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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 13 — Jun. 21, 2010
  • pp: 13451–13467
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Continuous adaptive beam pointing and tracking for laser power transmission

Christian A. Schäfer  »View Author Affiliations


Optics Express, Vol. 18, Issue 13, pp. 13451-13467 (2010)
http://dx.doi.org/10.1364/OE.18.013451


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Abstract

The adaptive beam pointing concept has been revisited for the purpose of controlled transmission of laser energy from an optical transmitter to a target. After illumination, a bidirectional link is established by a retro-reflector on the target and an amplifier-phase conjugate mirror (A-PCM) on the transmitter. By setting the retro-reflector’s aperture smaller than the diffraction limited spot size but big enough to provide sufficient amount of optical feedback, a stable link can be maintained and light that hits the retro-reflector’s surrounded area can simultaneously be reconverted into usable electric energy. The phase conjugate feedback ensures that amplifier’s distortions are compensated and the target tracked accurately. After deriving basic arithmetic expressions for the proposed system, a section is devoted for the motivation of free-space laser power transmission which is supposed to find varied applicability in space. As an example, power transmission from a satellite to the earth is described where recently proposed solar power generating structures on high-altitudes receive the power above the clouds to provide constant energy supply. In the experimental part, an A-PCM setup with reflectivity of about RA-PCM = 100 was realized using a semiconductor optical amplifier and a photorefractive self-pumped PCM. Simulation results show that a reflectivity of RA-PCM>1000 could be obtained by improving the self-pumped PCM’s efficiency. That would lead to a transmission efficiency of η>90%.

© 2010 OSA

1. Introduction

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

7. P. E. Glaser, “Power from the Sun: Its Future,” Science 162(3856), 857–861 (1968). [CrossRef] [PubMed]

]. Mainly microwave systems have been considered and analyzed for efficiency and cost-effectiveness in the past due to their mature level of technology [3

3. W. C. Brown, “The technology and application of free-space power transmission by microwave beam,” Proc. IEEE 62(1), 11–25 (1974). [CrossRef]

,8

8. J. C. Mankins, “A fresh look at space solar power: New architectures, concepts and technologies,” Acta Astronaut. 41(4-10), 347–359 (1997). [CrossRef]

]. Regardless of their significant advantage in the ability to penetrate through clouds, laser systems [9

9. R. L. Fork, “High Energy lasers may put power in space,” Laser Focus World 37, 113–117 (2001).

, 10

10. M. Smith, R. L. Fork, and S. Cole, “Safe delivery of optical power from space,” Opt. Express 8(10), 537–546 (2001). [CrossRef] [PubMed]

] 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

11. Znamya space mirror, e.g. V. Syromiatnikov, “Znamya-2 demonstration flight experiment,” http://src.space.ru/page_30e.htm.

] 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

8. J. C. Mankins, “A fresh look at space solar power: New architectures, concepts and technologies,” Acta Astronaut. 41(4-10), 347–359 (1997). [CrossRef]

]. 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

12. G. S. Aglietti, S. Redi, A. R. Tatnall, and T. Markvart, “Harnessing High-Altitude Solar Power,” IEEE J. Energy Conversion 24(2), 442–451 (2009). [CrossRef]

].

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

13. N. Kawashima, “The Importance of Development of a Rover for the Direct Confirmation of the Existence of Ice on the Moon,” Trans. Jpn. Soc. Aeronaut. Space Sci. 43(139), 34–35 (2000). [CrossRef]

].

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

14. G. Landis, “Satellite eclipse power by laser illumination,” Acta Astronaut. 25(4), 229–233 (1991). [CrossRef]

] or transfer orbits [15

15. G. A. Landis, and M. Stavnes, S., Oleson, and J. Bozek, “Space Transfer with Ground-based Laser / Electric Propulsion,” presented at the AIAA-92–3213: Laser Power Beaming 1992, Nashville, TN (United States), 6–8 Jul 1992.

], or structures on the moon during the lunar night [16

16. G. A. Landis, “Moonbase Night Power by Laser Illumination,” AIAA J. Propulsion and Power 8(1), 251–254 (1992). [CrossRef]

].

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

6. A. K. Majumdar, and J. C. Ricklin, Free-Space Laser Communications (Springer, 2008).

], 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

23. H. Bruesselbach, D. C. Jones, D. A. Rockwell, R. C. Lind, and G. Vogel, “Real-time atmospheric compensation by stimulated Brillouin-scattering phase conjugation,” J. Opt. Soc. Am. B 12(8), 1434–1447 (1995). [CrossRef]

].

