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Chinese Physics Letters

Effects of Turbulent Aberrations on Probability Distribution of Orbital Angular Momentum for Optical Communication

Yixin Zhang, Ji Cang

Published Jul 1, 2009• 15 citations
Publisher

Abstract

Effects of atmospheric turbulence tilt, defocus, astigmatism and coma aberrations on the orbital angular momentum measurement probability of photons propagating in weak turbulent regime are modeled with Rytov approximation. By considering the resulting wave as a superposition of angular momentum eigenstates, the orbital angular momentum measurement probabilities of the transmitted digit are presented. Our results show that the effect of turbulent tilt aberration on the orbital angular momentum measurement probabilities of photons is the maximum among these four kinds of aberrations. As the aberration order increases, the effects of turbulence aberrations on the measurement probabilities of orbital angular momentum generally decrease, whereas the effect of turbulence defocus can be ignored. For tilt aberration, as the difference between the measured orbital angular momentum and the original orbital angular momentum increases, the orbital angular momentum measurement probability decreases.

DOI
10.1088/0256-307x/26/7/074220

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Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.
The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.
The well defined spin and orbital angular momentum states of photons offers a practical realization of quantum digits and a means of secure single-photon optical communication. The orbital angular momentum is associated with the spatial distribution of the wavefunction and the number of orbital angular momentum eigenstates is unlimited, giving the possibility of arbitrary base-N digits. In this paper, free-space optical communications using angular momentum states of single photons is investigated and in particular the effect of atmospheric turbulence on the angular momentum of the photons is modelled. The refractive index fluctuations in the atmosphere perturb the complex amplitude of a propagating beam so that the photons that were launched in an eigenstate of orbital angular momentum are no longer guaranteed to be in the original eigenstate after propagation. By considering the resulting wave as a superposition of angular momentum states, the probability of obtaining correct or incorrect measurements of the transmitted digit is calculated. The effect on a free-space optical communication using orbital angular momentum and the use of adaptive optics is discussed. The information capacity per photon is quantified and compared to that using polarization states for binary digits.
The effect of atmospheric turbulence on quantum optical communication systems based on angular momentum states of single photons is investigated and the detection probabilities of the orbital angular momentum of the photons propagation in slant atmospheric turbulence channel is modeled with Rytov approximation and modified von Karman spectrum model of index-of-refraction fluctuation.The statistical averaging of the orbital angular momentum  of single photon in quantum communication channel is given.
The well defined orbital angular momentum states of photons offer a practical realization of quantum digits and a means of secure single-photon optical communication. The orbital angular momentum is associated with the spatial distribution of the wave function and the number of orbital angular momentum eigenstates is unlimited, giving the possibility of arbitrary base-N digits. The free-space optical communications using angular momentum states of single photons is investigated and the effect of slant path atmospheric turbulence on the angular momentum of the photons is modeled with Rytov approximation and modified von Karman spectrum model of index-of-refraction fluctuation. The analytical modeling for the angular momentum scattering due to the atmospheric turbulence and the orbital angular momentum quantum number for photons propagation in slant path atmospheric turbulence are presented. The refractive index fluctuations in the atmosphere perturb the complex amplitude of a propagating beam so that the photons that were launched in an eigenstate of orbital angular momentum are no longer guaranteed to be in the original eigenstate after propagation.
Abstract The entangled orbital angular momentum (OAM) photons propagating across a weakly turbulent atmosphere are investigated. Here, the paper uses the single-phase screen model based on the Kolmogorov theory of turbulence, and focuses on the influence of the backward scattering on OAM evolution. The results indicate that backward scattering plays an important role in the analysis of OAM entanglement evolution in the turbulent atmosphere. It cannot be negligible especially for higher-order OAM mode. Moreover, when OAM mode is greater than 4, entangled photon pairs composed of higher OAM modes are not more robust in turbulence within the weak scintillation regime. These results will be useful in future investigations of OAM-based optical wave propagation through turbulent atmosphere.