were enhanced, using a broadband white chaos generated by optical heterodyne of two chaotic external cavity semiconductor lasers [20]. In 2018, Cheng et al. employ self-homodyning and time gating to generate a pulse homodyned chaos radar to boost the energy-utilization efficiency [21]. As a result, they realized the target ranging accuracy of millimeter level and the detection range of more than 100m. Recently, we implemented the real-time ranging of two targets by using synchronized chaotic polarization radars in the drive-response vertical cavity surface-emitting lasers (VCSELs) system [22], and explored the ranging of the six orientational targets in there-node VCSEL network using the six chaotic polarization radars [23].
The resolution of the correlated CLR ranging is largely limited by the bandwidth of the chaotic laser in the previously reported works. An ultra-fast chaotic laser with large modulation bandwidth is required to further improve the ranging resolution. The optically pumped spin-controlled VCSELs proposed in [24] might provide properties superior to those of their conventional counterparts. For example, they promise to have faster modulation dynamics and larger modulation bandwidth [25–29], to operate with lower threshold [30–35] and to offer a stronger polarization determination than conventional VCSELs with up to a 100$\%$ polarization control [32,36–41]. The ultra-fast chaos radar wave originated from the optically pumped spin-VCSEL with optical injection or optical feedback is expected to be used for improving the resolution and accuracy of target ranging. In addition, in the previously reported works on the correlated CLR ranging, the CLR was usually utilized for the ranging of a fixed point in the target. The schemes and methods of the correlated CLR ranging proposed in the reported works cannot fully detect the distance of different regions in the target, and were unsuitable for the precision ranging of the whole region in a target. Therefore, the previously reported works on the correlated CLR ranging can difficultly applied in quality detection for the multi-region targets. To overcome these problems, it is necessary to further explore the theoretical and physical mechanism of the CLR ranging for multi-region targets, and explore the new scheme and method for its realization. Motivated by these, in this paper, based on the optically pumped spin-VCSEL with optical injection, we propose a novel scheme to realize the precise ranging for the multi-region in a rectangular shape target by using a chaotic polarization component. In our scheme, two chaotic polarization components emitted by the optically pumped spin-VCSEL have superior properties to chaotic wave emitted by convention lasers, such as uncorrelation in time and space, fast dynamic with femtosecond magnitude, large modulation bandwidth and stronger polarization determination. Utilizing these properties, the scheme presented by this paper might steadily realize high resolution and low relative errors ranging for multi-region targets. For this purpose, we further explore the mechanism and implementation method of the ranging to the multi-region targets, based on the correlation of the multi beams of the time-delay reflected chaotic polarization probe waveforms with their corresponding reference waveforms. Finally, we demonstrate the resolutions and the relative errors of the multi-region targets.
2. Theory and model
Figure 1 depicts the implementation scheme of the precise ranging for the multi-region by using chaotic x polarization components (x-PCs) in the optically pumped spin-VCSEL with optical injection. Here, the chaotic laser sours (CLSs) with the number of $N$ generate the $N$ beams of probe signals, which are utilized for the ranging of the multi-region in a rectangular shape target. Each CLS consists of the distributed feedback laser (DFB), the optically pumped spin-VCSEL and some passive optical components including the opticalisolators (OIs), the polarization control optical circuit (PCOC), the neutral density filter (NDF) and fiber polarization beam splitter (FPBS). Here, all spin-VCSELs are configured with the same wavelength (1550nm). When the DFB as an external optical source is injected into each optically pumped spin-VCSEL, the bandwidths of each chaotic x-PC is enhanced greatly under a certain value of the pump light power, which is beneficial to improve the range resolution. In each CLS, the OIs with the subscripts of 1-2 are used to ensure the unidirectional propagation of light wave. The NDF is used to control the strength of the injected light field from the DFB. To ensure that the polarized light wave of the DFB is parallelly injected into the x-PC and y-PC of the optically pumped spin-VCSEL, the polarized light wave from the DFB output need to be divided and adjusted