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
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.
. 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.

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

24. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical Phased Array Technology,” Proc. IEEE 84(2), 268–298 (1996). [CrossRef]

] 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

25. C. A. Schäfer, O. Matoba, and N. Kaya, “Tracking system by phase conjugation for laser energy transmission,” Proc. SPIE 6454, 64540A (2007). [CrossRef]

]. The following equations are therefore limited to a single transmitter for simplicity.

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

27. E. Jakeman and K. D. Ridley, “Incomplete phase conjugation through a random-phase screen. I. Theory,” J. Opt. Soc. Am. A 13(11), 2279–2287 (1996). [CrossRef]

] which derives theory about fidelity and beam spread in the case where parts of the original beam falls out of the PCM’s aperture.

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

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.

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

30. S. van Riesen, U. Schubert, and A. W. Bett, “GaAs photovoltaic cells for laser power beaming at high power densities,” in Proc. 17th Eur. PV Solar Energy Conf., Munich, Germany, 2001, 18−21, Paper VA1/26.

] and even 60% seem to be achievable [30

30. S. van Riesen, U. Schubert, and A. W. Bett, “GaAs photovoltaic cells for laser power beaming at high power densities,” in Proc. 17th Eur. PV Solar Energy Conf., Munich, Germany, 2001, 18−21, Paper VA1/26.

] when using laser light between 790 nm-850 nm. However, conventional Si-based cells might not achieve the same [5

5. H. Miyakawa, Y. Tanaka, and T. Kurokawa, “Design approaches to power-over-optical local-area-network systems,” Appl. Opt. 43(6), 1379-1389 (2004). [CrossRef] [PubMed]

]. 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

31. D. Krut, “PV Devices for Laser Power Conversion,” presented at the International Workshop on the Laser Energy Transmission for Space Exploration and Ground Applications, Nara, Japan 6.-7. Jun. 2004.

].

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

32. M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovolt. Res. Appl. 17(5), 320–326 (2009). [CrossRef]

] might be more suitable than most common Si-based solar cells because of better potential conversion efficiencies for laser light.

In Fig. 4, the conversion efficiency of sunlight is assumed to be 25% which is close to recent results for modules [32

32. M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovolt. Res. Appl. 17(5), 320–326 (2009). [CrossRef]

]. 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 pGround, pHAP and PGEO, respectively. Since the weather conditions have an influence to solar cells on the ground, there is a fundamental difference between pGround to pHAP and pGEO because the latter two are predictable in time and amount. Therefore, they can be employed for base load energy generation. pHAP depends on the altitude h of the HAP. It has been derived that pHAP(h = 6 km)≈35% and pHAP(h = 12 km)≈45% [12

12. G. S. Aglietti, S. Redi, A. R. Tatnall, and T. Markvart, “Harnessing High-Altitude Solar Power,” IEEE J. Energy Conversion 24(2), 442–451 (2009). [CrossRef]

]. PGEO is less than 1 because of the earth’s shadow which sometimes falls onto the satellite. However, pGEO is still about 99% [3

3. W. C. Brown, “The technology and application of free-space power transmission by microwave beam,” Proc. IEEE 62(1), 11–25 (1974). [CrossRef]

].

In contrast, the terrestrial availability pGround depends on the local weather conditions. For middle European conditions, pGround is about 10%. Furthermore, transmission through the atmosphere (indicated by τATM 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. τATM≈0.74) [33

33. ASTM International, Designation G173–03e1, Standard tables for reference solar spectral irradiance: direct normal and hemispherical 37° tilted surface (2006).

].

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

9. R. L. Fork, “High Energy lasers may put power in space,” Laser Focus World 37, 113–117 (2001).

, 34

34. O. Graydon, “Solar power: A sunny solution,” Nat. Photonics 1(9), 495–496 (2007). [CrossRef]

]. 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

3. W. C. Brown, “The technology and application of free-space power transmission by microwave beam,” Proc. IEEE 62(1), 11–25 (1974). [CrossRef]

, 35

35. R. M. Dickenson, “Wireless Power Transmission Technology State of the Art,” Acta Astronaut. 53(4-10), 561–570 (2003). [CrossRef]

].

