1. Introduction

Over the last decades, electromagnetic radiation has been used extensively to transmit and broadcast information over wires in the radio frequencies and over free-space through the atmosphere up to microwave frequencies. Although proposed long ago [1], the transmission of power in particular by microwaves over free-space has been developed and tested subsequently [2] but didn’t get applied into commercial product due to the availability of inexpensive cables and the necessity of a directed link between transmitter and receiver. Potential applications were identified to be virtually but in space where the radiation can propagate unobstructed over a very large distance. Systems that require large structures to efficiently focus the microwave radiation onto a receiver were designed and analyzed already long ago [3].

Over the last few decades, optical fiber communication has become a mature technology and has been employed especially for high speed data links. Recently, optical fiber links for power transmission were proposed and tested as well to provide additional power to optical communications networks [4, 5]. Although not being used for broadcasting, free-space laser communications (FSLC) has become an active research field and links through the atmosphere and between satellites have been tested [6]. Terrestrial power transmission by laser radiation is likely not to be applied in other form but through fibers due to the same reasons as for microwaves. However, it is likely that in the future laser power transmission (LPT) will become the most practicable way to transmit power efficiently in space due to its superior beam focusability.

Since decades, wireless power transmission has been discussed for the application of sending energy from orbital solar power satellites (SPS) down to the earth to generate clean energy [7]. Mainly microwave systems have been considered and analyzed for efficiency and cost-effectiveness in the past due to their mature level of technology [3,8]. Regardless of their significant advantage in the ability to penetrate through clouds, laser systems [9, 10] might become an alternative in the near future. Over the last years, the rapid progress in laser physics lets technology become mature and critical parameters as e.g. electrical-optical conversion efficiencies improve quickly. Furthermore, laser systems are considerably smaller because the shorter wavelength can be focused onto the distant receiver more easily. Besides these two techniques, directly reflecting the sunlight has been proposed and tested in the past as an alternative way [11] but this approach makes very complex optical systems necessary due to the sun’s largely incoherent emitted light and its extended size.

SPSs based on either way are in principle feasible, although it still requires on the progress in several technical details as e.g. the construction of large structures in space. It is mainly the cost which hampers the realization of such concepts. To be economically competitive to other forms of power generation, it has been shown that the launch cost per kg must be reduced significantly [8]. It is thus to be expected that “off-shore” solar energy conversion won’t begin directly by SPSs but by using high-altitude aerostatic platforms (HAPs) which generate solar power at 12 km~20 km altitude above the clouds. A recently proposed concept reveals their substantive benefits [12].

Due to the existence of the earth’s atmosphere a laser beam experiences distortions and absorption. Moreover, statistical cloud coverage makes a link from space to the earth unreliable. This is the main disadvantage of optical wavelengths compared to microwaves regarding this application. However, one can avoid this problem by pointing the laser beam on such a HAP which is placed above the clouds so that propagation through most part of the atmosphere is avoided. By selecting an appropriate wavelength, the same photovoltaic-cells on the HAP can convert the incident sun and laser light efficiently and simultaneously. It is due to these advantages why this scenario is likely to become superior to other concepts related to power from space.

Although power from space represents the most discussed application of wireless power transmission, other scenarios have also been proposed in the past. It has been given thoughts to remotely power a planetary rover by laser power at places where sunlight for solar power generation is weak or not available at all. One of these scenarios describes a rover that enters a permanent dark crater near the moon’s poles where it is supplied by a satellite or a laser/light beam from a station on the edge of the crater where sunlight is available almost permanently [13].

The most ambitious scenario for LPT might be a form of power grid established by laser beams to supply spacecrafts and structures in near-earth orbits and on the moon. In this case, the power would be generated on the earth or on power satellites on Lagrange points around the earth/moon which point their laser beams onto e.g. spacecrafts during eclipses [14] or transfer orbits [15], or structures on the moon during the lunar night [16].

