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Journal of Physics B Atomic Molecular and Optical Physics

Dipole nano-laser: the effect of an external electric field

Talal Ghannam

Published Jul 20, 2010• 5 citations
Publisher

Abstract

Using the Langevin formalism we study the effects an external electromagnetic field induces in a system made of a pumped two-level system (TLS) and a metallic nano-particle (NP) that interact together via their near-fields. The surface plasmons of the NP greatly enhance the scattered light. With the absence of the external EM field the spectral width of the scattered light is broader than that of the system, covering almost the entire optical range. However, with the inclusion the external EM field, a reduction in the spectral width of the scattered light of order of 10–50 times below that of the system is observed for certain parameter regimes.This system exhibits also bistability in the population difference of the TLS with the external field acting as an order parameter, but only for certain values of the noise quanta.

DOI
10.1088/0953-4075/43/15/155505

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Using the Langevin formalism we study the effects an external electromagnetic field induces in a system made of a pumped two-level system (TLS) and a metallic nano-particle (NP) that interact together via their near-fields. The surface plasmons of the NP greatly enhance the scattered light. With the absence of the external EM field the spectral width of the scattered light is broader than that of the system, covering almost the entire optical range. However, with the inclusion the external EM field, a reduction in the spectral width of the scattered light of order of 10–50 times below that of the system is observed for certain parameter regimes.This system exhibits also bistability in the population difference of the TLS with the external field acting as an order parameter, but only for certain values of the noise quanta.
Theoretically predicted ''dipole lasing'', i.e., spontaneous excitation of coherent metal nano-particle dipole oscillations through interaction with a quantum-dot two-level system subject to population inversion is demonstrated. Equations for dipole lasing are the same as equations for ordinary laser, where the dipole momentum of nano-particle stands for the electromagnetic field cavity mode. Dipole lasing frequency corresponds to the localized plasmon resonance of the nano-particle. Dipole momentum of nano-particle leads to coherent dipole radiation. Optical cavity is not necessary, the size of the dipole laser can be smaller than the optical wavelength, i.e. it is dipole nano-laser. Threshold conditions and optical bistability in dipole nano-lasers are considered.
The effect of a nearby metallic particle on the quantum optical properties of a quantum particle in the four-level double Raman configuration is studied using the quantum Langevin approach. We obtain analytical expressions for the correlated quantum fields of Stokes and anti-Stokes photons emitted from the system and perform analysis on how the interparticle distance, the direction of observation or detection, the strengths of controllable laser fields, the presence of surface plasmon resonance, and the number density of the quantum particle affect the quantum spectra of the Stokes and anti-Stokes fields. We explore the physics behind the quantum-particle--metallic-nanoparticle interaction within the dipole approximation, that is, when the interparticle distance is much larger than the sizes of the particles. Our results show the dependence of the spectra on the interparticle distance in the form of oscillatory behavior with damping as the interparticle distance increases. At weaker laser fields the enhancement of quantum fields which manifests itself in the form of a Fano dip in the central peak of the spectra becomes significant. Also, the quantum-particle--metallic-nanoparticle coupling, which is affected by the size of the metallic nanoparticle and the number density of the quantum particle, changes the angular dependence of the spectra by breaking the angular rotational symmetry. In the presence of surface plasmon resonance the oscillatory dependence of the spectra on the interparticle distance and angles of observation becomes even stronger due to the plasmonic enhancement effect.
Recent technological advances allow entire optical systems to be lithographically implanted on small silicon chips. These systems include tiny semiconductor lasers that function as light sources for digital optical signals. Future advances will rely on even smaller components. At the theoretical limit of this process, the smallest lasers will have an active medium consisting of a single atom (natural or artificial). Several suggestions for how this can be accomplished have already been published, such as nano-lasers based on photonic crystals and nano wires. In particular, the "dipole nanolaser" consists of a single quantum dot functioning as the active medium. It is optically coupled to a metal nanoparticles that form a resonant cavity. Laser light is generated from the near-field optical signal. The proposed work is a theoretical exploration of the nature of the resulting laser light.\nThe dynamics of the system will be studied and relevant time scales described. These will form the basis for a set of operator equations describing the quantum properties of the emitted light. The dynamics will be studied in both density matrix and quantum Langevin formulations, with attention directed to noise sources. The equations will be linearized and solved using standard techniques. The result of the study will be a set of predicted noise spectra describing the statistics of the emitted light. The goal will be to identify the major noise contributions and suggest methods for suppressing them. This will be done by studying the probability of getting squeezed light from the nanoparticle for the certain scheme of parameters.
This review is devoted to the study of effects of quantum optics in nanostructures. The mechanisms by which the rates of radiative and nonradiative decay are modified are considered in the model of a two-level quantum emitter (QE) near a plasmonic nanoparticle (NP). The distributions of the intensity and polarization of the near field around an NP are analyzed, which substantially depend on the polarization of the external field and parameters of plasmon resonances of the NP. The effects of quantum optics in the system NP + QE plus external laser field are analyzed-modification of the resonance fluorescence spectrum of a QE in the near field, bunching/antibunching phenomena, quantum statistics of photons in the spectrum, formation of squeezed states of light, and quantum entangled states in these systems.
A ``dipole'' laser is proposed consisting of a nanoparticle and a two-level system with population inversion. If the threshold conditions are fulfilled, the dipole interaction between the two-level system and the nanoparticle leads to coherent oscillations in the polarization of the particles, even in the absence of an external electromagnetic field. The emitted radiation has a dipolar distribution. It does not need an optical cavity, and has a very small volume, $\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{3}$, which can be important for applications in microelectronics. Estimates of the threshold conditions are carried out for a dipole laser composed of a quantum dot and a silver nanoparticle.
Abstract This review is devoted to studies of quantum optics effects for quantum emitters (QEs) in the near field of nanoparticles (NPs). In the simple model of a two-level QE located near a plasmon NP, we analyze the mechanisms for modifying the radiative and nonradiative decay rates and discuss the distribution of the near-field intensity and polarization around the NP. This distribution has a complex structure, being significantly dependent on the polarization of the external radiation field and on the parameters of NP plasmon resonances. The quantum optics effects in the system (NP + QE + external laser field) are analyzed, including the near-field modification of the resonance fluorescence spectrum of a QE, the bunching/antibunching effects and photon quantum statistics effects in the spectrum, the formation of squeezed light states, and quantum entangled states in such systems.