In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called magnetically silent variants of atomic magnetometers have been developed. While in conventional magnetometers the magnetic resonance transitions between atomic sublevels are phase-coherently driven by a weak oscillating magnetic field, silent magnetometers use schemes in which either the frequency or the amplitude of the light beam is modulated. Here we present a theoretical model that yields algebraic expressions for the parameters of the multiple resonances that occur when either amplitude-, frequency-, or polarization-modulated light of circular polarization is used to drive the magnetic resonance transition in a transverse magnetic field. The relative magnitudes of the resonances that are observed in the transmitted light intensity at harmonic
m of the Larmor frequency ${\ensuremath{\omega}}_{L}$ (either by DC or phase sensitive detection at harmonics
q of the modulation frequency ${\ensuremath{\omega}}_{\mathrm{mod}}$) of the transmitted light are expressed in terms of the Fourier coefficients of the modulation function. Our approach is based on an atomic multipole moment representation that is valid for spin-oriented atomic states with arbitrary angular momentum
F in the low light power limit. We find excellent quantitative agreement with an experimental case study using (square-wave) amplitude-modulated light.
Frequency-modulated light was generated by the application of a magnetic field oscillating at frequencies in the range 1-10 MHz to mercury vapour undergoing resonance fluorescence. The characteristics of the fluorescent light have been studied. When the primary illumination in the plane perpendicular to the field is anisotropic the sigma components are coherently excited. The light emitted along the field is then polarization-modulated. It becomes intensity-modulated if it is passed through a linear analyser. The light emitted obliquely to the magnetic field is intensity-modulated without passing through an analyser. The amplitudes of these modulations show resonance behaviour under the application of an additional static field parallel to the oscillating field. The polarization-modulated light was used to excite resonance fluorescence in a second cell of mercury vapour. The fluorescent light is intensity-modulated. The amplitude of modulation shows resonance behaviour when harmonics of the driving frequency coincide with Zeeman intervals in the excited atoms. These resonances have been explored in detail. They are satisfactorily interpreted by a theory given in an accompanying paper.