Although an optical system with the purpose to transmit power is similar to related technologies, there are fundamental differences. While e.g. in FSLC only a fraction of the transmitted beam is usually detected, an optical system for energy transmission requires the beam to fall almost entirely onto the detection area. This can only be achieved by an increased size of the transmitter’s and receiver’s aperture. Furthermore, while target tracking and pointing for FSLC is usually achieved by open-loop control, closed-loop pointing and tracking becomes necessary to fulfill the required increased precision for LPT. Special closed-loop laser beam pointing mechanisms have been proposed and developed in the past where the laser beam’s direction is modulated so that the back-reflected light gives conclusion about the position of the beam spot on the target [17–19]. A link based on such a method was successfully tested to supply entirely a moving vehicle by laser power over more than 100 m distance [20].

A different approach for closed-loop fine steering and tracking system is related to direct laser energy efficiently onto a target by nonlinear optical methods. This has been first proposed 30 years ago [21] and developed since then in particular for pulsed laser sources [22,23]. In these adaptive beam pointing concepts, positive optical feedback is created by initially illuminating a retro-reflector on the target before amplifying and phase conjugating its reflected light. Here, purpose of using phase conjugation is to maximize the amount of energy onto the target by the dynamic compensation of atmospheric turbulence induced beam distortions.

This paper proposes the modification of this method for the utilization in a continuous-wave (CW) power transmission link. While the target carries the retro-reflector in the middle of the detection area, the transmitter consists of an optical amplifier followed by a phase conjugate mirror (PCM) used with CW radiation. In contrast to the traditional concept but familiar to FSLC [6], it is favorable to place the initial illuminator here on the target. To find an expression for its acting range, the étendue which is defined by the product of aperture diameter and the full-angle field of view has been used for similar systems in the past. An étendue of ~100 mm mrad which has been demonstrated earlier is also considered here [23].

The paper is organized as followed: Section 2 describes the proposed concept and its background with some basic considerations about the control behavior. Section 3 deals with an experiment concerning a high reflective phase conjugate mirror as the core part of the target system. This consists of a self-pumped phase conjugator and an optical amplifier which is used in both directions. Section 4 summarizes and concludes the experimental results with respect to the target application before Section 5 concludes this study.

2. Laser power transmission by high reflective phase conjugate optical feedback

This chapter shall give an overview about the proposed concept in general. Section 2.1 characterizes the optical transmission system while Section 2.2 introduces the different use of photovoltaic (PV)-cells in combination with the sunlight and laser light before Section 2.3 describes briefly the concept of the high reflective PCM. Although various applications of laser power transmission have been discussed in the past, this paper motivates this study by a consideration for the frequently discussed energy-from-space-scenario. With small modifications, the proposed method is applicable to most applications of LPT in space.

2.1 The optical link for transmitting power by a laser beam

The setup for the proposed optical system is shown in Fig. 1 . Initially, the receiver, in this scenario a HAP, illuminates the transmitter, in this scenario a satellite, with a coherent light source (a). The transmitter sends the phase conjugate beam towards the receiver where a corner cube reflector (CCR) (as an example for retro-reflector) is placed. This reflects parts of the light back to the transmitter which closes the optical feedback loop. The idea for achieving power transmission requires the CCR to be smaller than the (diffraction limited) spot size of the transmitted beam. This will let a notable amount of the power be incident on the CCR surrounded area where photovoltaic cells convert the incident light into useable electric energy.

 

Fig. 1 Shown is the intended optical system for power transmission. (a) Initially, the transmitter, in this scenario a satellite, with integrated phase conjugate mirror is illuminated by a light source which is placed in the center on the receiver, in this scenario a high altitude platform (HAP). (b) Incident light is amplified, phase conjugated and transmitted back to the receiver where it is incident on the photovoltaic cell area and on a sub-diffraction limited spot size CCR. The light incident on the latter is reflected back to the transmitter in order to keep the process running. Power transmission is achieved by the remaining light that is converted into useable electric power by the surrounded photovoltaic cells.

