A modified projection approach to line mixing

This paper presents a simple approach to combine the high-resolution narrowband features of some desired isolated line models with the projection based strong collision (SC) method to line mixing which was introduced by Bulanin, Dokuchaev, Tonkov and Filippov. The method can be viewed in terms of a small diagonal perturbation of the SC relaxation matrix providing the required narrowband accuracy and resolution close to the line centers, at the same time as the SC line coupling transfer rates can be fine tuned to accurately match some given far wing absorption data. The method can conveniently be placed in the framework of the Boltzmann-Liouville transport equation where a rigorous diagonalization of the line mixing problem requires that molecular phase and velocity changes are assumed to be uncorrelated. Exact solutions and numerical examples are provided for the case with pure pressure broadening and velocity independent parameters. A detailed analysis for the general Doppler case is given based on the first order Rosenkranz approximation, including the possibility to incorporate quadratically speed dependent parameters such as with the Hartmann-Tran (HT) profile in the case with uncorrelated collisions

On the interpretation and significance of the fluctuation-dissipation theorem in infrared spectroscopy

In this paper we revisit the classical fluctuation-dissipation theorem with derivations and interpretations based on quantum electrodynamics (QED). As a starting point we take the widely cited semiclassical expression of the theorem connecting the absorption coefficient with the correlation spectra of a radiating molecular dipole. The literature is suggesting how this connection can be derived in terms of quantum mechanical statistical averages, but the corresponding results in terms of QED seems to be very difficult to trace in detail. The problem is therefore addressed here based on first principles. Interestingly, it turns out that the QED approach applied to the aforementioned statistical averages does not only prove the validity of the fluctuation-dissipation theorem, but it also provides a derivation and a quantum mechanical interpretation of Schwarzschild's equation for radiative transfer. In particular, it is found that the classical Beer-Bouguer-Lambert law is due to absorption as well as of stimulated emission, and furthermore that the source term in Schwarzschild's equation (Kirchhoff's law) is due solely to spontaneous emission. The significance of the fluctuation-dissipation theorem is finally elaborated on in terms of the appropriate scaling of line strength parameters (including line mixing) which is relevant in far infrared and millimeter wave broadband applications

Dispersion modeling and analysis for multilayered open coaxial waveguides

This paper presents a detailed modeling and analysis regarding the dispersion characteristics of multilayered open coaxial waveguides. The study is motivated by the need of improved modeling and an increased physical understanding about the wave propagation phenomena on very long power cables which has a potential industrial application with fault localization and monitoring. The electromagnetic model is based on a layer recursive computation of axial-symmetric fields in connection with a magnetic frill generator excitation that can be calibrated to the current measured at the input of the cable. The layer recursive formulation enables a stable and efficient numerical computation of the related dispersion functions as well as a detailed analysis regarding the analytic and asymptotic properties of the associated determinants. Modal contributions as well as the contribution from the associated branch-cut (non-discrete radiating modes) are defined and analyzed. Measurements and modeling of pulse propagation on an 82 km long HVDC power cable are presented as a concrete example. In this example, it is concluded that the contribution from the second TM mode as well as from the branch-cut is negligible for all practical purposes. However, it is also shown that for extremely long power cables the contribution from the branch-cut can in fact dominate over the quasi-TEM mode for some frequency intervals. The main contribution of this paper is to provide the necessary analysis tools for a quantitative study of these phenomena

Fundamental Limitations for DOA Estimation by a Sphere

In this paper we consider fundamental limitations for DOA estimation with arbitrary lossless antennas or antenna arrays inserted inside a sphere. Spherical vector modes and their associated equivalent circuits and Q factor approximations are employed as a general framework for the analysis. The classical broadband matching theory by Fano is extended to a general multiport S–parameter model of the antennas and fundamental bounds are given for the scattering parameters with respect to bandwidth and electrical size of the sphere. Finally, assuming a statistical signal model with Gaussian receiver noise, the Cramer–Rao lower bound is used to derive fundamental upper bounds for the performance of DOA estimation by a sphere

Antenna currents for optimal Q, superdirectivity, and radiation patterns using convex optimization

The high Q-factor (low bandwidth) and low efficiency make the design of small antennas challenging. Here, convex optimization is used to determine current distributions that give upper bounds on the antenna performance. Optimization formulations for maximal gain Q-factor quotient, minimal Q-factor for superdirectivity, and minimum Q for given far-field are presented. The effects of antennas embedded in structures are also discussed. The results are illustrated for planar geometries

Bandwidth, Q factor, and resonance models of antennas

In this paper, we introduce a first order accurate resonance model based on a second order Pade approximation of the reflection coefficient of a narrowband antenna. The resonance model is characterized by its Q factor, given by the frequency derivative of the reflection coefficient. The Bode-Fano matching theory is used to determine the bandwidth of the resonance model and it is shown that it also determines the bandwidth of the antenna for sufficiently narrow bandwidths. The bandwidth is expressed in the Q factor of the resonance model and the threshold limit on the reflection coefficient. Spherical vector modes are used to illustrate the results. Finally, we demonstrate the fundamental difficulty of finding a simple relation between the Q of the resonance model, and the classical Q defined as the quotient between the stored and radiated energies, even though there is usually a close resemblance between these entities for many real antennas