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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 452–461
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Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states

S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 452-461 (2012)
http://dx.doi.org/10.1364/OE.20.000452


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Abstract

The effect of atmosphere turbulence on light’s spatial structure compromises the information capacity of photons carrying the Orbital Angular Momentum (OAM) in free-space optical (FSO) communications. In this paper, we study two aberration correction methods to mitigate this effect. The first one is the Shack-Hartmann wavefront correction method, which is based on the Zernike polynomials, and the second is a phase correction method specific to OAM states. Our numerical results show that the phase correction method for OAM states outperforms the Shark-Hartmann wavefront correction method, although both methods improve significantly purity of a single OAM state and the channel capacities of FSO communication link. At the same time, our experimental results show that the values of participation functions go down at the phase correction method for OAM states, i.e., the correction method ameliorates effectively the bad effect of atmosphere turbulence.

© 2011 OSA

1. Introduction

In 1992, Allen et. al. showed that light can carry orbital angular momentum (OAM), and that an azimuthal phase dependence exp(ilθ) of a light beam corresponds to units of OAM [1

1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]

]. In principle, there is an infinite number of OAM eigenstates by a single-photon, which offer the possibilities of realizing arbitrary base-N quantum digits per single photon for free space optical communications (FSO) and quantum communications [2

2. J. Wang, J. Yang, I. Fazal, N. Ahmed, Y. Yan, B. Shamee, A. Willner, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, and M. Tur, “Demonstration of 12.8-bit/s/Hz spectral efficiency using 16-QAM signals over multiple orbital-angular-momentum modes,” in 37th European Conference and Exhibition on Optical Communication, paper We.10.P1.76 (2011).

5

5. M. Gruneisen, W. Miller, R. Dymale, and A. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47, A32–A42 (2008). [CrossRef] [PubMed]

]. In contrast to the polarization degree of freedom, which provides only a two dimensional Hilbert space, OAM states of one photon may carry more information. Furthermore, the orthogonality among beams with different OAM states allows a simultaneous information transmission by different users with their own separate states [6

6. J. Garcia-Escartin and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 062320 (2008). [CrossRef]

]. At the same time, experiments demonstrated the possibility of information transmission using OAM states [7

7. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004). [CrossRef] [PubMed]

], and the information encoded in OAM states was resistant to any eavesdropping. Therefore, OAM states provide a promising method to increase the transmission rates and the security of FSO and quantum communications.

In this paper, we first shortly review turbulent aberrations and the two phase correction methods. Then, we study an atmospheric turbulence model [14

14. L. Andrews and R. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005). [CrossRef]

, 15

15. R. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978). [CrossRef]

] and discuss the two methods to mitigate the decoherence effect of turbulent aberrations by numerical simulations. One is the Shack-Hartmann wavefront correction method, and the other is a phase correction method for OAM states. Finally, we testify the phase correction method for OAM states by experiments.

2. Turbulent aberrations and phase correction methods

The spatial variation in atmospheric aberration can be approximated using several thin sheets that modify the phase profile of the propagating beam. Usually, phase fluctuations result in amplitude fluctuations as the beam propagates. In simulations, the plane of the aberration can be modeled by an N × N array of random complex numbers with statistics that matches the fluctuations of the index of refraction. Many numerical methods have been proposed to simulate atmosphere turbulence [14