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Initial illumination is necessary to overcome a possible threshold for the PCM to start. It is the equivalent of a seed laser without that only light from spontaneous emission noise from the gain material would be present. This might not be coherent enough for the PCM to start. The choice for the type of mirror considered on each side is made according to the traditional concept. A CCR is an easy-to-align retro-reflector which is necessary to reflect incident light back towards the transmitter. There, a phase conjugate mirror is preferred over another CCR, for example, because it can clean up distortions coming from the thermal lens of an optical amplifier. Beam clean-up might not be perfect so a laser beam with common divergence, described by the beam quality factor M², is assumed below.

For the transfer of large amounts of energy, a single transmitter might result in too high intensities or very big optics. In this case, an optical phased array [24] as transmitter can provide advantages because it multiplies the total amount of transmitted power by the number of single elements and it further increases the étendue of the optical system. On the other hand, it makes the system more complex because of the adjustment of each element’s absolute phase which is crucial to form a proper beam pattern [25]. The following equations are therefore limited to a single transmitter for simplicity.

Figure 2 shows the power receiver for the tested method (a) [20] and for the proposed method and their intensity distributions (b). How much power must fall on the retro-reflector area is determined by the link distance and the sensitivity of the photo-detector in (a) and by the required amount of optical feedback in b). In this example, the optics of the illuminator is integrated into the CCR, indicated by the bright in the center of the receiver in Fig. 2 (b).

 

Fig. 2 Power receiver architecture for (a) the setup successfully tested in [20] and (b) the setup proposed in this study. Dark, hatched areas represent the solar cell area and gray triangular areas represent a CCR/CCRs. The bright spot in the center in (b) indicates the illuminator’s aperture. The intended illuminance on the receiver is plotted below.

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In order to make the link efficient for power transmission, the size of the CCR reflector is to be minimized such that the amount of reflected light is still sufficient for the feedback system to work properly. For a laser beam, the 1/e²-intensity half-width divergence angle θ_Div in the far field is given by [26]:

For stable operation, the transmitted power P_trans must be equal to the incident light’s power on the optical transmitter P_inc multiplied by the PCM’s reflectivity.

As a numerical example, consider a satellite with D_T = 3 m aperture transmitting a Gaussian beam (M² = 1) at λ = 850 nm from geostationary orbit to a HAP (L = 36000 km). For achieving a link-efficiency of η = 95% (T = 20), it requires to have R_PCM≈1600 and D_CCR≈1.8 m while the spot size is w_T≈13 m. Considering a planetary rover which is remotely powered by a Gaussian laser beam from a L = 10 km distant station with D_T = 10 cm and laser wavelength λ = 532 nm, one needs D_CCR≈1 cm (spot size w_T≈6.7 cm) for η≈95% / R_PCM = 1600. An étendue of 100 mm mrad leads to a tracking angular range of 1.2 km and 10 m for the HAP and the rover, respectively.

So far, it was assumed that incident back-reflected light is ideally phase conjugated and the transmitted beam being a collimated laser beam with beam quality M². However, the incoming beam is not identical to the transmitted beam since it has been spatially sampled by the CCR and only a fraction of this is finally incident on the PCM. It is therefore of interest how accurate phase conjugation can theoretically be in such a case. This can be tackled by the theory of incomplete phase conjugation [27] which derives theory about fidelity and beam spread in the case where parts of the original beam falls out of the PCM’s aperture.

The expressions derived in [27] indicates that in the limiting case of a spherical wave which means a small CCR the phase conjugated beam only contains terms of the coherent parts which should lead to ideal phase conjugation. (Eq. (12) in [27] with W = D_T and m₀ = 0 i.e. no distortions). In the presence of atmospheric distortions, loss of information of the original wavefront will occur and it is then of interest how much these aberrations will degrade the link performance. But since mainly quiet environment with no or negligible wavefront aberrations are assumed here, such an analysis is out of the scope of this paper.

Figure 3 shows a scheme for the closed-loop optical control. The two actuating variables are the position $\overrightarrow{r}$and the phase conjugate reflectivity R_PCM. While the PCM tracks $\overrightarrow{r}$ automatically by its dynamic holographic processing, R_PCM needs to behave in the following way for a stable control. If the back-reflected, on the transmitter incident power P_inc is too high which is the case if the target is too close, R_PCM must decrease so that the output power stays within bounds. In case P_inc is too small, R_PCM must increase since otherwise the output power would tend to zero.

