Resonant oscillating field

In the probe area, where the sample is placed, resonance is obtained by superimposing a weak oscillating field B on the field B0 generated by a coil that is fed by an AC radiofrequency. In order for B to have the proper space orientation, the propagation axis of the radiofrequency has to be perpendicular to the Oz axis (Fig. 9.8). The transfer of energy from the source to the nuclei occurs when the radio-frequency of the source and the frequency of precession are the same. When this occurs, nuclei in energy state E can pass to energy state E2 the relative populations become modified. 

Fig. 10.11 Schematic picture of a multicycle Landau-Zener transition. In combined static and microwave fields the oscillating field brings the atom to the avoided crossing on successive cycles, and the transition amplitudes due to successive cycles add, leading to interference, or resonances (from ref. 12).

The magnetic moment of a particle in a magnetic field B evolves according to the equation of (damped) precession, and in the absence of damping the resonance occurs when the oscillating field frequency exactly equals the precession frequency. For simplicity, we assume the nanoparticles to have an ellipsoidal form with principal axes x, y and z. In this instance, the free energy density in a particle to the first order in the magnetic symmetry can be expressed as [13] ... 

The application of the oscillating field satisfying the resonance condition deviates the system from equilibrium and induces transitions between the two states. On the other hand, the relaxation processes lead the system to equilibrium, in agreement with the Bloch equations (for a static field perpendicular to z) ... 

If we apply a resonant external field to a two-level system, we can observe a Rabi oscillation. In such a case, the quantum state is well described by... 

Figure 6.1-13 To illustrate the electromagnetic (EM) enhancement of SERS a simple model of a small metal sphere (radius is much less than the wavelength) experienced by an electromagnetic oscillating field is considered. If the sphere is illuminated at the plasma resonance frequency of the metal electrons a high electric field on the metal surface is generated, whose efectric field lines are shown (Creighton, 1988).

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