Abstract

A relativistically intense, ultrashort laser pulse with purely spin angular momentum produces second-harmonic radiation with equal parts of both spin and orbital angular momentum when focused into a plasma. The orbital contribution is due to an azimuthal phase variation that arises in the nonlinear current density. This phase variation is associated with the radial nonuniformity driven by ponderomotive blowout.

© 2009 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  2. L. Allen and M. Padgett, Opt. Commun. 184, 67 (2000).
    [CrossRef]
  3. M. Haines, Phys. Rev. Lett. 87, 135005 (2001).
    [CrossRef] [PubMed]
  4. M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5)35 (2004).
    [CrossRef]
  5. S. Franke-Arnold and A. Arnold, Am. Sci. 96, 226 (2008).
  6. E. Merzbacher, Quantum Mechanics (Wiley, 1970).
  7. J. Jackson, Classical Electrodynamics (Wiley, 1975).
  8. D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
    [CrossRef] [PubMed]
  9. A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002).
    [CrossRef]
  10. D. F. Gordon, W. B. Mori, and T. M. Antonsen, Jr., IEEE Trans. Plasma Sci. 28, 1224 (2000).
    [CrossRef]

2008

S. Franke-Arnold and A. Arnold, Am. Sci. 96, 226 (2008).

D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
[CrossRef] [PubMed]

2004

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5)35 (2004).
[CrossRef]

2002

A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002).
[CrossRef]

2001

M. Haines, Phys. Rev. Lett. 87, 135005 (2001).
[CrossRef] [PubMed]

2000

L. Allen and M. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

D. F. Gordon, W. B. Mori, and T. M. Antonsen, Jr., IEEE Trans. Plasma Sci. 28, 1224 (2000).
[CrossRef]

1992

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

Allen, L.

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5)35 (2004).
[CrossRef]

L. Allen and M. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

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

Antonsen, T. M.

D. F. Gordon, W. B. Mori, and T. M. Antonsen, Jr., IEEE Trans. Plasma Sci. 28, 1224 (2000).
[CrossRef]

Arnold, A.

S. Franke-Arnold and A. Arnold, Am. Sci. 96, 226 (2008).

Beijersbergen, M. W.

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

Courtial, J.

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5)35 (2004).
[CrossRef]

Franke-Arnold, S.

S. Franke-Arnold and A. Arnold, Am. Sci. 96, 226 (2008).

Gordon, D. F.

D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
[CrossRef] [PubMed]

D. F. Gordon, W. B. Mori, and T. M. Antonsen, Jr., IEEE Trans. Plasma Sci. 28, 1224 (2000).
[CrossRef]

Hafizi, B.

D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
[CrossRef] [PubMed]

Haines, M.

M. Haines, Phys. Rev. Lett. 87, 135005 (2001).
[CrossRef] [PubMed]

Jackson, J.

J. Jackson, Classical Electrodynamics (Wiley, 1975).

Kaganovich, D.

D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
[CrossRef] [PubMed]

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, 1970).

Meyer-ter-Vehn, J.

A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002).
[CrossRef]

Mori, W. B.

D. F. Gordon, W. B. Mori, and T. M. Antonsen, Jr., IEEE Trans. Plasma Sci. 28, 1224 (2000).
[CrossRef]

Padgett, M.

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5)35 (2004).
[CrossRef]

L. Allen and M. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

Pukhov, A.

A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002).
[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] [PubMed]

Ting, A.

D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
[CrossRef] [PubMed]

Woerdman, J. P.

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

Am. Sci.

S. Franke-Arnold and A. Arnold, Am. Sci. 96, 226 (2008).

Appl. Phys.

A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B74, 355 (2002).
[CrossRef]

IEEE Trans. Plasma Sci.

D. F. Gordon, W. B. Mori, and T. M. Antonsen, Jr., IEEE Trans. Plasma Sci. 28, 1224 (2000).
[CrossRef]

Opt. Commun.

L. Allen and M. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

Phys. Rev. A

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

Phys. Rev. Lett.

D. F. Gordon, B. Hafizi, D. Kaganovich, and A. Ting, Phys. Rev. Lett. 101, 045004 (2008).
[CrossRef] [PubMed]

M. Haines, Phys. Rev. Lett. 87, 135005 (2001).
[CrossRef] [PubMed]

Phys. Today

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5)35 (2004).
[CrossRef]

Other

E. Merzbacher, Quantum Mechanics (Wiley, 1970).

J. Jackson, Classical Electrodynamics (Wiley, 1975).

Supplementary Material (2)

» Media 1: MOV (1243 KB)     
» Media 2: MOV (26753 KB)     

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Figures (3)

Fig. 1
Fig. 1

Diagram for the nonlinear conversion of spin to orbital angular momentum. The lines are labeled by ( 1 ) | p , J z , where p is the momentum and J is the angular momentum (for paraxial rays [ p , J z ] 0 ). Wavy lines represent photons and braided lines represent plasmons. Time increases upward.

Fig. 2
Fig. 2

Density wave on a cylindrical shell of electrons, corresponding to the virtual plasmon of Fig. 1. Electrons are shown in green (lower density) and yellow (higher density). The centerline of the unperturbed electrons is shown as a dashed black circle. Electrons bunch in the direction opposite the electric field (white arrow). As the polarization vector rotates, so does the phase of the density wave (Media 1).

Fig. 3
Fig. 3

Transverse slices of the simulated E x field after applying a Fourier filter to suppress the pump. Light colors are positive and dark are negative. The constant phase contours are rotating spirals, which are characteristic of orbital angular momentum. The relatively large transverse wavenumber associated with conical emission is also evident (Media 2).

Equations (8)

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J = 1 2 π c d 3 r [ E × A + i E i ( r × ) A i ] ,
t n ( 1 ) = c n ( 0 ) a .
a 1 = a 0 2 ( x ̂ + i s y ̂ ) ,
j 2 = e c 2 a 0 2 4 i ω 0 ( x + i s y ) n ( 0 ) ( x ̂ + i s y ̂ ) .
θ c = cos 1 ε ( ω 0 ) ε ( 2 ω 0 )
n ( 0 ) = n 0 Δ ρ δ ( ρ ρ 0 ) rect [ ( z v b t ) l ] h ( z ) ,
j 2 = e c 2 n ( 0 ) 4 i ω 0 ρ a 0 2 ( x ̂ + i s y ̂ ) e i s φ .
A ( 2 ) = m c 2 e h ( c τ θ c 2 ) ( x ̂ + i s y ̂ ) e i s φ a 2 e i ψ 2 + c.c. ,

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