Radiation resistance and irreversible power of antennas in gyroelectric media

Abstract

In recent years, many investigators have been working on the problem of calculating the radiation resistance of a dipole antenna immersed in an anisotropic medium [1]. The central difficulty of their method of calculation is that it yields an infinite value for the radiation resistance. They hare attributed this infinity to the infinitesimal size of the source, and have suggested that if the source were of finite spatial extent the difficulty would not arise. It is our contention that the difficulty is of a more basic nature and is not due to the size of the source but to the method of calculation. The purpose of this letter is to show that if the radiation resistance is calculated with proper conformity to the thermodynamical laws of reversibility and irreversibility, the value of the radiation resistance will turn out to be finite. Clearly, radiation resistance is on the same footing as ordinary circuit resistance in the sense that they both are measures of irreversible power, and hence in calculating radiation resistance it is necessary that only the irreversible part of the power be used. Accordingly, we shall construct an expression for the irreversible part of the power emitted by a source, and show that the expression so constructed is finite and hence leads to a finite value for the radiation resistance. To construct the required expression, we recall that in the case of an accelerating point electron in vacuum, the combination of half the retarded minus half the advanced field is free from singularity [2] and corresponds to the irreversible power radiated by the electron [3]. We shall extend this idea of taking a combination field to the case of a monochro matic source Re(Je^(iWt)) radiating into a lossless anisotropic medium.