Density operator approach to the modulation effects in magnetic resonance

Abstract

The density operator method is employed for testing the extent of the equivalence of the (sideband) structures resulting from the frequency and field modulations in magnetic resonance. The two structures and their equivalence were previously established by Anderson and others with the Bloch equation method. The results indicate rather limited equivalence between the two structures. The field-modulation-induced structure remains the same in the two methods. In an approximation of small modulation index ( γH m ω m ), the present work predicts: (1) each rf (dispersion and absorption) signal under the field modulation contains a dominant first harmonic at modulation frequency ω m which is in phase with the modulation; (2) with the frequency modulation, however, each rf signal consists of two dominant first harmonics at ω m the in-phase component above and an out-of-phase component. The two components are proportional to γH m and γH m ω m , respectively.