 

Fig. 3 Block diagram of the optical control loop.

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Ρ_PCM,ref is the reference reflectivity which is determined by the desired link efficiency η. Using a similar setup discussed in Section 2.3 below, R_PCM can be controlled by adjusting the gain of the optical amplifier. $\overrightarrow{r}$ _ref is the reference direction for the phase conjugate beam. This needs to be adjusted e.g. in the case of an existing point-ahead angle. This can be achieved by an orthogonal polarization scheme for incident and phase conjugated beam.

2.2 Conversion efficiency of laser light

Using laser light to transmit power requires the generation and reconversion from electrical energy. This section reviews the most common ways and describes how LPT can be beneficial for the generation of clean energy in space.

Recent fiber power links usually generate laser light efficiently by a GaAs-based laser diode (LD) with wavelength in the near-infrared between 800 nm and 980 nm [4,5]. Here, larger wavelength LD’s are able to achieve higher efficiency and power. Commercial devices are available with efficiency between 50% and 60% [28, 29]. To achieve kW-output power with high beam quality, a solid state or fiber laser can be pumped by LD’s. This optical-optical conversion can exhibit an efficiency of 80% especially in fibers so that it leads to commercial high power lasers with wall-plug efficiency of up to about 30%. However, the longer wavelength of usually 1.06 µm is more difficult to reconvert and that’s why second harmonic generation is sometimes used to create a shorter wavelength.

For reconversion, a photovoltaic power converter (PPC) using photovoltaic (or solar) cells are used. While conventional solar cells are designed for solar light with a broad spectrum, efficient conversion of laser light can be obtained if its wavelength is tuned to be near the cut-off wavelength of the semiconductor material where the quantum efficiency (QE) has its peak value. The QE is the ratio of excited electrons per incident photon. Although the QE has its peak-value near the cut-off wavelength, it doesn’t decrease strongly for wavelengths of a few 10s of nm below. GaAs cells reach efficiencies of 50% [30] and even 60% seem to be achievable [30] when using laser light between 790 nm-850 nm. However, conventional Si-based cells might not achieve the same [5]. Optimum reconversion of a given laser emitting in the visible or near-IR is achieved by a wavelength-adapted band-gap design of GaAlAs or InP semiconductor compounds. They are capable to achieve efficiencies between 50% and 60% by a slight increase towards shorter wavelengths [31].

The intended energy-from-space scenario requires the conversion from sun-and laser light by the same PPC. Although no experimental data have been reported to the best knowledge of the author, GaAs or triple-junction cells [32] might be more suitable than most common Si-based solar cells because of better potential conversion efficiencies for laser light.

Following these arguments, the most efficient laser power link uses near-IR LD’s and GaAs based PPCs and a high power long range free-space link uses and additional amplification with fibers and GaAlAs-based PPCs. For both, sun- and laser light, near-IR LDs in combination with GaAs PPC are supposed to give optimum performance.

When collecting sunlight from space, one further has to regard its availability. Figure 4 depicts three different ways to produce energy from solar power: Terrestrial power generation, high-altitude power generation and satellite power generation.

 

Fig. 4 Efficiency scheme for different ways to collect solar energy. P_Ground, P_HAP and P_GEO embodies the availability of the link from the sun to the ground, to the HAP and to the satellite in geostationary orbit, respectively. Power transmission from the satellite to the HAP is considered to be done by laser while the transmission from the HAP to the ground by a cable or microwaves.

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In Fig. 4, the conversion efficiency of sunlight is assumed to be 25% which is close to recent results for modules [32]. Some solar cells can reach more than 40% under concentration but this requires additional optics and directional control so that it is not further considered here for comparison.

