Wireless optical communication system based on multiplexing and demultiplexing of orbital angular momentum modes

Abstract

FIELD: data transmission systems; laser technology; fiber optics.SUBSTANCE: invention can be used for wireless optical communications, quantum communications and data protection. A wireless optical communication device is proposed, which includes an optical transmitter comprising: a first optical element dividing an incident beam into a given number of spatially separated beams – channels and forming a grid of spatially separated beams, implementing modulation of the complex amplitude of the spatially separated beams, encoding information data; combining the channels into a single multiplexed beam; an optical receiver receiving the multiplexed beam and comprising a second optical element implementing spatial separation by modes for demultiplexing the received beam and decoding the information; a detector configured to receive demultiplexed modes from the second optical element, a control module including: a control computer setting the parameters of the information signal, a computing unit implementing a discrete Fourier transform of the binary information signal and converting the binary information signal into a discrete set of signals for controlling a multichannel optimizing phase processor and an amplitude controller.EFFECT: forming a phased optical array that generates a synthesized beam having a spectrum of orbital angular momentum modes that correspond to a set of orthogonal modes determined by the Fourier transform of an information signal, propagating the synthesized beam through the free atmosphere, receiving the synthesized beam and demultiplexing the received radiation by an orbital angular momentum mode sorter into a certain number of spatially separated modes corresponding to different modes of the orbital angular momentum of the received radiation and recording them, wherein the set of registered modes at each moment in time determines a binary sequence corresponding to the information signal.2 cl, 12 dwg

Description

[0001] The invention relates to data transmission systems, laser technology and fiber optics and can be used for wireless optical communications, quantum communications and data protection by increasing the effective number of degrees of freedom of electromagnetic radiation as a result of using orthogonal vortex modes, which are the result of decomposing an electromagnetic wave into a spectrum of orbital angular momentum modes.

[0002] The proposed device is based on the principles of beam formation by an optical phased array and decomposition of the formed beams into orthogonal modes.

[0003] After it was shown in 1992 (Allen L., Beijersbergen MW, Spreeuw RJC, Woerdman JP Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. / / Phys. Rev. A. 1992. V. 45, P. 8115-8189) that Laguerre-Gaussian beams containing an azimuthal phase factor in the analytical formulation have an orbital angular momentum (OAM), and the OAM modes are orthogonal, i.e. can be independently registered, an idea arose, along with other effective applications, to use OAM beams for transmitting information in fiber and wireless optical communication systems (Gibson G., Courtial J., Padgett M.J. Vasnetsov M., Pas'ko V., Barnett SM, Franke-Arnold S. Free-space information transfer using light beams carrying orbital angular momentum. / / Opt. Express. 2004. V. 12, N. 22, P. 5448-5456).The interest in using OAM waves as information carriers is due to the fact that traditional methods of signal modulation in time, amplitude, frequency, phase and polarization have practically reached their limit in expanding the bandwidth of the information channel, and the use of OAM provides additional degrees of freedom for signal modulation and multiplexing (Willner AE, Zhao Z., Liu C., Zhang R., et al. Perspectives on advances in high-capacity, free-space communications using multiplexing of orbital-angular-momentum beams. / / APL Photonics. 2021. V.6, N. 030901, P. 1-28). Currently, using OAM multiplexing, a data transmission rate of 1.036 Pbps has been achieved in a laboratory environment using 26 OAM modes and 368 wavelengths, and in a real atmosphere, a signal transmission distance of 260 m and a data transmission rate of 80 Gbps have been achieved using two OAM modes and quadrature amplitude modulation (16-QAM) (Hu Z., Li Y., Chen Z., Benton DMet al. Aiming for high-capacity multi-modal free-space optical transmission leveraging complete modal basis sets. / / Opt. Communs. 2023. V. 541, N. 129-531, pp. 1-16). At the same time, the practical use of OAM waves is constrained by the need to generate, multiplex, and demultiplex a large number of OAM modes, high intermode crosstalk between the multiplexer and demultiplexer, and the low power of the information signal. In this case, OAM modes are used only as a means of multiplexing / demultiplexing, and the modulation of the information signal carried by the OAM mode occurs using traditional methods. On the other hand, the potential for scaling the transmitted power inherent in systems based on coherent laser beam combining (CLB), for which data transmission distances of more than 10 km have been achieved, is not sufficiently utilized (Balasiano O., Wohlgemuth E., Attia I., Roizman A., Falk T., Vered R., Sadot D.Demonstration of coherent beam combining for atmospheric free space optical communication over 10 km. / / J. Lightwave Technol. 2024. V. 42, N. 20, P.7085-7094).

