The Q of dipole, TM radiation fields

We first critically review earlier attempts to define and calculate Q in unconfined radiation fields and decide that none are fully satisfactory. We then define Q to be the product of ω times the ratio of the peak standing energy to the time average output power, and use that definition to obtain the exact Q of a single electric dipole. The result is identical with the result based upon Chu´s model. Although in exact agreement for a single mode, our methodology shows that significant differences arise in mixed modal fields. As an example we characterize two ideal, collocated and perpendicularly oriented electric dipoles and calculate the standing energy. The equations show that Q is reduced by two factors. The first, shown by Chu in his original paper (1948), is that if collocated, parallel TM and TE dipoles ate driven with circular polarization the fields are unaffected but, very nearly, the standing energy is counted once and the output power counted twice, dropping Q by about a factor of two. With our collocated, circularly polarized, and properly driven TM dipoles some of the standing energies cancel and some standing energy associated with the source when the dipoles are in phase appears to become dissociated from it when the dipoles are phased π/2 apart. The result is a net reduction of Q by 1/3