Optical Waveguide Theory

The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

https://publikationen.bibliothek.kit.edu/1000010981/754615

Periodic nanostructures for photonics

Foundations For Microwave Engineering

We analyze the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity epsilon and permeability micro. Our study concerns metamaterial structures composed of periodic arrangements of wires, cut wires, split ring resonators (SRRs), closed SRRs, and both wires and SRRs. We find that the SRRs have a strong electric response, equivalent to that of cut wires, which dominates the behavior of left-handed materials (LHM). Analytical expressions for the effective parameters of the different structures are given, which can be used to explain the transmission characteristics of LHMs. Of particular relevance is the criterion introduced by our studies to identify if an experimental transmission peak is left or right handed.

Effective medium theory of left-handed materials

A simple approximate expression is derived for the resonant frequency of a singly split single ring that is among the first microwave resonators designed to be small relative to the wavelength. In addition to the usual gap capacitance the concept of surface capacitance is introduced. The surface capacitance is determined analytically by two different methods, first using analytical expressions for the electric field of a split cylinder, and second by using conformal mapping. Taking two practical examples the resonant frequency, found analytically, is shown to agree with that obtained by numerical simulations. The model could be used for studies of the resonant properties of split rings in the terahertz region.

Analytical formulation for the resonant frequency of split rings

Because the refractive index of hemoglobin in the visible range is sensitive to the hemoglobin concentration, optical investigations of hemoglobin are important for medical diagnostics and treatment. Direct measurements of the refractive index are, however, challenging; few such measurements have previously been reported, especially in a wide wavelength range. We directly measured the refractive index of human deoxygenated and oxygenated hemoglobin for nine wavelengths between 400 and 700 nm for the hemoglobin concentrations up to 140 g l−1. This paper analyzes the results and suggests a set of model functions to calculate the refractive index depending on the concentration. At all wavelengths, the measured values of the refractive index depended on the concentration linearly. Analyzing the slope of the lines, we determined the specific refraction increments, derived a set of model functions for the refractive index depending on the concentration, and compared our results with those available in the literature. Based on the model functions, we further calculated the refractive index at the physiological concentration within the erythrocytes of 320 g l−1. The results can be used to calculate the refractive index in the visible range for arbitrary concentrations provided that the refractive indices depend on the concentration linearly.

https://iopscience.iop.org/article/10.1088/0031-9155/56/13/017/pdf

The refractive index of human hemoglobin in the visible range

A generalized equivalence theorem for polarization theory is formulated and proven. It is shown that anisotropic properties of homogeneous nondepolarizing media can be presented as a combination of four basic mechanisms: linear and circular phase and linear and circular amplitude anisotropy. Expressions for the generalized effect operators of algebraic (or operator) optics are obtained and the inverse problem of crystal optics is solved in terms of physically realizable anisotropy parameters.

Generalized matrix equivalence theorem for polarization theory.

The dispersion characteristics of magnetoinductive (MI) waves for a one-dimensional array of metamaterial elements are investigated for the case where the element properties vary in a bi-periodic manner. It is shown that, by this means (analogously to acoustic waves in a solid), a variety of dispersion curves can be obtained including those displaying an “optical” branch. The flexibility of the metamaterial design makes it possible to apply this approach for obtaining specified dispersion properties. A design permitting parametric amplification is proposed.

Phonon-like dispersion curves of magnetoinductive waves

A theoretical and experimental study of magnetic metamaterials with unit cells containing two resonant elements is presented. The properties of these structures, consisting of split rings, are governed by strongly anisotropic magnetic coupling between individual elements. This coupling leads to propagation of slow magnetoinductive waves in the vicinity of the resonant frequency. The wavelength of magnetoinductive waves is much smaller than the free-space wavelength of the electromagnetic radiation. This opens up the possibility of manipulating the near field on a subwavelength scale. We develop a theoretical formulation for coupled chains of metamaterial elements allowing the tailoring of their guiding properties in the near field. In a comprehensive analysis modes of coupled waveguides supporting forward and/or backward waves are identified and the corresponding hybridization mechanisms for dispersion equations of magnetoinductive waves are determined. Analytical predictions are verified both experimentally and numerically on a variety of coupled waveguides. The approach can be employed for the design of near-field manipulating devices.

Oleksiy Sydoruk

Papers

Analytical formulation for the resonant frequency of split rings

The refractive index of human hemoglobin in the visible range

Generalized matrix equivalence theorem for polarization theory.

Phonon-like dispersion curves of magnetoinductive waves

Tailoring the near-field guiding properties of magnetic metamaterials with two resonant elements per unit cell