[0004] In the paper by Shu B., Zhang Y., Chang H. et al. Integrated coherent combining system for optical-angular-momentum shift-keying-based free space optical links. / / Adv. Photonics Nexus. 2024. V. 3, N. 3, P. 036003-1 – 036003-11 an integrated system of coherent beam combining for optical communication lines in free space based on digital signal transmission by means of orbital angular momentum modulation (OAM) is described. The system consists of three parts: OAM multiplexing, OAM filtering and propagation, and OAM demultiplexing. Generation and multiplexing of multiple (N) beams possessing orbital angular momentum is performed by a multi-aperture OAM beam array, similar to the beam array in the coherent combining system. In this solution, a multi-aperture array of OAM beams, which multiplexes them in space,is created by converting a narrow-band laser beam as it passes through two sequentially located binary amplitude and phase holograms formed by amplitude-spatial (A-SLM) and phase-spatial (PSLM) light modulators, respectively, forming an analogue of a phased optical array, and is a set of a certain number of sub-arrays concentrically nested within each other, consisting of a certain number of apertures of optical collimators located along the perimeter of a circle, and the number of collimator apertures in each sub-array corresponds to the number of beams required to form a synthesized sub-beam with a certain angular momentum and modulated by amplitude, while the set of beams coaxially propagating along one channel (multiplexed) OAM, formed in this way, after passing through a spatial filtration system,which suppresses unwanted side lobes in the interference pattern, is fed to the receiving aperture of the demultiplexer based on a phase holographic diffraction grating generated by the PSLM, which is a series of branching gratings, each of which is a superposition of a spiral phase and an echelette (flaming grating) and performs spatial separation of the amplitude-modulated OAM modes.

[0005] The device presented in this paper utilizes OAM modes as a means of channel multiplexing / demultiplexing. The information signal carried by each channel is amplitude-modulated, limited by A-SLM (up to a few kHz). It also requires a large number of collimator apertures to transmit a byte of information per cycle. Thus, to transmit data in four-bit binary coding mode with binary intensity modulation (BIM) of 8 bits of information (1 byte) per cycle or per pixel of the transmitted image, the system requires four collimator aperture subarrays carrying topological charges of 1, 3, 5, and 7, containing, according to the example given in the paper, 6, 9, 15, and 21 optical collimators, respectively, for a total of 50 array elements.

[0006] The closest to the claimed invention is the device of the optical communication system US20200092028A1, containing an optical transmitter containing a first optical element that can be selected from a group including a diffractive optical element, an aspherical optical element and a phase spatial light modulator that divides the incident beam into a given number of spatial modes (beams that have an individual value of the orbital angular momentum), by means of a hologram that performs modulation of the complex amplitude of the propagating beam, and forms a grating of a given number of spatially separated modes, combining the formed spatial modes into a single multiplexed light beam, wherein the spatial modes are used as channels of the carrier frequency and bit modulation of the OAM;An optical receiver comprising a second optical element that can be selected from the group consisting of a diffractive optical element, an aspherical optical element, and a phase spatial light modulator that comprises a hologram that performs spatial separation by modes for demultiplexing a received beam and decoding information carried by each mode; a detector configured to receive the demultiplexed modes from the second optical element through a spatial filter and to detect a signal associated with each mode by determining the modulus of the mode weighting coefficients found by mode decomposition of the received multiplexed beam; a lens array located between the first and second optical elements for spatially separating the spatial modes in the Fourier plane.

[0007] The capabilities of this device can be characterized based on the example of its use given in the patent description. According to this example, the information transmitted from the transmitter to the receiver over free space represents an image recorded by a CCD matrix. Multi-bit encoding via a hologram and decoding are accomplished by defining and subsequently determining 256 levels of image contrast, corresponding to 256 possible permutations of 8 modes, each representing a specific gray level. This approach requires significant time and resources for subsequent processing of the received image and limits the amount of information transmitted per unit of time.In addition, another disadvantage of this optical communication device is that the frequency of mode permutations, and therefore the data transfer rate, is limited by the frequency of changing holograms by the spatial light modulator (~60÷100 Hz), which modulates the complex amplitude of the propagating beams.

[0008] The purpose of the invention is to create a device for a wireless optical communication system based on multiplexing and demultiplexing of OAM modes, ensuring a high data transmission rate.

[0009] The technical result consists in the formation by the first optical element of a phased optical array generating a synthesized beam having a spectrum of OAM modes, the topological charge and intensity of which correspond to a set of orthogonal modes determined by the Fourier transform of the information signal, the propagation of the synthesized beam through the free atmosphere, the reception of the synthesized beam and the demultiplexing of the received radiation by the second optical element into a certain number of spatially separated modes corresponding to different OAM modes of the received radiation, the registration of the spatially separated modes, wherein the set of registered modes and their intensities at each moment in time determines a binary sequence corresponding to the information signal.

[0010] The technical result is achieved in that the claimed device of a wireless optical communication system, like the prototype, includes an optical transmitter containing a first optical element that divides an incident beam into a given number of spatially separated beams (channels) and forms a lattice of spatially separated beams, implementing modulation of the complex amplitude of the spatially separated beams, encoding information data; combining channels into a single multiplexed beam; an optical receiver that receives the multiplexed beam and contains a second optical element that implements spatial separation by modes for demultiplexing the received beam and decoding information; a detector configured to receive demultiplexed modes from the second optical element.