14. L. Andrews and R. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005). [CrossRef]

18

18. M. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008). [CrossRef]

]. Here, we use the model developed by Hill [15

15. R. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978). [CrossRef]

] and defined analytically by Andrews [14

14. L. Andrews and R. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005). [CrossRef]

]. The spectrum of fluctuations in index of refraction Φn(kx, ky) is then given as
Φn(kx,ky)=0.033Cn2[1+1.802kx2+ky2kl20.254[kx2+ky2kl2]7/12]×exp[kx2+ky2kl2][kx2+ky2+1L02]11/6,
(1)
where Cn2 is the structure constant of the index of refraction, which represents the strength of turbulence, Lo2 is the outer scale of turbulence that is the largest eddy size formed by injection of turbulent energy, kl=3.3l0, l0 is equals to the inner scale of turbulence, and ki (i = x, y) is the wavenumber in i direction. Then, the phase spectrum Φ(kx, ky) is
Φ(kx,ky)=2πk02ΔZΦn(kx,ky),
(2)
where ΔZ is the spacing between the subsequent phase screens, and k0 is the wavenumber of the light. The phase screen φ(x,y) can be evaluated as the Fourier transform of a complex random distribution with the variance σ2 as follows:
φ(x,y)=FFT(Cσ(kx,ky)),
(3)
and
σ2(kx,ky)=(2πNΔx)2Φ(kx,ky),
(4)
where C is an N × N array of complex random numbers with zero mean and variance one, and Δx is the grid spacing. Here, the grid spacing in x direction is assumed to be equal to that in y direction.

As we discuss later, phase distortion will be produced by atmosphere turbulence for a propagating beam. We use a retrieval algorithm to obtain the distortion phase, and consequently include the information about imperfections into the beam by some device, such as Spatial Light Modulation (SLM). This way we can obtain the ’perfect’ image at the receiver.

In the following there are two retrieval algorithms. The first one is the Shack-Hartmann wavefront correction method (SH-algorithm), which is commonly used to reconstruct random phase distortions caused by the aberrations [19

19. B. Platt, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

,20

20. V. Voitsekhovich, “Hartmann test in atmospheric research,” J. Opt. Soc. Am. A 13, 1749–1757 (1996). [CrossRef]

]. Its principle is based on the measurement of local slops incoming to the Hartmann mask wavefront. The mask wavefronts are mathematical functions called Zernike polynomials. Any wavefront φ(x,y) can completely be described by a linear combination of Zernike polynomials Z0, Z1,..., ZN [19

19. B. Platt, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

]
φ(x,y)=k=0NakZk(x,y).
(5)
Now, assuming that φ(x,y) is the deformation wavefront caused by turbulent aberrations. By model estimation and using the least-squares method, the coefficients ai can be obtained by solving the equantion
φx(x,y)=k=1NakZkx(x,y),
(6)
and
φy(x,y)=k=0NakZky(x,y).
(7)
that is
(Gx(1)Gy(1)Gx(m)Gy(m))=(D1x(1)Dnx(1)D1y(1)Dny(1)D1x(m)Dnx(m)D1y(m)Dny(m))(a1an).
where, Gx(m) = φ′x (m), Gy(m) = φ′y (m), Dkx(m) = Zkx(m), and Dky(m) = Zky(m). This equation can be expressed in a simplified form
G=DA,
(8)
and the coefficients of Zernike polynomial A is can then be calculated by
A=D1G.
(9)
This way, we could get the phase of deformation wavefront caused by atmosphere turbulence using above coefficients and Eq. (5).

The second retrieval algorithm is a phase correction method for OAM states, which is proposed to measure and correct the surface defects of beam by using Gerchberg-Saxton phase retrieval algorithm (GS-algorithm) [21

21. A. Jesacher, A. Schwaighofer, S. Frhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007). [CrossRef] [PubMed]

]. GS-algorithm will deal there with the problem of finding the phase φ(x,y) of a light field by just determining the modulus A(kx, ky) of its Fourier transform as
A(kx,ky)exp[iΦ(kx,ky)]=F{exp[iφ(x,y)]}.
(10)
In [21

21. A. Jesacher, A. Schwaighofer, S. Frhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007). [CrossRef] [PubMed]

], φ(x,y) corresponds to the hologram function, and A(kx, ky) to the amplitude of the observed doughnut mode. GS-algorithm is iterative, and its procedure is as follows. A perfect phase spiral is used as a starting point, and the illumination beam profile is selected as the magnitude in the Spatial Light Modulation plane. A complex Fast Fourier Transform (FFT) is used to generate the phase in the diffraction plane. The magnitude part of a perfect ring is discarded and replaced with the distorted image generated by the SLM, and then transformed back to the SLM plane, where the magnitude is replaced with the illumination beam profile. After a few iterations of the loop, the phase will generally converge to a value, and the phase of the aberration can be retrieved. Moreover, it is shown that this retrieval algorithm can be implemented by experiment [22

22. R. Bowman, “Aberration correction for spatial light modulators,” Master’s thesis (Churchill College, 2007).

].

