Analysis of optical elements with the local plane-interface approximation

Abstract

The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.

Fourier optics heuristics for diffraction at infinity by an index discontinuity in a one-dimensional slab

“…This restriction is illustrated by the fact that we restrict the range of values of α 0 n from −n 2 ≤ α 0 n ≤ n 2 to −1 ≤ α 0 n ≤ 1 between Eqs. (5) and (8). The next section illustrates the validity of our approach.…”

“…The highest values of θ n such that n 2 sin θ n > 1 are associated to total internal reflection and are thus not taken into account in Eq. (8). Therefore, −1 ≤ α 0 n ≤ 1, and…”

“…Glytsis [5] further analyzed the limits of the scalar theory to periodic diffractive optical elements. References [6][7][8][9] detail calculation techniques that imply both geometric and Fourier optics and lead to acceptable results in the nonparaxial domain, and the inclusion of knife-edge diffraction has proven useful for near-field modeling of elements a few wavelengths thick [10]. In Ref.…”

Geometrical Optics Reloaded

“…2 (left) illustrates the interaction of a ray with a curved interface. If we interpret a ray locally as an electromagnetic plane wave and the interface locally as a planar one, then the results from physical optics about the interaction of an ideal plane wave with an ideal plane interface can be applied locally [3]. We have developed an algorithm which consequently applies this local electromagnetic plane wave concept and call it geometric field tracing [4].…”

Analysis of blazed diffractive optical elements formed with artificial dielectrics

“…Absorbing elements are then described as amplitude modulations of the incident wave field, refractive index distributions are described as phase-only modulations, and the phase delay is obtained by classical ray-tracing methods. For many applications, such as échelette-type elements or binary elements with local periodicities much larger than the wavelength of the incident wave, this approach and further extensions to incorporate finite-thickness effects [1,2] or other refinements [3,4] provide sufficient accuracy.…”