[0011] Unlike the prototype, in the first optical element, the spatial separation and formation of a lattice of spatially separated beams (channels) is carried out in accordance with the principles of coherent addition of laser beams and the formation of a phased optical lattice that generates a synthesized beam containing a certain number of collimated and parallel-propagating sub-beams - channels, where each channel of the optical lattice contains a series-connected phase modulator and an amplitude modulator that modulate the complex amplitude of the wave propagating in the channel, so that the values ​​​​of the amplitude and phase of the wave in each channel at each moment in time are determined by the values ​​​​of the signals controlling the modulators, which are the result of the discrete Fourier transform of the information signal specified in the form of a binary sequence,wherein each individual subbeam (channel) has zero orbital angular momentum relative to its propagation axis, but possesses a spectrum of orbital angular momentum modes relative to the propagation axis of the beam synthesized by the grating, and the synthesized beam represents the sum of orthogonal modes determined by the information signal. The second optical element receives and demultiplexes the radiation generated by the first optical element into a certain number of spatially separated modes corresponding to different OAM modes of the received radiation, recorded by the detector, and the set of recorded modes (modes with zero and non-zero intensity) at each moment in time determines the zero and non-zero values ​​in the binary sequence corresponding to the information signal.

[0012] The advantage of the proposed device is the high throughput of the communication channel, determined by the high modulation frequency of the information signal (tens of GHz) due to the use of high-frequency integrated optical phase and amplitude modulators, and the fact that, unlike bit modulation, a binary sequence of length N (N is the number of channels) is transmitted in one control cycle of the amplitude and phase modulators, which corresponds to the transmission of a decimal number in the range [0, 2 N-1]. In particular, for N = 8, a byte of information is transmitted per clock cycle, i.e., a decimal number in the range [0, 255]. All this, along with the ability to scale the signal power by placing fiber power amplifiers between the phase modulators and amplitude modulators, and to use the generated orthogonal modes as carrier frequency channels for traditional methods of modulation and encoding of the information signal, makes it possible to significantly increase the channel capacity and communication distance compared to the current level.

[0013] All components of the device (laser, fiber splitter, integrated optical phase and amplitude modulators, single-mode polarization-maintaining fiber, fiber optic amplifiers, volume optics, spatial light modulator, photodetectors, electronic components of the control module) are commercially available and are manufactured by various companies in Russia and abroad.

[0014] What's new for the device is that the device contains:

[0015] - A control module including: a control computer that sets the parameters of the information signal, a computing unit that performs a discrete Fourier transform of the binary information signal and converts the binary information signal into a discrete set of signals for controlling a multi-channel optimizing phase processor and an amplitude controller; a multi-channel amplitude controller that generates voltages for controlling the amplitude modulators in the channels in accordance with the results of the Fourier transform of the information signals;a multi-channel optimizing phase processor that generates voltages for controlling phase modulators in channels for periodic phase synchronization in channels based on maximizing a feedback signal - a metric using a stochastic optimization algorithm (SPGD), disabling the optimization procedure upon reaching a state of phase synchronization in channels for a period of time of phase "freezing", determined in accordance with the criterion of reaching a threshold level of a drop in the feedback signal, carrying out during this period high-frequency generation of voltage pulses for controlling phase modulators in channels in accordance with signals from the computing unit (the results of the Fourier transform of information signals) and switching to the phase synchronization mode after this period of time.

[0016] - The first optical element, including: a fiber coherent source of linearly polarized radiation; a fiber radiation splitter dividing the radiation into nine channels of equal power; a series-connected amplitude modulator and a phase modulator in each channel; nine fiber optic collimators forming an optical lattice and arranged so that eight collimators are uniformly distributed along the perimeter of a circle and form a synthesized aperture of eight collimated Gaussian beams propagating in free space parallel to each other, and one collimator is located in the center of the circle, has no outlet into free space and serves to provide the feedback necessary for synchronizing the phases of the beams propagating in free space;four parabolic feedback mirrors that intercept small fractions of the radiation from the peripheral sections of three adjacent Gaussian beams, including the central beam, and focus the intercepted radiation onto four photodetectors, whereby the total radiation power recorded by the photodetectors serves as a feedback signal (metric) for a multi-channel optimizing phase processor operating in accordance with a stochastic optimization algorithm.

[0017] - A second optical element that receives and demultiplexes radiation generated by the first optical element into a certain number of spatially separated modes determined by an information signal, including a receiving telescope, an orbital angular momentum mode sorter that forms a hologram located in the image plane of the synthesized emitting aperture, and a detector that is a matrix of eight photodetectors, each of which is located in the center of localization of the converted mode corresponding to the orbital angular momentum mode, and records the presence and intensity of the mode, and a decoding device that converts the detector signals into a binary sequence corresponding to the information signal.

[0018] Brief description of drawings

[0019] The drawings and description of the device use the same designations of the elements used.

[0020] Fig. 1 shows the structural principle of operation of the information signal transmitter – the first optical element.

[0021] An example demonstrating the decay of the phase synchronization state after disabling the stochastic optimization procedure (SPGD) in a real system is shown in Fig. 2.

[0022] An example demonstrating the vortex phase modulation (|m| = 1) after turning off the SPGD in a real system is shown in Fig. 3.

[0023] The operating principle of the internal feedback loop for phase synchronization of beams combined into a synthesized aperture is shown in Fig. 4.

[0024] The schematic diagram of the transmitter device, consisting of a control module and a first optical element, is shown in Fig. 5.

[0025] The schematic diagram of a variant of the transmitter device, including fiber-optic power amplifiers, is shown in Fig. 6.

[0026] Fig. 7 shows a structural diagram of the principle of receiving and decoding an information signal by means of a second optical element.

[0027] The general operating principle of the mode sorter based on conformal coordinate mapping is shown in Fig. 8.

