Abstract

Optical communication with high photon-efficiency (many bits/photon) and high spectral efficiency (SE) (many bits/s-Hz) cannot be achieved unless multiple spatial modes are employed. For vacuum propagation, it is known that achieving 10 bits/photon and 5 bits/s-Hz requires 189 low-loss spatial modes at the ultimate Holevo limit and 4500 such modes at the Shannon limit for on–off keying with direct detection. For terrestrial propagation paths, however, atmospheric turbulence corrupts multiple spatial-mode operation. This paper derives power-transmissivity bounds and average intermodal crosstalks for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green’s function. These statistics are then evaluated for $\sim$200 spatial-mode systems whose transmitters use either focused-beam, Hermite–Gaussian (HG), or Laguerre–Gaussian (LG) modes and whose receivers either do or do not employ adaptive optics. It is shown that: (1) adaptive optics are not necessary for achieving both high photon information efficiency (PIE) and high SE; (2) systems employing HG or LG modes achieve the same capacities through turbulence; and (3) the orbital angular momentum carried by LG modes does not provide turbulence immunity. In the companion paper [N. Chandrasekaran, J. H. Shapiro, and L. Wang, “Photon Information Efficient Communication Through Atmospheric Turbulence—Part II: Bounds on Ergodic Classical and Private Capacities,” J. Lightw. Technol., vol. 32, no. 6, pp. 1088–1097, Mar. 2014], the transmissivity bounds are used to quantify the turbulence-induced loss in PIE versus SE performance for these mode sets.

© 2013 IEEE

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2013 (2)

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaka, T. Kobayashi, M. Watanabe, "305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber ," J. Lightw. Technol 31, 554-562 (2013).

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R .W. Boyd, J. H. Shapiro, A. E. Willner, "Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing," Opt. Lett. 38, 4062-4065 (2013).

2012 (4)

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, R. W. Boyd, "Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding," Opt. Exp. 20, 13195-13200 (2012).

D. M. Boroson, B. S. Robinson, D. A. Burianek, A. Biswas, "Overview and status of the lunar laser communications demonstration," Proc. SPIE 8246, art. 82460C , (2012).

R. J. Essiambre, R. W. Tkach, "Capacity trends and limits of optical communication networks," Proc. IEEE 100, 1035-1055 (2012).

B. Zhu, J. M. Fini, M. F. Yan, X. Liu, S. Chandrasekhar, T. F. Taunay, M. Fishteyn, E. M. Monberg, F. V. Dimarcello, "High-capacity space-division-multiplexed DWDM transmission using multicore fiber," J. Lightw. Technol 30, 486-492 (2012).

2011 (1)

B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello, "112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber," Opt. Exp. 19, 16665-16671 (2011).

2009 (1)

2008 (1)

J. A. Anguita, M. A. Neifeld, B. V. Vasic, " Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space link," Appl. Opt 47, 2414-2429 (2008).

2006 (1)

B. S. Robinson, A. J. Kerman, E. A. Dauler, R. O. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. W. Yang, K. K. Berggren, "781 Mbit/s photon-counting optical communications using a superconducting nanowire detector," Opt. Lett 31, 444-446 (2006).

2005 (2)

C. Paterson, "Atmospheric turbulence and orbital angular momentum of single photons for optical communication," Phys. Rev. Lett. 94, (2005).

J. H. Shapiro, S. Guha, B. I. Erkmen, "Ultimate channel capacity of free-space optical communications," J. Opt. Netw. 4 , 501-516 (2005).

2004 (2)

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, H. P. Yuen, "Classical capacity of the lossy bosonic channel: The exact solution," Phys Rev. Lett 92 , (2004).

D. Kedar, S. Arnon, "Urban optical wireless communication networks: The main challenges and possible solutions ," IEEE Commun. Mag. 42, S2-S7 (2004).

2003 (1)

J. H. Shapiro, "Near-field turbulence effects on quantum key distribution," Phys Rev. A 67, (2003).

2002 (1)

A. Vaziri, G. Weihs, A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett 89, (2002).

2001 (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, "Entanglement of the orbital angular momentum states of photons ," Nature 412, 313-316 (2001).

