Abstract

The transmittance, ellipsometric parameters, and depolarization of transmission, diffraction, and reflection of two volume holographic gratings (VHGs) are measured at a wavelength of 632.8 nm. The measured data are in good agreement with the theoretical simulated results, which demonstrated the correlation between the diffraction strength and the polarization properties of a VHG. Vector electromagnetic theory and polarization characterization are necessary for complete interpretation of the diffraction property of a VHG. The diffraction efficiency is measured at 532 nm in a polarization-sensing experiment. The measured data and theoretical simulation have demonstrated the potential application of the holographic beam splitter for polarization-sensor technology.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. S. F. Nee, H. E. Bennett, “Accurate null polarimetry for measuring the refractive index of transparent materials,” J. Opt. Soc. Am. A 10, 2076–2083 (1993).
    [CrossRef]
  4. A. Knoesen, L.-M. Wu, “Absorption of polymers for optical waveguide applications measured by photothermal detection spectroscopy,” in Linear and Nonlinear Optics of Organic Materials, M. Eich, M. G. Kuzyk, eds., Proc. SPIE4461, 146–148 (2001).
    [CrossRef]
  5. S. F. Nee, “Polarization of specular reflection and near-specular scattering by a rough surface,” Appl. Opt. 35, 3570–3582 (1996).
    [CrossRef]
  6. S. F. Nee, “Depolarization and principal Mueller matrix measured by null ellipsometry,” Appl. Opt. 40, 4933–4939 (2001).
    [CrossRef]
  7. S. F. Nee, “Error analysis of null ellipsometry with depolarization,” Appl. Opt. 38, 5388–5398 (1999).
    [CrossRef]
  8. M. S. Shahriar, J. Riccobono, W. Weathers, “Holographic beam combiner,” in Proceedings of the IEEE International Conference on Microwaves and Optics (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 10–14.
  9. M. S. Shahriar, J. Riccobono, W. Weathers, “Highly Bragg selective holographic laser beam combiner,” presented at the Solid State and Diode Laser Technology Review, Albuquerque, N.M., June 5–8, 2000.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
    [CrossRef]
  15. M. S. Shahriar, J. T. Shen, R. Tripathi, M. W. Kleinschmit, T. Nee, S. F. Nee, “Ultrafast holographic Stokesmeter for active polarization imaging in real time,” Opt. Lett. 29, 298–300 (2004).
    [CrossRef] [PubMed]

2004 (2)

2001 (1)

1999 (1)

1996 (1)

1993 (1)

1975 (2)

S. Kessler, R. Kowarschik, “Diffraction efficiency of volume holograms,” Opt. Quantum Electron. 7, 1–14 (1975).
[CrossRef]

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

1973 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1966 (1)

Alferness, R.

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Bennett, H. E.

Burckhardt, C. B.

Kaspar, F. G.

Kessler, S.

S. Kessler, R. Kowarschik, “Diffraction efficiency of volume holograms,” Opt. Quantum Electron. 7, 1–14 (1975).
[CrossRef]

Kleinschmit, M. W.

Knoesen, A.

A. Knoesen, L.-M. Wu, “Absorption of polymers for optical waveguide applications measured by photothermal detection spectroscopy,” in Linear and Nonlinear Optics of Organic Materials, M. Eich, M. G. Kuzyk, eds., Proc. SPIE4461, 146–148 (2001).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kowarschik, R.

S. Kessler, R. Kowarschik, “Diffraction efficiency of volume holograms,” Opt. Quantum Electron. 7, 1–14 (1975).
[CrossRef]

Nee, S. F.

Nee, T.

Nee, T. W.

Riccobono, J.

M. S. Shahriar, J. Riccobono, W. Weathers, “Holographic beam combiner,” in Proceedings of the IEEE International Conference on Microwaves and Optics (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 10–14.

M. S. Shahriar, J. Riccobono, W. Weathers, “Highly Bragg selective holographic laser beam combiner,” presented at the Solid State and Diode Laser Technology Review, Albuquerque, N.M., June 5–8, 2000.

Shahriar, M. S.

M. S. Shahriar, J. T. Shen, R. Tripathi, M. W. Kleinschmit, T. Nee, S. F. Nee, “Ultrafast holographic Stokesmeter for active polarization imaging in real time,” Opt. Lett. 29, 298–300 (2004).
[CrossRef] [PubMed]

M. S. Shahriar, J. Riccobono, W. Weathers, “Holographic beam combiner,” in Proceedings of the IEEE International Conference on Microwaves and Optics (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 10–14.

M. S. Shahriar, J. Riccobono, W. Weathers, “Highly Bragg selective holographic laser beam combiner,” presented at the Solid State and Diode Laser Technology Review, Albuquerque, N.M., June 5–8, 2000.

Shen, J. T.

Tripathi, R.

Weathers, W.

M. S. Shahriar, J. Riccobono, W. Weathers, “Holographic beam combiner,” in Proceedings of the IEEE International Conference on Microwaves and Optics (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 10–14.

M. S. Shahriar, J. Riccobono, W. Weathers, “Highly Bragg selective holographic laser beam combiner,” presented at the Solid State and Diode Laser Technology Review, Albuquerque, N.M., June 5–8, 2000.

Wu, L.-M.