[0028] The schematic diagram of the device of the second optical element (receiver-demultiplexer) is shown in Fig. 9.

[0029] Fig. 10a) shows the theoretical spectrum of the information signal, which is the result of the discrete Fourier transform of the number 32 (00100000), containing the modes m = (2; -6). Fig. 10b) shows the corresponding intensity distribution of the synthesized beam in the plane G1. Fig. 10c) represents the calculated intensity distribution in the recording plane. Fig. 10d) represents the calculated intensity distribution along the x = 0 axis in the recording plane, corresponding to the spectrum of modes m = (2; -6).

[0030] Fig. 11a) shows the theoretical spectrum of the information signal, which is the result of the discrete Fourier transform of the number 45 (00101101), containing the modes m = (2; 4; 5; 7; -1; -3; -4; -6). Fig. 11b) shows the corresponding intensity distribution of the synthesized beam in the plane Г1. Fig. 11c) represents the calculated intensity distribution in the recording plane. Fig. 11d) represents the calculated intensity distribution along the x = 0 axis in the recording plane, corresponding to the spectrum of modes m = (2; 4; 5; 7; -1; -3; -4; -6).

[0031] Fig. 12a) shows the theoretical spectrum of the information signal, which is the result of the discrete Fourier transform of the number 255 (11111111), containing the entire spectrum of modes from m = -8 to m = 8. Fig. 12b) shows the corresponding intensity distribution of the synthesized beam in the plane G1. Fig. 12c) represents the calculated intensity distribution in the recording plane. Fig. 12d) represents the calculated intensity distribution along the x = 0 axis in the recording plane, corresponding to the spectrum of modes from m = -8 to m = 8.

[0032] Let us consider the operation of the information signal transmitter – the first optical element, the operating principle of which is shown in Fig. 1.

[0033] Linearly polarized radiation from a narrowband laser1 is divided by a fiber optic splitter2 into N channels (N = 8 is required to transmit 1 byte of information). Each channel contains a phase modulator3 and an amplitude modulator4, which are arranged in series to modulate the complex amplitude of the light beam. These modulator and amplitude modulator4 are integrated with a single-mode fiber that maintains the polarization state. The fiber output end of the last modulator in each channel is coupled to a lens collimator5, which generates a light beam with a Gaussian intensity distribution and diffraction-limited divergence. A set of collimators (subapertures), the centers of which are located on a circle of radius R, forms a synthesized aperture (grating)6, which emits a set of N collimated and parallel subbeams with unidirectional linear polarization, representing the synthesized beam.

[0034] Initially, the transmitted information is encoded in binary code, then the resulting sequence is converted into bytes. This allows the transmission of a number from 0 (byte [00000000]) to 255 (byte [11111111] – second column from the left in Fig. 1). For each byte, an information signal G is generated. l = A Gl exp(iϕ l ), in which the phases are equal to zero ϕ l = 0 (or phase difference ϕ l -ϕ k =0), and the amplitudes represent a sequence A Gn = [A G0, A G1 , A G2 , A G3 , A G4 , A G5 , A G6 , A G7 ] (in Fig. 1, first column on the left), where A Gl – takes the value zero or one, corresponding to the value in the byte. Next, the discrete Fourier transform of the vector G is performed. l , as a result of which we obtain control signals V n = exp(i ), which are generated by the control module of the amplifier. Signals proportional to , are fed to amplitude modulators4 in fiber channels to set the corresponding values ​​of the amplitude (intensity) of radiation in the channel; signals proportional to ϕ Vn , are fed to phase modulators3 to set the corresponding phase shift values

[0035] Transmitted Components G l information signal are associated with modulating complex amplitudes V n by means of the discrete Fourier transform:

[0036]

[0037] with the corresponding inverse transformation

[0038]

[0039] Then in cylindrical coordinates the field of the synthesized beam in the far zone in the paraxial approximation can be written as (Vinogradov M.E., Rudenko O.V., Sukhorukov A.P. Wave Theory. Moscow: Nauka, 1990. 432 p.)

[0040]

[0041] where And - coefficients depending on the coordinates, geometry of the synthetic aperture and the propagation distance z.

[0042] Expression (3) explicitly relates the field at the receiver to the components of G l transmitted information signals, i.e. – is a multiplexed field that is the result of the interaction of N signals.

[0043] Expression (3) is obtained under the assumption that the phases of all subbeams are stationary in time, and the specified relationships between the phases of the subbeams are unchanged. This condition is especially relevant for phased arrays based on optical fiber, since the phase of radiation propagating in the fiber experiences fluctuations caused by thermal and acoustic effects (Augst SJ, Fan TY, Sanchez A. Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers. / / Opt. Lett. 2004. V. 29, N. 5, P. 474-476).In systems of coherent combining of fiber laser beams aimed at achieving maximum brightness, the problem of synchronization of phases of sub-beams is solved by various methods, among which the most widely used are the method of heterodyning using a reference signal shifted in frequency, the LOCSET method, which uses radio-frequency phase modulation of each sub-beam with a certain frequency, the interference signal of all sub-beams is recorded by a separate photodetector and the phase error signal is determined, which is minimized in accordance with the optimization algorithm, and the stochastic optimization method SPGD (stochastic parallel gradient descent), which is an algorithm based on minimizing the phase error and achieving the maximum contrast of the interference pattern formed as a result of the superposition of beams on the receiving platform of the photodetector, limited by a small aperture (Brignon A. (ed.) Coherent beam combining.– John Wiley & Sons. 2013; M.A. Vorontsov, V.P. Sivokon. Stochastic parallel-gradient-descent technique for high-resolution wave-front phase distortion correction. / / J. Opt. Soc. Am. A. 1998. V. 15, N. 10, P. 2745-2758).