1998 (1)

D. J. T. Healey, D. R. Wisely, I. Neild, P. Cochrane, "Optical wireless: The story so far ," IEEE Commun. Mag 36, 72-74, 79–82 (1998).

1980 (1)

S. M. Wandzura, "Meaning of quadratic structure functions ," J. Opt. Soc. Amer. 70, 745-747 (1980).

1974 ()

1970 (1)

R. S. Kennedy, "Communication through optical scattering channels: An introduction," Proc. IEEE 58, 1651-1665 (1970).

1969 (1)

G. Toraldo di Francia, "Degrees of freedom of an image ," J. Opt. Soc. Amer. 59, 799-803 (1969).

1968 (1)

C. K. Rushforth, R. W. Harris, "Restoration, resolution, and noise," J. Opt. Soc. Amer 58, 539-544 (1968).

1967 (1)

A. A. M. Saleh, "An investigation of laser wave depolarization due to atmospheric transmission," IEEE J. Quantum Electron 3, 540-543 (1967).

1965 (1)

D. Slepian, "Analytical solution to two apodization problems ," J. Opt. Soc. Amer. 55, 1110-1114 (1965).

1964 (1)

D. Slepian, "Prolate spheroidal wave functions, Fourier analysis and uncertainty–IV: Extensions to many dimensions; generalized prolate spheroidal functions," Bell Syst. Tech. J. 43, 3009 -3057 (1964).

1962 (1)

J. P. Gordon, "Quantum effects in communication systems ," Proc. IRE 50, 1898-1908 (1962).

Adv. Opt. Photon. (1)

Appl. Opt (1)

J. A. Anguita, M. A. Neifeld, B. V. Vasic, " Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space link," Appl. Opt 47, 2414-2429 (2008).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Slepian, "Prolate spheroidal wave functions, Fourier analysis and uncertainty–IV: Extensions to many dimensions; generalized prolate spheroidal functions," Bell Syst. Tech. J. 43, 3009 -3057 (1964).

IEEE Commun. Mag (1)

D. J. T. Healey, D. R. Wisely, I. Neild, P. Cochrane, "Optical wireless: The story so far ," IEEE Commun. Mag 36, 72-74, 79–82 (1998).

IEEE Commun. Mag. (1)

D. Kedar, S. Arnon, "Urban optical wireless communication networks: The main challenges and possible solutions ," IEEE Commun. Mag. 42, S2-S7 (2004).

IEEE J. Quantum Electron (1)

A. A. M. Saleh, "An investigation of laser wave depolarization due to atmospheric transmission," IEEE J. Quantum Electron 3, 540-543 (1967).

J. Lightw. Technol (1)

B. Zhu, J. M. Fini, M. F. Yan, X. Liu, S. Chandrasekhar, T. F. Taunay, M. Fishteyn, E. M. Monberg, F. V. Dimarcello, "High-capacity space-division-multiplexed DWDM transmission using multicore fiber," J. Lightw. Technol 30, 486-492 (2012).

J. Lightw. Technol (1)

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaka, T. Kobayashi, M. Watanabe, "305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber ," J. Lightw. Technol 31, 554-562 (2013).

J. Opt. Netw. (1)

J. H. Shapiro, S. Guha, B. I. Erkmen, "Ultimate channel capacity of free-space optical communications," J. Opt. Netw. 4 , 501-516 (2005).

J. Opt. Soc. Amer (1)

C. K. Rushforth, R. W. Harris, "Restoration, resolution, and noise," J. Opt. Soc. Amer 58, 539-544 (1968).

J. Opt. Soc. Amer. (3)

G. Toraldo di Francia, "Degrees of freedom of an image ," J. Opt. Soc. Amer. 59, 799-803 (1969).

S. M. Wandzura, "Meaning of quadratic structure functions ," J. Opt. Soc. Amer. 70, 745-747 (1980).

D. Slepian, "Analytical solution to two apodization problems ," J. Opt. Soc. Amer. 55, 1110-1114 (1965).

Nature (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, "Entanglement of the orbital angular momentum states of photons ," Nature 412, 313-316 (2001).

