Abstract

This Letter concentrates on the transverse limitations imposed by a finite aperture optical propagation link that supports free space optical communication. Here it is assumed that a series of states, which are the spatial component of the message, are sent through the communication channel. The spatial bandwidth of the propagation link expressed as bits per transmitted photon is computed as the product of the average link efficiency times the entropy of the link. To facilitate the evaluation, it is assumed that the transmitted states are minimum energy loss orbital angular momentum states expressed in the form of fnm(r)exp(imθ), where the radial function is controlled to ensure that, for each quantum number denoted by the values of n and m, the minimum energy loss is obtained. The results illustrate that the bandwidth in units of bits per transmitted photon is very nearly equal to log2(Nf2), where log2(·) denotes the logarithm in base 2 and the Fresnel number, Nf=(π/4)D1D2/(λz), where D1 is the diameter of the transmitting aperture, D2 is the diameter of the receiving aperture, λ is the wavelength of the light used, and z is the propagation distance.

© 2011 Optical Society of America

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References

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  1. L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
    [CrossRef]
  2. N. Gisin and R. Thew, Nat. Photon. 1, 165 (2007).
    [CrossRef]
  3. I. M. Gelfand and S. V. Fomin, Calculus of Variations(Dover, 2000).
  4. W. H. Louisell, Quantum Statistical Properties of Radiation (Pure & Applied Optics) (Wiley, 1973).

2007

N. Gisin and R. Thew, Nat. Photon. 1, 165 (2007).
[CrossRef]

Allen, L.

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

Barnett, S. M.

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

Fomin, S. V.

I. M. Gelfand and S. V. Fomin, Calculus of Variations(Dover, 2000).

Gelfand, I. M.

I. M. Gelfand and S. V. Fomin, Calculus of Variations(Dover, 2000).

Gisin, N.

N. Gisin and R. Thew, Nat. Photon. 1, 165 (2007).
[CrossRef]

Louisell, W. H.

W. H. Louisell, Quantum Statistical Properties of Radiation (Pure & Applied Optics) (Wiley, 1973).

Padgett, M. J.

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

Thew, R.

N. Gisin and R. Thew, Nat. Photon. 1, 165 (2007).
[CrossRef]

Nat. Photon.

N. Gisin and R. Thew, Nat. Photon. 1, 165 (2007).
[CrossRef]

Other

I. M. Gelfand and S. V. Fomin, Calculus of Variations(Dover, 2000).

W. H. Louisell, Quantum Statistical Properties of Radiation (Pure & Applied Optics) (Wiley, 1973).

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Amplitude of minimum energy loss states.

Fig. 2
Fig. 2

Efficiency of minimum energy loss states.

Fig. 3
Fig. 3

Optimization for spatial bandwidth.

Equations (21)

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ψ nm ( r ) = f nm ( r ) e i m θ ,
T = η S ,
n , m , z = F n , m ,
P 0 = m , n n , m ,
P = z , m , n n , m , z = m , n F F n , m = m , n H n , m ,
H = F F .
P = m , n H n , m + ε nm ( P 0 m , n n , m ) ,
P ϵ nm = P 0 m , n n , m ,
P m , n = H n , m ϵ nm n , m .
H n , m = ε nm n , m ,
ε nm = m , n H n , m m , n n , m = P P 0 .
N f = π 4 D 1 D 2 λ z ,
η = 1 N p = 1 N ϵ p .
S = Tr ρ log 2 ρ ,
ρ = H / Tr H .
S = p = 1 N λ p log 2 λ p , λ p = ϵ p p = 1 N ϵ p ,
T = 1 N p = 1 N ϵ p p = 1 N λ p log 2 λ p .
T = { 0.76 + 2.12 log 2 N f , for all states ; 0.96 + 1.16 log 2 N f , for lowest loss radial state .
T log 2 N f 2 .
N 0 = 2 T .
N 0 = N f 2 .

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