[0044] However, this approach is unacceptable in problems where it is necessary to ensure the constancy of the specified phase relationships between the subbeams, in particular, for the formation of vortex beams, since these beams are characterized by zero intensity on the propagation axis (T. Hou, Y. Zhang, Q. Chang, P. Ma, R. Su, J. Wu, Y. Ma, and P. Zhou. High-power vortex beam generation enabled by a phased beam array fed at the nonfocal-plane / / Optical Express. 2019. V. 27. N. 4. P. 4046–4059). To solve this problem, we use a simple and effective approach in which synchronization and phase modulation modes are alternated. Initially, phase synchronization is performed in the channels, and then, when the synchronization state is achieved, the phase synchronization procedure is stopped, and the phases in the channels are modulated in accordance with the results of the Fourier transform of the information signal.

[0045] This approach is based on the fact that after achieving phase synchronization, due to the slowness of the change in the phase state of the fiber system as a result of thermal and acoustic fluctuations of the refractive index in the fiber, there is a state of “frozen” phase specific to this system, which can last from 0.5 seconds to several seconds (VP ​​Aksenov, VV Atuchin, VV Dudorov, VV Kolosov, ME Levitsky, TD Petukhov. Vortex beam formation by means of control of the piston shift of a fiber array / / Proc. SPIE. 2019. V. 11322. P. 1132214; Kolosov V.V., Levitsky M.E., Aksenov V.P., Dudorov V.V., Filimonov G.A. Method for producing a scalar vortex beam and device for its implementation / / Russian Federation Patent No. 2648975). An example demonstrating the decay of the phase synchronization state after disabling the SPGD procedure in a real system is shown in Fig. 2.In this implementation, phase synchronization corresponds to the maximum radiation intensity recorded by the feedback photodetector as a result of the SPGD algorithm (SPGD level). When SPGD is disabled, the phase synchronization of the subbeams begins to slowly decay. However, during the phase "freezing" time, the system remains close to phase synchronization. The "freezing" time can be determined based on the criterion defining the acceptable signal drop at the photodetector. Thus, a signal drop to a level of 0.9 SPGD corresponded to a "freezing" time of τ. f (0.9) = 1.58 seconds, and the fall to the level of (1 / √2) SPGD corresponded to τ f(1 / √2) = 2.34 seconds. This time is sufficient for high-frequency (up to tens of GHz, typical for modern integrated optical modulators) modulation of the phase and amplitude of the subbeams and the formation of arbitrarily specified phase relationships between the grating subbeams, after which the phase synchronization procedure should be repeated. An example demonstrating the modulation of the vortex phase (|m| = 1) after turning off the SPGD in a real system is shown in Fig. 3. The phase synchronization state corresponds to the maximum signal on the photodetector (level (SPGD). After reaching the SPGD level, the phase controller stopped the SPGD procedure and periodically, with a given frequency, generated voltage levels on the phase modulators in the channels corresponding to the formation of a vortex beam with a topological charge m = 1, while the signal level on the photodetector dropped to zero, corresponding to the zero intensity value on the vortex beam axis.In this example, the signal drop to the level of 0.9 SPGD corresponded to a “freezing” time of τ. f (0.9) = 2.85 seconds, and the fall to the level of (1 / √2) SPGD corresponded to τ f (1 / √2) = 3.88 seconds. This allows us to define a criterion according to which a given value of the permissible signal drop determines the moment of termination of the phase modulation mode (information transmission) and return to the phase synchronization mode. Note that it takes ~10 -4 ÷10 -3 s, which is much shorter than the phase "frozen" time. This approach, implemented using a phase-optimizing processor6 and an amplitude controller7 within the first optical element, enables high-frequency modulation of the information signal and the transmission of large volumes of information per unit of time.

