<p>In this exercise, we present a simple classical approach to describe the atom-fied interaction. We will describe the interaction of a classical field with an harmonically bound charge. This is admittedly a rather naive model of an atom (often called Thomson model, and proposed at the end of the 19th century when the existence of the electron was first revealed). However, it captures many essential aspects of the interaction and its predictions coincide rather well with those of a more refined semi-classical model.</p>
<p>We consider a single electron of mass $m$ and charge $q = -e$ bounded to the origin (the atom is motionless) by a harmonic force. The position of the electron being $\mathbf{r}$, the motion equation is</p>
<p>The situation described above is not physical. To make it more physical, we should include some damping to reflect the finite lifetime of the excited states. We will consider here only damping corresponding to the emission of light by the accelerated electron. We assume that the total average power radiated by the electron is given by the Larmor formula</p>
$$<p>with $\mathbf{a}$ the acceleration of the electron and $\epsilon_0 = 8.9 \times 10^{-12} ~ \rm F \cdot m^{-1}$ the vacuum permittivity.</p>
<ol>
<li>We integrate the power between $t_1$ and $t_2$, with $\Delta t = t_2 - t_1$ large compared to the oscillation period and small compared to the characteristic time of energy dissipation</li>
</ol>
$$
\Delta E = m \tau \int_{t_1}^{t_2} \textbf{a}^2 \mathrm{d} t = m \tau \left( \underbrace{\left[\textbf{a}.\textbf{v} \right]_{t_1}^{t_2}}_{(1)} - \underbrace{\int_{t_1}^{t_2} \frac{\mathrm{d}^2 \textbf{v}}{\mathrm{d} t^2} \textbf{v} \mathrm{d} t}_{(2)} \right)
$$<p>Term $(2)$ becomes dominant compared to term $(1)$ for time intervals $\Delta t$ much larger than the oscillation period. One way to see this is to set $\textbf{r} = r_0 e^{i \omega_0 t} \textbf{e}_r$. Because $\mathrm{d} \textbf{l} = \textbf{v} \mathrm{d} t$,</p>
$$
\Delta E = - m \tau \int_{r(t_1)}^{r(t_2)} \frac{\mathrm{d}^2 \textbf{v}}{\mathrm{d} t^2} \mathrm{d} \textbf{l} = - \int \textbf{f}\mathrm{d} \textbf{l}
$$<p>thus</p>
$$
\boxed{
\textbf{f} = m \tau \frac{\mathrm{d} \textbf{a}}{\mathrm{d} t}
}
$$<ol start="2">
<li>Since the motion is quasi-harmonic, it can be approximated to first order as $\textbf{r} = \textbf{r}_0 \cos (\omega_0 t)$, thus $\textbf{a} = - \omega_0^2 \textbf{r}$ and</li>
</ol>
$$
\boxed{
\textbf{f} = - m \omega_0^2 \tau \frac{\mathrm{d} \textbf{r}}{\mathrm{d} t}
<li>The total average radiated power is given by Larmor's formula, $P = m \tau a^2$, with $\langle a \rangle = \omega_0^4 \left| r_0 \right|^2 / 2$. Thus, using the expression for the classical polarizabilty</li>
</ol>
$$
\boxed{
P = \frac{\epsilon_0}{12 \pi c^3} \left| \alpha_c \right|^2 \omega^4 E_0^2
$$<p>The energy released is proportionnal to the imaginary part of the classical polarisability. For the elastically bound model, $\mathrm{Im} (\alpha_c) $ is always positive, meaning that the field is absorbed (then scattered in other directions since $\gamma$ only describes the radiation damping). There is no possible amplification of a light field in the steady state in our classical mode.</p>
<p>This exercise is a logical continuation of the previous one, in which we set out to explain, still using a classical model, the principle of emission, absorption and scattering by an atom or group of atoms.</p>
<p>We analyse the interaction of a single atom, desribed as a pointlike classical dipole oscillator, with a Gaussian TEM$_{00}$ mode of wavenumber $k = 2 \pi / \lambda = \omega /c$ and a waist $w$ that is at least somewhat larger than an optical wavelength $\lambda$ such that the paraxial appximation for the propagation of Gaussian beams is valid.</p>
<p>The atom polarisability $\alpha$ is given by</p>
$$<p>In presence of a driving field $\textbf{E}_I = 1/2 E_I e^{- i \omega t} \textbf{e} + \rm c.c$, the oscillating dipole emits a radiation field whose amplitude at large distance $R \gg \lambda$ from the atom is given by</p>
$$<p>where $\theta$ is the angle between the polarisation $\textbf{e}$ of the driving field and the direction of observation.</p>
<p>The field radiated into the same mode as the driving field can interfere with the latter, resulting in absorption and emission effects.</p>
<p><strong>Scattering into a free space mode: emission</strong></p>
<p>An incident field $E_I$ is polarized perpendicular to the TEM$_{00}$ mode and drives an atomic dipole oscillator that emits an electromagnetic field $E_{\rm rad}$ at large distance $R$ from the atom. The atom is located on the axis at the waist of the TEM$_{00}$ mode, as shown in the figure below.</p>
<p>The TEM$_{00}$ field at position $(\rho,z)$ can be written for $z \gg z_R$ as
$$
E (\rho, z) = \frac{\mathcal{E}}{\sqrt{\epsilon_0 c }} e(\rho, z), e(\rho, z) \simeq \sqrt{\frac{2}{\pi \tilde{w}^2}} \mathrm{exp} \left( - \frac{\rho^2}{\tilde{w}^2} + i k z + i k \frac{\rho^2}{2z} - i \frac{\pi}{2} \right)
$$</p>
<p>with $\mathcal{E}$ the mode amplitude which can be related to the total power $P = \left| \mathcal{E} \right|^2 / 2$ and to the electric field at waist $\mathcal{E} = E (0,0) \sqrt{\epsilon_0 c A}$ where $A = \pi w^2 / 2$ is the effective mode area. We can similarly define a mode amplitude for the driving field $\mathcal{E}_I = E_I \sqrt{\epsilon_0 c A}$, even if the driving field is some arbitrary mode.</p>
<ol>
<li>The amplitude of the Gaussian mode can be obtained by projecting the radiated field onto $e$. This gives</li>
<li>The radiated power in all directions can be calculated by integrating the intensity $I_{\rm rad} = \epsilon_0 c \left| E_{\rm rad} \right|^2/2$ over the surface of a sphere with radius $R$.</li>
<li><p>We have directly $2 P = \left| \mathcal{E} \right|^2$</p>
</li>
<li><p>By calculating the ratio of radiated power to emitted power in Gaussian mode,</p>
</li>
</ol>
$$
\boxed{
\frac{2P}{P_{\rm rad}} = \eta
}
$$<p>The cooperativity $\eta$ can be seen here as a geometric quantity representing the overlap between the mode of interest subtending the solid angle $\Delta \Omega = 4/ (kw)^2$.</p>
<p><strong>Scattering from a free space mode: absorption and dispersion</strong></p>
<p>We consider the same TEM$_{00}$ mode as in the previous section but now take the light to be incident in that mode with power $P_{I} = \frac{\left| \mathcal{E}_I \right|^2}{2}$, as shown in the figure below.</p>
<li>a) Using the principle of energy conservation, the power $P_{\rm rad}$ radiated by the atom must be equal to the power of the driven field absorbed by it. Thus,</li>
<li>b) The absorbed power can also be seen as resulting from destructive interference between the incident field $\mathcal{E}_I$ and the field $\mathcal{E}= i \beta \mathcal{E}_I$.</li>
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"/>