Applicability of geometrical optics to in-plane liquid-crystal configurations

Abstract

We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices n o = 1.5 and n e = 1.7. To this end, we compare the results of advanced ray-and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths. © 2010 Optical Society of America OCIS codes: 080.3095, 160.1190, 260.1440 In geometrical optics, optical laws are obtained in the limit where the wavelength of the light vanishes. Also, the material properties are allowed to change with position, provided that the change is sufficiently small over the distance of a wavelength. One important question that has not received much attention so far is how much change in the material properties per unit wavelength is allowed in geometrical optics. In this Letter, our purpose is to provide some insight into this subject for typical in-plane (dielectric nongyrotropic) liquid-crystal configurations with refractive indices n o = 1.5 and n e = 1.7 and give a first approximation to the maximum change in material properties per unit wavelength that is allowed in geometrical optics.If the wave character of light is taken into account, a widely used approach consists of expanding the wave amplitude in terms of 1 / ͑ik 0 ͒, called a Debye expansion (cf. [1], p. 7). When we substitute this expansion into the Maxwell equations, we obtain a set of first-order partial differential equations that are called the transport equations [2]. In geometrical optics, the optical wave field satisfies the zeroth-order transport equation. The transport equations of higher order are difficult to solve, and they do not provide additional physical insight into the modeling of anisotropic media. In that sense, the use of the transport equations does not form an attractive route to investigate the applicability of geometrical optics. Other criteria for the applicability of geometrical optics, such as Fresnel zones discussed by Kravtsov and Orlov (cf. [1], p. 80), are also difficult to apply in practice.A different approach to investigate the validity of geometrical optics can be deduced from the following consideration. Consider an anisotropic medium in which the director (i.e., the local optical axis) is rotated gradually by an angle of 90°over a distance L, see Fig. 1. Then L is the distance over which a maximum change in optical properties occurs (for fixed principal refractive indices). We define the dimensionless wavelength by / L, where is the wavelength of the light. In the limit where / L → 0, a medium has homogeneous material properties. The limit where / L → ϱ corresponds to a discontinuity in the material properties. For sufficiently small / L, geometrical optics and wave optics agree. The main question is then up to wha...

Wide angle conoscopic interference patterns in uniaxial crystals

“…As known, ray tracing is widely used in optics, due to the fact that it is a fundamental tool for the design of optical instruments. Moreover, it has been used to analyze the first order geometrical deformations that a limited beam suffers when it propagates, reflects, or transmits through an optical device for isotropic or anisotropic media [15][16][17][18][19][20]. The paraxial or the nonparaxial approaches are used in accordance with the characteristics of the device (material, shape, use, etc.)…”