High brightness solid-state phase-conjugate lasers for space applications
Even today, the experience of using lasers in space covers a wide range of tasks: laser scanning devices are used for docking space vehicles [1–3], spaceborne lidars carry out remote sensing of the Earth and other celestial bodies [4–7], near-Earth space is controlled by laser locators [8–10], high-speed space laser links are implemented [11, 12].
Laser equipment for solving these problems is a part of the service load of the space vehicles with relatively low mass and dimensional characteristics, it consumes, on average, no more than 100–150 W in the active mode.
In the long term [13, 14], the lasers are in demand to remove space debris from near-Earth space [15–17], remote power supply of space vehicles [18, 19], anti-asteroid protection of the Earth , as well as acceleration of space vehicles [21, 22] for interorbital flights in near-Earth space and flights to the outer space. Laser systems (Fig. 1) for these applications require power supply with a power of more than 100 kW and, in many ways, determine the shape of the carrier vehicle.
In this article, based on the system method, the role and place of lasers in modern space technology are evaluated, the requirements and approaches to the construction of lasers for a number of space applications are justified, and the results of studies of high brightness solid-state phase-conjugate lasers which, in the opinion of the authors, are of practical interest for application in outer space, are given.
LASER REQUIREMENTS FOR SPACE APPLICATIONS
The potential of a large-scale application of lasers in space is due to the fact that it is in this medium that the narrowly directed transmission of energy and information over long distances along the laser beam is the least exposed to physical limitations. Therefore, lasers will be most in demand in solving similar problems.
On the one hand, there is no disturbing effect of the optical inhomogeneities of the atmosphere in space. This makes it possible, with distance focusing of the radiation, to approach the limitations caused by the diffraction limit. Furthermore, there is no absorption of radiation along the space path.
On the other hand, high brightness laser sources are needed for space applications. The reason is that the energy density of radiation delivered to the probed object (scope) is inversely proportional to the second power of the range value:
ED = ( 4 · Ep ) / ( π θ2 · L2 ),
θ = M2 · 1,06 · λ / dt,
where ED is the energy density [J / m2] of the radiation on the target, Ep is the energy of the pulse, L is the distance to the object of detection, θ is the divergence of the laser radiation at half the energy level, M2 is the parameter of the optical quality of the radiation, λ is the laser wavelength, dt is the diameter of transmitting telescope with filled aperture.
In the problems of locating small remote objects, the energy Er of the radiation scattered by the object detected by the receiving laser locator system is inversely proportional to the range in the fourth power:
Er = ( Ep · A · Seff · dr2 ) / ( 2 π · θ2 · L4 ),
where, A is the albedo of the detection object, Seff is the effective reflection cross-section, and dr is the diameter of the receiving aperture.
Thus, at long distances (over 100 km), the main requirement for lasers for space applications is to provide simultaneously high energy and the minimum possible divergence of the laser beam. In other words, the high brightness sources of laser radiation are needed . Depending on the task, the requirements are imposed on the energy, time, spatial and spectral parameters of the space laser.
LASERS FOR SPACEBORNE LIDARS
Laser location and lidar systems are widely used  on the Earth and in space, where laser sources are usually used [4, 6–8, 25] with a pulse energy of 0.1–10 J, duration 0.1–10 ns, repetition frequency 1–100 Hz, peak power over 1 MW and optical quality of radiation M2 ~ 1.1–1.5.
Lasers for energy transmission in space
The vast majority of scientific results in the field of remote transmission of electric energy by means of directed electromagnetic radiation are related to the problems of creating large space solar power plants (SSPP) , transforming solar energy into electrical energy and its subsequent delivery to the Earth by means of laser or microwave radiation.
At the current moment, the estimates of the capital and operating costs of creating SSPPs with the corresponding ground infrastructure did not allowe us to talk about how a reasonable cost of kW-h thus obtained on the Earth. At the same time, the SSPP technology is quite competitive for the creation of a heavy space platform with an energy capacity of tens and hundreds of kilowatts, and in combination with a powerful high brightness laser system – for remote power supply to potential spaceborne consumers.
For these space applications, it is rational to use continuous solid-state lasers, including fiber and semiconductor ones, that provide an acceptable efficiency of the entire energy circuit [18, 19].
Lasers for removing space debris and space vehicles acceleration
Steady growth in the number of objects classified as space debris (SD), in conditions of increasingly intensive development of near-Earth space, has already become critical today. It threatens the safety and efficiency of space flights. 
A far-reaching and perhaps the only real method for large-scale removal of small debris from near-Earth orbit is remote SD exposure to laser radiation in the ablation regime. As a result of such an exposer, the SD object is given a reactive pulse that corrects its trajectory in order to prevent collisions of the SD with the active space vehicle and with each other. It also removes SD to either the burial orbit, or to dense layers of the Earth’s atmosphere with subsequent combustion.