as the x-PC and y-PC by using the PCOC. The polarization control function of the PCOC is given in [23]. In the PCOC, the switch between the x-PC and y-PC is realized by some passive devices such as the fiber polarizer (FP), fiber polarization controller (FPCO), fiber depolarizer (FD) and fiber polarization coupler (FPC). In each CLS, the spin-VCSEL is pumped by the total normalized power $\eta$ of pump light, where $\eta$ = $\eta _{+}$+$\eta _{-}$, with $\eta _{+}$ and $\eta _{-}$ being dimensionless circularly polarized pump components. $\eta$ = 1 represents the pump threshold. In addition, the target (T) is a rectangular shape target to be measured. The PD is photodetector. The EA is electric amplifier. The TA and RA are the transmitting antenna and receiving one, respectively. The chaotic x-PC emitted by each CLS is divided into two beams by the 1:1 FBS. One of them is considered as the reference signal (RS), the other is utilized for the probe signal (PS). For arbitrary one-region ranging in the target T, the $j$th beam of the PS from the $j$th CLS is firstly converted into the probe current signal by the PD$_{{1},{j}}$, then amplified by the EA$_{{1},{j}}$. finally transmitted to one-region in the target T by the transmitting antenna TA$_{j}$ ($j = 1, 2, 3. {\dots }, N$, the same below). The other beams of the PSs are processed in the same way. After being reflected or scattered by the multi-region of the target T, the $N$ beams of the PSs are first delayed, then received by the receiving antenna RA1 and amplified by the electric amplifier EA1. On other hand, the $N$ beams of the RSs are converted into $N$ branches of the reference current signals by the PDs with subscripts of 21-2$N$ and further be amplified by the EAs with the subscripts of 21-2$N$ in turn. The correlations of the PSs with their corresponding RSs are calculated by using the correlation function calculation module (CFCM). By the observation of the time locations of the maximum expected values of correlations, the position vectors of the multi-region in the target T can be further calculated by using the target ranging calculation module (TRCM).
Fig. 1. Schematic diagram of the precise ranging for the multi-region in a rectangular shape target by using a chaotic x-polarization component in the optically pumped spin-VCSEL with optical injection. Here, DFB: distributed feedback laser; OI: optical isolator; FBS: fiber beam splitter; PCOC: polarization control optical circuit; NDF: neutral density filter; Spin-VCSEL: spin vertical cavity surface-emitting laser; FPBS: fiber polarization beam splitter; FP: fiber polarizer; FD: fiber depolarizer; FPC: fiber polarization coupler; FPCO: fiber polarization controller; x-PC; x polarization component; y-PC: y polarization component; CLS; chaotic laser source; PD: photodetector; EA: electric amplifier; TA: transmitting antenna; CFCM: correlation function calculation module; TRCM: target ranging calculation module; $\eta$: total normalized pump power.
For the spin-VCSEL, the left- and right-circularly polarized components of the optical field are rewritten in terms of the orthogonal linear components
3. Results and discussions
As shown in Fig. 1, arbitrary one-region in the target T is detected by using the $N$ beams of the chaotic x-polarization radar probe waveforms simultaneously. After being reflected or scattered by this region, the $N$ beams of the chaotic x-polarization radar probe waveforms with different delays are received by the RA simultaneously. Under the condition, according to the correlation theory [45], to detect easily the position vector of each small area, these chaotic lidars need to satisfy time-space uncorrelation. When these chaos radar probe signals from different spin-VCSELs presented in Fig. 1 can meet with time-space uncorrelation when these spin-VCSELs are subjected to different optical injections. To further explain their time-space uncorrelations, we rewrite the expression of the $j$th beam of the probe signal as follows:
Here, if $t_1$=$t_2$ and $j$=$l$, there appears the maximum peak of the $\textrm{C}_{R{T_1}}$ . The time-space correlation of the $j$th beam of the probe radar signal with its corresponding reference signal is written as
According to Eq. (17), we can solve the position vectors of the A-point with the numbers of $C_N^2$ , which are almost equal. We take their mean value as the accurate position vector of the A-point, which is described as
Fig. 2. Geometry diagram of the ranging for arbitrary one-region of the rectangular shape target T. Here, A: a target point in one-region; $\textbf{r}_{A}$ : the position vector of the target point-A; $\textbf{r}_{T_{1}}$ - $\textbf{r}_{T_{N}}$ : the position vectors of the transmitting antennas TA$_1$-TA$_N$ in turn: $\textbf{r}_{R}$: the position of the receiving antenna RA1.