Altogether, the average collection efficiency ηc is derived for the three different collecting paths by multiplying their total efficiencies with the probabilities: ηc,Ground≈2%, ηc,HAP≈8% and ηc,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

36. K. Reed and H. J. Willenberg, “Early commercial demonstration of space solar power using ultra-lightweight arrays,” Acta Astronaut. 65(9-10), 1250–1260 (2009). [CrossRef]

]. 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

37. T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate fourwave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75(4-5), 493–495 (2002). [CrossRef]

39

39. Y. A. Zakharenkov, T. O. Clatterbuck, V. V. Shkunov, A. A. Betin, D. M. Filgas, E. P. Ostby, F. P. Strohkendl, D. A. Rockwell, and R. S. Baltimore, “2-kW Average Power CW Phase-Conjugate Solid-State Laser,” IEEE J. Sel. Top. Quantum Electron. 13(3), 473–479 (2007). [CrossRef]

].

Figure 5
Fig. 5 High-reflective phase conjugate mirror (PCM) consisting of a self-pumped PCM and an optical amplifier.
shows the arrangement of the amplifier and PCM. Henceforth, RPCM refers to the reflectivity of the self-pumped PCM alone while RA-PCM describes the total reflectivity of the amplifier-PCM (A-PCM) setup. For small incident powers, the optical amplifier‘s single-pass gain Gsp is given by its specified small signal gain G0 and it follows that the reflectivity RA-PCM is simply given by:
RAPCM=G0RPCMG0.
(7)
However, increasing the incident power will lead to gain saturation of the amplifier which reduces the overall reflectivity.

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

40. e.g. M. Summerfield, “Optical Amplifiers (Semiconductor),” in Encyclopedia of Physical Science and Technology, R. A. Meyers, eds. (Elsevier Science Ltd. 2004), pp.219–235.

]:
dPdz=[g(P)γsc]P,
(8)
where P is the optical power, z is the coordinate inside the amplifier, g the gain coefficient and γsc the internal loss. The power dependent gain coefficient g(P) is given by:
g(P)=g01+PPsat,
(9)
where g0 is the gain coefficient for a small signal and Psat a constant depending on the characteristics of the amplifier. For amplifiers with large gain (G0≳100) and no internal losses (γsc = 0), Psat is characterized by:
PsatG0Ps,in2/ln2,
(10)
where Ps,in is the input power at which the output power is equal to Psat [41

41. N. K. Dutta, and Q. Wang, Semiconductor Optical Amplifiers (World Scientific, 2006).

].

Beside the amplified incident signal Pin, optical amplified spontaneous emission (ASE) noise is added to the signal so that the output power is given by:
Pout=GspPin+PASE,
(11)
with:
PASE=μhυΔυ(G01),
(12)
where h is the Planck’s constant, ν the optical frequency and Δν the optical bandwidth of interest. µ is the population inversion factor given by μ=N2/(N2N1) where N1 and N2 are electrons in the ground and exited state, respectively.

For small signals, PASE doesn’t depend much on the input power. For large input power, N2 becomes significantly smaller so that PASE 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

40. e.g. M. Summerfield, “Optical Amplifiers (Semiconductor),” in Encyclopedia of Physical Science and Technology, R. A. Meyers, eds. (Elsevier Science Ltd. 2004), pp.219–235.

].

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

42. A. Minassian, G. J. Crofts, and M. J. Damzen, “A tunable self-pumped phase-conjugate laser using Ti:sapphire slab amplifiers,” Opt. Commun. 161(4-6), 338–344 (1999). [CrossRef]

], 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

43. N. Huot, J.-M. C. Jonathan, and G. Roosen, “Dynamic Wavefront Correction of Nd:YAG Lasers by Self Pumped Phase Conjugation in Photorefractive BaTiO3:Rh,” Proc. IEEE 87(12), 2059–2073 (1999). [CrossRef]

]. 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
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.
. 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.

Phase conjugation was achieved by degenerate four-wave mixing (FWM) [44

44. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20(1), 12–30 (1984). [CrossRef]

]. 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

45. X. Yi and P. Yeh, “Effect of partial coherence on phase conjugation,” Opt. Commun. 147(1-3), 126–130 (1998). [CrossRef]

].

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

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

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

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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indicate a nonlinear dependence with significant reduction below Pin = 20 µW.

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 Icur = 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
Fig. 9 Output power and reflectivity of the PCM-SOA setup as a function of the input power.
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 RA-PCM>90 was obtained which decreased to RA-PCM = 80 for Pin = 23 µW which was the maximum input due to the limited laser’s power of P = 1 mW. The desired decrease of RA-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 Pin≈5 µW is near the “minimum detectable power” which is defined as Pmin = hνΔν [41

41. N. K. Dutta, and Q. Wang, Semiconductor Optical Amplifiers (World Scientific, 2006).

] where h is the Plank’s constant, ν light’s frequency and Δν the FWHM of the emission spectrum and which is Pmin≈4.9 µW for the used SOA.