3. Simulation results

3.1. A single OAM state propagating through turbulence and its purity

Fig. 1 shows the aberration caused by the atmosphere turbulence and a single OAM state propagating through turbulent atmosphere with and without aberration correction. The parameters for the simulation of atmosphere turbulence are the following: Cn2=5×1013m2/3, L0 = 50m, l0 = 0.0002m, N =140, Δx=0.0003m, and ΔZ=50m. In the simulation, there are supposed five phase screens during the beam propagation. The results show that the purity of the input OAM state, l = −3, is damaged by the turbulent atmosphere, and the OAM state can be recovered by an aberration correction method.

Fig. 1 The aberration caused by atmosphere turbulence and the mitigation effect of the aberration correction methods. (a) propagation through turbulent atmosphere without aberration correction (b) propagation through turbulent atmosphere with aberration correction.

In order to express the damaged effect of atmosphere turbulence and the recovery impact of aberration correction, we use decomposition in Fig. 1. Since LG modes are an orthogonal set of functions, they will compose a complete basis. Any state can be decomposed using this orthogonal basis, which is
Ψ(r,θ,z)=plap,l(z)LGp,l(r,θ).
(11)
The probability of obtaining a measurement, lz = ℓh̄, is obtained by summing all probabilities associated with that eigenvalue
P(l)=p|ap,l(z)|2,
(12)
where the superposition coefficients ap,l(z) are given by the inner products
ap,l(z)=LGp,l(r,θ)|Ψ(r,θ,z).
(13)

In order to compare the mitigation effect of SH-algorithm and GS-algorithm presented in section 2, Fig. 2 shows the decomposition of the received state with the two correction methods in strong aberration case. The results show that for OAM =0 state, the probability of the OAM state keeping on =0 is only 25.3% in the atmospheric turbulence enviroment with Cn2=1×1012m2/3, L0 = 50m, l0 = 0.0002m, N = 128, Δx=0.0003m, ΔZ=100m. This probability can be improved to 63.8% by using SH-algorithm, where 12th order of Zernike polynomials have been used to estimate the wavefront. And this probability can be enhanced to 69% by using GS-algorithm. The results show that the two aberration correction methods have improved the beam quality significantly, then the phase correction method for OAM states show a better performance.

Fig. 2 Decomposition of the beam after passing through atmospheric turbulence with and without a correction. (a) original decomposition (b) without a correction (c) corrected by the Shark-Hartmann wavefront correction method (d) corrected by the phase correction method for OAM states.

3.2. A communication system on OAM and its capacity

Fig. 3 shows that the probability of keeping original OAM state varies with the strength of turbulent aberration. The results show that the probability of obtaining the original LG mode (corresponding to Δ = 0) decreases as Cn2 increases. At the same time, the probability for shifting to adjacent one LG mode (Δ = ±1) is higher than those to shift to two (Δ = ±2) or more modes. As the adjacent azimuthal modes increase, the probabilities of obtaining the original LG modes (Δ ≠ 0) decrease significantly.

Fig. 3 The effect of turbulence on the propagating OAM quantum states as functions of Cn2, where Cn2 varies from 1 × 10−14m−2/3 to 1 × 10−11m−2/3, representing the strength of turbulent aberration changing from weak to strong. The distance of propagating is 100m, the outer scale is 50m, and the inner scale is 0.0002m. The simulation grid comprises 128 × 128 elements, and the grid spacing size is 0.0003m.