For the convenience of discussion, here $N$=10, i.e., we take the chaotic laser sources with the number of 10 (CLS$_1$-CLS$_{10}$) as an example to elaborate the ranging for the multi-region in the target T. In the following calculations, we take common parameter values for the CLSs of 10 as those presented in Table 1. The different parameters ($k_{xinj}$, $k_{yinj}$, $E_{yinj}$) for them are given in Table 2. By utilizing these parameters presented in Tables 1 and 2, we make the x polarization probe radar signals from the chaotic laser sources (CLS$_1$-CLS$_{10}$) to satisfy high uncorrelation in time-space. To elaborate their time-space uncorrelations, we first calculate the temporal traces of the first two beams of the x polarization probe radar signals (S$_{11}$ and S$_{12}$) from the CLS$_1$ and CLS$_2$, using Eqs. (6)–(7. One sees from Fig. 3 that the temporal traces of the S$_{11}$ and S$_{12}$ both appear chaotic state and fast dynamics with femtosecond magnitude. Other probe radar signals originated from the CLS$_3$ to CLS$_{10}$ also show fast chaotic dynamics. These denote that all probe radar signals exhibit chaotic temporal traces with fast dynamics. Moreover, we take the 5th and 6th beams of the probe radar signals as two examples to calculate their auto-correlations in time, as shown in Fig. 4. It is found from Fig. 4 that the maximum peaks of these two auto-correlations are 0.15 and 0.17, respectively, which occur at $t$=0. Their values are 0.112 and 0.13 at the other time except for $t$=0. Figures 5(a) and 5(b) further presents the space cross-correlation of the 5th beam of the probe radar signal with 10 beams of ones andthat of the 6th beam of the probe radar signal with 10 beams of ones, respectively. As seen from these two figures, for the 5th and 6th beams of the probe radar signals, the maximum peaks of their space cross-correlations are both 1, which occur at $j$=5 and 6, respectively. However, their cross-correlations are almost equal to 0 except for $j$=5 and 6. Since the reference signal is the replica of the probe radar signal, the space cross-correlation ($R_{PR}$) of the 5th beam of the probe radar signal with 10 beams of the reference signals is identical to the $R_P$ presented in Fig. 5(a). The time cross-correlation ($T_{PT}$) of the 5th beam of the probe radar signal with 5th beam of the reference signal is the same with the $T_P$ given in Fig. 4(a). Finally, for 10 beams of the probe radar signals and the reference signals, Figs. 6(a) and 6(b) depict the evolutions of the time-space correlations ( $\textrm{C}_{R{T_1}}$ and $\textrm{C}_{R{T_2}}$ ), respectively. As observed from Figs. 6(a) and 6(b), the maximum peak of the $\textrm{C}_{R{T_1}}$ for the $N$th beam of the probe radar signal appears at $t$=0 and $j$=$N$ ($N = 1, 2, 3, {\ldots }, 10$, the same below). The maximum peak for the $\textrm{C}_{R{T_2}}$ of the $N$th beam of the probe radar signal with 10 beams of the reference signals can be achieved at $t$=0 and $j$=$N$. These results denote that $N$ beams of the probe radar signals have the feature of the uncorrelation in time and space. For the same reason, the time-space uncorrelations of $N$ beams of the probe radar signals with their corresponding reference signals can be achieved since the reference signals are the replica of the probe radar signals. In the following, using their time-space uncorrelations, we take the 16-region in the target T as the examples to discuss their ranging.
Fig. 3. (a) Temporal traces of the x polarization radar signal S$_{11}$ from the CLS$_1$; (b) those of the x polarization radar signal S$_{12}$ from the CLS$_2$.
Fig. 4. (a) Auto-correlation in time ($T_P$) of the 5th beam of the probe radar signal at different times; (b) that of the 6th beam of the probe radar signal at different times.
Fig. 5. (a) Cross-correlation in space ($R_P$) of the 5th beam of the probe radar signal with 10 beams of ones. (b) that of the 6th beam of the probe radar signal with 10 beams of ones.
Fig. 6. (a) Time-space correlations (${C_{R{T_1}}}$) of 10 beams of the probe radar signals with themselves. (b) Time-space correlations (${C_{R{T_2}}}$) of 10 beams of the probe radar signals with 10 beams of the reference signals.