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 g0sc = 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: Psat = 32mW, γsc = 1mm−1. In general, simulated results could be fitted well to the measured data. Differences are found for low input powers because RPCM was assumed to be constant. In reality, RPCM 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

43. N. Huot, J.-M. C. Jonathan, and G. Roosen, “Dynamic Wavefront Correction of Nd:YAG Lasers by Self Pumped Phase Conjugation in Photorefractive BaTiO3:Rh,” Proc. IEEE 87(12), 2059–2073 (1999). [CrossRef]

, 46

46. M. Jazbinšek, D. Haertle, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Wavelength dependence of visible and near-infrared photorefraction and phase conjugation in Sn2P2S6,” J. Opt. Soc. Am. B 22(11), 2459–2467 (2005). [CrossRef]

].

Compared to the single-pass gain of >100, the obtained overall reflectivity RA-PCM is relatively low and originates in the low reflectivity of the self pumped PCM which was only about RPCM ≈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

47. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7(10), 486–488 (1982). [CrossRef] [PubMed]

] or a ring-cavity phase conjugator [48

48. M. Cronin‐Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self‐induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42(11), 919–921 (1983). [CrossRef]

] 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

49. B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz, “Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate,” Opt. Lett. 19(8), 536–538 (1994). [CrossRef] [PubMed]

] 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

50. G. W. Ross and R. W. Eason, “Highly efficient self-pumped phase conjugation at near-infrared wavelengths by using nominally undoped BaTiO(3),” Opt. Lett. 17(16), 1104–1106 (1992). [CrossRef] [PubMed]

]. Finally, other optical losses like fiber coupling further reduced the PCM’s reflectivity.

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.

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

21. V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978). [CrossRef] [PubMed]

] 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 RA-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 RA-PCM≈2000 is reachable using the same amplifier.

Acknowledgments

The author would like to thank V. Shidlovski from Superlum for useful discussions.

References and links

1.

N. Tesla, “The transmission of electrical energy without wires,” Elec. World Eng. 35, 429–431 (1904).

2.

R. M. Dickinson, “Performance of a High-Power, 2.388-GHz Receiving Array in Wireless Power Transmission Over 1.54 km,” MTT-S Int. Microwave Symp. Digest 76, 139–141 (1976). [CrossRef]

3.

W. C. Brown, “The technology and application of free-space power transmission by microwave beam,” Proc. IEEE 62(1), 11–25 (1974). [CrossRef]

4.

M. Röger, G. Böttger, M. Dreschmann, C. Klamouris, M. Huebner, A. W. Bett, J. Becker, W. Freude, and J. Leuthold, “Optically powered fiber networks,” Opt. Express 16(26), 21821–21834 (2008). [CrossRef] [PubMed]

5.

H. Miyakawa, Y. Tanaka, and T. Kurokawa, “Design approaches to power-over-optical local-area-network systems,” Appl. Opt. 43(6), 1379-1389 (2004). [CrossRef] [PubMed]

6.

A. K. Majumdar, and J. C. Ricklin, Free-Space Laser Communications (Springer, 2008).

7.

P. E. Glaser, “Power from the Sun: Its Future,” Science 162(3856), 857–861 (1968). [CrossRef] [PubMed]

8.

J. C. Mankins, “A fresh look at space solar power: New architectures, concepts and technologies,” Acta Astronaut. 41(4-10), 347–359 (1997). [CrossRef]

9.

R. L. Fork, “High Energy lasers may put power in space,” Laser Focus World 37, 113–117 (2001).

10.

M. Smith, R. L. Fork, and S. Cole, “Safe delivery of optical power from space,” Opt. Express 8(10), 537–546 (2001). [CrossRef] [PubMed]

11.

Znamya space mirror, e.g. V. Syromiatnikov, “Znamya-2 demonstration flight experiment,” http://src.space.ru/page_30e.htm.

12.

G. S. Aglietti, S. Redi, A. R. Tatnall, and T. Markvart, “Harnessing High-Altitude Solar Power,” IEEE J. Energy Conversion 24(2), 442–451 (2009). [CrossRef]

13.

N. Kawashima, “The Importance of Development of a Rover for the Direct Confirmation of the Existence of Ice on the Moon,” Trans. Jpn. Soc. Aeronaut. Space Sci. 43(139), 34–35 (2000). [CrossRef]

14.