The availability of sunlight on the ground, the HAP and the satellite in geostationary orbit are expressed by p_Ground, p_HAP and P_GEO, respectively. Since the weather conditions have an influence to solar cells on the ground, there is a fundamental difference between p_Ground to p_HAP and p_GEO because the latter two are predictable in time and amount. Therefore, they can be employed for base load energy generation. p_HAP depends on the altitude h of the HAP. It has been derived that p_HAP(h = 6 km)≈35% and p_HAP(h = 12 km)≈45% [12]. P_GEO is less than 1 because of the earth’s shadow which sometimes falls onto the satellite. However, p_GEO is still about 99% [3].

In contrast, the terrestrial availability p_Ground depends on the local weather conditions. For middle European conditions, p_Ground is about 10%. Furthermore, transmission through the atmosphere (indicated by τ_ATM in Fig. 4) is reduced due to absorption which also depends on the location. Usually, the air-mass 1.5 (AM1.5) (Global) spectrum is used to describe the spectral irradiance of the sunlight in most developed countries on the earth. Compared to the AM0 spectrum in space, the integrated irradiance is reduced from about 1.35 kW / m² to about 1.0 kW / m², respectively (i.e. τ_ATM≈0.74) [33].

On the satellite, electric energy is converted into laser light by LDs in the aforementioned way. Alternative methods propose to convert sunlight directly into laser light [9, 34]. This promising idea could about double the efficiency in the future but is not considered here due to its early stage of development. Choosing carefully a wavelength in the near-IR absorption by the atmosphere can be neglected, especially when considering the illumination of HAPs. The efficiency for beaming laser power from the satellite onto the HAP is thus assumed to be about ~50%.

Finally, a cable or cloud penetrating microwave power transmission is assumed to bring the power from the HAP down to the Earth. Its efficiency, which includes power transformation, transmission and reconversion, is assumed here to be about 80% [3, 35].

Altogether, the average collection efficiency η_c is derived for the three different collecting paths by multiplying their total efficiencies with the probabilities: η_c,Ground≈2%, η_c,HAP≈8% and η_c,GEO≈5%. This concludes that solar cells installed on the satellite provide more energy than on earth but less than solar cells on a HAP over a whole year. Their main benefit will thus be its constant power supply over a whole day and its vast expandability.

The efficiency is of importance at places where space for sunlight collection is limited. This will be the case especially for power generation on a HAP since its size is limited. Not less for HAPs but more important for geo-stationary satellites is the power/mass or efficiency/mass ratio of the solar cells since payload to space is very costly. For that reasons, extreme light solar cells have been proposed in the past [36]. Although a very promising idea, one has to challenge various technical problems until directly applicable.

2.3 The amplifier-Phase Conjugate Mirror

PCM’s in combination with amplifiers have been demonstrated in the past by using optical amplifiers. Combining a PCM with 2-way amplification brings the benefit of improved beam quality because phase conjugation compensates beam distortions occurring due to the thermal material deformations of the amplifying material. Master oscillator power amplifier systems with high output power have been achieved with such techniques [37–39].

Figure 5 shows the arrangement of the amplifier and PCM. Henceforth, R_PCM refers to the reflectivity of the self-pumped PCM alone while R_A-PCM describes the total reflectivity of the amplifier-PCM (A-PCM) setup. For small incident powers, the optical amplifier‘s single-pass gain G_sp is given by its specified small signal gain G₀ and it follows that the reflectivity R_A-PCM is simply given by:

 

Fig. 5 High-reflective phase conjugate mirror (PCM) consisting of a self-pumped PCM and an optical amplifier.

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A simple model which assumes constant charge carrier distribution inside the amplifier describes the amplifier’s gain and its saturation behavior. For this, the following differential equation for the optical power P is used [40]:

Beside the amplified incident signal P_in, optical amplified spontaneous emission (ASE) noise is added to the signal so that the output power is given by:

For small signals, P_ASE doesn’t depend much on the input power. For large input power, N₂ becomes significantly smaller so that P_ASE is reduced. Especially when using the amplifier in both directions, a significant reduction of ASE noise can be expected compared to a single directional usage because in the latter most of the noise is created at the low power input end [40].