[0046] Another important aspect that ensures the system's operability is the method of constructing the feedback loop, which is used to initially synchronize the phases in the optical collimator array. A key condition for the feedback loop's effectiveness is the requirement of the absence of additional phase distortions introduced by the elements of the feedback loop itself. To solve this problem, we use our previously proposed solution (Kolosov VV, Levitskii ME, Petukhov TD, Simonova GV Formation of the Feedback Loop for Phase Control of a Fiber Laser Array. Atmos Ocean Opt (2019) 32(6):716-23; Kolosov VV, Levitskii ME, Simonova GVA method for organizing an internal feedback loop for phase synchronization of a fiber laser array in coherent beam combining systems and a device for implementing it / / Russian Federation Patent 2720263 C1), using peripheral sections (wings) of Gaussian radiation beams intercepted at the output of optical array collimators as a control signal. The operating principle of this method is presented in Fig. 4, which depicts a portion of the synthesized aperture forming a subbeam array. Let us consider three subbeams, two of which represent information channels, located in the vicinity and whose centers are located on the diameter of a circle of radius R. The third subbeam is located at the center of the circle, does not participate in the formation of the information signal, and serves as a reference for synchronizing the phases of the information subbeams.The radiation emerging from the end of a single-mode fiber is collimated by a lens, which forms a plane wave with a Gaussian intensity distribution characterized by infinite width. The aperture of the collimating lens limits the width of the Gaussian beam, cutting off the weak wings of the Gaussian distribution. Thus, an aperture with a diameter of D = , Where - focal length of the collimating lens and - the numerical aperture of a single-mode fiber transmits 95.85% of the incident power, with the remaining power lost through the aperture. If the diameters of the collimating lenses are selected to be 10% larger than the aperture diameters and the adjacent sections of the three collimating lenses 7 are freed from the limiting apertures, as shown in Fig. 4, so that the free sections of the wings of three adjacent Gaussian beams are collimated and extend into free space, these three sections can be intercepted using a parabolic focusing mirror 11 and focused onto the receiving pad of the photodetector 6. These three sections of the Gaussian beams will superimpose and interfere on the receiving pad of the photodetector, limited by a small aperture, while the maximum signal level of the photodetector will correspond to the phase co-ordination of the corresponding Gaussian beams. An important feature of the chosen solution is that it ensures the compactness of the device, which is necessary in many applications.

[0047] The schematic diagram of the transmitter device, consisting of a control module and a first optical element, is shown in Fig. 5.

[0048] The first optical element works as follows:

[0049] - Narrow-band linearly polarized laser radiation 1 with a fiber output is divided by a fiber splitter 2 into 9 channels of equal power. In each channel, integrated optical phase 3 and amplitude 4 modulators are installed, arranged in series, controlled by signals from the control module. The emitting ends of single-mode optical fibers 5 at the output of the modulators 4, together with collimator lenses 7, form a synthesized aperture 9 - an array of 9 collimator lenses, one of which is located in the center of the aperture and forms a reference radiation channel, which is used to synchronize the phases of 8 radiation channels - parallel Gaussian beams formed by the remaining collimator lenses, radially located relative to the center of the synthesized aperture 9. In accordance with the principle shown in Fig.4, the parabolic feedback mirror 11 intercepts, reflects through the feedback aperture 10 and collects the peripheral sections (the wings of the Gaussians) of the radiation of two adjacent radially located channels and the central channel on the receiving platform of the photodetector 6, limited by a small aperture. In order not to limit the propagation of the peripheral sections of the radiation, the mounts 8 (apertures) of the collimator lenses have releases, as shown in Fig. 6. The photodetector 6 generates a feedback signal proportional to the intensity at the maximum of the interference pattern resulting from the superposition of a small fraction of the radiation of the three channels, which serves as a metric for the optimizing phase processor 15. By dividing the synthesized aperture into four sections and using four parabolic mirrors 11, as well as four photodetectors 6, we obtain four feedback signals locked to the phase of the central channel.The feedback signals are amplified and summed by a four-channel amplifier13, which generates a feedback signal that is fed to one of the inputs of a multi-channel optimizing processor15, which is part of the control module, which generates voltages supplied to the phase modulators in accordance with the SPGD algorithm, ensuring phase synchronization in the channels.

[0050] One of the key factors determining the communication range is the transmitted signal power. To increase the transmitted signal power, fiber-optic power amplifiers26 can be used, placed in each channel between the phase modulator and the amplitude modulator, as shown in Fig. 6.

[0051] - The control module works as follows.

[0052] The control computer17 generates a binary information signal, which is transmitted to the computing unit16, and also controls the multi-channel phase optimizing processor15; the computing unit16 receives the binary information signal, performs a discrete Fourier transform of the binary information signal, and transforms the binary information signal into a discrete set of signals to control the multi-channel phase optimizing processor15 and the amplitude controller14; the multi-channel amplitude controller14 controls the amplitude modulators4 in the channels, generating voltages in accordance with the results of the Fourier transform;a multi-channel optimizing phase processor15 controls phase modulators3, generating voltages for controlling phase modulators in channels for periodic phase synchronization in channels based on maximization of a feedback signal (metric) using a stochastic optimization algorithm, disabling the optimization procedure upon reaching a state of phase synchronization in channels for a period of phase "freezing" time determined in accordance with the criterion of reaching a threshold level of a drop in the feedback signal, implementing during this period high-frequency generation of voltage pulses for controlling phase modulators in channels in accordance with signals from the computing unit (the results of the Fourier transform of information signals) and switching to the phase synchronization mode after this period of time);

[0053] The optical information signal generated by the transmitter (the first optical element) propagates in free space and arrives at the receiving aperture of the second optical element, the operating principle of which is shown in Fig. 7. Let us consider how the second optical element performs demultiplexing – divides the field into N components (OAM modes) associated with only one information signal.

[0054] For this, we use the expansion of the field (3) in vortex modes, amplitude S m which are defined as follows:

[0055]

[0056] a mod power C m (z) –

[0057]

[0058] In this case, the sum of the powers of the modes P must correspond to the total radiation power:

[0059]

[0060] The inverse transformation of expansion (3) defines the field through the spectrum of vortex modes:

[0061]

[0062] Whereas , and from (1) and (2) it follows

[0063]

[0064] After transformations we obtain an expression for the amplitude of the vortex mode:

[0065]

[0066] where - a function depending on m, on the coordinates, the propagation distance z and on .

