Free space optical communication system and simulation method for suppressing atmospheric turbulence

Abstract

The application provides a free space optical communication system and a simulation method for suppressing atmospheric turbulence, the system comprising a transmitting end and a receiving end, the transmitting end being used for generating a fundamental mode Gaussian light beam, modulating and collimating the Gaussian light beam, and converting the Gaussian light beam into a combined Bessel Gaussian light beam; the receiving end being used for receiving the combined Bessel Gaussian light beam, performing position detection and signal restoration on the combined Bessel Gaussian light beam, and obtaining original digital information; wherein the combined Bessel Gaussian light beam is formed by superimposing Bessel Gaussian light beams of different orders which are orthogonal to each other. The non-diffraction characteristic, self-repairing capability and spatial diversity gain of the combined Bessel Gaussian light beam are utilized to reduce the influence of atmospheric turbulence on the communication link, reduce the pointing error and light intensity flicker of the space laser communication, and convert the optical signal into an electrical signal for demodulation by using a photoelectric detector in the receiving end, so that the transmission performance and stability of the free space optical transmission system in a complex environment can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of space optical communication, and in particular to a free-space optical communication system and a simulation method for suppressing atmospheric turbulence. Background Art

[0002] With the rapid development of the information society, the demand for data communications is growing exponentially. Existing wireless communication technologies face unprecedented challenges in bandwidth, speed, and transmission distance. Space laser communication, with its advantages such as high bandwidth, high speed, strong anti-interference capabilities, and lack of spectrum resource constraints, has gradually become an effective solution for large-capacity data transmission. In particular, space laser communication technology, due to its unique advantages, has been widely researched and applied in fields such as deep space exploration, satellite communications, ocean communications, and military communications.

[0003] However, in practical applications, space laser communication systems are susceptible to atmospheric turbulence, which can cause pointing errors and light intensity flicker. These can cause the beam to deviate from the receiving end, leading to received power jitter and severely impacting the link stability and communication quality of the communication system. Pointing errors and light intensity flicker are particularly significant in high-precision, high-speed space laser communication systems, potentially increasing the system's bit error rate and even leading to communication interruption. Summary of the Invention

[0004] The purpose of the present invention is to provide a free-space optical communication system and simulation method that suppresses atmospheric turbulence, so as to solve the problem that space laser communication systems are easily affected by atmospheric turbulence in practical applications, resulting in the light beam deviating from the receiving end and the receiving power jitter, which seriously affects the link stability and communication quality of the communication system.

[0005] To achieve the above objectives, the present invention proposes a free-space optical communication system and simulation method for suppressing atmospheric turbulence. This system generates a combined Bessel-Gaussian beam optical signal in an on-off keying modulation format at the transmitter. This system utilizes the non-diffraction properties, self-repair capabilities, and spatial diversity gain of the combined Bessel-Gaussian beam to reduce the impact of atmospheric turbulence on the communication link. The specific technical solutions of the present invention are as follows:

[0006] A free-space optical communication system for suppressing atmospheric turbulence, comprising:

[0007] The transmitting end is used to generate a fundamental mode Gaussian beam, modulate and collimate it, and convert the Gaussian beam into a combined Bessel-Gaussian beam;

[0008] The receiving end is used to receive the combined Bessel-Gaussian beam and perform position detection and signal restoration on it to obtain the original digital information;

[0009] The combined Bessel-Gaussian beam is formed by superimposing Bessel-Gaussian beams of different orders that are orthogonal to each other.

[0010] Furthermore, the transmitting end includes: a laser and a modulator connected to the output end of the laser, a collimator connected to the output end of the modulator, a combined Bessel-Gaussian beam converter connected to the output end of the collimator, and a beam expander connected to the output end of the combined Bessel-Gaussian beam converter;

[0011] The laser is used to generate and emit a fundamental mode Gaussian beam;

[0012] The modulator is used to load an electrical signal into the fundamental mode Gaussian beam;

[0013] The collimator is used to collimate the divergent light beam to form a collimated fundamental mode Gaussian beam;

[0014] The combined Bessel-Gaussian beam converter is used to convert the fundamental mode Gaussian beam into a combined Bessel-Gaussian beam;

[0015] The beam expander is used to expand the combined Bessel-Gaussian beam.

