| Free-space optical communication constructs an important part of the information transmission network.Implementing vortex beams that carry orbital angular momentum(OAM)as carriers can meet the increasing demand for information capacity.At the same time,high-dimensional quantum entanglement based on orbital angular momentum furtherly expands the application range of vortex beams.However,the turbulent medium in the free space will greatly distort the orbital angular momentum,which directly affects the performance of the communication system.To have better establishment and optimization of communication systems,it is crucial to carry out research on the transmission characteristics of orbital angular momentum in turbulence.In this paper,effects of turbulent medium on the orbital angular momentum are analyzed in two dimensions: detection probability and concurrence,including the discussion of classical single photon and quantum entanglement.We mainly use the pure phase perturbation model,combining the multi-phase-screen method with experimental data for comparative study.The main work of this paper is as follows:(1)The single-photon phase-only perturbation model is extended to the entangled biphoton state.Based on the initial Bell state,considering the independence of the two channels,the expression of the detection probability distribution for entangled two-photons is derived.It is analytically shown that the mutual conversion between the initially entangled OAM provides additional turbulence resistance to the signal photons and indicates the advantage of low-order OAM entanglement.(2)The phase correlation arc is proposed,and the universal law of entanglement decay of orbital angular momentum is revealed.To solve the finite-size effect in the phase correlation length,the phase correlation arc is established to explore the attenuation mechanism of OAM entanglement in turbulence.Meanwhile,the phase correlation arc can be compatible with vortex beams with phase drift characteristics,indicating that it is more universal than the phase correlation length.On the other hand,the phase correlation arc includes the influence of diffraction effect on the entanglement.Numerical simulations prove the importance of considering the actual transmission distance rather than the light source plane.Based on the phase correlation arc and the universal decay law of entanglement,the maximum distance of entanglement survival in turbulence is given,and the independence of orbital angular momentum can be degenerated to the previous experimental conclusion under the specific experimental condition.This distance formula possesses more physical significance and wider application scenarios than the existing experimental conclusion.(3)The detection probability distribution of a pure vortex beam in random turbulence medium with complete turbulence strength range is constructed.Based on the phase-only perturbation model of single photon,the calculation of turbulence effect is largely simplified by the quadratic phase approximation.Firstly,for the atmospheric turbulence environment,the accuracy of the model is verified by using the experimental data of the real atmosphere.Compared with the previous results,the minimum or maximum conditions of turbulence strength are too strict,but the model presented in this paper can maintain good accuracy in the whole strength interval,especially in the moderate strength interval.Secondly,the spatial coherence radius is used in the model,and the applicability of the model in all kinds of turbulence is demonstrated by using simulated oceanic turbulence data in the laboratory and simulated data generated by the multiphase screen method.(4)The propagation characteristics of entangled auto-focusing Airy beam in oceanic turbulence are studied.In this chapter,the evolution process of auto-focusing and entanglement in turbulence is discussed from the perspective of detection probability.Oceanic turbulence is affected by many factors such as salinity,temperature and stratification,and the variation of turbulence strength in oceanic turbulence is discussed.The propagation process of Airy beam is simulated accurately by generalized Huygens-Fresnel principle,and the influences of light source factors on auto-focusing are analyzed.Under the influence of oceanic turbulence,the auto-focusing characteristics decrease with the increment of turbulence strength.With growing strength,the focus distance and focus intensity reduce,and the beam spread becomes more serious.Both auto-focusing and entanglement have a certain improvement effect on the detection probability.The improvement of auto-focusing comes from the entire OAM subspace,while the entanglement is only affected by the initial entanglement space.Although there is competition between them,the common effect of auto-focusing and entanglement finally improves the detection probability of OAM,suggesting the potential advantages of the auto-focusing beams in quantum communication links. |
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