Abstract

When a light beam passes through a cascade of biaxial crystals (BCs) with aligned optic axes, the resulting transverse intensity pattern consists of multiple concentric rings. We provide a simple formulation for the pattern formation for both circularly and linearly polarized input beams, that could be applied for a cascade of an arbitrary number of BCs. We have experimentally investigated multiple ring formation with up to three cascade BCs, showing that the theoretical formulation is in full agreement with the experimental results.

© 2013 Optical Society of America

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References

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    [CrossRef]
  4. C. F. Phelan, K. E. Ballantine, P. R. Eastham, J. F. Donegan, and J. G. Lunney, Opt. Express 20, 13201 (2012).
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  5. A. Abdolvand, Appl. Phys B 103, 281 (2011).
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  6. S. D. Grant and A. Abdolvand, Opt. Lett. 37, 5226 (2012).
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  7. D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, Opt. Express 18, 27319 (2010).
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  8. D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 21119 (2012).
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  9. A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, Opt. Lett. 37, 4197 (2012).
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  10. A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).
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    [CrossRef]
  12. A. Turpin, Yu. V. Loiko, T. K. Kalkandjiev, and J. Mompart, Opt. Express 21, 4503 (2013).
    [CrossRef]
  13. Y. Loiko, M. A. Bursukova, T. K. Kalkanjiev, E. U. Rafailov, and J. Mompart, Proc. SPIE 7950, 79500D (2011).
    [CrossRef]

2013 (1)

2012 (4)

2011 (2)

A. Abdolvand, Appl. Phys B 103, 281 (2011).
[CrossRef]

Y. Loiko, M. A. Bursukova, T. K. Kalkanjiev, E. U. Rafailov, and J. Mompart, Proc. SPIE 7950, 79500D (2011).
[CrossRef]

2010 (3)

2008 (1)

T. K. Kalkandjiev and M. Bursukova, Proc. SPIE 6994, 69940B (2008).
[CrossRef]

2007 (1)

M. V. Berry and M. R. Jeffrey, Prog. Opt. 50, 13 (2007).
[CrossRef]

1978 (1)

A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).

Abdolvand, A.

Ballantine, K. E.

Belskii, A. M.

A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).

Berry, M. V.

M. V. Berry, J. Opt. 12, 075704 (2010).
[CrossRef]

M. V. Berry and M. R. Jeffrey, Prog. Opt. 50, 13 (2007).
[CrossRef]

Bursukova, M.

T. K. Kalkandjiev and M. Bursukova, Proc. SPIE 6994, 69940B (2008).
[CrossRef]

Bursukova, M. A.

Y. Loiko, M. A. Bursukova, T. K. Kalkanjiev, E. U. Rafailov, and J. Mompart, Proc. SPIE 7950, 79500D (2011).
[CrossRef]

Donegan, J. F.

Eastham, P. R.

Grant, S. D.

Jeffrey, M. R.

M. V. Berry and M. R. Jeffrey, Prog. Opt. 50, 13 (2007).
[CrossRef]

Kalkandjiev, T. K.

Kalkanjiev, T. K.

Y. Loiko, M. A. Bursukova, T. K. Kalkanjiev, E. U. Rafailov, and J. Mompart, Proc. SPIE 7950, 79500D (2011).
[CrossRef]

Khapalyuk, A. P.

A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).

Loiko, Y.

Y. Loiko, M. A. Bursukova, T. K. Kalkanjiev, E. U. Rafailov, and J. Mompart, Proc. SPIE 7950, 79500D (2011).
[CrossRef]

Loiko, Yu. V.

Lunney, J. G.

Mompart, J.

O’Dwyer, D. P.

Phelan, C. F.

Rafailov, E. U.

Y. Loiko, M. A. Bursukova, T. K. Kalkanjiev, E. U. Rafailov, and J. Mompart, Proc. SPIE 7950, 79500D (2011).
[CrossRef]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 18, 2753 (2010).
[CrossRef]

Rakovich, Y. P.

Turpin, A.

Wilcox, K. G.

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Figures (3)

Fig. 1.
Fig. 1.

(a) CR ring at the focal plane for a circularly polarized input beam. Orange double arrows show the polarization distribution at each point of the CR ring. See text for parameters’ definition. (b) CR pattern for a vertically LP input beam.

Fig. 2.
Fig. 2.

Experimental setup. An input beam propagating along the optic axis of a cascade of BCs (BCi) (with orientation φi) is focused with a lens (FL) and transformed by the CR phenomenon in the cascade. An imaging lens (IL) projects the final pattern into the CCD camera.

Fig. 3.
Fig. 3.

Transverse intensity patterns for a cascade of two (two concentric rings patterns) and three (four concentric rings patterns) BCs. Figures (a)–(d) are experimental data and (e)–(h) the corresponding theoretical simulations. First and third columns correspond to a circularly polarized input beam, while second and fourth columns correspond to a LP input beam with azimuth Φ0=0°. Experimental parameters of the BCs: L1=27.31mm, φ1=0°; L2=10.66mm, φ2=90°; L3=18.29mm, φ3=180°. The focal length of the focusing lens (FL, see Fig. 2) is 200 mm.

Equations (23)

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r⃗1=r⃗0+G⃗1.
r⃗1(χ)=r⃗0+G⃗1+|G⃗1|[cos(χ),sin(χ)].
Φχ=χ+φ12.
r⃗2=r⃗1+G⃗2=r⃗0+G⃗1+G⃗2,
χ2(1)=χ,χ2(2)=χ+π;
r⃗2(χ2(1,2))=r⃗1(χ)+G⃗2±|G⃗2|[cos(χ),sin(χ)],
r⃗2(χ2(1,2))=r⃗2±R2(1,2)[cos(χ),sin(χ)],
I2(1)=Iχcos2(Φχ2(1)Φχ)=Iχcos2(φ212),
I2(2)=Iχcos2(Φχ2(2)Φχ)=Iχsin2(φ212),
r⃗2=r⃗0+G⃗1+G⃗2,
R2(i)=||G⃗1|±|G⃗2||(i=1,2),
I2,CP(1)=P0A2(1)cos2(φ212),
I2,CP(2)=P0A2(2)sin2(φ212),
I2,LP(1)=2I2,CP(1)cos2(χ+φ12Φ0),
I2,LP(2)=2I2,CP(2)cos2(χ+φ12Φ0+π2),
I2,LP(1)=2I2,CP(1)cos2(χ+φ12Φ0),
I2,LP(2)=2I2,CP(2)cos2(χ+φ12Φ0),
r⃗3=r⃗0+G⃗1+G⃗2+G⃗3,
R3(i)=|||G⃗1|±|G⃗2||±|G⃗3||(i=1,2,3,4),
I3(1)=P0A3(1)cos2(φ212)cos2(φ212),
I3(2)=P0A3(2)sin2(φ322)cos2(φ212),
I3(3)=P0A3(3)cos2(φ322)sin2(φ212),
I3(4)=P0A3(4)sin2(φ322)sin2(φ212),

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