## Abstract

A theory is formulated to describe the modulation which has been observed in fluorescent light from atoms subjected simultaneously to optical and radio-frequency radiation. The optical field stimulates one or more of a set of excited states of the atom, between which the radio-frequency field establishes coherence. This coherence is manifest in the fluorescent radiation. Interference between radiations of different frequency leads to modulation. General expressions are given for the intensity of the fluorescent light as a function of time. The Zeeman structure of the transition (6$^3$P$_1$ - 6$^1$S$_0$), $\lambda$2537 $\overset{\circ}{\mathrm A}$, in mercury is studied in detail. Modulation at frequencies, 1, 2, 3 and 4 times that of the radio-frequency field, $\omega_0$, is predicted, and resonant effects at static magnetic fields, 0, $\frac{1}{2}$, 1, $\frac{3}{2}$, 2 and 3 times H$_0$, the field for which $\omega_0$ is the Larmor frequency. Resonances at fields other than H$_0$ are due to excitation with light of mixed polarization. Most of the predicted effects have been found experimentally. A `frequency diagram' is introduced and discussed, to represent the combined effects of static and radio-frequency magnetic fields. To each excited state belong a set of r frequencies, where r is the number of states linked by the radio-frequency perturbation. The 9 levels are drawn, as functions of H, for the states m$_J$ = 0, $\pm$1, of $^3$P$_1$. The resonances at fields other than H$_0$ may be associated with intersections of frequency levels belonging to different m$_J$.