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Timestamp: 2019-04-22 20:59:14+00:00

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In recent works, we demonstrated the accuracy and physical relevance of a highly simplified reverse-engineering analytical model for a parallel-aligned liquid crystal on silicon devices (PA-LCoS). Both experimental measurements and computational simulations applying the rigorous split-field finite difference time domain (SF-FDTD) technique led to this conclusion in the low applied voltages range. In this paper, we develop a complete rigorous validation covering the full range of possible applied voltages, including highly non-linear liquid crystal (LC) tilt angle profiles. We demonstrate the applicability of the model for spectral and angular retardation calculations, of interest in spatial light modulation applications. We also show that our analytical model enables the calculation of the retardance for novel PA-LC devices as a function of the LC compound and cell gap, becoming an appealing alternative to the usual numerical approaches for PA-LC devices design.
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Fig. 1 Diagram for the PA-LC cell considered in the model proposed.
Fig. 2 LC director tilt angle profiles across the thickness of the cell and for various voltages.
Fig. 3 Retardance measurements obtained in the SF-FDTD simulated experiment for 18 wavelengths and 61 voltages and the incidence angles: (a) 3°, (b) 25°, (c) 35°, and (d) 45°.
Fig. 4 Retardance simulated measurements for the various incidence angles (in the legend) and for the wavelengths: (a) 633 nm, (b) 532 nm, and (c) 473 nm.
Fig. 5 SF-FDTD experiment (dots) and theoretical fitting with the proposed simplified model (continuous line) for the wavelengths 633, 532 and 473 nm and for incidence at: (a) 3°; (b) 35°.
Fig. 6 Tilt angle as a function of voltage.
Fig. 7 Difference between theoretical and SF-FDTD-experimental retardance normalized by the theoretical value for wavelengths 633, 532 and 473 nm and for incidence at: (a) 3°, and (b) 35°.
Fig. 8 SF-FDTD experiment (dots) and prediction with the proposed simplified model (continuous line) for the wavelengths 633, 532 and 473 nm and for incidence at: (a) 25°; (b) 45°.
Fig. 9 Difference between predicted and SF-FDTD experimental retardance normalized by the predicted value for wavelengths 633, 532 and 473 nm and for incidence at: (a) 25°, and (b) 45°.
Fig. 10 Relation for α max (sine profile), (a) vs. tilt angle of an equivalent homogenous slab and, (b) vs. voltage.
Fig. 11 Comparison between the realistic and the sine tilt profiles for a series of voltages.
Fig. 12 Tilt angle as a function of gray level for the commercial PA-LCoS in .
Fig. 13 From the experimental data for the commercial PA-LCoS in . Relation between (sine profile), (a) vs. tilt angle of an equivalent homogenous slab and, (b) vs. gray level (applied voltage).
Fig. 14 Sine tilt profiles as a function of the gray level.
Fig. 15 Proposed simplified model (continuous line) and SF-FDTD experimental (dots) retardance versus wavelength and for three incidences. (a) Maximum and (b) minimum retardance values.
Fig. 16 Retardance dynamic range. Proposed simplified model (continuous line) and SF-FDTD experimental (dots) retardance versus wavelength and for three incidences.
Fig. 17 With the simplified model, usage of the true OPL to calculate the retardance. Normalized retardance difference in the: (a) Off-state, against the true off-state retardance, and (b) On-state, for an angle of incidence of 45°, against the calculation using the fitted OPL.
Fig. 18 Values for OPD, in (a), and OPL, in (b), for two LC compounds and two temperatures, for a cell gap of 2 µm. Data points in the plots are the sample values use to fit the extended Cauchy relation across the visible.
Fig. 19 Using the proposed simplified model, simulated retardance at 633 nm, at incidence angles: (a) 0°; (b) 45°.
Fig. 20 Using the proposed simplified model, simulated retardance at 473 nm, at incidence angles: (a) 0°; (b) 45°.
Table 1 Values for the parameters used to simulate the performance of the PA-LC cell.
Table 2 Values for the retardance in the off-state.
Table 3 True OPD and OPL parameters calculated from the cell gap and the indices of refraction in Table 1.
Table 4 Fitted OPD and OPL values for different values for nLC, and values for the figures of merit for the off-state χ2 and for the on-state MSE comparison between theoretical and experimental results.
Table 5 OPD and OPL parameters obtained for the commercial PA-LCoS in .
(1) Γ= 2π λ OPL cos θ LC [ 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ −1 ].
(4) ΔΓ= 2π λ ( OPL/d ) cos θ LC ( 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ −1 )Δz.
(5) Γ total hom ( θ inc , α hom )= 2π λ ( OPL cos θ LC ( θ inc ) [ 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ( θ inc , α hom ) + 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ( − θ inc , α hom ) −2 ] ).
Values for the parameters used to simulate the performance of the PA-LC cell.
Values for the retardance in the off-state.
True OPD and OPL parameters calculated from the cell gap and the indices of refraction in Table 1.
Fitted OPD and OPL values for different values for nLC, and values for the figures of merit for the off-state χ2 and for the on-state MSE comparison between theoretical and experimental results.
OPD and OPL parameters obtained for the commercial PA-LCoS in .

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