Oscillator-strength enhancement of electric-dipole-forbidden transitions in evanescent light at total reflection

The absorption line strengths of electric-dipole-forbidden (magnetic dipole and electric quadrupole) transitions have been calculated in the evanescent light field that accompanies the total reflection of light. Owing to the complex wave and polarization vectors of the evanescent light, the apparent oscillator strength is enhanced from that in the propagating light and the enhancement for the electric quadrupole transition depends on the polarization vector of the incident light. Separation of the contribution from each component of the wave and polarization vectors is proposed with a magnetic-sublevel-resolved measurement for the $\left(s\text{−}d\right)$ electric quadrupole transition.

Figure 1

A schematic illustration of the internal total reflection and the relevant evanescent field with the wave and polarization vectors for $p$ (left) and $s$ (right) polarizations.

Figure 2

The ${\theta }_1$ dependence of the enhancement factor for the $\left(s\text{−}d\right)$ electric quadrupole transition in the $m_L$ basis for $s$ (a) and $p$ (b) polarizations (solid lines). The dotted lines in both figures show the contribution to the enhancement factor from the relevant matrix element; the magnetic sublevels are shown in the figure.

Figure 3

Zeeman effects on the energy levels relevant to the Cs $(6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2})$ electric quadrupole transition (the nuclear spin $I=7∕2$) up to 3 T.

Figure 4

Contribution to the enhancement factor for the $(S_{1∕2}\to D_{5∕2})$ electric quadrupole transition in the $m_J$ basis for $s$ (a) and $p$ (b) polarizations.

Figure 5

Calculated spectra of the Cs $(6{}^{2}S_{1∕2}\to 5{}^{2}D_{5∕2})$ electric quadrupole transition at 3 T for $s$ polarization (a),(c),(e) and for $p$ polarization (b),(d),(f). (a),(b) ${\theta }_1={\theta }_c\left(43.38\mathrm{°}\right)$; (c),(d) ${\theta }_1=45\mathrm{°}$; (e),(f) ${\theta }_1=70\mathrm{°}$.