[0067] Expression (8) shows that each mode amplitude S m depends on only one information signal G m , i.e. the information transmission channels are divided, and the received signal S m proportional to the original signal G m .

[0068] The multiplexed sum field carries within the measured range as many modes as there are single amplitude values ​​in the sequence A Gl = [A G0, A G1 , AG2 , A G3 , A G4 , A G5 , A G6 , A G7 ] (the first column on the left in Fig. 7). The multiplexed signal is received by the telescope 18 (Fig. 7), in the image plane of which the mode sorter SM is located. The corresponding amplitudes of the separated modes are presented in the first column on the right. According to formula (17), the following relationship is realized between the OAM value m carried by the mode radiation and the amplitude value A Gl : m(l) = [0, 1, 2, 3, 4, -3, -2, -1]. For example, when transmitting the byte [11111111], corresponding to the decimal number 255, the radiation carries eight modes with OAM values ​​m: m(0) = 0, m(1) = 1, m(2) = 2, m(3) = 3, m(4) = 4, m(5) = -1, m(6) = -2, m(7) = -3. When transmitting the byte [00101101], corresponding to the decimal number 45, the radiation carries four modes with OAM values ​​m: m(2) = 2, m(4) = 4, m(5) = –3, m(7) = -1.

[0069] To separate modes by space, we use the principles of sorting vortex beams.

[0070] The most promising approach is based on conformal mapping of coordinates, which transforms the spiral (azimuthal) phase gradients of OAM modes into linear phase gradients in the form of inclined beams, which can be spatially separated in the recording plane using a Fourier lens (Berkhout GCG, Lavery MPJ, Courtial J., Beijersbergen MW, Padgett MJ Efficient sorting of orbital angular momentum states of lights / / Phys. Rev. Lett. 2010. V. 105, P.153601-153604). The operating principle of the mode sorter based on conformal mapping is shown in Fig. 8. Four optical elements are required for sorting. The first phase optical element (G1) transforms the coordinates of the input images of beams with azimuthal phase gradients corresponding to the OAM modes (m=1, 2, 3,…) into the coordinates of the output images of beams with a transverse phase gradient corresponding to the OAM modes (m=1, 2, 3,…).An inevitable consequence of such a transformation is the variability of the optical path length for each beam trajectory, which leads to phase distortions. To compensate for phase distortions, a phase element (G2) is placed in the Fourier plane (the rear focal plane of lens FL1) of element G1. Thus, in the Fourier plane (the rear focal plane of lens FL2) of element G2, spatially separated images of the beams are observed, representing a system of narrow bands parallel to the X-axis with centers lying on the Y-axis. The total radiation power in each band is equal to the radiation power of the OAM mode in the original beam. Photodetectors placed in the Fourier plane of element G2 record the radiation intensity of these bands on the Y-axis. Thus, the set of registered OAM modes (modes with zero and non-zero intensity) at each moment in time determines the zero and non-zero values ​​in the binary sequence corresponding to the information signal.

[0071] A number of vortex mode sorters based on different conformal coordinate mappings, differing in efficiency, are presented in the scientific and patent literature. The corresponding OAM mode sorters can be made using diffractive optical elements, aspherical optics and phase spatial light modulators (Lavery MPJ, Robretson DJ, Berkhout GCG, Love GD, Padgett MJ, Courtial J. Refractive elements for measuring the orbital angular momentum of a single photon / / Opt. Express. 2012.V.20, No.3, P.2110-2115; Ruffato G., Massari M., Romanato F. Compact sorting of optical vortices by media of diffractive transform optic / / Opt. Letters. 2017. V.42, No.3, P.551-554; Wan C., Chen J., Zhan Q. Compact and high-resolution optical angular momentum sorter / / APL Photonics. 2017. V.2, P. 031302-1 – 031302-6; Wen Y., Chremmos I., Bhen Y., Zhu J., Zhang Y., Yu S.Spiral transformation for high-resolution and efficient sorting of optical vortex modes / / Phys.Rev.Lett. 2018. V.120, No.19, P. 193904(1-6); CN 110161681 A1; WO 20192074381 A1; RU 2777799 C1).

[0072] The basic diagram of the device of the second optical element (receiver-demultiplexer), consisting of a receiving telescope18, beam-splitting prisms19,21, holographic elements20,22, a photodetector matrix23 and a decoding device24,25, is shown in Fig. 9. Reflective phase spatial light modulators are shown as holographic elements 20, 22 in the given diagram, however, they can be replaced by corresponding diffractive and refractive elements, as well as metasurfaces with minor changes in the device circuit without changing the principle of its operation. The second optical element operates as follows. The receiving telescope18 matches the dimensions of the received synthesized beam with the aperture of the first holographic element20, located in the image plane of the telescope18. The holographic element20 performs a conformal mapping of coordinates onto the second holographic element22.Holographic element 22 performs phase correction of the transformed beams. Fourier lenses (FL1 and FL2 in Figure 7 are included in holographic elements 20 and 22 as phase components and are not shown in Fig. 8). Beams separated by vortex modes fall on a photodetector matrix 23, in which each photodetector element is located at the center of the corresponding mode localization, registers the presence and intensity of the modes, and transmits the signals to a decoding device 24, which, together with a computer 25, converts the photodetector signals into a binary sequence corresponding to the information signal.

