An extension of the second quantization scheme based on the quasinormal-modes theory to one-dimensional photonic band gap (PBG) structures is discussed. Such structures, treated as double open optical cavities, are studied as part of a compound closed system including the electromagnetic radiative external bath. The electromagnetic field inside the photonic crystal is successfully represented by a new class of modes called quasinormal modes. Starting from this representation we introduce the Feynman’s propagator to calculate the decay rate of a dipole inside a PBG structure, related to the density of modes, in the presence of the vacuum fluctuations outside the one-dimensional cavity.

The three‐dimensional (3‐D) electron density representation of the ionosphere computed by the assimilative IRI‐SIRMUP‐P (ISP) model was tested using IONORT (IONOspheric Ray‐Tracing), a software tool for calculating a 3‐D ray‐tracing for high‐frequency waves in the ionospheric medium. A radio link was established between Rome (41.8°N, 12.5°E) in Italy, and Chania (35.7°N, 24.0°E) in Greece, within the ISP validity area, and for which oblique soundings are conducted. The ionospheric reference stations, from which the autoscaled foF2 and M(3000)F2 data and real‐time vertical electron density profiles were assimilated by the ISP model, were Rome (41.8°N, 12.5°E) and Gibilmanna (37.9°N, 14.0°E) in Italy, and Athens (38.0°N, 23.5°E) in Greece. IONORT was used, in conjunction with the ISP and the International Reference Ionosphere 3‐D electron density grids, to synthesize oblique ionograms. The comparison between synthesized and measured oblique ionograms, both in terms of the ionogram shape and the maximum usable frequency characterizing the radio path, demonstrates both that the ISP model can more accurately represent real conditions in the ionosphere than the IRI, and that the ray‐tracing results computed by IONORT are reasonably reliable.

The present paper proposes a comparison between the extinction theorem and the Sturm–Liouville theory approaches for calculating the electromagnetic (e.m.) field inside an optical cavity. We discuss for the first time to the best of our knowledge, in the framework of classical electrodynamics, a simple link between the quasi normal modes (QNMs) and the natural modes (NMs) for one-dimensional (1D), two-sided, open cavities. The QNM eigenfrequencies and eigenfunctions are calculated for a linear Fabry–Pérot (FP) cavity. The first-order Born approximation is applied to the same cavity in order to compare the first-order Born approximated and the actual QNM eigenfunctions of the cavity. We demonstrate that the first-order Born approximation for an FP cavity introduces symmetry breaking: in fact, each Born approximated QNM eigenfunction produces values below or above the actual QNM eigenfunction value on the terminal surfaces of the same cavity. Consequently, the two error-functions for an approximated QNM are not equal in proximity to the two terminal surfaces of the cavity.

The present study proposes a theoretical modeling of simultaneous and noninvasive measurements of electrical resistivity and dielectric permittivity using a quadrupole probe on a subjacent medium. A mathematical–physical model is applied to the propagation of errors in the measurement of resistivity and permittivity based on a sensitivity functions tool. The findings are also compared with results of the classical method of analysis in the frequency domain, which is useful for determining the behavior of zero and pole frequencies in the linear time invariant circuit of the quadrupole. This study underlines that average values of electrical resistivity and dielectric permittivity can be used to estimate complex impedance over various terrains and concretes, especially when they are characterized by low levels of water saturation (content), and are analyzed within a bandwidth ranging only from low to middle frequencies. To meet the design specifications, that ensure satisfactory performances of the probe (inaccuracies of no more than 10%), the forecasts provided by the sensitivity functions approach are discussed in comparison with those foreseen by the transfer functions method (in terms of both the band of frequency f and the measurable range of resistivity ρ, or permittivity εr).