Table of Contents:
- Phasor Analysis
- Electric Polarization and Susceptibility
- Atomic Susceptibility
- Resonant Susceptibility
- Lorentzian Lineshape
- Magnitude of the Steady-State Atomic Response
PHASOR ANALYSIS
ELECTRIC POLARIZATION AND SUSCEPTIBILITY
\begin{equation} D = \epsilon_0E + P \end{equation}
\begin{equation} P(\omega) = \chi(\omega)\epsilon_0E(\omega) \end{equation}
\begin{equation} \chi(\omega) = \frac{P(\omega)}{\epsilon_0E(\omega)} \end{equation}
\begin{equation} D = \epsilon_0[1+\chi]E = \epsilon{E} \end{equation}
\begin{equation} \epsilon(\omega) = \epsilon_0(1+\chi) \end{equation}
ATOMIC SUSCEPTIBILITY
RESONANT SUSCEPTIBILITY
\begin{equation} \chi_{at}(\omega) = \frac{P_x}{\epsilon{E_x}} = \frac{Ne^2}{m\epsilon}\frac{1}{\omega_a^2-\omega^2+j\omega\Delta\omega_a} \end{equation}
\begin{equation} \Delta\omega_a = \gamma + 2/T_2 \end{equation}
LORENTZIAN LINESHAPE
\begin{equation} \Delta{x} = 2\frac{\omega-\omega_a}{\Delta\omega_a} \end{equation}
MAGNITUDE OF THE STEADY-STATE ATOMIC RESPONSE