[0073] Examples of numerical simulation of decoding of information signals in the form of a decimal code or a binary sequence are shown in Fig. 10-12.

[0074] Calculations were performed for the following parameters:

[0075] - diffraction radius of the subbeam in the plane of the element G1, ω0 = 0.6 mm;

[0076] - radius of the circle on which the centers of the sub-bundles are located in the plane G1, R′ = 3.35* ω0;

[0077] - working wavelength, λ = 1.064 μm;

[0078] - working area of ​​elements G1 and G2, 7.68*7.68 mm 2 ;

[0079] - distance between elements G1 and G2 – 100 mm;

[0080] - distance between element G1 and registration plane – 200 mm.

[0081] Fig. 10a) demonstrates the theoretical spectrum of the information signal, which is the result of the discrete Fourier transform of the number 32 (00100000), containing the modes m = (2; -6). Fig. 10b) shows the intensity distribution of the synthesized beam in the plane G1. Fig. 10c) represents the calculated intensity distribution in the recording plane. Fig. 10d) represents the calculated intensity distribution along the x = 0 axis in the recording plane, corresponding to the spectrum of the modes m = (2; -6).

[0082] Fig. 11a) demonstrates the form of the theoretical spectrum of the information signal, which is the result of the discrete Fourier transform of the number 45 (00101101), containing the modes m = (2; 4; 5; 7; -1; -3; -4; -6). Fig. 11b) shows the intensity distribution of the synthesized beam in the plane Г1. Fig. 11c) represents the calculated intensity distribution in the recording plane. Fig. 11d) represents the calculated intensity distribution along the x = 0 axis in the recording plane, corresponding to the spectrum of modes m = (2; 4; 5; 7; -1; -3; -4; -6).

[0083] Fig. 12a) shows the theoretical spectrum of the information signal, which is the result of the discrete Fourier transform of the number 255 (11111111), containing the entire spectrum of modes from m = -8 to m = 8. Fig. 12b) shows the intensity distribution of the synthesized beam in the plane G1. Fig. 12c) represents the calculated intensity distribution in the recording plane. Fig. 12d) represents the calculated intensity distribution along the x = 0 axis in the recording plane, corresponding to the spectrum of modes from m = -8 to m = 8.

Claims

1. A wireless optical communication device comprising an optical transmitter containing: a first optical element dividing an incident beam into a given number of spatially spaced beams - channels and forming a grid of spatially spaced beams, implementing modulation of the complex amplitude of the spatially spaced beams, encoding information data; combining the channels into a single multiplexed beam; an optical receiver receiving the multiplexed beam and containing a second optical element implementing spatial division by modes for demultiplexing the received beam and decoding the information;a detector configured to receive demultiplexed modes from a second optical element, characterized in that it comprises a control module including: a control computer that sets the parameters of the information signal, a computing unit that performs a discrete Fourier transform of the binary information signal and converts the binary information signal into a discrete set of signals for controlling a multi-channel optimizing phase processor and an amplitude controller; a multi-channel amplitude controller that generates voltages for controlling amplitude modulators in the channels in accordance with the results of the Fourier transform;a multi-channel optimizing phase processor that generates voltages for controlling phase modulators in channels for periodic phase synchronization in channels based on maximizing a feedback signal - a metric using a stochastic optimization algorithm, disabling the optimization procedure upon reaching a state of phase synchronization in channels for a period of time of "frozen" phase, determined in accordance with the criterion of reaching a threshold level of a drop in the feedback signal, implementing during this period high-frequency generation of voltage pulses for controlling phase modulators in channels in accordance with the results of the Fourier transform of information signals and switching to the phase synchronization mode after this period of time has elapsed;the first optical element includes a fiber coherent source of linearly polarized radiation, a fiber radiation splitter dividing the radiation into nine channels of equal power, a series-connected amplitude modulator and a phase modulator in each channel, and nine fiber optic collimators, eight of which are distributed along the perimeter of the circle and form a grid of spatially separated collimated Gaussian beams propagating in free space parallel to each other, which are used as carrier frequency and digital coding channels, and the ninth collimator is located in the center of the circle, has no outlet into free space, and serves to provide feedback necessary for synchronizing the phases of the beams propagating in free space;four parabolic feedback mirrors that intercept small fractions of the radiation from the peripheral sections of three adjacent Gaussian beams, including the central beam, and focus the intercepted radiation onto four photodetectors, wherein the total radiation power recorded by the photodetectors serves as a feedback signal - a metric for a multichannel optimizing phase processor operating in accordance with a stochastic optimization algorithm; the second optical element includes a receiving telescope and an orbital angular momentum mode sorter that forms a hologram located in the image plane of the receiving telescope; the detector contains a matrix of eight photodetectors, each of which is located at the center of localization of the corresponding orbital angular momentum mode and records the presence and intensity of the mode, and a decoding device that converts the signals from the photodetectors into a binary sequence corresponding to the information signal.

2. The device according to claim 1, characterized in that fiber power amplifiers are placed between the phase modulators and the amplitude modulators in each channel.

Images