Broadband Matching Limitations for Higher Order Spherical Modes

On the Relation Between Optimal Wideband Matching and Scattering of Spherical Waves

“…They have also been used recently to derive a series of new sum rules for the scattering of electromagnetic waves [3,25,26], with applications in antenna theory [11,29,30].…”

“…Hence, under the assumptions of linearity, continuity, time-translational invariance and passivity, sum rules can be derived from the analytic properties of the forward scattering dyadic, see e.g., [25,26], and have also applications in antenna theory, see e.g., [11,12,24,29,30]. In [23], similar relations are used to determine the ultimate thickness to bandwidth ratio of radar absorbers.…”

“…By using Fano's approach, optimum broadband tuning limits of the higher-order spherical waves are considered in [29,30], giving important physical insight into the matching limitations for UWB antennas, see also [9,14,15,18,31,32,34]. Previously, the Fano broadband matching bounds have been applied mainly to the lowest order spherical waves, and there is hence a need to further develop analytical results as an aid in the related numerical analysis.…”

“…Previously, the Fano broadband matching bounds have been applied mainly to the lowest order spherical waves, and there is hence a need to further develop analytical results as an aid in the related numerical analysis. In [29,30], it is conjectured that the lowfrequency asymptotics of the positive real function − log ρ τ l is of the form − log(±ρ τ l ) = 2 a c 0 s + 2(−1) l ( a c 0 ) 2l+1 c τ l s 2l+1 + · · · , (1.1) where ρ τ l is the re ection coe cient corresponding to a TE (τ = 1) or TM (τ = 2) spherical wave of order l, s the Laplace variable, a the radius of a circumscribing sphere, c 0 the speed of light in free space, and c τ l constants to be determined from network analysis and the circuit analogy of the spherical wave impedance.…”

“…In this contribution, an exact circuit analogy for the scattering of spherical waves is used similar to [6,28], to show how the problem of determining the scattering limitations for a homogeneous sphere in its high-contrast limit becomes identical to the closely related, and yet very di erent problem of nding the broadband tuning limits of the spherical waves [29,30]. Furthermore, the scattering view of the matching problem yields explicitly the necessary low-frequency asymptotics of the re ection coe cient (1.1), i.e., the coe cients c τ l that are used with Fano's broadband matching bounds for spherical waves.…”