Preliminary estimates of the laser accommodation with an average power of 25 kW on a space platform indicate an acceptable performance of removing small debris from the low near-Earth orbits. A laser system with a wavelength of ~ 1 µm, a pulse energy of 500 J, a pulse duration of 10–8 s, a transmitting telescope with a diameter of 1.5 m, as a result of a single 10 s ablative effect on SD with a pulse repetition rate of 50 Hz, will decelerate small SD with the overall mass ratio ~ 10 cm2/g at ΔV ~ 300 km/h. For the same deceleration of the SD with a ratio of ~ 1 cm2/g, several sessions of laser pulses with a total amount of ~ 5000 are required.
Thus, lasers with an average power exceeding 25 kW, generating pulses with an energy of 0.1–1.5 kJ, a duration of 0.1–10 ns, a repetition frequency of 50–100 Hz, a peak power of more than 1 GW and an optical quality of radiation M2 ~ 1.2–2.5 are considered for ablation exposure on space debris [15, 16].
A further increase in energy in the pulse opens the possibility of ablation deceleration of dangerous asteroids  in order to prevent their collision with the Earth, as well as ablation acceleration of the space vehicles [21, 22] in order to provide interorbital maneuvering in the near-Earth space and long-range space flights.
Solid-state phase-conjugate lasers
Achieving high brightness of laser radiation, and therefore high energy in the pulse with a relatively small divergence, is possible by phase conjugation. During the last decades, the variety of solid-state lasers based on the phase conjugation effect, which has a unique set of energy, temporal, spatial and spectral characteristics of radiation, has increased significantly. The key difference between lasers with phase conjugation from the analogs is the selection of longitudinal and transverse modes resulting from self-Q-switching of the resonator, obtained as a result of self-action, rather than artificially formed with the help of additional optical elements. The corresponding gain in the mass and dimensional characteristics of phase-conjugated lasers enhances the attractiveness of their use in outer space.
The propagation of radiation in a laser resonator with self-intersecting beams in an active third-order nonlinear medium leads to a change in its optical properties. As a result of four-wave mixing, gratings of the refractive index, the absorption index and the gain factor are formed in response to the volume periodic distribution of the radiation intensity in the region of intersection of the beams (Fig. 2). Diffraction on the gratings of the gain leads to an energy exchange between the beams, which makes it possible to create a self-pumping PC mirror that supports positive feedback.
The effect of phase conjugation by mixing waves in an active medium can be implemented in any nonlinear medium of the third order. In the media with a high absorption cross section, the generation of the radiation from a PC laser is formed by a relatively small number of passes through the resonator and is close in spatial and spectral characteristics to spontaneous luminescence, since an insufficient number of cycles of the grating re-recording leads to insufficient mode selection. On the other hand, in the media with a low absorption cross section and a high generation threshold, the amplification factor necessary for the development of lasing will be higher. At a sufficiently high pump energy, it is possible to generate lasing without an output mirror of a PC laser resonator.
The rational solution is to use the available medium: YAG : Nd3+ with a relatively low absorption cross section, while increasing the efficiency of the resonator by increasing the number of self-intersections of the beams in the active medium and recording additional gratings. The joint operation of a large number of gratings leads to an increase in the efficiency of phase conjugation and an improvement in the radiation parameters.
In phase-conjugate lasers, the traditional decrease in the quality of radiation with increasing energy parameters does not occur, due to the increase in the diffraction efficiency of the gratings of the gain factor, proportional to the contrast V of the grating:
V = 2 · ( I1 · I2 )0,5 / ( I1 + I2 ),
where I1, I2 are the intensities of the beams recording the grating.
In , the characteristics of the YAG : Nd3+ PC laser radiation with diode multi-kilowatt pumping were compared with different configurations of the loop resonator (Fig. 3). It is shown that an increase in the number of loops from two to four leads to a twofold increase in the energy in the pulse at equal pump energies due to an increase in the number of gratings and their diffraction efficiency.
In combination with the compensation of distortions due to the propagation of phase-conjugate radiation, this leads to a paradoxical increase in the quality of radiation with increasing power. Furthermore, the dynamic gain gratings produce an angular selection of the radiation, which makes it possible to obtain radiation with a divergence close to the diffraction limit. Thus, in the free-running regime, the energy in a train of pulses, depending on the configuration of the resonator, reached a level of 0.5–1.25 J with a radiation quality parameter M2 = 1.15–1.5, while the energy growth in the train was accompanied by an increase in the optical quality.
Since the grating diffraction efficiency of the gain factor depends directly on the intensities of the interfering beams, a longitudinal mode competition arises in the phase-conjugate laser, which leads to the natural selection of a single frequency mode. This makes it possible to obtain single pulses with a bandwidth equal to the width of one 350 MHz mode using a loop resonator (instead of 30 GHz, the bandwidth of multimode laser generation with a Fabry-Perot resonator). In this case, the bandwidth of the pulse train generation remains equal to the width of the laser generation band with the Fabry-Perot resonator, since the amplification of various longitudinal modes has a random character and the dominant frequency is randomly selected in the amplification band range.
