Abstract

An analysis of the operators of some widespread nonorthogonal polarizers is performed on the basis of the polar factorization theorem, in pure operatorial (nonmatrix) Dirac algebraic language. The role of the unitary polar component as a converter of the two sets of singular eigenvectors of the operator, one in the other, is emphasized in each case; this role is maintained for the singular operators corresponding to these special nonorthogonal polarizers.

© 2014 Optical Society of America

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    [CrossRef]
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  23. O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, Opt. Express 17, 15623 (2009).
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2013 (2)

2012 (1)

2010 (1)

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702 (2010).
[CrossRef]

2009 (1)

2007 (3)

S. N. Savenkov, O. I. Sydoruk, and R. S. Muttiah, Appl. Opt. 46, 6700 (2007).
[CrossRef]

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (2)

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

J. Morio and F. Goudail, Opt. Lett. 29, 2234 (2004).
[CrossRef]

2003 (1)

1996 (2)

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
[CrossRef]

1994 (1)

1992 (1)

Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
[CrossRef]

1987 (1)

J. J. Gil and E. Bernabeu, Optik 76, 67 (1987).

1971 (1)

Anastasiadou, M.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Angelsky, O. V.

Ben Hatit, S.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Bernabeu, E.

J. J. Gil and E. Bernabeu, Optik 76, 67 (1987).

Berry, M. V.

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

Chipman, R. A.

De Martino, A.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Dennis, M. R.

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

Gantmacher, F. R.

F. R. Gantmacher, Theory of Matrices (AMS Chelsea, 2000).

Gil, J. J.

Gorodyns’ka, N. V.

Gorsky, M. P.

Goudail, F.

Guyot, S.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Hanson, S. G.

Klein, S.

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

Lancaster, P.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985).

Lu, S.-Y.

Miller, D. A. B.

Morio, J.

Muttiah, R. S.

Ossikovski, R.

J. J. Gil, I. San José, and R. Ossikovski, J. Opt. Soc. Am. A 30, 32 (2013).
[CrossRef]

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, Collected Works of S. Pancharatnam (Oxford University, 1975).

San José, I.

Savenkov, S. N.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard University, 1962).

Sydoruk, O.

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702 (2010).
[CrossRef]

Sydoruk, O. I.

Tismenetsky, M.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985).

Tudor, T.

Whitney, C.

Xing, Z.-F.

Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
[CrossRef]

Zenkova, C. Yu.

Appl. Opt. (1)

Eur. Phys. J. Appl. Phys. (1)

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

J. Eur. Opt. Soc. Rapid Pub. (1)

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007).
[CrossRef]

J. Mod. Opt. (2)

Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
[CrossRef]

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

J. Opt. (1)

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702 (2010).
[CrossRef]

J. Opt. A (1)

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Opt. Express (2)

Opt. Lett. (1)

Optik (1)

J. J. Gil and E. Bernabeu, Optik 76, 67 (1987).

Other (4)

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985).

F. R. Gantmacher, Theory of Matrices (AMS Chelsea, 2000).

S. Pancharatnam, Collected Works of S. Pancharatnam (Oxford University, 1975).

W. A. Shurcliff, Polarized Light (Harvard University, 1962).

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Equations (44)

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D=UHr=HlU,
Hr=DD,Hl=DD.
Hr=DD=σ1|W1W1|+σ2|W2W2|,
Hl=DD=σ1|V1V1|+σ2|V2V2|,
W1|W2=0,V1|V2=0,
Hl=UHrU,DD=UDDU.
σ1|UW1UW1|+σ2|UW2UW2|=σ1|V1V1|+σ2|V2V2|.
|V1=U|W1,|V2=U|W2.
|W1=U|V1,|W2=U|V2.
U=|V1W1|+|V2W2|.
U{|W1,|W2}{|V1,|V2}.
U=|W1V1|+|W2V2|
U|V1=|W1,U|V2=|W2,
U{|V1,|V2}{|W1,|W2}.
D=UHr=[|V1W1|+|V2W2|][σ1|W1W1|+σ2|W2W2|]=σ1|V1W1|+σ2|V2W2|.
D|W1=σ1|V1,D|W2=σ2|V2,
D{|W1,|W2}{σ1|V1,σ2|V2}.
D=σ1|W1V1|+σ2|W2V2|,
D|V1=σ1|W1,D|V2=σ2|W2.
P|PθP|Px=|PθPθ|PxPx|=cosθ|PθPx|.
|Pθ,withλ1=cosθPx|Pθ=cos2θ,|Py,withλ2=0.
|Pθ|Py|=sinθ.
P=cosθ|PxPθ|,
Hr=PP=cosθ|PxPx|,Hl=PP=cosθ|PθPθ|.
U=|PθPx|+|Pθ+90°Py|.
U=|PxPθ|+|PyPθ+90°|,
U|Px=|Pθ,U|Py=|Pθ+90°,
U|Pθ=|Px,U|Pθ+90°=|Py.
U|S=[|PθPx|+|Pθ+90°Py|]|S=Px|S|Pθ+Py|S|Pθ+90°.
P=cosθ|PθPx|+0·|Pθ+90°Py|.
P|S=cosθPx|S|Pθ,
C=R|Px(π/2)P|P45°,
C=eiπ4|LP45°|.
C|LP45°|,
|L|P45°|=1/2,
C=eiπ4|P45°L|.
Hr=CC=|P45°P45°|,Hl=CC=|LL|,
U=|LP45°|+|RP45°|,
U=|P45°L|+|P45°R|.
U|P45°=|L,U|P45°=|R,
U|L=|P45°,U|R=|P45°.
C=eiπ4|LP45°|+0·|RP45°|.
C|SP45°|S|L,
|LL|S=L|S|L.

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