Abstract

We present a unique method for real-time polarization measurement by use of a discrete space-variant subwavelength grating. The formation of the grating is done by discrete orientation of the local subwavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the discrete subwavelength dielectric grating followed by a subwavelength metal polarizer. We discuss a theoretical analysis based on Stokes–Mueller formalism, as well as on Jones calculus, and experimentally demonstrate our approach with polarization measurements of infrared radiation at a wavelength of 10.6 µm.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2003 (1)

E. Hasman, V. Kleiner, G. Biener, A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[CrossRef]

2002 (1)

2001 (3)

P. C. Deguzman, G. P. Nordin, “Stacked subwavelength gratings as circular polarization filters,” Appl. Opt. 40, 5731–5737 (2001).
[CrossRef]

P. C. Chou, J. M. Fini, H. A. Haus, “Real-time principle state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Space-variant polarization state manipulation with computer-generatedsubwavelength metal stripe gratings,” Opt. Commun. 192, 169–181 (2001).
[CrossRef]

2000 (1)

1999 (3)

1996 (1)

1987 (2)

Azzam, R. M. A.

Biener, G.

E. Hasman, V. Kleiner, G. Biener, A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, E. Hasman, “Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating,” Opt. Lett. 27, 188–190 (2002).
[CrossRef]

Bomzon, Z.

Z. Bomzon, G. Biener, V. Kleiner, E. Hasman, “Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating,” Opt. Lett. 27, 188–190 (2002).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Space-variant polarization state manipulation with computer-generatedsubwavelength metal stripe gratings,” Opt. Commun. 192, 169–181 (2001).
[CrossRef]

Chou, P. C.

P. C. Chou, J. M. Fini, H. A. Haus, “Real-time principle state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Collet, E.

E. Collet, Polarized Light (Marcel Dekker, New York, 1993).

Collins, R. W.

Deguzman, P. C.

Everett, M. J.

Fini, J. M.

P. C. Chou, J. M. Fini, H. A. Haus, “Real-time principle state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Gori, F.

Hasman, E.

E. Hasman, V. Kleiner, G. Biener, A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, E. Hasman, “Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating,” Opt. Lett. 27, 188–190 (2002).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Space-variant polarization state manipulation with computer-generatedsubwavelength metal stripe gratings,” Opt. Commun. 192, 169–181 (2001).
[CrossRef]

Haus, H. A.

P. C. Chou, J. M. Fini, H. A. Haus, “Real-time principle state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Jellison, G. E.

Jones, M. W.

Kleiner, V.

E. Hasman, V. Kleiner, G. Biener, A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, E. Hasman, “Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating,” Opt. Lett. 27, 188–190 (2002).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Space-variant polarization state manipulation with computer-generatedsubwavelength metal stripe gratings,” Opt. Commun. 192, 169–181 (2001).
[CrossRef]

Koh, J.

Lalanne, P.

Lee, J.

Maitland, D. J.

Meier, J. T.

Morris, G. M.

Niv, A.

E. Hasman, V. Kleiner, G. Biener, A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[CrossRef]

Nordin, G. P.

Sankaran, V.

Walsh, J. T.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. Hasman, V. Kleiner, G. Biener, A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. C. Chou, J. M. Fini, H. A. Haus, “Real-time principle state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

Z. Bomzon, V. Kleiner, E. Hasman, “Space-variant polarization state manipulation with computer-generatedsubwavelength metal stripe gratings,” Opt. Commun. 192, 169–181 (2001).
[CrossRef]

Opt. Lett. (6)

Other (1)

E. Collet, Polarized Light (Marcel Dekker, New York, 1993).

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Figures (7)

Fig. 1
Fig. 1

Schematic presentation of near-field Fourier transform polarimetry based on a discrete space-variant subwavelength dielectric grating followed by a subwavelength metal polarizer.

Fig. 2
Fig. 2

(a) Magnified geometry of the discrete space-variant dielectric grating with a number of discrete levels N=4. (b) Discrete rotation angle of the subwavelength grating as a function of x coordinate; the local groove orientations are indicated. (c) Scanning electron microscopy image of a region on the subwavelength structure. (d) Scanning electron microscopy image of a cross section of the subwavelength grooves.

Fig. 3
Fig. 3

Measured (circles) and predicted (solid curves) values of the normalized transmitted intensity as a function of the x coordinate along the DSG when the fast axis of the rotating QWP was at angles (a) 0°, (b) 20°, and (c) 45°; the insets show the experimental images of the near-field transmitted intensities.