[0016] Furthermore, the electrical signal is an on-off keying modulation signal.

[0017] Furthermore, the combined Bessel-Gaussian beam converter includes:

[0018] Linear polarizer, used to change the polarization state of the fundamental mode Gaussian beam;

[0019] a spatial light modulator for loading a combined Bessel-Gaussian beam phase hologram to generate a combined Bessel-Gaussian beam;

[0020] The reflecting mirror is used to reflect the combined Bessel-Gaussian beam outward.

[0021] Furthermore, the receiving end includes: a receiving aperture and a beam reducer connected to an output end of the receiving aperture, a beam splitter connected to an output end of the beam reducer, a camera and a photodetector connected to an output end of the beam splitter, and a signal processing unit connected to an output end of the photodetector;

[0022] The receiving aperture is used to receive the combined Bessel-Gaussian beam;

[0023] The beam reducer is used to focus the combined Bessel-Gaussian beam;

[0024] The beam splitter is used to split the focused combined Bessel-Gaussian beam into two beams, one beam irradiating the photodetector and the other beam irradiating the camera;

[0025] The camera is used to obtain the transverse electric field distribution and the center position of the combined Bessel-Gaussian beam;

[0026] The photodetector is used to perform photoelectric conversion on the combined Bessel-Gaussian beam, converting the optical signal into an electrical signal;

[0027] The signal processing unit is used to restore the electrical signal to obtain original digital information and analyze the original digital information.

[0028] Furthermore, the method for analyzing the original digital information by the signal processing unit is to set a decision threshold, record the electrical pulse sequence signals above the decision threshold as binary symbol 1, and record the electrical pulse sequence signals below the decision threshold as binary symbol 0, thereby forming a binary digital sequence of the electrical pulse sequence signal, and compare this binary digital sequence with the digital sequence in the on-off keying modulation signal of the transmitting end to obtain the bit error rate characteristics of the original digital information.

[0029] The present invention also provides a free-space optical communication simulation method for suppressing atmospheric turbulence, the method comprising:

[0030] Establish a simulation model of the above-mentioned free-space optical communication system for suppressing atmospheric turbulence, and set simulation conditions and simulation parameters;

[0031] By changing the simulation parameters, the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam were simulated. After the two beams experienced the same intensity of atmospheric turbulence, the simulation results were calculated.

[0032] Furthermore, the simulation conditions include at least one of the beam wavelength, grid length, beam waist radius, angular index and radial index, receiving aperture, atmospheric turbulence intensity and simulation times, and the simulation parameters include the transmission distance of the beam.

[0033] Furthermore, the simulation results include a first simulation result and a second simulation result;

[0034] The first simulation result includes the diameters of the beam distribution circles of the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam at the receiving surface of the camera at the receiving end under strong turbulence, and the beam distribution circle diameter at the receiving end is twice the distance between the center of the camera receiving surface and the farthest beam center point;

[0035] The second simulation result includes the aperture scintillation index of the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam under strong turbulence and the beam power received by the photodetector at the receiving end at a fixed receiving aperture.

[0036] The free-space optical communication system and simulation method for suppressing atmospheric turbulence provided by the present invention have the following beneficial effects compared with the prior art:

[0037] 1. The present invention proposes a free-space optical communication system for suppressing atmospheric turbulence, in which a combined Bessel-Gaussian beam has spatial diversity gain compared to a single Bessel-Gaussian beam, and beam shaping can be achieved by freely combining Bessel-Gaussian beams of different orders, thereby obtaining a beam that is more conducive to free-space optical transmission.

[0038] 2. In a free-space optical communication system for suppressing atmospheric turbulence proposed by the present invention, a combined Bessel-Gaussian beam is used for tracking and aiming and communication parts of the free-space optical communication system. During the tracking and aiming process, the combined Bessel-Gaussian beam has a smaller jitter error. During the communication process, the combined Bessel-Gaussian beam has a lower power jitter. The combined Bessel-Gaussian beam can effectively reduce the impact of atmospheric turbulence during long-distance free-space optical transmission.

