Theoretical analysis of an electrically addressed viscoelastic spatial light modulator

The time behavior and the spatial-frequency response of a deformable viscoelastic control layer are analyzed in view of its intended use as a spatial light modulator in a solid-state light valve. Direct electrical addressing of the viscoelastic spatial light modulator (VSLM) is incorporated in the analytical model by means of electrostatic potentials that vary sinusoidally in one lateral dimension. First, the electrostatic boundary-value problem of the VSLM is solved, and the resulting compressional forces are determined; then the elastohydrodynamic boundary-value problem is solved on the basis of the so-called Voigt model and the mechanical stresses acting on the VSLM are calculated. Finally, analytical solutions for the deformation amplitude are found by use of equilibrium conditions for the electrostatic and the viscoelastic stresses. The resulting deformation amplitudes of the VSLM are given as functions of time and of spatial frequency with viscosity, shear modulus, surface tension, layer thickness, electric bias, and spatial modulation depth as parameters. An extensive discussion of these results concludes the present study.