Materials described by the constitutive equations D = εE + βε ∇ × E and B = μH + βμ ∇ × H lack inversion symmetry due to chirality or handedness in their microstructure. In this paper, we describe the first direct measurements of the material properties ε, μ, and β for microwave chiral composite materials prepared in our laboratory in the frequency range of 8–40 GHz. We have used both reflection and transmission measurements for normally incident, linearly polarized plane waves in a specially designed free‐space facility using spot focusing antennas. Different concentrations of the chiral inclusions in the form of miniature metallic springs that are left‐handed only, right‐handed only or equally mixed (racemic) have been studied. It is shown that ε and μ are comparable for all three samples at a given concentration, but β has equal but opposite values for the left‐ and right‐handed samples, whereas it is nearly zero for the equichiral sample. The values of β thus obtained are compared to estimated values for suspensions of naturally occurring chiral molecules. The accuracy of the measurements is assessed by using the experimental procedure and inversion algorithm for standard materials like quartz. A new technique involving time domain repines has been used to remove the ambiguity that is usually encountered in the inversion of measured S parameters.
Abstract-In this paper, the coupled mode theory is used to analyze apodized fiber Bragg gratings (FBGs). Since the profile of gratings varies with the propagation distance, the coupled mode equations (CMEs) of apodized FBGs are solved by the fourth-order Runge-Kutta method (RKM) and piecewise-uniform approach (PUA). We present two discretization techniques of PUA to analyze the apodization profile of gratings. A uniform profile FBG can be expressed as a system
Abstract-The coupled mode theory (CMT) is used to analyze uniform Fiber Bragg gratings. The multi-mode CMT is expressed as the first-order vector ordinary differential equations (ODEs) with coefficients depending on the propagation distance. We show in this paper that by changing variables, the original couple mode equations (CMEs) can be re-casted as constant coefficient ODEs. The eigenvalue and eigenvector technique (EVVT), the analytic method for solving constant coefficient ODEs, is then applied to solve the coupled mode equations. Furthermore, we also investigate the application of RungeKutta method (RKM) to the calculation of the global transfer-function matrix for CMEs. We compare the transmission and the reflection
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.