[0039] 3. The present invention proposes a free-space optical communication system that suppresses atmospheric turbulence. The combined Bessel-Gaussian beam has non-diffraction and self-repairing characteristics, which enables the combined Bessel-Gaussian beam to self-recover when encountering obstacles that partially block the transmission during long-distance transmission in space, effectively improving the transmission performance of the free-space optical transmission system in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0041] Figure 1 1 is a schematic structural diagram of a free-space optical communication system for suppressing atmospheric turbulence provided by the present invention;

[0042] Figure 2 2 is a schematic structural diagram of a combined Bessel-Gaussian beam converter according to an embodiment of the present invention;

[0043] Figure 3 Schematic diagram of the change in the diameter of the center distribution circle of the light beam on the receiving surface of the camera at the receiving end according to the light beam transmission distance in an embodiment of the present invention;

[0044] Figure 4 Schematic diagram of the change of the aperture scintillation index of the received light beam power of the photoelectric detector at the receiving end with the light beam transmission distance in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the accompanying drawings provided by the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are all in a very simplified form and are not in exact proportions. They are only used to facilitate and clearly illustrate the purpose of the embodiments of the present invention.

[0046] In the description of the present invention, unless otherwise clearly specified and limited, the terms "connection" and "connected" should be interpreted broadly. For example, it can be a fixed connection, a detachable connection, or an integrated connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0047] In the description of the present invention, terms such as "up", "down", "left", "right", "front", "back", "center", "horizontal", "vertical", "top", "bottom", "inside", and "outside" and other orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings and are only for the convenience of description and simplification of operation, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, they should not be understood as limiting the present invention.

[0048] Example 1

[0049] This embodiment provides a free-space optical communication system for suppressing atmospheric turbulence. Figure 1 As shown, the system includes a transmitter and a receiver. The optical transmission method between the transmitter and the receiver is free space transmission, that is, the light beam is transmitted from the transmitter to the receiver via free space. The transmitter is used to generate a fundamental mode Gaussian beam and modulate and collimate it, and convert the Gaussian beam into a combined Bessel-Gaussian beam. The receiver is used to receive the combined Bessel-Gaussian beam and perform position detection and signal restoration on it to obtain the original digital information. The Bessel-Gaussian beam is a structured beam with non-diffraction characteristics and self-repairing capabilities. During transmission, the Bessel-Gaussian beam can maintain its cross-sectional intensity distribution unchanged. Even when encountering partial obstruction or interference, it can automatically repair the wavefront and maintain the transmission characteristics of the beam. Bessel beams of different orders are orthogonal to each other. By combining the beams, not only can the beam shaping design be realized to meet the required beam shape, but also spatial diversity can be achieved to reduce the impact of atmospheric turbulence.

[0050] The free-space optical communication system for suppressing atmospheric turbulence provided by this embodiment is described in detail below.

[0051] In one embodiment of the present invention, the transmitting end includes a laser, a modulator, a collimator, a combined Bessel-Gaussian beam converter, and a beam expander in sequence. The output of the laser is connected to the input of the modulator, the output of the modulator is connected to the input of the collimator, the output of the collimator is connected to the input of the combined Bessel-Gaussian beam converter, and the output of the combined Bessel-Gaussian beam converter is connected to the input of the beam expander. The laser is used to generate and emit a fundamental mode Gaussian beam; the modulator is used to load an electrical signal into the fundamental mode Gaussian beam, the electrical signal being an on-off keying modulation signal; the collimator is used to collimate the divergent beam to form a collimated fundamental mode Gaussian beam; the combined Bessel-Gaussian beam converter is used to convert the fundamental mode Gaussian beam into a combined Bessel-Gaussian beam; and the beam expander is used to expand the combined Bessel-Gaussian beam.