3. Experiment

In this study, a state of the art single mode fiber pigtailed multiple quantum well type semiconductor optical amplifier (SOA) (Superlum, SOA-372) was used as amplifier. A SOA is one of the few possibilities to amplify radiation in the near-IR from ~700 nm-900 nm without nonlinear wavelength conversion processes. Compared to a Ti:Sapphire crystal [42], its efficiency should be superior since other optical-optical conversion processes aren’t necessary. On the other hand, in the used version, high gain is only available in single mode operation so that it can be only of use as single element of a phase array due to the loss of directional information when. A Rh:BaTiO₃ photorefractive crystal was employed as material for building a self-pumped PCM operating in the near-IR [43]. The used crystal measured 8 mm x 6 mm x 5.5 mm with the c-axis along the longest side, and Rh-doping concentration was specified by <10ppm.

The experimental setup is shown in Fig. 6 . A fiber coupled laser diode (OzOptics) at λ = 850 nm was used in combination with a free space polarization control setup plus a tunable narrow band-pass (BP)-filter with full-with-half maximum (FWHM) Δλ≈1 nm to produce a quasi single frequency input signal. Polarization control was performed in a free space setup consisting of a λ/2-plate and a polarizer. It is necessary due to the polarization dependency of the SOA’s gain. Two 50/50 couplers were integrated in order to measure the input and output power of the following SOA-PCM setup. Photodiodes converted the optical into an electrical signal which was observed on the oscilloscope.

 

Fig. 6 Experimental setup for testing the SOA-PCM system. M1-M3: mirrors, BS: beamsplitter, POL: polarizer, λ/2: half-wave plate, BP-Filter: band-pass filter, ND-Filter: neutral density filter.

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Phase conjugation was achieved by degenerate four-wave mixing (FWM) [44]. An isolator was added in order to prevent the counter-propagating pump beam to return into the fiber. The polarization was controlled by a polarizer and the isolator to be incident extra-ordinary on the crystal. An 11 dB beamsplitter was placed into the beam path to reflect parts of the phase conjugate beam’s light onto a CCD camera and to display its pattern on a screen. The λ/2 wave plate placed before the 3 dB-beamsplitter was first set to maximize incident light on the crystal and then adjusted to obtain maximum phase conjugate power.

In order to describe its influence on the PCM, the output signal was examined for its spectrum and its degree of coherence (DOC). It is known that partially coherent light reduces the reflectivity of photorefractive phase conjugators according to the DOC of the used laser light [45].

For examination, an optical spectrum analyzer (Advantest, model: Q8347 Optical Spectrum Analyzer) was used which could measure both, the spectrum and the DOC, directly. This is accomplished with a built-in Michelson interferometer that additionally uses a He-Ne Laser as reference to increase its accuracy by determining precisely the mirror positions. Two interferograms are taken simultaneously by recording 4096 data point over a definite interval. This allows determining the spectrum by a Fourier transformation. Due to the phase information obtained by the interferogram, each data point is then taken as a complex value so that the DOC is determined by its normalized absolute value.

Figure 7 presents the measured spectrum of the amplified signal for different input signals. One can recognize 2 “hills” belonging to two quantum states of the MQW-type SOA. It can be observed that by increasing the input power, the hill at smaller wavelength decreases.

 

Fig. 7 Spectra of the output signal for several input powers.

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Figure 8 shows the measured DOC for an input power of 27 µW. A peak can be found for the DOC at a delay of Δx = 0 cm. Its FWHM is about Δx≈20 µm which is due to the noise spectrum with FWHM of about Δλ≈50 nm. Beyond Δx = ± 10 µm, the DOC is almost constant for several cm length since the linewidth of the input signal was narrow with about Δν≈3 GHz.

 

Fig. 8 The measured degree of coherence of the output signal at P_in = 27µW input power.

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The recorded diffraction grating in the FWM setup is dependent on the DOC of the writing beams over the whole interaction length of about 0.8 cm. Since the peak’s width of Δx = 20 µm is small against the interaction length of 0.8 cm, it can be neglected and it is the constant value beyond Δx = ± 10µm which is significant for the PCM’s efficiency. The path-length difference of the two writing beams was <5 cm and therefore the DOC at Δx≈ ± 1 cm as a function of the input power was measured as significant parameter for the recording process. The data in Table 1 indicate a nonlinear dependence with significant reduction below P_in = 20 µW.