G. Landis, “Satellite eclipse power by laser illumination,” Acta Astronaut. 25(4), 229–233 (1991). [CrossRef]

15.

G. A. Landis, and M. Stavnes, S., Oleson, and J. Bozek, “Space Transfer with Ground-based Laser / Electric Propulsion,” presented at the AIAA-92–3213: Laser Power Beaming 1992, Nashville, TN (United States), 6–8 Jul 1992.

16.

G. A. Landis, “Moonbase Night Power by Laser Illumination,” AIAA J. Propulsion and Power 8(1), 251–254 (1992). [CrossRef]

17.

F. Steinsiek, W. P. Foth, K. H. Weber, C. A. Schäfer, and H. J. Foth, “Method and apparatus for transmitting energy via a laser beam,” European Patent 1566902 (2005), US Patent 7423767 (2008).

18.

A. Erteza, “Boresighting a Gaussian beam on a specular target point: a method using conical scan,” Appl. Opt. 15(3), 656–660 (1976). [CrossRef] [PubMed]

19.

I. Buske and W. Riede, “Sub-µrad laser beam tracking,” Proc. SPIE 6397, 63970J (2006). [CrossRef]

20.

F. Steinsiek, W. P. Foth, K. H. Weber, C. A. Schäfer, and H. J. Foth, “Wireless power transmission experiments an early contribution to planetary exploration missions,” in Proc. 54th International Astronautical Congress, Bremen, Germany, 29 Sept.–4 Oct. 2003, Paper IAC-03-R.3.06.

21.

V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978). [CrossRef] [PubMed]

22.

P. S. Lebow and J. R. Ackerman, “Phase conjugation through Brillouin-enhanced four-wave mixing over an extended atmospheric path,” Opt. Lett. 14(4), 236–238 (1989). [CrossRef] [PubMed]

23.

H. Bruesselbach, D. C. Jones, D. A. Rockwell, R. C. Lind, and G. Vogel, “Real-time atmospheric compensation by stimulated Brillouin-scattering phase conjugation,” J. Opt. Soc. Am. B 12(8), 1434–1447 (1995). [CrossRef]

24.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical Phased Array Technology,” Proc. IEEE 84(2), 268–298 (1996). [CrossRef]

25.

C. A. Schäfer, O. Matoba, and N. Kaya, “Tracking system by phase conjugation for laser energy transmission,” Proc. SPIE 6454, 64540A (2007). [CrossRef]

26.

R. Pascotta, “Encyclopedia of Laser Physics and Technology-Beam Quality,” http://www.rp-photonics.com/beam_quality.html.

27.

E. Jakeman and K. D. Ridley, “Incomplete phase conjugation through a random-phase screen. I. Theory,” J. Opt. Soc. Am. A 13(11), 2279–2287 (1996). [CrossRef]

28.

R. Pascotta, “Encyclopedia of Laser Physics and Technology-Laser Diodes,” http://www.rp-photonics.com/laser_diodes.html.

29.

e.g. “ EksmaOptics,” http://www.eksmaoptics.com/en, or “Jenoptik,” http://www.jold.com.

30.

S. van Riesen, U. Schubert, and A. W. Bett, “GaAs photovoltaic cells for laser power beaming at high power densities,” in Proc. 17th Eur. PV Solar Energy Conf., Munich, Germany, 2001, 18−21, Paper VA1/26.

31.

D. Krut, “PV Devices for Laser Power Conversion,” presented at the International Workshop on the Laser Energy Transmission for Space Exploration and Ground Applications, Nara, Japan 6.-7. Jun. 2004.

32.

M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovolt. Res. Appl. 17(5), 320–326 (2009). [CrossRef]

33.

ASTM International, Designation G173–03e1, Standard tables for reference solar spectral irradiance: direct normal and hemispherical 37° tilted surface (2006).

34.

O. Graydon, “Solar power: A sunny solution,” Nat. Photonics 1(9), 495–496 (2007). [CrossRef]

35.

R. M. Dickenson, “Wireless Power Transmission Technology State of the Art,” Acta Astronaut. 53(4-10), 561–570 (2003). [CrossRef]

36.

K. Reed and H. J. Willenberg, “Early commercial demonstration of space solar power using ultra-lightweight arrays,” Acta Astronaut. 65(9-10), 1250–1260 (2009). [CrossRef]

37.

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate fourwave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75(4-5), 493–495 (2002). [CrossRef]

38.

