We show applications of our analytical approach to predict the performance of multilayer metallo-dielectric bandpass filters, which also enables estimation of their effective permittivity without relying on homogenization techniques. The approach is based on the one-dimensional dispersion relation for an infinite metallo-dielectric structure that accounts for the complex nature of the permittivities for the metal and dielectric constituents. The dispersion relation clearly reveals the band structure (often comprising multiple passbands), directly provides transmittance characteristics such as center wavelengths and bandwidths and enables the calculation of effective propagation constant and effective attenuation. In this work, we evaluate the dispersion relations for metallo-dielectric structures with complex refractive index data for the metal, viz., Ag, acquired from different sources to show the differences in the center wavelength and the cutoff wavelengths. We verify the accuracy of our method numerically by comparing the transmittance spectrum of finite metallo-dielectric structures using the transfer matrix method. We also plot the dispersion relation using Al as the metal and show the differences in the dispersion relations of the infinite structure and the transmittances of the finite structures relative to Ag. Extension to determination of dispersion relations for other polarizations, viz., transverse magnetic, is discussed, along with corresponding transmittance spectra for oblique incidence.
Combining multilayer metallo-dielectric metamaterials with tunable liquid crystals and electro-optical materials provides a unique approach to develop multifunctional devices for spectral filtering and custom control over light propagation.
Metallo-dielectric structures are used as optical filters whose transmission and reflection characteristics can be changed by varying the thicknesses of the metal and dielectric, and the number of layers. A first estimate of their performance can be found by using effective medium theory and Berreman analysis. Incorporation of an electro-optic material within a metallo-dielectric sandwich can enable electronic tuning of the structure through application of an external voltage. We analyze the performance of metallo-dielectric electro-optic sandwiches using effective medium theory for the metallo-dielectric multilayers and the transfer matrix method for the three-layered sandwich.
We summarize our analyses of optical wave and beam propagation in layered media using the transfer matrix method and the Berreman technique using effective medium theory. Examples include multilayer metallodielectric structures which can exhibit hyperbolic dispersion, multilayer dielectric-phase change materials, multilayers of positive index and negative index materials, and multilayers of linear and nonlinear materials. The Berreman technique is used to derive a transfer function of propagation to model beam propagation in hyperbolic metamaterials.
Anisotropic materials can be multilayer stacks made from isotropic-isotropic, uniaxial-uniaxial or uniaxial-isotropic layers. Under certain conditions, these multilayer stacks can be modeled as a bulk anisotropic medium using effective medium theory. In this work, the effective permittivity tensor of arbitrary anisotropic layers is first derived using effective medium theory. Thereafter the Berreman matrix method is used to analyze electromagnetic propagation in this effective bulk medium. The overall transmittance and reflectance are investigated as a function of the thickness of the layers, number of layers, wavelength and the incident angle. Illustrative examples of stacks made from uniaxial-uniaxial layers and uniaxial-isotropic layers are provided. The uniaxial layers are, in turn, made from a sandwich of two isotropic layers. An example of a transmission filter comprising a multilayer stack on a substrate is also discussed, along with comparison with experimental observations.
Anisotropic materials can comprise multilayer stacks, where each anisotropic layer is, in turn, made from uniaxial-uniaxial or uniaxial-isotropic materials. Each uniaxial layer can be made from two dissimilar isotropic materials, e.g., a metal and a dielectric. Similar to usual metallo-dielectric structures, these multilayer structures can be used to achieve unique optical filters, and can be modeled as a bulk structure using effective medium theory. The optical properties of these anisotropic media can be described in terms of effective parameters such as permittivity and permeability tensors. In this work, optical propagation through such layered media is analyzed using Berreman 4 × 4 matrix along with appropriate boundary conditions. Reflection and transmission are investigated as functions of the incident angle and wavelength. Results are compared with those obtained using the transfer matrix approach. This analysis can be extended to Gaussian beam propagation through such anisotropic materials using angular plane wave approach.
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