The use of the output mirror as a source of additional feedback leads to an increase in the energy in the pulse, but it affects the spectral properties, in this case there is no selection of longitudinal modes. The use of additional intracavity selectors, such as the stationary Bragg grating or the Sagnac interferometer, leads to an additional selection of longitudinal modes, which leads to an increase in the efficiency of the gratings.
Since pulse development and feedback enhancement occur in the phase-conjugate laser as the intensity of the intra-resonator beams increases, self-Q-switching occurs, which leads to a shortening of the radiation pulse duration from 400–500 ns to 200–300 ns and an increase in the peak radiation power.
In the case of insufficient self-Q-switching of the resonator, which arises from the PC effect, it is possible to use passive saturable absorbers. They make it possible to increase the peak power of the generated radiation, not only due to the intrinsic modulation of the generation threshold, but also due to the influence on the intensity of intracavity beams recording the grating gain factor. Variation of the initial gate transmission coefficient allows changing the peak power and energy in the pulse within several orders of magnitude.
It was shown in  that the use of a saturable YAG : Cr4+ absorber with a transmission coefficient of 5% in a YAG : Nd3+ laser with diode multi-kilowatt pumping and a loop resonator makes it possible to obtain pulses with a peak power of up to 30 MW. The variation of the initial transmission of the YAG : Cr4+ and GSGG : Cr4+ gates in the range of 5–55% makes it possible to change the peak power in the pulse from 250 kW to 30 MW with a change in the energy in the lasing train within 20% (Fig. 4). Such a significant range of peak radiation power makes it possible to implement the same effect at distances differing by several orders of magnitude without a significant change in the thermal regime of the laser operation.
Further increase of energy in the pulse can be achieved by increasing the pump energy or by adding, including coherent, radiation from several laser channels. In , the characteristics of the radiation of a YAG : Nd3+ laser based on a high power laser head have been studied. In a passive Q-switched mode with beam intersection in a saturable LiF: F2 absorber with an initial transmission of 10%, a pulse train with an energy of 2.55 J and a radiation quality parameter M2 ≤ 1.2 were obtained with a divergence of 0.35 mrad and a spatial brightness of 7 · 1014 W · cm–2 · sr–1. Peak power of single-frequency pulses exceeded 21 MW at their energy of 230 mJ. An increase in the peak power of the radiation from the phase-conjugate laser can be achieved by active Q-switching.
Thus, phase-conjugate lasers are the tools with the possibility of varying energy and spectral characteristics in a wide range. This ensures the versatility of the laser installation for a wide range of applications and the ability to quickly change the generation parameters both within the same or different applications.
APPROACHES TO BUILDING THE LASERS FOR SPACE APPLICATIONS
Solid-state lasers, including fiber and semiconductor lasers, remain in the focus of attention of developers of spaceborne lidar and location technology due to acceptable energy efficiency, operational experience in space conditions, relative simplicity and ease of use.
The power of solid-state lasers is limited by the radiation stability of their active media, the limiting dimensions of which, in turn, are restricted by the technologies of growth (manufacture). The problem of amplified spontaneous emission, especially relevant in the case of wide-aperture disk active elements, is also limiting. The issues of ensuring thermal regimes are of critical importance.
High brightness of radiation in solid-state lasers is achieved using the "master oscillator + amplifier" architecture. An alternative to this solution can be implemented in a solid-state laser with the help of the phase conjugation effect with four-wave mixing. Solid-state phase-conjugate lasers provide the possibility of varying the radiation characteristics over a wide range while maintaining high brightness, which makes it possible to use them optimally in lidar and location space technology.
For solid-state lasers of large average power, including those capable of providing pulsed-periodic operation modes with extremely high pulse energies, required for ablation, long negative optical quality of radiation was considered the main drawback, which did not allow them to be considered for long-distance applications.
However, as has been shown recently [31–34], obtaining high brightness at a high average power of laser radiation becomes an achievable task if several physical phenomena are used: phase conjugation (to compensate for the wave front distortion in the amplifying stage) and the coherent addition of the emission of several channels (allowing to increase the total brightness of radiation in proportion to the square of the number of laser channels).
Modern approaches to the coherent addition consist in phasing and synchronizing the emission of individual laser channels by implementing the phase conjugation effect in stimulated Brillouin scattering or four-wave mixing in a laser active medium. The options of lasers for space applications are summarized in the table below.
High brightness solid-state phase-conjugate lasers remain an up-to-date research area, including in the interests of practical applications in space technology for solving lidar and location problems, energy transfer, ablation removal of space debris from the near-Earth orbits and ablation acceleration of space vehicles.