1. Introduction

Optical tracking is an essential element in free-space optical communication [1,2], small-size space debris removal [3,4], and laser propulsion [5]. In these applications, optical transmitters must have a priori knowledge of the three-dimensional location of a target in order to transmit a light beam to it. In the case of moving targets, the information needs to be kept updated so that illumination is maintained. Such optical target acquisition, tracking, and pointing functions have mostly been studied using gimbal-based systems composed of a motorized beam-steering mirror system and servos [6–8]. However, mechanical beam-steering systems are usually slow, bulky, heavy, and power consuming. Rotating stages also cause unwanted effects such as mechanical vibration and torques that affect satellite attitudes if the system is incorporated into a satellite. These disadvantages are serious problems, especially for air- or space-borne systems. Although several non-mechanical optical beam-steering methods have also been proposed [9–12], heavy energy loss is inevitable due to beam divergence caused by diffraction and phase aberration during propagation. Moreover, air turbulence causes beam spot dancing and deflects the light beam from the target [13]. As an established means to correct wavefront distortions, adaptive optics has been used in astronomical observations. However, this technique requires a guide star, and wavefront correction is applicable only when a target is in close proximity to the guide star. Therefore, adaptive optics cannot be applied to target tracking because such guide stars are not commonly available. Furthermore, adaptive optics systems are expensive and complex because they require a wavefront sensor, a deformable mirror, and feedback control.

Given the aforementioned considerations, phase conjugate light (PCL) can be an effective means of optical transmission owing to its automatic targeting, tracking, and pointing properties. A phase conjugate mirror reflects the incident light beam so that the output beam follows the incident beam’s exact reverse path. Subsequently, PCL reconstructs the original wavefront and returns to its source despite the aberration in the light path. The time-reversal property enables near-diffraction-limited focusing to a point light source. Although PCL can be also generated through an electro-optics process [14], the nonlinear optical method is favorable for tracking a fast moving target because the process is all-optical and rapid. In fact, the nonlinear process is by far the fastest among all the aforementioned processes. Another advantage of PCL is that it can simultaneously track more than one target. This property is unique to PCL; moreover, novel applications such as simultaneous removal of small-sized debris, optical signal transmission when more than one target needs to receive signals, and broadcasting through moving nodes (e.g., unmanned small aircrafts with communication repeaters) can be employed. Although the merits of using PCL have been discussed in several studies [15–18], none have discussed a case wherein multiple targets exist. Therefore, in this study, we demonstrate two-target tracking and pointing as well as measure the effect on the PCL output. Moreover, we expand the field of view using collector optics, which is also important for tracking moving targets. PCL output behavior and tracking accuracy are investigated in relation to the enhancement of the field of view.

In our scenario, diverging probe light illuminates a relatively large area. If the target of interest is within the illuminated area, a small portion of the probe light is reflected off the target and returns to the system. The system then generates PCL, and major energy transfer to the target occurs. An optical amplifier can be added in front of the system so that both the target-reflected incoming beam and PCL are amplified; thereby increasing the overall reflectivity to a desired level.

2. Experiment and results

The experimental setup is based on the setup described in ref. 19. PCL is generated in a self-starting, self-pumped Fabry–Perot resonator-type phase conjugator with a 160-cm cavity length. A 90 J-flash-lamp-pumped Nd:YAG rod with a length of 10 cm and a diameter of 1 cm was placed between two mirrors of 100% and 40% reflectivity; this system generated a 1.4 J, 400-μs pulse at 1064 nm. An aperture with a diameter of 2 mm was placed inside the cavity to make the top-hat beam a narrow Gaussian beam. The target was a beam splitter with 95% reflectivity that was positioned 20 cm away from the optical coupler. The target-reflected laser beam was forwarded back to the Nd:YAG rod as an object beam to induce the four-wave mixing (FWM) process.

The proposed system has a distinct advantage of simplicity compared to other systems. Although it utilizes the FWM process, the phase-matching condition is automatically satisfied because light waves propagating back and forth in the cavity are used as the counter-propagating reference and readout light, and the laser output serves as the prove light; hence, no additional light source is required. The system is also capable of handling high power; unlike other processes such as photorefraction, saturable-gain FWM does not involve light absorption. Moreover, laser crystals (e.g., Nd:YAG) are chemically stable and have good durability. Other gain materials such as diode-pumped, high-efficiency ceramic gain materials can also be used; these materials offer greater doping concentrations at lower cost and with arbitrary shapes and size.

2.1 Two-target tracking and pointing

For the two-target experiment, the laser output was spatially separated into two beams (hereinafter referred to as object light waves E3-1 and E3-2) by beam splitters BS1 and BS2 (Fig. 1). The two object beams interfere with reference light E1 inside the rod and induce stimulated emission at the constructively interfered region. This process produces modulated gain in the rod and diffracts the readout light (E2), thereby generating two PCL beams (E4-1 and 2), which are monitored by the beam profiler (BP).

 

Fig. 1 Experimental setup for the two-target experiment. E1, reference light; E2, readout light; E3-1 and 2, object beams; E4-1 and 2, phase-conjugated beams; M0–6, mirrors; BW, Brewster window; A, 2-mm-diameter aperture; OC, optical coupler; BS1–3, beam splitters; ND, neutral density filter; BP, beam profiler.

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A snapshot captured by the beam profiler (Fig. 2) shows that two PCL beams were simultaneously generated. Each PCL beam diameter measured at the 1/e² is suppressed to approximately 1.2 times the original laser output beam spot size, whereas the beam diameter of normal light that propagated the same path became more than two times in size due to diffraction, as listed in Table 1. This result indicates that the diffraction effect was canceled by the time-reversal property of PCL and that the original beam shapes were reconstructed. No grating lobe was observed, unlike the case of a phased array system, because the proposed system acted as a volume grating. The two beams were separated by 730 μrad; however, angular resolution can be further narrowed in the system.