T. Omatsu and M. J. Damzen, “Multi-watt CW output from a double-pass diode side-pumped Nd:YVO4 amplifier with a Rh:BaTiO3 phase conjugator,” Opt. Commun. 198(1-3), 135–139 (2001). [CrossRef]

39.

Y. A. Zakharenkov, T. O. Clatterbuck, V. V. Shkunov, A. A. Betin, D. M. Filgas, E. P. Ostby, F. P. Strohkendl, D. A. Rockwell, and R. S. Baltimore, “2-kW Average Power CW Phase-Conjugate Solid-State Laser,” IEEE J. Sel. Top. Quantum Electron. 13(3), 473–479 (2007). [CrossRef]

40.

e.g. M. Summerfield, “Optical Amplifiers (Semiconductor),” in Encyclopedia of Physical Science and Technology, R. A. Meyers, eds. (Elsevier Science Ltd. 2004), pp.219–235.

41.

N. K. Dutta, and Q. Wang, Semiconductor Optical Amplifiers (World Scientific, 2006).

42.

A. Minassian, G. J. Crofts, and M. J. Damzen, “A tunable self-pumped phase-conjugate laser using Ti:sapphire slab amplifiers,” Opt. Commun. 161(4-6), 338–344 (1999). [CrossRef]

43.

N. Huot, J.-M. C. Jonathan, and G. Roosen, “Dynamic Wavefront Correction of Nd:YAG Lasers by Self Pumped Phase Conjugation in Photorefractive BaTiO3:Rh,” Proc. IEEE 87(12), 2059–2073 (1999). [CrossRef]

44.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20(1), 12–30 (1984). [CrossRef]

45.

X. Yi and P. Yeh, “Effect of partial coherence on phase conjugation,” Opt. Commun. 147(1-3), 126–130 (1998). [CrossRef]

46.

M. Jazbinšek, D. Haertle, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Wavelength dependence of visible and near-infrared photorefraction and phase conjugation in Sn2P2S6,” J. Opt. Soc. Am. B 22(11), 2459–2467 (2005). [CrossRef]

47.

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7(10), 486–488 (1982). [CrossRef] [PubMed]

48.

M. Cronin‐Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self‐induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42(11), 919–921 (1983). [CrossRef]

49.

B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz, “Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate,” Opt. Lett. 19(8), 536–538 (1994). [CrossRef] [PubMed]

50.

G. W. Ross and R. W. Eason, “Highly efficient self-pumped phase conjugation at near-infrared wavelengths by using nominally undoped BaTiO(3),” Opt. Lett. 17(16), 1104–1106 (1992). [CrossRef] [PubMed]

51.

I. V. Kedyk, P. Mathey, G. Gadret, O. Bidault, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Enhanced photorefractive properties of Bi-doped Sn2P2S6,” J. Opt. Soc. Am. B 25(2), 180–186 (2008). [CrossRef]

52.

T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt. 44(30), 6388–6401 (2005). [CrossRef] [PubMed]

53.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garrett, and D. Rytz, “Impurity enhanced self-pumped phase conjugation in the near infrared in `blue' BaTiO3,” Opt. Commun. 101(1-2), 60–64 (1993). [CrossRef]

54.

T. Omatsu, A. Minassian, and M. J. Damzen, “High Quality 7.5 W Continuous-Wave Operation of a Nd:YVO4 Laser with a Rh:BaTiO3 Phase Conjugate Mirror,” Jpn. J. Appl. Phys. 41(Part 1, No. 4A), 2024–2027 (2002). [CrossRef]

55.

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5(10), 1550–1567 (1966). [CrossRef] [PubMed]

56.

D. Udaiyan, G. J. Crofts, T. Omatsu, and M. J. Damzen, “Self-consistent spatial mode analysis of self-adaptive laser oscillators,” J. Opt. Soc. Am. B 15(4), 1346–1352 (1998). [CrossRef]

OCIS Codes
(070.5040) Fourier optics and signal processing : Phase conjugation
(260.2160) Physical optics : Energy transfer
(230.4480) Optical devices : Optical amplifiers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 26, 2010
Revised Manuscript: May 31, 2010
Manuscript Accepted: May 31, 2010
Published: June 8, 2010

Citation
Christian A. Schäfer, "Continuous adaptive beam pointing and tracking for laser power transmission," Opt. Express 18, 13451-13467 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13451