Table 1. The common parameter values for the chaotic laser sources with the number of 10 (CLS$_1$-CLS$_{10}$).
Table 2. The different parameter values for the chaotic laser sources with the number of 10 (CLS$_1$-CLS$_{10}$).
We present the geometry diagram of the ranging for the 16-region in the target T, as displayed in Fig. 7. Here, we define the 16-region targets as T$_1$-T$_{16}$ in turn. In the $j$th region ($j$=1, 2, 3,…, 16, the same below), the distances of two target points ( $T_j^{(1)}$ and $T_j^{(2)}$ ) are to be measured. As shown in Fig. 6, the position vectors of the target points $T_j^{(1)}$ and $T_j^{(1)}$ are considered as $\textbf{r}_{T_{j}}^{(1)}$ and $\textbf{r}_{T_{j}}^{(2)}$, respectively. The 10 beams of the probe radar signals radiated by the transmitting antennas (TA$_{1}$-TA$_{10}$) are used to detect the distance of one arbitrary target point simultaneously. The position vectors of these transmitting antennas are supposed as $\textbf{r}_{T_{1}}$ - ${\textbf{r}_{T_{10}}}$ in turn. Moreover, the transmitting antennas (TA$_{1}$-TA$_{10}$) are arranged linearly, which have an edge-to-edge separation of 0.5 m. To verify the feasibility of the ranging for these target points, we suppose that the actual distances of the target points $T_j^{(1)}$ and $T_j^{(2)}$ are $\textbf{d}_{T_{j}}^{(1)}$ and $\textbf{d}_{T_{j}}^{(2)}$, respectively. Their values are given in Table 4. The position vectors of the transmitting antennas (TA$_1$-TA$_{10}$) are presented in Table 3. To further describe the accuracy of these target points, we introduce their relative errors as follows,
Fig. 7. Geometry diagram of the ranging for the small areas of 16 in the targets T (see texts for the detailed descriptions).
Fig. 8. Figure 8. (a) For the target point-$\textrm{T}_3^{(1)}$, the cross-correlations in time of the received signal from the RA1 with 10 beams of the reference signals; (b) For the target point-$\textrm{T}_3^{(1)}$, the time-space cross-correlation of the received signal from the RA1 with 10 beams of the reference signals; (c) For the target point-$\textrm{T}_3^{(1)}$, the cross-correlation in time of the received signal from the RA1 with the 4th beam of the reference signal.
Table 3. The position vectors of the transmitting radars (TA$_{1}$-TA$_{10}$).
Table 4. The actual position vectors (${\textbf{r}_T}$) and the measured position vectors (${\textbf{d}_T}$) of the targets points in the 16-region of the T, as well as their relative errors.
For the correlated chaotic lidar ranging, the full width at half maximum (FWHM) of the time- correlation peak is used to describe the range resolution ($RR$). As seen in Fig. 8(c), the CC$_4$ is the time-correlation of the received signal from the RA1 with the 4th beam of the reference signal. The FWHM of its peak is 10ps. According to the expression that RR=(c$\times$FWHM)/2, we obtain $RR$ as 1.2mm. We utilize the 4th beam of the probe radar signal from the CLS$_4$ for the ranging of the target point-$\textrm{T}_3^{(1)}$, to calculate dependences of $RR$ and ${\Delta} f$ on some key parameters. The related calculation results are displayed in Fig. 9. Here, $d$ is the distance between the target