Abstract

A simple optical system for the self-homodyne detection of the orbital angular momentum (OAM) carried by optical beams is introduced. We propose two different schemes based on the use of optical hybrids, which could detect the OAM mode number, even when the input beam might be slightly distorted. A balanced receiver is used to perform a self-homodyne measure of the optical signal from two different locations at the beam wavefront.

© 2012 Optical Society of America

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References

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  1. J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  3. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef]
  4. A. Yao and M. Padgett, Adv. Opt. Photon. 3, 161 (2011).
    [CrossRef]
  5. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef]
  6. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
    [CrossRef]
  7. K. Murphy and C. Dainty, Opt. Express 20, 4988 (2012).
    [CrossRef]
  8. G. Li, Adv. Opt. Photon. 1, 279 (2009).
    [CrossRef]
  9. A. Belmonte and J. M. Kahn, Opt. Express 17, 2763 (2009).
    [CrossRef]
  10. L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, Appl. Opt. 26, 437 (1987).
    [CrossRef]
  11. R. Bracewell, “The Hilbert transform,” in The Fourier Transform and Its Applications (McGraw-Hill, 1999).
  12. T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
    [CrossRef]

2012 (1)

2011 (1)

2010 (1)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

2009 (2)

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1988 (1)

T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
[CrossRef]

1987 (1)

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Belmonte, A.

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Bracewell, R.

R. Bracewell, “The Hilbert transform,” in The Fourier Transform and Its Applications (McGraw-Hill, 1999).

Cheung, N. K.

Chidgey, P. J.

T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
[CrossRef]

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Curtis, L.

Dainty, C.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Harmon, R. A.

T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
[CrossRef]

Hodgkinson, T. G.

T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
[CrossRef]

Kahn, J. M.

Kazovsky, L. G.

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Li, G.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Murphy, K.

Padgett, M.

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Smith, D. W.

T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Torner, L.

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

Torres, J. P.

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yao, A.

Young, W. C.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

IEE Proc. (1)

T. G. Hodgkinson, R. A. Harmon, D. W. Smith, and P. J. Chidgey, IEE Proc. 135, 260 (1988).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett. (3)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Other (2)

J. P. Torres and L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

R. Bracewell, “The Hilbert transform,” in The Fourier Transform and Its Applications (McGraw-Hill, 1999).

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Figures (2)

Fig. 1.
Fig. 1.

Scheme of the coherent technique. An OAM beam wavefront is sampled at two different positions, and the signals are combined into a self-homodyne receiver.

Fig. 2.
Fig. 2.

Homodyne signal retrieved with two different versions of optical hybrids (shown in the figure). In (a) represents the desired self-homodyne term, and in (b) the signal is the complex phasor.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

U(ρ,ϕ)=Rm(ρ)exp(imϕ),
E1(r1,t)=I1exp{i[2πft+Φ(r1)+χ1]},E2(r2,t)=I2exp{i[2πft+Φ(r2)+χ2]}.
i1=R/2(I1+I2+2I{I1I2exp[i(ΔΦ+Δχ)]}),i2=R/2(I1+I22I{I1I2exp[i(ΔΦ+Δχ)]}),
V=2RrI1I2sin(Φ+χ).
ΔΦ=mΔϕ.
v=2Rrsin(mΔϕ).
v=2Rr[cos(mΔϕ)+isin(mΔϕ)].
|δΔϕ|Δϕ/4|m|,

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