No abstract

We derive a new expression for the two-photon spontaneous emission (TPSE) rate of an excited quantum emitter in the presence of arbitrary bodies in its vicinities. After investigating the influence of a perfectly conducting plate on the TPSE spectral distribution (Purcell effect), we demonstrate the equivalence of our expression with the more usual formula written in terms of the corresponding dyadic Green's function. We establish a general and convenient relation between the TPSE spectral distribution and the corresponding Purcell factors of the system. Next, we consider an emitter close to a dielectric medium and show that, in the near field regime, the TPSE spectral distribution is substantially enhanced and changes abruptly at the resonance frequencies. Finally, motivated by the suppression that may occur in the one-photon spontaneous emission of an excited atom between two parallel conducting plates, we discuss the TPSE for this same situation and show that complete suppression can never occur for s → s transitions.

A combination of the magnetotelluric phase tensor and the quadratic algorithm provides a fast and simple solution to the problem of a 2D impedance tensor distorted by 3D electrogalvanic effects. The strike direction is provided by the phase tensor, which is known to provide unstable estimates for noisy data. We obtain stable directions in three steps. First, we use bootstrapping to find the most stable estimate among the different periods. Second, this value is used as the seed to select the neighbor strikes assuming continuity over periods. This second step is repeated several times to compute variances. The third step, which we call prerotating, consists of rotating the original impedance tensor to a most favorable angle for optimal stability and then rotating it back for compensation. The procedure is developed as a progressing algorithm through its application to the gradually more difficult data sets COPROD2S1, COPROD2, far-hi, and BC87, all available for testing new ideas. Alternately, using the Groom-Bailey terminology, the quadratic algorithm provides the amplitudes and phases independently of the strike direction and twist. The amplitudes and phases still need to be tuned up by the correct shear. The correct shear is obtained by contrasting the phases from the phase tensor and from the quadratic equation until they match for all available periods. The results are the undistorted impedances. Uncertainties are computed using formulas derived for the quadratic equation. We use the same data sets as for the strike to illustrate the recovery of impedances and their uncertainties.

After reviewing how the Dirac delta contributions to the electrostatic and magnetostatic fields of a point electric dipole and a point magnetic dipole are usually introduced, we present an alternative procedure for obtaining these terms based on a regularization prescription similar to that used in the computation of the transverse and longitudinal delta functions. We think this method may be useful for the students in other analogous calculations.