point-$\textrm{T}_3^{(1)}$ and the transmitting antenna TA$_1$; ${\Delta} f$ is the bandwidth of the 4th-beam of the probe radar signal from the CLS$_{4}$. As shown in Fig. 9(a) where $k_{yinj}^{(4)}$ = $k_{xinj}^{(4)}$, $E_{xinj}^{(4)}$ = 2.8, $E_{yinj}^{(4)}$ = 0.8, $\beta$ = 4$\times 10^9$, $\gamma$ = 8 ns$^{-1}$, $\gamma _{a}$ = 20 ns$^{-1}$, $\gamma _{p}$ = 30ns$^{-1}$, $\gamma _{s}$ = 120ns$^{-1}$ and $d$=6m, with the increase of $k_{xinj}^{(4)}$ from 20ns$^{-1}$ to 100ns$^{-1}$, $RR$ is decreased step by step, and ${\Delta} f$ gradually increases from 200GHz to 360GHz. A smaller $RR$ is accompanied by a larger value of ${\Delta} f$. If $k_{xinj}^{(4)}$ increases from 20ns$^{-1}$ to 25ns$^{-1}$, RR decreases from 1.8 to 1.5 when ${\Delta} f$ increases from 200GHz to 210GHz. If $k_{xinj}^{(4)}$ is between 25ns$^{-1}$ and 55ns$^{-1}$, $RR$ keeps the value of 1.5mm while ${\Delta} f$ further increases from 210GHz to 290GHz. With the further increase of $k_{xinj}^{(4)}$ from 55ns$^{-1}$ to 60ns$^{-1}$, $RR$ further decreases to 1.2mm since ${\Delta} f$ increases from 290GHz to 300GHz. When $k_{xinj}^{(4)}$ varies from 60ns$^{-1}$ to 90ns$^{-1}$, $RR$ keeps a constant as 1.2mm, with the increase of ${\Delta} f$ from 300GHz to 360GHz. If $k_{xinj}^{(4)}$ even further increases from 90ns$^{-1}$ to 100ns$^{-1}$, $RR$ firstly decreases to 0.9mm, then keeps it unchanged under ${\Delta} f$ =360GHz. One sees from Fig. 9(b) that when $\beta$ varies in a certain range, $RR$ and ${\Delta} f$ are independent of them. As seen from Fig. 9(c), if $E_{yinj}^{(4)}$ increases from 0.6 to 0.7, $RR$ decreases from 1.5mm to 1.2mm, owing to the increase of ${\Delta} f$ from 260GHz to 290GHz. When $E_{yinj}^{(4)}$ is between 0.7 and 2.1, $RR$ keeps a value of 1.2mm since ${\Delta} f$ appears an oscillatory variation in a small range from 290GHz to 330GHz. While $E_{yinj}^{(4)}$ further increases from 2.1 to 2.2, it further decreases to 0.9mm, due to the further increase of ${\Delta} f$. As displayed in Fig. 9(d), if $\gamma$ is between 5ns$^{-1}$ and 10ns$^{-1}$, $RR$ first keeps the value of 1.5mm, then decreases to 1.2mm, finally keeps it unchanged, since ${\Delta} f$ firstly shows a rise in oscillation from 260GHz to 300GHz, then appears an oscillation change in a small range from 290GHz to 300GHz. As seen from Fig. 9(e), $RR$ is independent of $\gamma _a$, due to the slow change of ${\Delta} f$ between 290GHz and 300GHz. It is observed from Fig. 9(f) that with the increase of $\gamma _p$ from 30ns$^{-1}$ to 100ns$^{-1}$, $RR$ firstly keeps the value of 1.2mm, then linearly decreases to 0.9mm, finally holds this value unchanged since ${\Delta} f$ firstly increases step by step from 270GHz to 320GHz, then almost stays at 320GHz. It is found in Fig. 9(g) that with the increase of $\gamma _s$ from 10ns$^{-1}$ to 130ns$^{-1}$, $RR$ firstly keeps the value of 0.9mm, then linearly increases to 1.2mm, finally stays at 1.2mm since ${\Delta} f$ gradually decreases from 420GHz to 310GHz. One further sees from Fig. 9(h) that when $d$ varies in a certain range, $RR$ is independent of it. The range resolutions of the other target points have the similar change with the above-mentioned parameters.
