Optics Express
Vol. 13,
Issue 7,
pp. 2303-2320
(2005)
•https://doi.org/10.1364/OPEX.13.002303

Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon

M. Xu, H.P. Urbach, D.K.G de Boer, and H.J. Cornelissen

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M. Xu, H.P. Urbach, D.K.G de Boer, and H.J. Cornelissen, "Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon," Opt. Express 13, 2303-2320 (2005)

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Abstract

The application of wire grid polarizers as efficient polarizing beam splitters for visible light is studied. The large differences between the transmissivity for different polarizations are explained qualitatively by using the theory of metallic wave guides. The results of rigorous calculations obtained by using the finite element method are compared with experiments for both classical and conical mount. Furthermore the application of wire-grid polarizers in liquid crystal on silicon display systems is considered.

©2005 Optical Society of America

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Figures (18)

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Fig. 1.

Fig. 1. An example of a WGP. When unpolarized light incident on the polarizer, polarization with electric field parallel to wire grid is reflected and polarization with electric field perpendicular to the wire grid is transmitted.

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Fig. 2.

Fig. 2. (a) Coordinate system. (b) Cone of incident rays with respect to normal of the WGP surface.

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Fig. 3.

Fig. 3. Infinitely long slab waveguide, independent of y-axis.

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Fig. 4.

Fig. 4. Propagation constant of the lowest TE and TM modes in the complex plane as function of the width of the groove. The wavelength of the incident light is 550 nm. Left is TM polarization, and right is TE polarization. The axes are normalized by the wave number in vacuum.

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Fig. 5.

Fig. 5. Field in unit cell at normal incidence for green light (with wavelength of 550 nm). At the left the field is s-polarized and the amplitude of the electric field component along the grooves is shown. At the right the field is p-polarized and the amplitude of the magnetic field component parallel to the grooves is shown. The field has been calculated by the rigorous finite element model described in Section 3.1. (Note that the y-axis in these figures is called the z-axis in Fig. 1).

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Fig. 6.

Fig. 6. Set up for measurement of transmission (a) and reflection (b).

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Fig. 7.

Fig. 7. Reflection and transmission for 550 nm wavelength at classical mount (ϕ=90°) as functions of the depths of the grooves. Green line: normal incidence (θ=0°). Blue line: oblique incidence (θ=45°). Tp and Ts are the transmitted intensities for p- and s-polarization in the z-direction, respectively. Rp and Rs are the reflected intensities for p-and s-polarization in the z-direction respectively.

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Fig. 8.

Fig. 8. SEM photos of a WGP sample.

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Fig. 9.

Fig. 9. Comparison between simulated (solid line) and measured (star-dotted line) reflected and transmitted intensities for classical mount (ϕ=90°) as function of θ. The light is incident from the wire grid side. Thus for transmitted measurements, the glass side faces the detector, and for reflected measurements, the wire grid side faces the detector.

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Fig. 10.

Fig. 10. Real (red curve) and imaginary part (black curve) of the refractive index of aluminum (top), silver (left bottom) and gold (right bottom) as function of wavelength in the range of visible light.

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Fig. 11.

Fig. 11. Performance of three metals at classical mount, θ=45° and ϕ=90°, as function of wavelength.

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Fig. 12.

Fig. 12. Conical incident angle with respect to normal at θ=45°.

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Fig. 13.

Fig. 13. Polarization states for 550 nm wavelength as function of angle ϕ(0≤ϕ≤90°) and for θ=45°. The ϕ-axis is also the direction of E_ϕ and the vertical axis is also the direction of E_θ .

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Fig. 14.

Fig. 14. Comparison between simulations (star-dotted lines) and measurements (solid lines) at conical mount with θ=45° for 550 nm wavelength incident radiation. The computed results of R_sp are overlapped by those of R_ps .

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Fig. 15.

Fig. 15. Reflectivity and transmissivity of a WGP for incident s-polarized (a) and p-polarized (b) light at a wavelength of 550 nm and at θ=45° as functions of ϕ. Solid lines: calculated with Berreman’s method and effective-medium theory. Dotted lines: calculated with rigorous diffraction theory (finite-element method).

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Fig. 16.

Fig. 16. Orientation of the polarization ellipse and the ellipticity defined in the text for incident s-polarized (a) and p-polarized light (b) at λ=500 nm and θ=45° as a function of ϕ. Solid lines: calculated with Berremans method and effective-medium theory. Dotted lines: calculated with finite-element method.

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Fig. 17.

Fig. 17. (a) Single LCoS panel rear projection display.(b) A cone of incident rays with the chief incident ray of ϕ=90°,θ=45° as axis of the cone.

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Fig. 18.

Fig. 18. Polarization states for 550 nm wavelength incident light for varying field angle α of the cone, with the chief ray at θ=45°, ϕ=90°. Numbers around the ellipses are the total reflectivity or transmissivity.

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Tables (1)

Table 1. Values of ϕ and θ for varying α in degrees.

Equations (9)

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

k^{pl} = (k_{x}^{pl}, k_{y}^{pl}, k_{z}^{pl}),

{(k_{x}^{pl})}^{2} + {(k_{y}^{pl})}^{2} \equiv {(k_{∥}^{pl})}^{2} \overset{>}{\approx} k_{0}^{2} n^{2},

(k_{x} + \frac{2 π m}{p}, k_{y}, k_{z}^{m}),

{(k_{x} + \frac{2 π m}{p})}^{2} + {(k_{y})}^{2} \approx {(k_{∥}^{pl})}^{2} .

n = {\begin{matrix} n_{0}, & - w ⁄ 2 < x < w ⁄ 2, \\ n_{1}, & ∣ x ∣ \geq w ⁄ 2 . \end{matrix}

β_{m} = \sqrt{k_{0}^{2} n_{0}^{2} - \frac{m^{2} π^{2}}{w^{2}}}, m = 1, 2, 3, \dots For TE modes,

β_{1} = k_{0} n_{0}, β_{m} = \sqrt{k_{0}^{2} n_{0}^{2} - \frac{{(m - 1)}^{2} π^{2}}{w^{2}}}, m = 1, 2, 3, \dots For TM modes .

ϕ = \arctan (\frac{\sqrt{2}}{2 \tan α}),

θ = \arccos (\frac{\sqrt{2} \cos α}{2}) .

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