Perfect Reflection of Light by an Oscillating Dipole

We show theoretically that a directional dipole wave can be perfectly reflected by a single pointlike oscillating dipole. Furthermore, we find that, in the case of a strongly focused plane wave, up to 85% of the incident light can be reflected by the dipole. Our results hold for the full spectrum of the electromagnetic interactions and have immediate implications for achieving strong coupling between a single propagating photon and a single quantum emitter.

Figure 1

(a) Incident light propagating along the $z$ axis is focused with a spherical phase front onto a dipole placed in vacuum. GRS: Gaussian reference sphere; $a$: entrance-aperture radius; $\alpha$: entrance half angle; $\beta$: collection half angle; $f$: focal length. (b) The dashed curve plots the transmittance for the focused plane wave and displays an attenuation of $\mathcal{T}\simeq 80\%$ at resonance for $\alpha =\beta =\pi /3$. The solid curve shows that a directional dipolar wave can be completely attenuated for $\alpha =\beta =\pi /2$.

Figure 2

(a) The $z$ component of the Poynting vector $S_z$ (solid curve) and the electric energy density $W_{\mathrm{inc}}^{\mathrm{el}}$ (dashed curve), both along the positive $x$ axis in the focal plane and normalized to their respective values at $x=0$. (b) Scattering ratio ${\mathcal{K}}_0$ as a function of $\alpha$ for several focused waves. $p_z$ denotes the dipole wave with the electric dipole along the $z$ axis, pw signifies the focused plane wave, $p+m$ shows the combined electric and magnetic dipole fields, and $p_x$ notes the wave of an electric dipole oriented along the $x$ axis. ${\mathcal{K}}_0=2$ is reached at $\alpha =\pi /2$ for $p_x$ and $p_z$. The horizontal dashed line separates the regimes ${\mathcal{K}}_0\gtrless 1$.

Figure 3

Transmittance $\mathcal{T}$ of a focused plane wave as a function of the angles $\alpha$ and $\beta$ as defined in Fig. 1a. The dashed curve indicates the edge at the geometrical shadow boundary $\alpha =\beta$, and the vertical arrow indicates the location $\alpha =\beta \simeq 0.43\pi$ of the minimum value approximately equal to 10%. $\mathcal{T}$ values for the cases $\alpha =\pi /2$, $\beta \to 0$, and $\alpha =\beta =\pi /2$ are also noted.