Fig. 4 Comparison of the channel capacity for a communication link employing OAM states of single photon through atmospheric turbulence, corrected by Shark-Hartmann wavefront correction method and the phase correction method for OAM states.

4. Experimental results

From the above section, we find that the phase correction method for OAM states is more useful to overcome turbulent aberration in numerical simulations. On the other hand, if we use the observed intensity pattern in CCD as the deformation wavefront caused by turbulent aberration to Gerchberg-Saxton algorithm [22

22. R. Bowman, “Aberration correction for spatial light modulators,” Master’s thesis (Churchill College, 2007).

], the phase correction method for OAM states can be implemented experimentally. Therefore, we will discuss the effect of the phase correction method for OAM states as has been shown by the following experiments.

4.1. Experimental setup

Because LG modes of small helical charge have high sensitivity to the phase errors, even small phase irregularities cause significant deviations from their rotational symmetric ’doughnut’ shape, we utilize = 1 LG mode to determine the ’hologram’ of the turbulent atmosphere aberration from the distorted shape of a focused doughnut mode. Unfortunely, this mode does not explain the change numerically. In order to illustrate the improvement of the phase correction method for OAM states to the turbulent aberration, we will design a referenced spot mode ( = 0) besides the doughnut, and we will use the participation function (also named as sharpness metric) to measure the spot quality. The participation function of the referenced spot is defined as following
P=(i,jNIi,j)2i,jNIi,j2,
(14)
where Ii, j is the intensity of the (i, j)th pixel of the referenced spot. It is shown that the smaller value corresponds to the more tightly focused spot [24

24. J. R. Fienup and J. J. Miller, “Aberration correction by maximizing generalized sharpness metrics,” J. Opt. Soc. Am. A 20, 609–620 (2003). [CrossRef]

].

Fig. 5 shows the experimental system to test the turbulent aberration correction method. The reflective computer-controlled spatial light modulator shows a diffractive vortex lens, which transforms a collimated laser beam into an optical vortex of helical charge ( = 1 in the Fig. 5) and a referenced spot ( = 0) under somewhat turbulent aberration. As usual, the vortex lens is superposed by a grating in order to spatially separate the optical vortex generated in the first diffraction order from other orders. In order to detect the referenced spot besides the LG mode, different grating is assigned to LG mode and the referenced spot. The Fourier plane corresponds to the far-field diffraction pattern. A len (L3) is used to focus the image on CCD in the Fourier plane, and several mirrors are arranged so as to get the biggest image in CCD as possible.

Fig. 5 The sketch of the experimental setup.

4.2. improvement of the participation function

At first, we get a deformated doughnut and referenced spot when we include phase screen from the simulations about the turbulent aberration on the SLM, then we use the phase correction method for OAM states to obtain the ”correction hologram” of the turbulent aberration, and add it on the SLM. Finally, we can get an improved doughnut and referenced spot in CCD. The participation function of the reference spot with and without the correction method show the improvement of the correction method. In order to calculate the participation function with and without the correction method, we divide the CCD into two interesting areas, one for showing the correction procedures ( = 1 LG mode), and one for participation function calculations (( = 0 LG mode).

According to the atmosphere turbulence model, the random phase screen caused by atmosphere turbulence is mainly determined by the constant of the index of refraction. In order to understand the mitigation effect of the correction method, we measure the participation function of referenced spot with and without the correction method. We let the index of refraction change while keeping the other simulation parameters be constant during the experiments. Since the phase screen caused by atmospheric turbulence is random, phase screen obtained from the simulation is different from time to time, even with the same simulation parameters. We give the average value of the participation function in each case over 20 values.

Fig. 6 shows the variances of participation function with the constant of index of refraction varying from 10−15 to 10−12. The experimental results show that the values of participation function go down with the correction method, and the correction method is an effective way to mitigate the turbulent aberration. We get 45% maximum improvement and 17% average improvement by the change of strength of aberration.

Fig. 6 The variance of the participation functions for the reference spot with the change of the index of refraction by the phase correction method for OAM states.