Table 1. Measured DOC of the amplified signal at a delay of Δx = 1 cm as a function of the input power.

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Although an optical feedback loop was proposed in section 2.1, it was not employed yet and the reflected light simply detected by a photo-diode. However, a very small part of the light returned into the laser source and provided optical feedback which didn’t affect the experiment much. It was observed that it seemed to stabilize the emission by reducing the occurrence of mode-hopping inside the laser diode. The SOA’s input-output behavior was measured with a driving current of I_cur = 125 mA.

Alignment of the crystal and mirrors M2 and M3 were critical since the phase conjugated beam not only had to have a round beam spot but also needed to couple back into the single mode fiber. Hence, the signal of photo-detector 2 was maximized besides optimizing the spot’s shape which was recorded by the CCD-camera and displayed on a screen.

Due to the slow response of the crystal, maximum phase conjugate power was reached after several minutes. Once it was built up, operation was relatively stable and a short decrease of the input power did not affect the reflectivity much. Input power was then changed by turning the λ/2-plate which changes the transmission through the following polarizer.

4. Experimental results and estimations with regard to applications

Figure 9 presents the results of the tested SOA-PCM system. Phase conjugate output power could be observed above a certain threshold. Beyond the threshold, a reflectivity of R_A-PCM>90 was obtained which decreased to R_A-PCM = 80 for P_in = 23 µW which was the maximum input due to the limited laser’s power of P = 1 mW. The desired decrease of R_A-PCM for increased input power which is required for stable operation as discussed in section 2.1 has thus been observed. It is worth to remark that the threshold of P_in≈5 µW is near the “minimum detectable power” which is defined as P_min = hνΔν [41] where h is the Plank’s constant, ν light’s frequency and Δν the FWHM of the emission spectrum and which is P_min≈4.9 µW for the used SOA.

 

Fig. 9 Output power and reflectivity of the PCM-SOA setup as a function of the input power.

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Data were also fitted using the model of Section 2.3 by numerically integrating Eq. (8) after inserting Eq. (9) for both directions. A small signal gain of G₀ = 250 (24 dB) was assumed which leads to g₀-γ_sc = 5.02 mm⁻¹ knowing the length of the SOA of L = 1.1 mm. The two remaining parameters were fitted to the graph with: P_sat = 32mW, γ_sc = 1mm⁻¹. In general, simulated results could be fitted well to the measured data. Differences are found for low input powers because R_PCM was assumed to be constant. In reality, R_PCM changes due to the dependence of the light’s DOC which is reduced at low input powers. The existence of a threshold can be explained by an existing dark current which is created due to thermally excited charge carriers [43, 46].

Compared to the single-pass gain of >100, the obtained overall reflectivity R_A-PCM is relatively low and originates in the low reflectivity of the self pumped PCM which was only about R_PCM ≈0.2% including the 3 dB beam splitter and the other optical components. The reason for this low value was the selected relatively ineffective FWM-type PCM. A more efficient type which functions with self-induced oscillations and that is usually used like a CAT mirror [47] or a ring-cavity phase conjugator [48] was difficult to achieve under the given resources. One important factor was the relatively low incident power of a few mW but also the observed low coupling coefficient of the used Rh:BaTiO₃-crystal. This might be due to the Rh-doping concentration of <10 ppm which was untypically low [49] for this only available crystal of this type. Rh-doping is supposed to be the main active center in the process because it increases the sensitivity at near-IR wavelengths beyond 800 nm where un-doped BaTiO₃ becomes less sensitive [50]. Finally, other optical losses like fiber coupling further reduced the PCM’s reflectivity.