Fig. 9. For the target point-$\textrm{T}_3^{(1)}$ ranging by using the 4th beam of the probe radar signal from the CLS$_4$, the dependences of the range resolution ($RR$) and the bandwidth (${\Delta} f$) on some key parameters, where ${\Delta} f$ is the bandwidth of this probe radar signal. Here, black line: $RR$; light-red line: ${\Delta} f$; (a) $RR$ and ${\Delta} f$ versus $k_{xinj}^{(4)}$, where $k_{yinj}^{(4)} = k_{xinj}^{(4)}$, $E_{xinj}^{(4)} = 2.8$, $E_{yinj}^{(4)} = 0.8$, $\beta = 4 \times 10^9$, $\gamma = 8 \textrm {ns}^{-1}$, $\gamma _{a} = 20\textrm {ns}^{-1}$, $\gamma _{p} = 30\textrm {ns}^{-1}$, $\gamma _{s} = 120\textrm {ns}^{-1}$ and $d$=6m; (b) $RR$ and ${\Delta} f$ versus $\beta$; (c) $RR$ and ${\Delta} f$ versus $E_{yinj}^{(4)}$; (d) $RR$ and ${\Delta} f$ versus $\gamma$; (e) $RR$ and ${\Delta} f$ versus $\gamma _{a}$; (f) $RR$ and ${\Delta} f$ versus $\gamma _{p}$; (g) $RR$ and ${\Delta} f$ versus $\gamma _{s}$; (h) $RR$ versus $d$. In (b)-(h), $k_{yinj}^{(4)} = k_{xinj}^{(4)} = 60\textrm {ns}^{-1}$ and the other parameters are the same as those in (a).
These results show that, with the total normalized pump power $\eta$ fixed at 9, the resolution of the ranging to the multi-region targets can be achieved as high as 0.9mm by the optimization of some key parameters such as the injection strength, the amplitude of external light, linear birefringence, spin relaxation rate. The larger linear birefringence, the smaller spin relaxation rate, and the stronger injection strength and amplitude of external light can result in the higher resolution, owing to the larger response-bandwidth (over 310GHz) of the optically pumped spin-VCSEL. It is worth noting that if the optically pumped spin-VCSEL is replaced with the conventional laser in our scheme, the range resolutions might be achieved as high as several centimeters [8], due to the restriction of the response-bandwidth (about several tens of GHz) of the conventional laser subject to strong injection [8]. In addition, the range resolutions exhibit excellent strong anti-noise performance and strong stability when $d$ and $\beta$ change in a certain range. In addition, we calculate the influences of the distance ($d_1$) between the transmitting antenna TA$_1$ and the arbitrary point in the target T on the relative error of the ranging, as presented in Fig. 10. One sees from Fig. 10 that if $d_1$ is between 5.42m and 6.24m, the relative error ($RE$) oscillates between 0 and 0.28$\%$. The $RE$ has similar change with the distance between the other transmitting antenna and the arbitrary point. These indicate that the distance between arbitrary transmitting antenna and any one target point has little effect on the relative error.
Fig. 10. Dependence of the relative error ($RE$) on the distance between the transmitting antenna TA$_1$ and arbitrary one point in the target T.
4. Conclusion
To sum up, we propose a novel scheme for the precise ranging of the multi-region in a rectangular shape target by utilizing numbers of the chaotic x polarization components emitted by the multiple parallel optically pumped spin-VCSEL with optical injection. These chaotic x polarization components have the attractive features of fast dynamics with femtosecond magnitude, and the time-space uncorrelation under different optical injection strengths. Utilizing these features, the delay times from the multi-region targets can be obtained by the observation of the time locations of the maximum expected values of the cross-correlations of the chaotic polarization probe waveforms with their corresponding reference waveforms. Based on these delay times, the position vectors of the multi-region targets can be accurately measured. The investigation results show that the ranging to the multi-region targets has very low relative error and less than 0.28$\%$. The ranging to the multi-region targets can be achieved the higher resolution under the larger linear birefringence, the smaller spin relaxation rate, and the stronger injection strength and amplitude of external light. When these above-mentioned parameters reach a certain value, their resolutions can be achieved as high as 0.9mm. The ranging resolutions for the multi-region targets have excellent strong anti-noise performance. The attractive advantages of our proposed scheme for the ranging to the multi-region targets show as follows: high range resolution, strong anti-noise performance, and low relative error. Our investigation results have the potential for the quality detection of the multi-region surfaces.
Funding
Special project in key fields of Guangdong Universities: the new generation of communication technology (2020ZDZX3052); GuangDong Basic and Applied Basic Research Foundation (2020A1515010088); Major Project of Basic Research and Applied Research for Natural Science in GuangDong Province (2017KZDXM086); National Natural Science Foundation of China (62075168).
Disclosures
The authors declare no conflicts of interest.
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