Fig. 4
Fig. 4

Measured (circles) and predicted (solid curves) values of the normalized Stokes parameters (a) S1/S0, (b) S2/S0, and (c) S3/S0 as a function of the orientation of the QWP.

Fig. 5
Fig. 5

Measured (circles) and predicted (solid curves) values for (a) azimuthal angle ψ and (b) ellipticity angle χ as a function of orientation of the QWP.

Fig. 6
Fig. 6

Calculated (solid curve) and measured (circles) DOP as a function of intensity ratio of the two independent lasers having orthogonal linear polarization states, as used in a setup depicted in the top inset. The bottom inset shows calculated (solid curves) and measured (circles) intensity cross sections for the two extremes, I1=I2 (DOP=0.059) and I2=0 (DOP=0.975).

Fig. 7
Fig. 7

Diffraction orders emerging from the DSG: zero order (dashed), first order for |R〉 and |L〉 polarized beams (solid), and higher order for |R〉 and |L〉 polarized beams (dotted–dashed).

Equations (27)

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M=PR(-θ)WR(θ),
R(θ)=10000cos(2θ)sin(2θ)00-sin(2θ)cos(2θ)00001
W=12tx2+ty2tx2-ty200tx2-ty2tx2+ty200002txty cos ϕ-2txty sin ϕ002txty sin ϕ2txty cos ϕ
P=121100110000000000
S0(x)=14(AS0+12(A+C)S1+B(S1+S0)cos[2θ(x)]+(BS2-DS3)sin[2θ(x)]+12(A-C)×{S1 cos[4θ(x)]+S2 sin[4θ(x)]}),
θ(x)=0,0<x<dNπN,dN<x<2dNπ(m-1)N,d(m-1)N<x<dmNπ(N-1)N,d(N-1)N<x<d,
4S0(x)=AS0+12 (A+C)S1+B(S1+S0)×n=1[an cos(2πnx/d)+bn sin(2πnx/d)]+(BS2-DS3)n=1[cn sin(2πnx/d)+dn cos(2πnx/d)]+12 (A-C)×S1n=1[en cos(4πnx/d)+fn sin(4πnx/d)]+S2n=1[gn sin(4πnx/d)+hn cos(4πnx/d)].
an=cn=N2πnsin2πN, bn=dn=Nπnsin2πN, en=gn=N4πnsin4πN, fn=hn=N2πnsin22πN
AS0+12 (A+C)S1=4d0dS0(x)dx,
B(S1+S0)a1+(BS2-DS3)b1=8d0dS0(x)cos2πxddx,
(BS2-DS3)a1+B(S1+S0)b1=8d0dS0(x)sin2πxddx,
(A-C)(S1e1+S2f1)=16d0dS0(x)cos4πxddx,
(A-C)(S1f1+S2e1)=16d0dS0(x)sin4πxddx.
J=tx00ty exp(iϕ),
TC(x)=M(θ(x))JM-1(θ(x)),
T(x)=12 [tx+ty exp(iϕ)]1001+12 [tx-ty exp(iϕ)]×0exp[i2θ(x)]exp[-i2θ(x)]0.
|Eout=ηE|Ein+ηR exp[i2θ(x, y)]|R+ηL exp[-i2θ(x, y)]|L,
ηE=12[tx+ty exp(iϕ)], ηR=12[tx-ty exp(iϕ)]Ein|L, ηL=12[tx-ty exp(iϕ)]Ein|R
|Eout=ηE|Ein+ηRm=-αm exp(i2πmx/d)|R+ηLm=-α-m*exp(i2πmx/d)|L,
P=121111.
E˜out=12ηE(Ein|R+Ein|L)+ηRm=-αm exp(i2πmx/d)+ηLm=-α-m* exp(i2πmx/d).
α=4d0dS0(x)dx,β=8d0dS0(x)sin(2πx/d)dx, γ=16d0dS0(x)cos(4πx/d)dx, δ=16d0dS0(x)sin(4πx/d)dx,
H=A(A+C)/200Bb1Bb1Ba1-Da10(A-C)e1(A-C)f100(A-C)f1(A-C)e10.
S0=1Aα-12 A+CA-C γe1-δf1e12-f12,
S1=1A-Cγe1-δf1e12-f12,
S2=1A-Cδe1-γf1e12-f12,
S3=1Da1-β+BA b1α+B(e12-f12)×b1e12A+a1f1A-Cγ-b1f12A+a1e1A-Cδ.

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