[0052] For details, see Figure 2 As shown, the combined Bessel-Gaussian beam converter at the transmitting end includes a linear polarizer, a spatial light modulator and a reflector. The linear polarizer is used to change the polarization state of the fundamental mode Gaussian beam, the spatial light modulator is used to load the combined Bessel-Gaussian beam phase hologram to generate a combined Bessel-Gaussian beam, and the reflector is used to reflect and emit the combined Bessel-Gaussian beam.

[0053] Among them, the combined Bessel-Gaussian beam is the superposition of Bessel-Gaussian beams of different orders orthogonal to each other, and its light field expression is:

[0054]

[0055] In the above formula, E represents the light field, r and φ represent the radial and angular coordinates respectively, A is the amplitude term, ω0 is the Gaussian envelope waist, and J l is the lth-order Bessel function (l=0, 1, ..., n), β is the width parameter, and exp(jlφ) is the spiral phase factor. By superimposing Bessel-Gaussian beams of different amplitudes and orders, combined Bessel-Gaussian beams with different light field distributions are formed.

[0056] In another embodiment of the present invention, the receiving end includes a receiving aperture, a beam shrinker, a beam splitter, a camera, a photodetector and a signal processing unit in sequence, the output end of the receiving aperture is connected to the input end of the beam shrinker, the output end of the beam shrinker is connected to the input end of the beam splitter, the output end of the beam splitter is connected to the input ends of the camera and the photodetector, and the output end of the photodetector is connected to the input end of the signal processing unit. The receiving aperture is used to receive the combined Bessel-Gaussian beam; the beam reducer is used to focus the combined Bessel-Gaussian beam; the beam splitter is used to split the focused combined Bessel-Gaussian beam into two beams according to a specific power ratio, one beam is irradiated onto the photodetector, and the other beam is irradiated onto the camera; the camera is used to obtain the transverse electric field distribution and the center position of the combined Bessel-Gaussian beam; the photodetector is used to perform photoelectric conversion on the combined Bessel-Gaussian beam, and convert the optical signal into an electrical signal; the signal processing unit is used to restore the electrical signal, obtain the original digital information and analyze the original digital information, set a decision threshold, record the electrical pulse sequence signal above the decision threshold as a binary symbol 1, and record the electrical pulse sequence signal below the decision threshold as a binary symbol 0, to form a binary digital sequence of the electrical pulse sequence signal, and compare this binary digital sequence with the digital sequence in the on-off keying modulation signal at the transmitting end to obtain the bit error rate characteristics of the original digital information.

[0057] This embodiment proposes a free-space optical communication system that suppresses atmospheric turbulence. A combined Bessel-Gaussian beam optical signal in an on-off keying modulation format is generated at the transmitting end. The non-diffraction characteristics, self-repair capabilities, and spatial diversity gain of the combined Bessel-Gaussian beam are utilized to reduce the impact of atmospheric turbulence on the communication link, minimize pointing errors and light intensity flicker in space laser communications, and utilize photodetectors to convert optical signals into electrical signals for demodulation. This can effectively improve the transmission performance and stability of the free-space optical transmission system in complex environments.

[0058] Example 2

[0059] This embodiment provides a simulation method for suppressing atmospheric turbulence based on a combined Bessel-Gaussian beam, which specifically includes:

[0060] Establish a simulation model of the system as in the above embodiment 1, and set simulation conditions and simulation parameters;

[0061] Specifically, the simulation conditions include beam wavelength, grid length, beam waist radius, angular index and radial index, receiving aperture, atmospheric turbulence intensity, number of simulations, etc., and the simulation parameters include the transmission distance of the beam.

[0062] In a specific implementation process, after establishing the simulation model of the free-space optical transmission system described above, the beam wavelength is set to 1550 nm, the simulation grid is 2000×2000, the length of each grid is 10 μm, and the Bessel-Gaussian beam order is set to 0, 3, and -3 to generate a combined Bessel-Gaussian beam. The waist radius of the Gaussian beam is 20 mm, and the width parameter is 100.

[0063] By changing the simulation parameters, the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam were simulated. After the two beams experienced the same intensity of atmospheric turbulence, the simulation results were calculated.