A. Knoesen, L.-M. Wu, “Absorption of polymers for optical waveguide applications measured by photothermal detection spectroscopy,” in Linear and Nonlinear Optics of Organic Materials, M. Eich, M. G. Kuzyk, eds., Proc. SPIE4461, 146–148 (2001).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. (1)

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Lett. (1)

Opt. Quantum Electron. (1)

S. Kessler, R. Kowarschik, “Diffraction efficiency of volume holograms,” Opt. Quantum Electron. 7, 1–14 (1975).
[CrossRef]

Other (4)

S. F. Nee, “Measurement of reflective index of transparent materials using null polarimetry near Brewster angle,” in Optical Diagnostic Methods for Inorganic Transmissive Materials, R. V. Datla, L. M. Hanssen, eds., Proc. SPIE3425, 248–257 (1998).
[CrossRef]

A. Knoesen, L.-M. Wu, “Absorption of polymers for optical waveguide applications measured by photothermal detection spectroscopy,” in Linear and Nonlinear Optics of Organic Materials, M. Eich, M. G. Kuzyk, eds., Proc. SPIE4461, 146–148 (2001).
[CrossRef]

M. S. Shahriar, J. Riccobono, W. Weathers, “Holographic beam combiner,” in Proceedings of the IEEE International Conference on Microwaves and Optics (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 10–14.

M. S. Shahriar, J. Riccobono, W. Weathers, “Highly Bragg selective holographic laser beam combiner,” presented at the Solid State and Diode Laser Technology Review, Albuquerque, N.M., June 5–8, 2000.

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Figures (9)

Fig. 1
Fig. 1

Measured optical properties of the PMMA substrate material: top, refractive index; bottom, extinction coefficient in the spectral range 450–1700 nm.

Fig. 2
Fig. 2

Reflected, transmitted, and diffracted beams of the holographic grating sample.

Fig. 3
Fig. 3

Calculated transmittance of transmitted and diffracted beams (Tt and Td) and transmission diffraction efficiency η for sample A. The parameters are listed in Table 2. The fitted points are marked by x.

Fig. 4
Fig. 4

Calculated ψ and Δ of sample A. Horizontal lines are the measured data; the fitted points are marked by x. Parameters are the same as in Fig. 3.

Fig. 5
Fig. 5

Calculated transmittance of the transmitted and the three diffracted beams at wavelength 532 nm for sample B. Parameters are n=1.4942, u0=0.2821 µm, sample thickness=1.71 mm. Other parameters are listed in Tables 1 and 4.

Fig. 6
Fig. 6

Polarization-sensing experiment of sample B. HWP, half-wave plate.

Fig. 7
Fig. 7

HWP rotating angle (δ) dependence of the diffraction efficiency η at wavelength 532 nm. The measured data are marked by x. With Apol=4.327×10-6, the solid curve is the calculated result with incident Stokes parameter (1, 0, 0.22, 0). Other parameters are listed in Table 4.

Fig. 8
Fig. 8

Calculated diffraction efficiency η of grating #1 of sample B at wavelength 532 nm. Other parameters are listed in Table 4.

Fig. 9
Fig. 9

HWP rotating angle (δ) dependence of the calculated transmittance of the transmitted and grating #1 diffracted beams at wavelength 532 nm. Parameters are the same as Fig. 8.

Tables (4)

Tables Icon

Table 1 Volume Gratings’ Diffraction Properties

Tables Icon

Table 2 Polarization Properties of Sample A at Wavelength 632.8 nma

Tables Icon

Table 3 Mueller Matrix Properties at Wavelength 632.8 nm for Sample B

Tables Icon

Table 4 Calculated Mueller Matrix Properties of Sample B, Grating #1, and Fitted Incident Stokes Vector (1, 0, U, 0) for Wavelength 532 nm, n=1.4942a

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

M=R1Px00Px1-2Dv0000PyPz00-PzPy,
P=(Px2+Py2+Pz2)1/2,
D=1-P=Du+Dv,
Px=-P cos 2ψ,
Py=P sin 2ψ cos Δ,
Pz=P sin 2ψ sin Δ,
Apol=α/(Aux0)
f(u)=1u0πexp-u2u02.
n(Өj, Φj)=n+n-/(n+2 sin2 δj+n-2 cos2 δj)1/2, j=ts, tp, ds, dp,
cos(δj-Δδj)=sin Өj cos θK cos(Φj-ϕK)+cos Өj sin θK.
dn=Cdn(Apol),
I(j)Q(j)U(j)V(j)=M(j)Mhwp(δ)IiQiUiVi,j=t, d,
Mhwp(δ)=Thwp10000cos 4δ-sin 4δ00-sin 4δ-cos 4δ0000-1
S(j)(δ)=sdI(j)(δ),j=t, d,
I(j)(δ)=Thwp{IjM11(j)+(Qj cos 4δ-Uj sin 4δ)M12(j)-(Qj sin 4δ+Uj cos 4δ)M13(j)-VjM14(j)},  j=t, d.
η(δ)=I(d)/(I(t)+I(d))=S(d)/(S(t)+S(d)).
S(j)(δ)=sdI(j),j=t, d1, d2, d3,
I(j)=Thwp{IiM11(j)+QiM12(j)+UiM13(j)+ViM14(j)}.

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