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.
A hologram is the 2D recording of the amplitude and phase of an object. Often the phase contains the information of the depth of a 3D object. In our previous work, the 3D mapping of different surfaces have been performed using digital holographic topography. For instance, multi-wavelength digital holography has been used to resolve deformations/depths which are in the order of several microns to centimeters. Now, 2D correlation has been extensively used as a pattern recognition tool to distinguish between different 2D objects. For 3D object correlation, a novel technique involving 2D correlation of holograms is proposed, enabling identification of the 3D object. As a proof-of-principle, in this work holograms of objects which have identical intensity features and different depth profiles are computer generated as well as optically recorded. Then 2D correlation is applied to distinguish the objects. An additional advantage of this method is that one can compare phase/depth information without performing additional numerical steps such as phase unwrapping.
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.
The Berreman matrix method has been previously used to model electromagnetic plane wave propagation through a hyperbolic metamaterial, and to determine transmission and reflection coefficients as a function of wavelength and varying angles of incidence. The Berreman matrix approach is now used to derive the propagation transfer function matrix in such materials. The eigenvalues of the Berreman matrix, which determine the transfer function, depend on the anisotropy. Beam propagation in such anisotropic materials are simulated using the transfer functions of all components of the electric (and magnetic) fields. Implications of this on negative refraction and the self-lensing of beams are explored.
Anisotropic metamaterials are widely used in the field of optics because of their unique electromagnetic properties. These metamaterials can be made from multilayer metallo-dielectric structures. Such stacks can be represented as an anisotropic bulk medium using effective medium theory. Optical properties of anisotropic media are mostly described in terms of effective parameters such as permittivity and permeability, or alternatively, refractive index and characteristic impedance. These properties depend not only on the wavelength and polarization but also the direction of the optical wave-vector. In this work optical wave propagation through such anisotropic media is studied in detail. The Berreman 4 × 4 matrix along with appropriate boundary conditions is used to determine all electric and magnetic fields inside and outside the structure. The overall transmission and reflection are investigated as a function of the thickness of each layer (metal/dielectric), the number of layers, and the wavelength for oblique incidence. The validity of the effective medium theory is also investigated by changing the thickness and number of layers.
The Berreman matrix method is used to analyze the polarization and propagation of electromagnetic waves and beams in anisotropic metamaterials. The metamaterial, comprising a multilayer structure of alternating metal and dielectric layers, is modeled as an effective anisotropic medium. The Maxwell’s equations for electromagnetic propagation are then represented as a set of coupled differential equations using the Berreman matrix. These coupled equations are then solved analytically and cross checked numerically using MATLAB® for plane wave propagation. The analysis can be extended to Gaussian beam propagation through such anisotropic metamaterials using the angular plane wave spectral approach.