On the determination of the boundary impedance from the far field pattern

We consider the Helmholtz equation in the half space and suggest two methods for determining the boundary impedance from knowledge of the far field pattern of the time-harmonic incident wave. We introduce a potential for which the far field patterns in specially selected directions represent its Fourier coefficients. The boundary impedance is then calculated from the potential by an explicit formula or from the WKB approximation. Numerical examples are given to demonstrate efficiency of the approaches. We also discuss the validity of the WKB approximation in determining the impedance of an obstacle.Comment: 10 pages, 4 figure

The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

Design and performance of duct acoustic treatment

The procedure for designing acoustic treatment panels used to line the walls of aircraft engine ducts and for estimating the resulting suppression of turbofan engine duct noise is discussed. This procedure is intended to be used for estimating noise suppression of existing designs or for designing new acoustic treatment panels and duct configurations to achieve desired suppression levels

Analysis, design, and test of acoustic treatment in a laboratory inlet duct

A suppression prediction program based on the method of modal analysis for spinning mode propagation in a circular duct was used in the analytical design of optimized, multielement, Kevlar bulk-absorber treatment configurations for an inlet duct. The NASA-Langley ANRL anechoic chamber using the spinning mode synthesizer as a sound source was used to obtain in-duct spinning mode measurements, radial mode measurements, and far-field traverses, as well as aerodynamic measurements. The measured suppression values were compared to predicted values, using the in-duct, forward-traveling, radial-mode content as the source for the prediction. The performance of the treatment panels was evaluated from the predicted and measured data. Although experimental difficulties were encountered at the design condition, sufficient information was obtained to confirm the expectation that it is the panel impedance components which are critical to suppression at a single frequency, not the particular construction materials. The agreement obtained between measurement and prediction indicates that the analytical program can be used as an accurate, reliable, and useful design tool

Impedance matching and emission properties of optical antennas in a nanophotonic circuit

An experimentally realizable prototype nanophotonic circuit consisting of a receiving and an emitting nano antenna connected by a two-wire optical transmission line is studied using finite-difference time- and frequency-domain simulations. To optimize the coupling between nanophotonic circuit elements we apply impedance matching concepts in analogy to radio frequency technology. We show that the degree of impedance matching, and in particular the impedance of the transmitting nano antenna, can be inferred from the experimentally accessible standing wave pattern on the transmission line. We demonstrate the possibility of matching the nano antenna impedance to the transmission line characteristic impedance by variations of the antenna length and width realizable by modern microfabrication techniques. The radiation efficiency of the transmitting antenna also depends on its geometry but is independent of the degree of impedance matching. Our systems approach to nanophotonics provides the basis for realizing general nanophotonic circuits and a large variety of derived novel devices