[0064] Specifically, during the simulation process, the parameter that needs to be changed to create a contrast effect is the beam transmission distance parameter. Changing the beam transmission distance simulates the initial fundamental mode Gaussian beam and the combined Bessel-Gaussian beam. The two beams are subjected to the same intensity of atmospheric turbulence for simulation, and the atmospheric coherence length r0 is used to represent the atmospheric turbulence intensity. The final simulation results are specifically described as the first simulation result and the second simulation result. The specific simulation process is as follows:

[0065] A beam transmission function is constructed, and the effect of atmospheric turbulence on the beam is equivalent to a phase screen. The Kolmogorov turbulence theory is used to simulate atmospheric turbulence and generate a phase screen with the same size as the beam cross section. In order to simulate atmospheric turbulence more realistically, the transmission distance of the beam is divided into n segments. For each transmission segment, the beam passes through the phase screen once. This process is repeated n times to obtain the light field distribution of the two beams after passing through the phase screen (atmospheric turbulence) respectively.

[0066] In this embodiment, the first simulation result includes the diameter of the beam center distribution circle of the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam at the receiving surface of the receiving end camera under strong turbulence. The diameter of the beam distribution circle at the receiving end is twice the distance between the center of the camera receiving surface and the farthest beam center point; the center of the beam at the receiving surface of the receiving end camera is calculated using the grayscale centroid method, and its expression is:

[0067]

[0068] Where xc and yc are the x and y coordinates of the center of the light beam, respectively. The number of pixels in the simulation area is m × n. I is the grayscale value of each pixel.

[0069] In this embodiment, the second simulation result includes the aperture scintillation index of the beam power received by the photodetector at the receiving end under a fixed receiving aperture for the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam under strong turbulence. The aperture scintillation index of the beam power received by the photodetector at the receiving end is expressed as

[0070]

[0071] Where m2 is the aperture scintillation index, Pr(L) is the received power, Ir is the light intensity, and L is the transmission distance.

[0072] In a specific implementation process, the transmission distance is set to 100m, the number of phase screens is 50, and the number of simulations is 100. Thus, the lateral spot distribution of 100 single combined Bessel-Gaussian beams and fundamental mode Gaussian beam pulses at the receiving surface of the receiving camera under strong turbulence conditions is obtained. Using the lateral spot distribution, the grayscale centroid method is used to calculate the beam center position distribution of the two beams after 100 simulations. The diameter of the beam distribution circle at the receiving end is calculated to be twice the distance between the center of the camera receiving surface and the farthest beam center point. The first simulation result is as follows: Figure 3 As shown; using the received beam power, the aperture scintillation index of the two beam simulations 100 times is calculated, and the second simulation result is as follows Figure 4 shown.

[0073] By simulating the combined Bessel-Gaussian beam obtained by the present invention, it can be found that the beam has non-diffraction characteristics, self-repair ability, and spatial diversity gain. Therefore, it can be seen in the simulation that it can effectively reduce the influence of atmospheric turbulence during long-distance transmission in free space, reduce the pointing error of space laser communication, and effectively improve the transmission performance of the free-space optical transmission system in complex environments.

[0074] Those skilled in the art should understand that the present invention can be implemented in many other specific forms without departing from the spirit and scope of the present invention. Based on the embodiments of the present invention, any changes and modifications made by ordinary technicians in the field of the present invention in accordance with the above disclosure are within the scope of protection of the claims.

Claims

1. A free-space optical communication system for suppressing atmospheric turbulence, characterized in that: include: The transmitting end is used to generate a fundamental mode Gaussian beam, modulate and collimate it, and convert the Gaussian beam into a combined Bessel-Gaussian beam; The receiving end is used to receive the combined Bessel-Gaussian beam and perform position detection and signal restoration on it to obtain the original digital information; The combined Bessel-Gaussian beam is formed by superimposing Bessel-Gaussian beams of different orders that are orthogonal to each other.

