Dielectric response of strongly damped resonances

Vladimir Leonardovich Derbov, S. N. Krasnobaev, Sergey K. Potapov

Ramy El‐Ganainy, Sajeev John

Using the electromagnetic response function of an electric dipole located within a dielectric geometry, we derive the mathematical equivalence between the classical response and quantum mechanical resonant dipole–dipole interaction between two quantum objects (atoms, quantum dots, etc). Cooperative spontaneous emission likewise emerges from this equivalence. We introduce a practical numerical technique using finite difference time domain for calculating both dipole–dipole interaction and collective spontaneous emission in confined dielectric structures, where strong light–matter coupling might arise. This method is capable of obtaining resonant dipole–dipole interaction over a wide range of frequencies in a single run. Our method recaptures the results of quantum mechanical second order perturbation theory for weak light–matter coupling. In strong coupling situations such as near a photonic band edge, second order Rayleigh–Schrödinger perturbation theory leads to divergences, and instead Brillouin–Wigner perturbation theory is required. This is equivalent to the use of a variational wavefunction to describe the exciton transfer between initial and final states. We introduce a system of coupled classical oscillators, that describes resonant dipole–dipole interaction and vacuum Rabi splitting in the strong-coupling regime, and that provides an effective numerical scheme based on the finite difference time domain method. This includes the effects of quantum entanglement and the correlation of quantum fluctuations. We discuss the crossover to Forster energy transfer when quantum correlations between the dipoles are damped by strong environmental interactions.

Joel I. Gersten, Abraham Nitzan

The optical response of small clusters made of two-level molecules is investigated with particular emphasis on the near-resonance region. It is seen that the dielectric-function concept is still useful for describing first-order properties such as particle polarizability and particle-absorption profile; however, near resonance the dielectric response is strongly affected by dephasing and by the energy-level shifts resulting from clustering of molecules in space. Finite-size effects on the dielectric response are also more pronounced near resonance. Second-order response (light scattering) cannot be described by the dielectric function if dephasing processes are important (as they usually are near resonance) and different response functions must be used for different observables. For a cluster of $N$ molecules the light-scattering cross section is made of two contributions: a coherent part (proportional to ${N}^{2}$) which may be described by the dielectric-function concept and an incoherent part (proportional to $N$). Implications for surface effects on the optical properties of molecules adsorbed on such clusters are considered.

Kazem Ardaneh, Mostafa Hassan, Jesús del Hoyo +6 more

B. Hönerlage, J.-Y. Bigot

Sajeev John, Tran Quang

We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipole-dipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.