Abstract

The circular polarization components of a vortex beam in a uniaxial crystal exhibit complex propagation characteristics. We demonstrate how the amount of splitting may be distinguished by use of a vortex beam. We predict and experimentally verify a threshold angle subtending the crystal and beam axes, below which the splitting is indistinguishable.

© 2007 Optical Society of America

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References

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  1. M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 459, 1261 (2003).
    [CrossRef]
  2. M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
    [CrossRef]
  3. A. Volyar and T. Fadeyeva, Opt. Spectrosc. 101, 297 (2006).
    [CrossRef]
  4. F. Flossmann, U. Schawarz, M. Maier, and M. Dennis, Opt. Express 14, 11402 (2006).
    [CrossRef] [PubMed]
  5. T. W. Stone and J. M. Battiato, Appl. Opt. 33, 182 (1994).
    [CrossRef] [PubMed]
  6. N. N. Rosanov, Opt. Spectrosc. 93, 746 (2002).
    [CrossRef]
  7. I. D. Maleev and G. A. Swartzlander, J. Opt. Soc. Am. B 20, 1169 (2003).
    [CrossRef]

2006 (2)

2003 (2)

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 459, 1261 (2003).
[CrossRef]

I. D. Maleev and G. A. Swartzlander, J. Opt. Soc. Am. B 20, 1169 (2003).
[CrossRef]

2002 (1)

N. N. Rosanov, Opt. Spectrosc. 93, 746 (2002).
[CrossRef]

2001 (1)

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

1994 (1)

Battiato, J. M.

Berry, M. V.

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 459, 1261 (2003).
[CrossRef]

Dennis, M.

Dennis, M. R.

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 459, 1261 (2003).
[CrossRef]

Fadeyeva, T.

A. Volyar and T. Fadeyeva, Opt. Spectrosc. 101, 297 (2006).
[CrossRef]

Flossmann, F.

Maier, M.

Maleev, I. D.

Rosanov, N. N.

N. N. Rosanov, Opt. Spectrosc. 93, 746 (2002).
[CrossRef]

Schawarz, U.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Stone, T. W.

Swartzlander, G. A.

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Volyar, A.

A. Volyar and T. Fadeyeva, Opt. Spectrosc. 101, 297 (2006).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Spectrosc. (2)

A. Volyar and T. Fadeyeva, Opt. Spectrosc. 101, 297 (2006).
[CrossRef]

N. N. Rosanov, Opt. Spectrosc. 93, 746 (2002).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 459, 1261 (2003).
[CrossRef]

Prog. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: P 1 , P2, polarizers; λ 4 , quarter wave plate; L 1 L 5 , lenses; W, optical wedge; D 1 D 3 , diaphragms; SM, semitransparent mirrors; M, mirrors; CCD, CCD camera. a, Beam axis trajectories in Li Nb O 3 crystal: c ̂ is a unit vector of the crystal optical axis; α in is the inclination angle at the crystal input z = 0 , α in = n o α o . b, Intensity profile of the beam at the crystal input.

Fig. 2
Fig. 2

Numerically determined vortex position in the E + component at z = 20 mm for a varying tilt angle. a, Region for the vortex position in the x , y plane. Experimental images of the beam for, b, α ¯ = 10.5 ; c, α ¯ = 11.08 ; d, α ¯ = 11.3 ; e, α ¯ = α ¯ c r = 22.7 ( α c r = 2.6 o ) ; f, α ¯ = 31.4 ; g, α ¯ = 32 ; h, α ¯ = 40 , X = x w 0 , Y = y w 0 , α ¯ = α o α diff .

Fig. 3
Fig. 3

Intensity profiles E + ( o ) 2 and E + ( e ) 2 for the cases n 1 = 2 , n 3 = ε 3 = 2.1 at the critical angle α ¯ cr = 22.7 ( α cr = 2.6 o , if w 0 = 50 μ m ) for the maxima matching Δ y = 0 , Y = y w 0 .

Fig. 4
Fig. 4

Indistinguishability limit as a function of the normalized propagation distance in the crystal and beam tilt from the crystal axis.

Equations (7)

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( 2 + 2 i k o z ) E ̃ = Δ ε ε 3 ( E ̃ ) ,
E ̃ + = x i ( y α o z ) w 0 σ o Ψ ̃ o + x i ( y α e z ) w 0 σ e Ψ ̃ e ,
E ̃ = x + i y o w 0 ( Ψ ̃ o σ o Ψ ̃ e σ e ) + α o z o w 0 ( x + i y o r o ) 2 [ w 0 2 r o 2 ( σ o Ψ ̃ o σ e Ψ ̃ e ) + ( Ψ ̃ o Ψ ̃ e ) ] ,
Ψ ̃ o , e = exp [ x 2 + ( y + i α o z o ) 2 w 0 2 σ o , e ] exp ( α e 2 k e z e 2 ) σ o , e ,
y front o = α o z + W o 2 , y back e = α e z W e 2 ,
z 2 ( α o 2 w 0 2 Δ ε 2 2 ε 3 2 1 z o 2 ) 1 .
α ut = 2 ε 3 Δ ε α diff .

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