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References

  1. N. Tesla, “The transmission of electrical energy without wires,” Elec. World Eng. 35, 429–431 (1904).
  2. R. M. Dickinson, “Performance of a High-Power, 2.388-GHz Receiving Array in Wireless Power Transmission Over 1.54 km,” MTT-S Int. Microwave Symp. Digest 76, 139–141 (1976). [CrossRef]
  3. W. C. Brown, “The technology and application of free-space power transmission by microwave beam,” Proc. IEEE 62(1), 11–25 (1974). [CrossRef]
  4. M. Röger, G. Böttger, M. Dreschmann, C. Klamouris, M. Huebner, A. W. Bett, J. Becker, W. Freude, and J. Leuthold, “Optically powered fiber networks,” Opt. Express 16(26), 21821–21834 (2008). [CrossRef] [PubMed]
  5. H. Miyakawa, Y. Tanaka, and T. Kurokawa, “Design approaches to power-over-optical local-area-network systems,” Appl. Opt. 43(6), 1379-1389 (2004). [CrossRef] [PubMed]
  6. A. K. Majumdar and J. C. Ricklin, Free-Space Laser Communications (Springer, 2008).
  7. P. E. Glaser, “Power from the Sun: Its Future,” Science 162(3856), 857–861 (1968). [CrossRef] [PubMed]
  8. J. C. Mankins, “A fresh look at space solar power: New architectures, concepts and technologies,” Acta Astronaut. 41(4-10), 347–359 (1997). [CrossRef]
  9. R. L. Fork, “High Energy lasers may put power in space,” Laser Focus World 37, 113–117 (2001).
  10. M. Smith, R. L. Fork, and S. Cole, “Safe delivery of optical power from space,” Opt. Express 8(10), 537–546 (2001). [CrossRef] [PubMed]
  11. Znamya space mirror, e.g. V. Syromiatnikov, “Znamya-2 demonstration flight experiment,” http://src.space.ru/page_30e.htm .
  12. G. S. Aglietti, S. Redi, A. R. Tatnall, and T. Markvart, “Harnessing High-Altitude Solar Power,” IEEE J. Energy Conversion 24(2), 442–451 (2009). [CrossRef]
  13. N. Kawashima, “The Importance of Development of a Rover for the Direct Confirmation of the Existence of Ice on the Moon,” Trans. Jpn. Soc. Aeronaut. Space Sci. 43(139), 34–35 (2000). [CrossRef]
  14. G. Landis, “Satellite eclipse power by laser illumination,” Acta Astronaut. 25(4), 229–233 (1991). [CrossRef]
  15. G. A. Landis, and M. Stavnes, S., Oleson, and J. Bozek, “Space Transfer with Ground-based Laser / Electric Propulsion,” presented at the AIAA-92–3213: Laser Power Beaming 1992, Nashville, TN (United States), 6–8 Jul 1992.
  16. G. A. Landis, “Moonbase Night Power by Laser Illumination,” AIAA J. Propulsion and Power 8(1), 251–254 (1992). [CrossRef]
  17. F. Steinsiek, W. P. Foth, K. H. Weber, C. A. Schäfer, and H. J. Foth, “Method and apparatus for transmitting energy via a laser beam,” European Patent 1566902 (2005), US Patent 7423767 (2008).
  18. A. Erteza, “Boresighting a Gaussian beam on a specular target point: a method using conical scan,” Appl. Opt. 15(3), 656–660 (1976). [CrossRef] [PubMed]
  19. I. Buske and W. Riede, “Sub-µrad laser beam tracking,” Proc. SPIE 6397, 63970J (2006). [CrossRef]
  20. F. Steinsiek, W. P. Foth, K. H. Weber, C. A. Schäfer, and H. J. Foth, “Wireless power transmission experiments an early contribution to planetary exploration missions,” in Proc. 54th International Astronautical Congress, Bremen, Germany, 29 Sept.–4 Oct. 2003, Paper IAC-03-R.3.06.
  21. V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978). [CrossRef] [PubMed]
  22. P. S. Lebow and J. R. Ackerman, “Phase conjugation through Brillouin-enhanced four-wave mixing over an extended atmospheric path,” Opt. Lett. 14(4), 236–238 (1989). [CrossRef] [PubMed]
  23. H. Bruesselbach, D. C. Jones, D. A. Rockwell, R. C. Lind, and G. Vogel, “Real-time atmospheric compensation by stimulated Brillouin-scattering phase conjugation,” J. Opt. Soc. Am. B 12(8), 1434–1447 (1995). [CrossRef]
  24. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical Phased Array Technology,” Proc. IEEE 84(2), 268–298 (1996). [CrossRef]
  25. C. A. Schäfer, O. Matoba, and N. Kaya, “Tracking system by phase conjugation for laser energy transmission,” Proc. SPIE 6454, 64540A (2007). [CrossRef]