 

Fig. 2 Beam profile of two phase-conjugated beams generated simultaneously.

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Table 1. Beam Spot Sizes of the Original Object Beam, the Two Phase-Conjugated Beams in Fig. 3, and Non-Phase Conjugated Light that Propagated the Same Distance as the PCL

View Table

2.2 Expansion of field of view

In the case of sending optical energy to moving targets, having a wide field of view is an important subject. However, in the scheme of PCL generation inside a nonlinear material, a long interaction length is required for efficient energy coupling; hence, a wide field of view is difficult to achieve. A large incident angle also degrades the efficiency because it results in extremely small fringe spacing where the gratings can easily be washed out.

As shown in Fig. 3, a pair of lenses with different focal lengths was inserted in the object light path to widen the field of view while maintaining a small incident angle. These lenses collect incident light beams from a wide area and steer them into the rod at a smaller incident angle.

 

Fig. 3 Schematic of the field-of-view experiment. M0–4, mirrors; BW, Brewster window; A1 and 2, apertures; OC, optical coupler; L1 and 2, lenses with f = 100 and 500 mm, respectively; BP, beam profiler.

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In our experiments, the wavefront correction property was first verified using a phase aberrator comprising a 3-mm-thick plastic sheet inserted in the object light path between L1 and A2. A PCL profile that passed through the aberrator is shown in Fig. 4(b), where the beam size was approximately the same as the case without the aberrator (Fig. 4(a)). In contrast, Fig. 4(c) shows a strong wavefront distortion observed for the light that experienced the same aberrating path, but it was reflected by a normal flat mirror placed closely in front of the rod. These results confirmed the wavefront correction capability of PCL with the collector lenses inserted in the object light path.

 

Fig. 4 Beam profiles of (a) PCL when no aberrator was used; (b) PCL when a plastic sheet was placed in the object light path as a phase aberrator; and (c) normal light propagated the aberrator. Wavefront distortions caused by the collector lenses and aberrator can be canceled by optical phase conjugation.

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Next, we investigated the tracking ability of the PCL beam. A flat mirror target was shifted in small steps in the direction perpendicular to the object light path. If the generated light is perfect PCL, it would retrace the original light path and its beam spot on the beam splitter surface would remain at the same location. The results are shown in Fig. 5. The origin of the horizontal-axis was set to be the position where the target located closest to the optical coupler. In this setup, a field of view as wide as 21° was obtained, which is approximately five times larger than the case without the collector lenses. The rms deviation of the beam centroid determined by the first moment method [20] was 120 μrad, which is well within the target size of 8 mrad. Figure 5 also shows reflectivity at each location, where the reflectivity is defined as the ratio of PCL to the object light energy that was maintained at 23 mJ. The reflectivity was almost constant throughout this range. The pointing ability over such a wide angle without changes in the setup is highly advantageous compared to mechanical beam-steering systems that take time to be rotated.

 

Fig. 5 Phase conjugated-beam centroid position and output energy as functions of target position. The vertical axis for the beam wander is set to be the target size of 8 mrad.

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Finally, the collector lenses were inserted in the setup for the two-target experiments. PCL outputs for both one- and two-target cases were measured. For these experiments, the aperture shown in Fig. 1 was removed from inside the cavity to exclude the contribution of mere amplification produced at the outer non-interference region of the rod. A variable Neutral density (ND) filter was used to equalize the energy of the two object beams. The beams on BS3 were separated by 4 mrad. In the one-target case, one of the object beams was blocked. The test was conducted 20 times for each case. The change ratio of the PCL output for the two-target case with respect to the one-target case was 101 ± 19% for the beam that passed through the beam splitters and 94 ± 13% for the beam sent to M5 and M6. The results indicated that the PCL output was not substantially diminished as a result of the increase in the number of targets.

3. Discussion

In the proposed scheme, weak PCL can theoretically be amplified within the rod because of the large gain of the material; however, the measured reflectivity was 2%. Brignon and Huignard have reported that excess stimulated emission due to strong incoming light results in a low gain for PCL amplification [21]. Conceivably, the same phenomenon occurs in our case. To confirm this hypothesis, we measured the reflectivity by varying the object light energy using a variable ND filter. The reflectivity increased with decreasing object light, as shown in Fig. 6. The highest reflectivity of 205% was obtained when we decreased the object’s light energy to 0.2 mJ, which was just before PCL became indistinguishable from the background noise. The fact that the amplification factor decreased as the object light energy was increased is consistent with the aforementioned hypothesis. Therefore, the reduction in gain should be avoided by widening the aperture size of the medium to maintain the total energy at approximately the saturation fluence of the medium which is 500 mJ/cm² in the case of Nd:YAG.

 

Fig. 6 Phase conjugate light (PCL) energy and reflectivity as functions of the incoming object light energy, which was varied using a variable ND filter.

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4. Summary

We have demonstrated two-target pointing using PCL generated in a Nd:YAG laser. Two phase-conjugated beams with beam sizes approximately equal to that of the original object beam were verified, thereby demonstrating the pointing ability of PCL. A maximum field of view greater than 20° was also achieved through the use of collector lenses. Accurate tracking capability was confirmed by measuring the beam centroid positions, and the amount of beam wander was 120 μrad, which was well within the target size of 8 mrad. A constant PCL energy was also confirmed for the range of the field of view. We demonstrated that no reduction in PCL output due to the increase in the number of targets occurred. Our results indicate that the system is potentially applicable for wide-range, simultaneous multi-target tracking and pointing.