Photorefractive crystals possess a high sensitivity which is important for CW applications but their temporal response is usually very slow as for the used Rh:BaTiO₃ crystal. Hence, the tested configuration is only applicable for almost stationary links. For faster temporal response which is required for tracking applications, various optical materials based on 3^rd-order nonlinearity appear to be more suitable employed in aforementioned studies [22, 23] with pulse lasers. Nevertheless, a good candidate could be the Sn₂P₂S₆ photorefractive crystal [46, 51] since its temporal response is exceptionally high even in the near infrared. 100 Hz phase conjugation sampling seems achievable [46] which allows applying to moderate dynamic links while more than 1 kHz beam amplification could be demonstrated [51] which’s temporal response is comparable to fine steering mirrors in free space laser links [52].

Based on the obtained results, Eq. (6) reveals that the link efficiency for the obtained maximum R_A-PCM would be about η≈80%. In order to obtain higher efficiencies in the realized setup, R_PCM has to be increased by employing a more efficient self pumped PCM type. Once a self pumped PCM with reflectivity R_PCM in the double-digit percentage could be realized, R_A-PCM will strongly increase. Typical values using Rh:BaTiO₃ with higher incident power and (potentially) higher doping of nearly 70% for the same wavelength were reported using a CAT mirror [53] and about 40% using a ring-cavity phase conjugator integrated into a laser system at 1064nm wavelength [54].

Using the same parameters and assuming a 100 times more efficient PCM with R_PCM = 20% which is in the same order of magnitude of the reported values, simulated results in Table 2 reveal that a reflectivity of R_A-PCM>1000 is reachable that will lead to link efficiencies >90%. Although a 100 times more efficient PCM is assumed, R_A-PCM is only about one order of magnitude higher which is due to the strongly saturated gain. Single-pass gain G_sp is up to 8 dB smaller than the specified small signal gain G_AMP of the SOA.

Table 2. Simulated results assuming R_PCM = 20%. The link efficiency under stable operation is calculated using Eq. (6) with R_PCM = R_A-PCM.

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In a realistic link, input power might not be constant due to scintillations caused by vibrations of the transmitter or dynamic refractive index variations on the propagation path. Therefore, measurements have been performed using an amplitude modulated signal of 270 Hz and 1 kHz. No notably different results were obtained compared to the CW case expect that the time for grating built-up significantly increased, probably due to the decrease of average power. Scintillation will thus result in higher requirements on the material’s temporal response besides.

The signal in the conducted experiment didn’t contain any phase front distortions and is therefore not suitable to make conclusions on how e.g. a link through the atmosphere would change the A-PCM’s performance. Furthermore, in contrast to the final system, almost the entire beam is spatially incident. Hence, changes in the mode structure are to be expected in a setup closer to the application. By conducting a spatial mode analysis [55, 56], the transverse mode structure could be obtained assuming a resonator with large diffraction losses.

Therefore, the relevance of the conducted experiment is the demonstrated high reflectivity and the obtained saturation behavior of the A-PCM setup in the wavelength suitable for power transmission.

5. Conclusion

A modification of the adaptive beam pointing concept [21] is proposed for the use to transmit energy by laser continuously. A retro-reflector is installed on the target to give optical feedback to a high reflective phase conjugate mirror while diffracted light around it is collected to convert it into useable electric energy. An expression is derived that describes the required reflectivity of the PCM for a stable operation of the power link.

As part of the aspired system, a high reflective PCM was realized experimentally by combining a state of the art traveling wave SOA and a photorefractive self-pumped PCM. It has been shown that ASE noise which occurs during amplification reduces the coherence of the amplified signal which influences the reflectivity of the PCM. A power threshold has been found for the input power beyond that phase conjugation could be achieved with reflectivity of nearly R_A-PCM = 100. Further experimental studies will focus on increasing this by using a more efficient self-pumped PCM. Simulation results show that a reflectivity as high as R_A-PCM≈2000 is reachable using the same amplifier.

As a next step, the proposed setup for LPT will be subject of a further experimental study and more detailed theory that could include a spatial mode analysis similar to self-adaptive laser oscillators [56] as well as an analysis how much atmospheric beam distortions influence the link performance [27]. Especially over large distances in space where the diffraction limited spot size is spacious, the intended system should be found useful for application.