1. 
 Bernland, Anders
(författare)

Bandwidth limitations for scattering of higher order electromagnetic spherical waves with implications for the antenna scattering matrix
 2011

Rapport (övrigt vetenskapligt)abstract
 Various physical limitations in electromagnetic theory and antenna theory have received considerable attention recently. However, there are no previous limitations on the scattering of higher order electromagnetic vector spherical waves, despite the widespread use of spherical wave decompositions. In the present paper, bandwidth limitations on the scattering matrix are derived for a wide class of heterogeneous objects, in terms of their electrical size, shape and static material properties. In particular, it is seen that the order of the dominating term in the Rayleigh limit increases with the order of the spherical wave. Furthermore, it is shown how the limitations place bounds on the antenna scattering matrix, thus introducing a new approach to physical limitations on antennas. Comparisons to other types of antenna limitations are given, and numerical simulations for two folded spherical helix antennas and a directive YagiUda antenna are included to illuminate and validate the theory. The results in this paper are derived using a general approach to derive limitations for passive systems: First, the lowfrequency asymptotic expansion of the scattering matrix of a general scatterer is derived. This gives a set of sum rules, from which the limitations follow.


2. 
 Bernland, Anders, et al.
(författare)

Physical limitations on the scattering of electromagnetic vector spherical waves
 2010

Rapport (övrigt vetenskapligt)abstract
 Understanding the interaction between electromagnetic waves and matter is vital in applications ranging from classical optics to antenna theory. This paper derives physical limitations on the scattering of electromagnetic vector spherical waves. The assumptions made are that the heterogeneous scatterer is passive, and has constitutive relations which are on convolution form in the time domain and anisotropic in the static limit. The resulting bounds limit the reflection coefficient of the modes over a frequency interval, and can thus be interpreted as limitations on the absorption of power from a single mode. They can be used within a wide range of applications, and are particularly useful for electrically small scatterers. The derivation follows a general approach to derive sum rules and physical limitations on passive systems on convolution form. The time domain versions of the vector spherical waves are used to describe the passivity of the scatterer, and a set of integral identities for Herglotz functions are applied to derive sum rules from which the physical limitations follow.


3. 
 Bernland, Anders, et al.
(författare)

Sum rules and constraints on passive systems
 2010

Rapport (övrigt vetenskapligt)abstract
 A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system on convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic functions mapping the open upper half plane to the closed upper half plane, is closely related to the transfer functions of passive systems. Following a wellknown representation theorem, Herglotz functions can be represented by means of positive measures on the real line. This fact is exploited in this paper in order to rigorously prove a set of integral identities for Herglotz functions that relate weighted integrals of the function to its asymptotic expansions at the origin and infinity. The integral identities are the core of a general approach introduced here to derive sum rules and physical limitations on various passive physical systems. Although similar approaches have previously been applied to a wide range of specific applications, this paper is the first to deliver a general procedure together with the necessary proofs. This procedure is described thoroughly, and exemplified with examples from electromagnetic theory.


4. 
 Nordebo, Sven, et al.
(författare)

On the relation between optimal wideband matching and scattering of spherical waves
 2010

Rapport (övrigt vetenskapligt)abstract
 Using an exact circuit analogy for the scattering of vector spherical waves, it is shown how the problem of determining the optimal scattering bounds for a homogeneous sphere in its highcontrast limit is identical to the closely related, and yet very different problem of finding the broadband tuning limits of the spherical waves. Using integral relations similar to Fano's broadband matching bounds, the optimal scattering limitations are determined by the static response as well as the highfrequency asymptotics of the reflection coefficient. The scattering view of the matching problem yields explicitly the necessary lowfrequency asymptotics of the reflection coefficient that is used with Fano's broadband matching bounds for spherical waves, something that appears to be nontrivial to derive from the classical network point of view.


5. 

