Abstract

Anisotropic detectors (AD's) can be designed by coating a photosensitive surface (e.g., Si) with a birefringent thin film whose principal axes are in the plane of the film. An integrated polarimeter (IP) is described that uses four linear photodetectors, of which three are AD's. The light beam, whose Stokes parameters (SP's) are to be measured, is relayed from one detector to the next by near-normal-incidence partial specular reflection while remaining in one plane. By a suitable choice of surface properties and orientations of the AD's, the four output electrical signals of the four detectors determine completely and unambiguously all four SP's. This IP with AD's (IPAD) has all the advantages of the previously described four-detector polarimeter [Opt. Lett. 10, 309 (1985)]. In addition, the IPAD offers a compact design with small-area detectors.

© 1987 Optical Society of America

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References

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  1. R. M. A. Azzam, Opt. Lett. 10, 427 (1985);Appl. Opt. 25, 4224 (1986).
    [CrossRef] [PubMed]
  2. R. M. A. Azzam, Rev. Sci. Instrum. 56, 1746 (1985).
    [CrossRef]
  3. R. M. A. Azzam, Opt. Lett. 10, 309 (1985).
    [CrossRef] [PubMed]
  4. K. Berthold, W. Beinstingl, E. Gornik, Opt. Lett. 12, 69 (1987).
    [CrossRef] [PubMed]
  5. When α1 = α2 = 45°, r0 = r1 = r2 = r, ψ0 = ψ1 = ψ2 = ψ, and Δ1 = 90°, Eq. (4) gives det A = (k0k1k2k3)r6 sin3 2ψ cos3 2ψ. This result should replace Eq. (11) of Ref. 3, which was in error.
  6. R. M. A. Azzam, Opt. Commun. 20, 405 (1977). Equations (22)–(25) simplify for the present case of an isotropic substrate by setting N2x = N2y = N2.
    [CrossRef]
  7. D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983);H. R. Philipp, J. Appl. Phys. 43, 2835 (1972).
    [CrossRef]
  8. Coherent interference within the thin film is responsible for the large reflection anisotropy that results from a small refractive-index difference (birefringence).

1987 (1)

1985 (3)

1983 (1)

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983);H. R. Philipp, J. Appl. Phys. 43, 2835 (1972).
[CrossRef]

1977 (1)

R. M. A. Azzam, Opt. Commun. 20, 405 (1977). Equations (22)–(25) simplify for the present case of an isotropic substrate by setting N2x = N2y = N2.
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983);H. R. Philipp, J. Appl. Phys. 43, 2835 (1972).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, Opt. Lett. 10, 309 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, Opt. Lett. 10, 427 (1985);Appl. Opt. 25, 4224 (1986).
[CrossRef] [PubMed]

R. M. A. Azzam, Rev. Sci. Instrum. 56, 1746 (1985).
[CrossRef]

R. M. A. Azzam, Opt. Commun. 20, 405 (1977). Equations (22)–(25) simplify for the present case of an isotropic substrate by setting N2x = N2y = N2.
[CrossRef]

Beinstingl, W.

Berthold, K.

Gornik, E.

Studna, A. A.

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983);H. R. Philipp, J. Appl. Phys. 43, 2835 (1972).
[CrossRef]

Opt. Commun. (1)

R. M. A. Azzam, Opt. Commun. 20, 405 (1977). Equations (22)–(25) simplify for the present case of an isotropic substrate by setting N2x = N2y = N2.
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (1)

D. E. Aspnes, A. A. Studna, Phys. Rev. B 27, 985 (1983);H. R. Philipp, J. Appl. Phys. 43, 2835 (1972).
[CrossRef]

Rev. Sci. Instrum. (1)

R. M. A. Azzam, Rev. Sci. Instrum. 56, 1746 (1985).
[CrossRef]

Other (2)

When α1 = α2 = 45°, r0 = r1 = r2 = r, ψ0 = ψ1 = ψ2 = ψ, and Δ1 = 90°, Eq. (4) gives det A = (k0k1k2k3)r6 sin3 2ψ cos3 2ψ. This result should replace Eq. (11) of Ref. 3, which was in error.

Coherent interference within the thin film is responsible for the large reflection anisotropy that results from a small refractive-index difference (birefringence).

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Figures (5)

Fig. 1
Fig. 1

Integrated polarimeter with IPAD's. The surfaces of the first three detectors, D0, D1, and D2, are parallel, partially specularly reflecting, and uniaxially optically anisotropic in the plane of the surface with principal axes x0, x1, and x2, respectively. x1 is rotated with respect to x0 by the angle α1, and x2 is rotated with respect to x1 by α2. The fourth detector, D3, is isotropic and absorbs all the radiation reflected by D2. The light beam strikes each detector surface near normal incidence (θ ≲ 10°) and remains in one plane. The four output electrical signals, i0, i1, i2, and i3, of the four detectors determine the four unknown Stokes parameters, S0, S1, S2, and S3, of input light.

Fig. 2
Fig. 2

Imaginary part versus real part of the ratio of complex principal reflection coefficients at normal incidence, ρ = Ry/Rx, as the thickness d of a birefringent film on a Si substrate increases. The principal refractive indices of the film are taken as N1x = 1.55 and N1y = 1.50, while the complex refractive index of Si is N2 = 3.85 − j0.02 at an assumed wavelength of 0.6328 μm. The open-spiral trajectory of ρ starts at point S (ρ = 1) where d = 0 and ends at F(ρ = 0.81 − j0.80) where d = 2 μm. The thickness scale along the curve can be inferred from Figs. 3 and 4.

Fig. 3
Fig. 3

Arctangent of the relative amplitude attention on reflection of the x and y linear polarizations of normally incident light, ψ = tan−1 |ρ|, versus the thickness d of a birefringent film (N1x = 1.55, N1y = 1.50) on a Si substrate (N2 = 3.85 − j0.02) at wavelength λ = 0.6328 μm.

Fig. 4
Fig. 4

Differential reflection phase shift between the x and y linear polarizations of normally incident light, Δ = arg ρ, versus the thickness d of a birefringent film (N1x = 1.55, N1y = 1.50) on a Si substrate (N2 = 3.85 − j0.02) at wavelength λ = 0.6328 μm.

Fig. 5
Fig. 5

Modulation depth mL, Eq. (5), of the output signal of a RODE that uses a Si (N2 = 3.85 − j0.02) photodetector coated with a birefringent film (N1x = 1.55, N1y = 1.50) whose thickness d varies from 0 to 2 μm. A beam of linearly polarized monochromatic light (λ = 0.6328 μm) is assumed to strike such an anisotropic detector at or near normal incidence.

Equations (5)

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ρ = R y / R x = tan ψ exp ( j Δ ) ,
I = AS .
S = A 1 I .
det A = ( k 0 k 1 k 2 k 3 ) ( r 0 3 r 1 2 r 2 ) ( sin 2 α 1 sin 2 α 2 ) × ( sin 2 2 ψ 0 cos 2 ψ 0 sin 2 ψ 1 cos 2 ψ 1 cos 2 ψ 2 ) × ( sin Δ 1 ) .
m L = ( y x ) / ( 2 x y )

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