2. The free-space optical communication system for suppressing atmospheric turbulence according to claim 1, characterized in that: The transmitting end includes: a laser and a modulator connected to the output end of the laser, a collimator connected to the output end of the modulator, a combined Bessel-Gaussian beam converter connected to the output end of the collimator, and a beam expander connected to the output end of the combined Bessel-Gaussian beam converter; The laser is used to generate and emit a fundamental mode Gaussian beam; The modulator is used to load an electrical signal into the fundamental mode Gaussian beam; The collimator is used to collimate the divergent light beam to form a collimated fundamental mode Gaussian beam; The combined Bessel-Gaussian beam converter is used to convert the fundamental mode Gaussian beam into a combined Bessel-Gaussian beam; The beam expander is used to expand the combined Bessel-Gaussian beam.

3. The free-space optical communication system for suppressing atmospheric turbulence according to claim 2, wherein: The electrical signal is an on-off keying modulation signal.

4. The free-space optical communication system for suppressing atmospheric turbulence according to claim 2, wherein: The combined Bessel-Gaussian beam converter comprises: Linear polarizer, used to change the polarization state of the fundamental mode Gaussian beam; a spatial light modulator for loading a combined Bessel-Gaussian beam phase hologram to generate a combined Bessel-Gaussian beam; The reflecting mirror is used to reflect the combined Bessel-Gaussian beam outward.

5. The free-space optical communication system for suppressing atmospheric turbulence according to claim 3, wherein: The receiving end includes: a receiving aperture and a beam reducer connected to an output end of the receiving aperture, a beam splitter connected to an output end of the beam reducer, a camera and a photodetector connected to an output end of the beam splitter, and a signal processing unit connected to an output end of the photodetector; The receiving aperture is used to receive the combined Bessel-Gaussian beam; The beam reducer is used to focus the combined Bessel-Gaussian beam; The beam splitter is used to split the focused combined Bessel-Gaussian beam into two beams, one beam irradiating the photodetector and the other beam irradiating the camera; The camera is used to obtain the transverse electric field distribution and the center position of the combined Bessel-Gaussian beam; The photodetector is used to perform photoelectric conversion on the combined Bessel-Gaussian beam, converting the optical signal into an electrical signal; The signal processing unit is used to restore the electrical signal to obtain original digital information and analyze the original digital information.

6. The free-space optical communication system for suppressing atmospheric turbulence according to claim 5, characterized in that: The signal processing unit analyzes the original digital information by setting a decision threshold, recording the electrical pulse sequence signals above the decision threshold as binary symbols 1, and recording the electrical pulse sequence signals below the decision threshold as binary symbols 0, thereby forming a binary digital sequence of the electrical pulse sequence signal, and comparing this binary digital sequence with the digital sequence in the on-off keying modulation signal of the transmitting end to obtain the bit error rate characteristics of the original digital information.

7. A free-space optical communication simulation method for suppressing atmospheric turbulence, characterized in that: The method comprises: Establishing a simulation model of the free-space optical communication system for suppressing atmospheric turbulence according to any one of claims 1 to 6, and setting simulation conditions and simulation parameters; By changing the simulation parameters, simulating the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam, the simulation results are calculated after the two beams experience the same intensity of atmospheric turbulence.

8. The free-space optical communication simulation method for suppressing atmospheric turbulence according to claim 7, characterized in that: The simulation conditions include at least one of the following: beam wavelength, grid length, beam waist radius, angular index and radial index, receiving aperture, atmospheric turbulence intensity and simulation times; and the simulation parameters include the transmission distance of the beam.

9. The free-space optical communication method for suppressing atmospheric turbulence according to claim 7, wherein: The simulation results include a first simulation result and a second simulation result; The first simulation result includes the diameters of the beam distribution circles of the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam at the receiving surface of the camera at the receiving end under strong turbulence, and the beam distribution circle diameter at the receiving end is twice the distance between the center of the camera receiving surface and the farthest beam center point; The second simulation result includes the aperture scintillation index of the fundamental mode Gaussian beam and the combined Bessel-Gaussian beam under strong turbulence and the beam power received by the photodetector at the receiving end at a fixed receiving aperture.

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