Opt. Exp. (2)

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, R. W. Boyd, "Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding," Opt. Exp. 20, 13195-13200 (2012).

B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello, "112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber," Opt. Exp. 19, 16665-16671 (2011).

Opt. Lett (1)

B. S. Robinson, A. J. Kerman, E. A. Dauler, R. O. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. W. Yang, K. K. Berggren, "781 Mbit/s photon-counting optical communications using a superconducting nanowire detector," Opt. Lett 31, 444-446 (2006).

Opt. Lett. (1)

Phys Rev. A (1)

J. H. Shapiro, "Near-field turbulence effects on quantum key distribution," Phys Rev. A 67, (2003).

Phys Rev. Lett (1)

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, H. P. Yuen, "Classical capacity of the lossy bosonic channel: The exact solution," Phys Rev. Lett 92 , (2004).

Phys. Rev. Lett (1)

A. Vaziri, G. Weihs, A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett 89, (2002).

Phys. Rev. Lett. (1)

C. Paterson, "Atmospheric turbulence and orbital angular momentum of single photons for optical communication," Phys. Rev. Lett. 94, (2005).

Proc. IEEE (2)

R. J. Essiambre, R. W. Tkach, "Capacity trends and limits of optical communication networks," Proc. IEEE 100, 1035-1055 (2012).

R. S. Kennedy, "Communication through optical scattering channels: An introduction," Proc. IEEE 58, 1651-1665 (1970).

Proc. IRE (1)

J. P. Gordon, "Quantum effects in communication systems ," Proc. IRE 50, 1898-1908 (1962).

Proc. SPIE (1)

D. M. Boroson, B. S. Robinson, D. A. Burianek, A. Biswas, "Overview and status of the lunar laser communications demonstration," Proc. SPIE 8246, art. 82460C , (2012).

Other (12)

A. W. Marshall, I. Olkin, Inequalities: Theory of Majorization and Its Applications (Academic, 1979).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic , 1978).

L. C. Andrews, R. L. Phillips, Laser Beam Scintillation With Applications (SPIE, 2001).

L. C. Andrews, R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

B. Rodenburg, M. Mirhosseini, M. Malik, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating real-world turbulence in the lab: Orbital angular momentum communication through 1 km of atmosphere,” arXiv: 1301.7454 [physics.optics], 2013..

J. P. Gordon, Quantum Electronics and Coherent Light (Academic, 1964) pp. 156-181.

S. Guha, Z. Dutton, J. H. Shapiro, "On quantum limit of optical communications: concatenated codes and joint detection receivers," Dig. IEEE Int. Symp. Inform. Theory (2011) pp. 274-278 .

M. M. Wilde, S. Guha, S.-H. Tan, S. Lloyd, "Explicit capacity-achieving receivers for optical communication and quantum reading," Proc. IEEE Int. Symp. Inform. Theory (2012 ) pp. 551-555.

S. Dolinar, B. I. Erkmen, B. Moision, K. Birnbaum, D. Divsalar, "The ultimate limits of optical communication efficiency with photon-counting receivers ," Dig. IEEE Int. Symp. Inf. Theory (2012) pp. 541-545.

J. H. Shapiro, Laser Beam Propagation in the Atmosphere (Springer-Verlag, 1978, ch. 6 ).

N. Chandrasekaran, J. H. Shapiro, and L. Wang, “Photon information efficient communication through atmospheric turbulence—Part II: Bounds on ergodic classical and private capacities,” J. Lightw. Technol., vol. 32, no. 6, pp. 1088–1097, Mar. 2014..

B. I. Erkmen, J. H. Shapiro, "Performance analysis for near-field atmospheric optical communications," Proc. IEEE Global Telecommun. Conf. (2004) pp. 318 -324.

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