Propagation Of The Bessel Gaussian Beam In Turbulence And Application

Bessel beam is widely studied for its non-diffractive and self healing property.Moreover,there is the orbital angular momentum(OAM)of the high order Bessel beam.Therefore,the Bessel beam is widely applied to the free-space optical communication,the laser radar systems,the imaging systems analysis and the particle manipulation.And there are much more advantages of the Bessel beam over the OAM beam,such as the expression of the Bessel beam at the received plane is simpler,the energy is more concentrated and it can also carry more the information.These are all its advantages for the application in the laser communication.This paper majors in providing the theoretical basis for the Bessel Gaussian beams propagation through the turbulence and its application.The innovation of this paper is shown below.1.The statistical moment of the turbulence is derived based on the Rytov theory in this paper which can be used to calculate the average intensity and scintillation index.This study expands the research method of Bessel Gaussian beam propagating through the turbulence for the beam propagation properties is always studied by the extended Huygens–Fresnel principle in the past decades.The average intensity in this paper is simple in format and easy to conclude the propagation property,the result without the second order approximation of the wave structure function is more accurate when the turbulence inner scale is small.The minimum scintillation is in the bright ring of the average intensity which indicates that the information carried by the intensity has less influenced by the turbulence.Based on the result in this paper,an interesting phenomenon is found that for special width Bessel Gaussian beam,the central average intensity could not be influenced by the turbulence for the turbulence perturbation could be equal to 0 only when the propagation distance and the beam width satisfies a three order equation.Moreover,the beam will become to the flat top or flat bottom beam at this circumstance.These properties are beneficial for the laser communication.2.The intensity of the Gaussian like beam propagating through the turbulence is derived which includes the annular cosine Gaussian beam(acGB)and modified Bessel Gaussian beam.The acGB is proposed and its average intensity could be expressed as a summation of several polynomials.The acGB has the similar propagating properties to the Bessel Gaussian beams and it could approximate the low order Bessel Gaussian beams within specific parameters.3.The multiple Bessel Gaussian beam(mBGB)is proposed to investigate the beam multiplexing.It is proved that the turbulence influence on the angular distribution of the average intensity of any sub beam of the mBGB is the same and the turbulence only causes the beam diverge.Only when the order difference between each of two sub beams is the integer multiples of the minimum order difference,there is the rotational symmetry of the average intensity distribution and the rotational frequency is the minimum order difference.With the propagation distance increasing,the side lobes at the radial direction will combine to a large lobe which implies that the energy will be more focusing with the distance increasing.The scintillation of the mBGB is also studied and the symmetry of the scintillation is the same as that of the average intensity.These properties all also do benefit to the beam multiplexing.4.The multiplexing and demultiplexing method of the Bessel Gaussian beam is also studied in this paper.For different order Bessel function is linearly independent,the beam order and the information carried by the OAM could be detected in theory.Based on this theory,a demultiplexing method is proposed and the accuracy of the result is texted by the phase screen method.The applicable condition is also provided based on the probability and the statistics theory.There are 2 major advantages of the Bessel Gaussian beam in the field of the communication over the general vortex beam.One is that the expression of the Bessel Gaussian at the received plane is simpler and the energy is more concentrated than the general vortex beam.The other advantage is that there are two more beam width dimension of the Bessel Gaussian beam which can also carry information.And the demutiplexing method in this paper could realize these advantages.Therefore,this paper is of great significance to the beam multiplexing in the laser communication.This paper provides theoretical basis for the Bessel Gaussian beam propagating through the turbulence and the application in the laser communication.