Traditionally, the active material in a laser is modelled as independent emitters, but in recent years it has become increasingly clear that radiative coupling between emitters can significantly change the characteristics of small lasers. Collective effects in free space such as superradiance have been studied extensively [1,2], but the effects of inter-emitter correlation in micro- and nano-cavities need further examination to be put on firm theoretical ground. Several studies of collective effects in nano-cavities have been made [3-6], but the theoretical models employed are intricate, and numerical methods are needed both to generate the dynamic equations and to solve them. We propose a model where the complexity is strongly reduced, allowing analytical solutions .
We consider a collection of identical two-level emitters interacting with a single cavity mode. We start from Maxwell-Bloch equations, but instead of making the typical adiabatic elimination of the polarization, we allow the polarization decay rate to be of the same magnitude or smaller than other decay rates. Hence, the traditional laser rate equations for the photon number and the population inversion must be supplemented by equations for the emitter-field correlation and the emitter-emitter correlation. This gives us four generalized laser rate equations, which we solve analytically in steady state.
Comparing with the steady state results obtained from the traditional laser rate equations we see that inclusion of collective effects leads to a reduction of the photon number for small pump rates, similarly to what is found in . From the generalized laser rate equations, we derive a measure of the strength of collective effects in terms of laser parameters: This describes the difference between results with and without inter-emitter correlations, and it goes smoothly to zero as we approach parameter values where the traditional laser rate equations become valid.
To gain insight into the photon statistics of the laser, we construct dynamic equations for higher order correlations of operators. We derive an analytical expression for the zero-delay photon auto-correlation function, and for low pump rates we find that the interaction of emitters results in super-thermal values of the auto-correlation. This feature is observed in experiments and numerical models [4-5], and with our analytical expressions, we are able to pinpoint the parameter combinations for which the collective effects have the largest impact.
Considering the same model in terms of the Fourier components of the operators, we find results for the photon number that agree well with the previous approach, while allowing computation of the linewidth. Thus, we can examine how emitter-emitter correlation affects the line broadening of the laser.
Electrically driven optical antennas are attracting much attention, in particular, due to necessity to develop integrated electrical source of surface plasmons for future plasmonic nanocircuitries. By default, this term denotes a metal nanostructure, in which electromagnetic oscillations at optical frequencies are excited by electrons, tunneling between metallic parts of the structure when a bias voltage is applied between them. Instead of relying on an inefficient inelastic light emission in a tunnel gap, we are suggesting to use ballistic nanoconstrictions as the feed element of an optical antennas in order to excite electromagnetic plasmonic modes. Similarly to tunneling structures, the voltage applied at the constriction falls over the contact of nanoscale length. Electron passing through the contact ballistically can gain the energy provided by the bias ~1eV and exchange it into an mode of the optical antenna. We discussed the underlying mechanisms responsible for the optical emission, and show that with nanoscale contact, one can reach quantum efficiency orders of magnitude larger than with standard tunneling structures.
Quantum emitters, such as q-dots and dye molecules, in the immediate vicinity of plasmonic nanostructures, resonantly excite surface plasmon-polaritons (SPPs) under incoherent pump. The efficiency in the excitation of SPPs per emitter increases with the number of the emitters, because the SPP field synchronizes emission of the coupled emitters, in analogy with the superadiance (SR) in free space. Using fully quantum mechanical model for two emitters coupled with a metal nanorod, we predict up to 15% increase in the emission yield of single emitter compared to only one emitter near the nanorod. Such emission enhancement is stationary and should be observable even with strong dissipation and dephasing under incoherent pump of emitters. Solid-state quantum emitters with blinking behaviors may be utilized to demonstrate such plasmonic SR emission enhancement. Plasmonic SR may find implications in the excitation of nonradiative modes in plasmonic waveguides, in lowing threshold of plasmonic nanolasers.
Photoelectric properties of metamaterials comprising asymmetrically shaped, similarly oriented metallic nanoparticles embedded in a homogeneous semiconductor matrix are theoretically and numerically studied. The asymmetric shape of the nanoparticles is found to result in the existence of a preferred direction where “hot” photoelectrons are emitted from the nanoparticle surface under the action of the localized plasmonic resonance excited in the nanoparticles. The resulting directional photocurrent flow occurring when nanoparticles are uniformly illuminated by a homogeneous plane wave is the direct analogy of the photogalvanic effect known to exist in naturally occurring non-centrosymmetric media. This plasmonic bulk photovoltaic effect is intermediate between the inner photoelectric effect in bulk media and the outer photoelectric effect at macroscopic interfaces. The results obtained are valuable for characterizing photoemission and photoconductive properties of plasmonic nanostructures. They can find many uses for photodetection-related and photovoltaic applications.