T. W. Preist

Scattering-matrix approach to multilayer diffraction

A new modeling system to determine the optical response function of a multilayer structure with imposed periodicity in the plane of the layers, a multilayer diffraction grating, is described. This new model has two essential ingredients. This model is based on the well-established coordinate transformation procedure developed by Chandezon et al. [ J. Opt. Soc. Am.72, 839– 846 ( 1982)] in which a periodically modulated surface is transformed into a frame in which it is flat, permitting simpler use of Maxwell’s boundary conditions. Then, instead of using the conventional transfer-matrix method, we developed a scattering-matrix technique that permits the modeling of very thick (of the order of 1 μm or greater) multilayer systems with many field components without numerical instability. Model programs have been developed based on this new scattering-matrix approach and tested by comparison with other models and experimental data.

Photonic surfaces for surface-plasmon polaritons

We examine the propagation of surface-plasmon polaritons on textured surfaces. Specifically, we look at how a grating surface produces a band gap in the propagation of this mode and how the band gap depends on the propagation direction of the mode. This naturally leads to a discussion of a surface profile suitable for blocking surface mode propagation in all directions. By using a diffractive-optics-based theoretical modeling approach we examine the requirements for such a surface. We then confirm these expectations experimentally by producing a surface exhibiting a band gap for surface-plasmon polariton modes in all directions in the energy range 1.91–2.00 eV.

Optical response of bigratings

We present a differential theory to describe the optical response of multilayer bigrating structures. The formalism is based on an extension of the coordinate transformation method used by Chandezon et al. [ J. Opt. Soc. Am. A72, 839 ( 1982)] and is a rigorous differential theory capable of modeling highly modulated multilayer bigratings. The method is used to model experimental reflectivity data taken from bigratings and shows good agreement.

Differential formalism for multilayer diffraction gratings made with uniaxial materials

We present a theoretical analysis for multilayer gratings of arbitrary shape containing uniaxial materials in which all optic axes lie in the plane of incidence, which itself is perpendicular to the grating grooves. The analysis is based on the differential method with internal boundary conditions imposed by means of a scattering matrix. Our development allows for layer interfaces of different shape, although they must all share the same periodicity.

Conical diffraction from multicoated gratings containing uniaxial materials

The full optical response of multilayer gratings containing anisotropic layers until now has been the domain of the experimentalist with no suitable theoretical model available to investigate such systems. The introduction of such a model would clearly benefit this relatively unexplored area of diffractive optics. To this end we present a differential theory based on the work of Chandezon et al. [ J. Opt. Soc. Am. A72, 839 ( 1982)], extending our previous analysis to explore not only the in-plane diffraction with anisotropic layers but also the twisted grating, or conical diffraction, case. In this case there are now two possible mechanisms for transverse magnetic to transverse electric conversion, those being the twisted grating and the anisotropic, uniaxial layer. To illustrate the modeling, results of the new theory are compared with experimental data for a twisted grating anisotropic liquid-crystal system. Resonance mode position and intensity are in good agreement, showing the validity of the new mathematical procedure.

Standing-wave surface-plasmon resonances with overhanging zero-order metal gratings

We have found that a relatively unknown and little understood type of standing-wave surface-plasmon resonance may be excited in strongly blazed overhanging zero-order metallic gratings. A modeling code based on an oblique coordinate transformation has been implemented to evaluate the optical response of these structures. For certain dimensions of surface topography, very strong resonant absorption of light is found that is insensitive to the angle of incidence yet is sharply wavelength selective. These resonances are not the well-known geometrical cavity resonances but have smaller periodicities determined by the self-coupling of surface-plasmon modes on the overhanging surfaces.

Optical response of blazed and overhanging gratings using oblique chandezon transformations

In this work we present a new oblique transformation technique which allows the modelling of the optical response of highly blazed and overhanging grating surfaces using a differential method. The new technique when implemented as computer code is an order of magnitude faster than the conventional differential method when applied to blazed gratings with no overhang. Applying it to severely blazed overhanging gratings, which cannot be modelled with the conventional approach, yields new insight into an area of grating theory which has previously remained largely unexplored.

CALCULATION OF PHOTONIC BAND STRUCTURES OF PERIODIC MULTILAYER GRATING SYSTEMS BY USE OF A CURVILINEAR COORDINATE TRANSFORMATION

We present a theoretical study of photonic band structures of multilayer grating systems, in which the periodicity in one plane is provided by a grating and the periodicity perpendicular to the plane is obtained by multilayering repeat units. Our method is based on the Chandezon transformation technique together with a scattering matrix approach. It is numerically stable and computationally efficient. Calculations have been performed for several multilayer systems involving a monograting generating a solid with two-dimensional periodicity. Results are presented that show the effect of the amplitudes and the relative phase of the gratings on the subsequent optical band structure. It is found that when all interfaces have the same profile, there are no appreciable bandgaps in the direction of the grating. In contrast, if adjacent interfaces are out of phase, there are large bandgaps in all the directions in the two-dimensional plane containing the grating vector and the layer periodicity vector.

A new optical technique for characterizing reference artefacts for surface profilometry

We compare two methods for characterizing the profile of surface relief diffraction gratings. First a Talystep and an atomic force microscope (AFM) are used to sense the surface and generate profiles that are a convolution of the stylus and the shape of the gratings surface. Second the reflectivity of the grating is scanned as a function of the angle of incidence. The shape of the observed anomalies, caused by radiation coupling to surface plasmons, depends critically on the groove profile and can be used to determine the true form of the surface. By comparing the optical and mechanical measurements we show that it is possible to determine the effective radius of curvature of the Talystep and AFM styli.

Characterization of a grating-coupled liquid crystal cell using a rigorous theoretical model

We use a rigorous differential formalism to model the optical response of a multilayer structure having both a surface-relief grating and containing uniaxial materials. The uniaxial material is, in this case, a layer of liquid crystal that has its uniaxial axis defined by its director. By fitting experimental angle dependent reflectivity data to a multilayer grating model we are able to determine the spatial profile of the liquid crystal director, and show how accurately the optical response of such a system may be modelled.