5. Conclusion

In this work, we apply different aberration correction techniques [19

19. B. Platt, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

, 21

21. A. Jesacher, A. Schwaighofer, S. Frhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007). [CrossRef] [PubMed]

] to mitigate the deformation effect caused by the atmosphere turbulence. One is the Shack-Hartmann wavefront correction method, and the other is a phase correction method for OAM states. To quantify the improvements we calculate the channel capacities in a similar fashion to the method described in [8

8. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett 94, 153901 (2005). [CrossRef] [PubMed]

]. Our simulation results show that it is possible to recover the damaged LG mode caused by the atmosphere turbulence. The two correction methods have improved the purity of a single photon LG mode and the capacities of the free space optical communication channel produced by atmosphere turbulence significantly, and the phase correction method for OAM states outperforms the Shack-Hartmann wavefront correction method.

Using SLM, the phase correction method for OAM states is easier to implemented. We testify the correction method in a series of experiments. The experimental results show that the values of participation function decrease with the phase correction method for OAM states. The correction method is an effective way to mitigate the turbulent aberration both in simulations and experiments.

Acknowledgments

We would like to thank the anonymous referee for several useful comments. We are grateful to Prof. Jozef Gruska for careful reading the manuscript. Shengmei Zhao acknowledges support from the University Natural Science Research Foundation of JiangSu Province ( 11KJA510002), Foundation NJ210002, the project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the open research fund of Key Lab of Broadband Wireless Communication and Sensor Network Technology (Ministry of Education), China. Longyan Gong acknowledges support from the national natural science foundation of China(No. 10904074). The authors thank Optics group, School of Physics and Astronomy, Glasgow University for hosting Shengmei Zhao as a visitor while conducting this research.

References and links

1.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]

2.

J. Wang, J. Yang, I. Fazal, N. Ahmed, Y. Yan, B. Shamee, A. Willner, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, and M. Tur, “Demonstration of 12.8-bit/s/Hz spectral efficiency using 16-QAM signals over multiple orbital-angular-momentum modes,” in 37th European Conference and Exhibition on Optical Communication, paper We.10.P1.76 (2011).

3.

I. Djordjevic, “Deep-space and near-Earth optical communications by coded orbital angular momentum (OAM) modulation,” Opt. Express 19, 14277–14289 (2011). [CrossRef] [PubMed]

4.

I. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18, 24722–24728 (2010). [CrossRef] [PubMed]

5.

M. Gruneisen, W. Miller, R. Dymale, and A. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47, A32–A42 (2008). [CrossRef] [PubMed]

6.

J. Garcia-Escartin and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 062320 (2008). [CrossRef]

7.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004). [CrossRef] [PubMed]

8.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett 94, 153901 (2005). [CrossRef] [PubMed]

9.

J. Anguita, M. Neifeld, and B. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47, 2414–2429 (2008). [CrossRef] [PubMed]

10.

G. Tyler and R. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34, 142–144 (2009). [CrossRef] [PubMed]

11.

Y. X. Zhang and J. Chang, “Effects of turbulent aberrations on probability distribution of orbital angular momentum for optical communication,” Chin. Phys. Lett. 26, 074220 (2009). [CrossRef]

12.

C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys. 9, 94 (2007). [CrossRef]

13.

S. Zhao, J. Leach, and B. Zheng, “Correction Effect of Shark-Hartmann Algorithm on Turbulence Aberrations for free space Optical Communications Using Orbital Angular Momentum,” in 12th IEEE International Conference on Communication Technology (ICCT) , pp. 580–583 (2010). [CrossRef]

14.

L. Andrews and R. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005). [CrossRef]

15.

R. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978). [CrossRef]

16.

J. Strasburg and W. Harper, “Impact of atmospheric turbulence on beam propagation,” Proc. SPIE 5413, 93 (2004). [CrossRef]

17.

R. Frehlich, “Simulation of laser propagation in a turbulent atmosphere,” Appl. Opt. 39, 393–397 (2000). [CrossRef]

18.

M. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008). [CrossRef]

19.

B. Platt, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

20.

V. Voitsekhovich, “Hartmann test in atmospheric research,” J. Opt. Soc. Am. A 13, 1749–1757 (1996). [CrossRef]

21.

A. Jesacher, A. Schwaighofer, S. Frhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15, 5801–5808 (2007). [CrossRef] [PubMed]

22.

R. Bowman, “Aberration correction for spatial light modulators,” Master’s thesis (Churchill College, 2007).

23.

P. Vontobel, A. Kavcic, D. Arnold, and H. Loeliger, “A generalization of the Blahut–Arimoto algorithm to finite-state channels,” IEEE Trans. Inf. Theory 54, 1887–1918 (2008). [CrossRef]

24.

J. R. Fienup and J. J. Miller, “Aberration correction by maximizing generalized sharpness metrics,” J. Opt. Soc. Am. A 20, 609–620 (2003). [CrossRef]

OCIS Codes
(010.1285) Atmospheric and oceanic optics : Atmospheric correction
(060.2605) Fiber optics and optical communications : Free-space optical communication
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: September 7, 2011
Revised Manuscript: November 19, 2011
Manuscript Accepted: December 1, 2011
Published: December 21, 2011

Citation
S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, "Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states," Opt. Express 20, 452-461 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-452


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References

  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8189 (1992). [CrossRef] [PubMed]
  2. J. Wang, J. Yang, I. Fazal, N. Ahmed, Y. Yan, B. Shamee, A. Willner, K. Birnbaum, J. Choi, B. Erkmen, S. Dolinar, and M. Tur, “Demonstration of 12.8-bit/s/Hz spectral efficiency using 16-QAM signals over multiple orbital-angular-momentum modes,” in 37th European Conference and Exhibition on Optical Communication, paper We.10.P1.76 (2011).
  3. I. Djordjevic, “Deep-space and near-Earth optical communications by coded orbital angular momentum (OAM) modulation,” Opt. Express19, 14277–14289 (2011). [CrossRef] [PubMed]
  4. I. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express18, 24722–24728 (2010). [CrossRef] [PubMed]
  5. M. Gruneisen, W. Miller, R. Dymale, and A. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt.47, A32–A42 (2008). [CrossRef] [PubMed]
  6. J. Garcia-Escartin and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A78, 062320 (2008). [CrossRef]
  7. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12, 5448–5456 (2004). [CrossRef] [PubMed]
  8. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett94, 153901 (2005). [CrossRef] [PubMed]
  9. J. Anguita, M. Neifeld, and B. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt.47, 2414–2429 (2008). [CrossRef] [PubMed]
  10. G. Tyler and R. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett.34, 142–144 (2009). [CrossRef] [PubMed]
  11. Y. X. Zhang and J. Chang, “Effects of turbulent aberrations on probability distribution of orbital angular momentum for optical communication,” Chin. Phys. Lett.26, 074220 (2009). [CrossRef]
  12. C. Gopaul and R. Andrews, “The effect of atmospheric turbulence on entangled orbital angular momentum states,” New J. Phys.9, 94 (2007). [CrossRef]
  13. S. Zhao, J. Leach, and B. Zheng, “Correction Effect of Shark-Hartmann Algorithm on Turbulence Aberrations for free space Optical Communications Using Orbital Angular Momentum,” in 12th IEEE International Conference on Communication Technology (ICCT), pp. 580–583 (2010). [CrossRef]
  14. L. Andrews and R. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005). [CrossRef]
  15. R. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech.88, 541–562 (1978). [CrossRef]
  16. J. Strasburg and W. Harper, “Impact of atmospheric turbulence on beam propagation,” Proc. SPIE5413, 93 (2004). [CrossRef]
  17. R. Frehlich, “Simulation of laser propagation in a turbulent atmosphere,” Appl. Opt.39, 393–397 (2000). [CrossRef]
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