  26. R. Pascotta, “Encyclopedia of Laser Physics and Technology-Beam Quality,” http://www.rp-photonics.com/beam_quality.html .
  27. E. Jakeman and K. D. Ridley, “Incomplete phase conjugation through a random-phase screen. I. Theory,” J. Opt. Soc. Am. A 13(11), 2279–2287 (1996). [CrossRef]
  28. R. Pascotta, “Encyclopedia of Laser Physics and Technology-Laser Diodes,” http://www.rp-photonics.com/laser_diodes.html .
  29. e.g. “ EksmaOptics,” http://www.eksmaoptics.com/en , or “Jenoptik,” http://www.jold.com .
  30. S. van Riesen, U. Schubert, and A. W. Bett, “GaAs photovoltaic cells for laser power beaming at high power densities,” in Proc. 17th Eur. PV Solar Energy Conf., Munich, Germany, 2001, 18−21, Paper VA1/26.
  31. D. Krut, “PV Devices for Laser Power Conversion,” presented at the International Workshop on the Laser Energy Transmission for Space Exploration and Ground Applications, Nara, Japan 6.-7. Jun. 2004.
  32. M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, “Solar cell efficiency tables (Version 34),” Prog. Photovolt. Res. Appl. 17(5), 320–326 (2009). [CrossRef]
  33. ASTM International, Designation G173–03e1, Standard tables for reference solar spectral irradiance: direct normal and hemispherical 37° tilted surface (2006).
  34. O. Graydon, “Solar power: A sunny solution,” Nat. Photonics 1(9), 495–496 (2007). [CrossRef]
  35. R. M. Dickenson, “Wireless Power Transmission Technology State of the Art,” Acta Astronaut. 53(4-10), 561–570 (2003). [CrossRef]
  36. K. Reed and H. J. Willenberg, “Early commercial demonstration of space solar power using ultra-lightweight arrays,” Acta Astronaut. 65(9-10), 1250–1260 (2009). [CrossRef]
  37. T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate fourwave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75(4-5), 493–495 (2002). [CrossRef]
  38. T. Omatsu and M. J. Damzen, “Multi-watt CW output from a double-pass diode side-pumped Nd:YVO4 amplifier with a Rh:BaTiO3 phase conjugator,” Opt. Commun. 198(1-3), 135–139 (2001). [CrossRef]
  39. Y. A. Zakharenkov, T. O. Clatterbuck, V. V. Shkunov, A. A. Betin, D. M. Filgas, E. P. Ostby, F. P. Strohkendl, D. A. Rockwell, and R. S. Baltimore, “2-kW Average Power CW Phase-Conjugate Solid-State Laser,” IEEE J. Sel. Top. Quantum Electron. 13(3), 473–479 (2007). [CrossRef]
  40. e.g. M. Summerfield, “Optical Amplifiers (Semiconductor),” in Encyclopedia of Physical Science and Technology, R. A. Meyers, eds. (Elsevier Science Ltd. 2004), pp.219–235.
  41. N. K. Dutta and Q. Wang, Semiconductor Optical Amplifiers (World Scientific, 2006).
  42. A. Minassian, G. J. Crofts, and M. J. Damzen, “A tunable self-pumped phase-conjugate laser using Ti:sapphire slab amplifiers,” Opt. Commun. 161(4-6), 338–344 (1999). [CrossRef]
  43. N. Huot, J.-M. C. Jonathan, and G. Roosen, “Dynamic Wavefront Correction of Nd:YAG Lasers by Self Pumped Phase Conjugation in Photorefractive BaTiO3:Rh,” Proc. IEEE 87(12), 2059–2073 (1999). [CrossRef]
  44. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20(1), 12–30 (1984). [CrossRef]
  45. X. Yi and P. Yeh, “Effect of partial coherence on phase conjugation,” Opt. Commun. 147(1-3), 126–130 (1998). [CrossRef]
  46. M. Jazbinšek, D. Haertle, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Wavelength dependence of visible and near-infrared photorefraction and phase conjugation in Sn2P2S6,” J. Opt. Soc. Am. B 22(11), 2459–2467 (2005). [CrossRef]
  47. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7(10), 486–488 (1982). [CrossRef] [PubMed]
  48. M. Cronin‐Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self‐induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42(11), 919–921 (1983). [CrossRef]
  49. B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz, “Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate,” Opt. Lett. 19(8), 536–538 (1994). [CrossRef] [PubMed]
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