# Electromagnetic Field in Hybrid Quantum Plasmonic-Photonic Systems

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of Artificial Solids with Special Optical Properties

## 3. Hybrid Plasmonic-SQD Platform

^{3}W/cm

^{2}. The solid curve presents an asymmetric Fano shape for an SQD electric dipole μ = 0.25 e nm while the dashed line shows excitation induced transparency and a modified Fano shape, for an SQD electric dipole μ = 2 e nm. Clearly, the two curves are very different from a Lorentzian shape. In the present case, the standard density matrix time dependent treatment [33] is limited to a few building blocks since it considers a set of complex nonlinear ordinary differential equations (ODEs) as explained in [31]. In order to alleviate the computational bottleneck due to the system size, Hayati et al. have used a set of linear von Neumann equations of motion in the steady state for the density matrix of each SQD placed in an effective field calculated within the discrete dipole approximation [31]. In this regime, the method becomes scalable and its numerical efficiency allows the treatment of very large hybrid networks. Plasmonics components such as gold thin films can be also used to convert light in a current of electron by charge separation [11]. More specifically, resonant photons coupled to an optical gold nano-antenna relax into “hot”, energetic electrons [34], which, when driven over the Schottky barrier formed by the nanoantenna/semiconductor interface, generate a photocurrent. In general, electrons and positive holes once formed in a dye or SQD absorbing layer must be kept several nanometers apart before the charge recombination between the electron and hole occurs. The basic idea of charge separation is to move electrons from one side of a potential barrier to the other side as quickly and as efficiently as possible, so that the positive and negative charges become spatially remote.

## 4. SERS and Electromagnetic Field Localization

_{0}* = exp[(ε

_{1}/ε

_{0}– 1)/(3α)]r

_{0}

_{0}is the vacuum dielectric constant, α = 1/137 is the fine structure constant (i.e., the effective coupling when ε = ε

_{0}) while ε

_{1}is the real part of an effective dielectric function ε. The bare classical radius of the electron r

_{0}, has a very small size given by 2.82 × 10

^{−15}m. The effective cross section of a valence electron scattered by a photon is proportional to the square of r

_{0}

^{*}. Therefore, there are anomalous dispersions near the plasmonic absorption edges, that allow the Raman scattering cross section to be enhanced in the domain where ε

_{1}/ε

_{0}– 1 is positive. Interestingly, ε

_{1}/ε

_{0}= 1.3 can explain observed enhancements of 14 orders of magnitude [9]. A typical example of such a situation is the single crystal violet molecule detection by SERS in a colloidal silver solution [48]. That means that the ratio r

_{0}*/r

_{0}could be of the order of 10

^{7}and therefore the scale of r

_{0}

^{*}is about 100 nm. Clearly ε

_{1}/ε

_{0}> 1 is an important condition for the resonant enhancement of the stimulated electronic Raman Scattering. In fact, when ε

_{1}/ε

_{0}is smaller than one, the cross section weakens instead of growing. In resonant X-ray inelastic scattering [47,49,50], ε

_{1}can be evaluated by using first-principles quantum calculations but for SERS the ab initio determination of ε

_{1}is still lacking. Therefore, the connection with first-principles calculations has to be established to verify the present model. We turn now to the discussion of the electromagnetic field confinement in the SERS process. According to Mael Melvin [51], an electronic charge distribution described by a renormalized r

_{0}

^{*}and coupled to a classical electromagnetic field leads to an analogue of the London penetration depth for the electromagnetic field that can be expressed as

_{s}[4π/3 r

_{s}/r

_{0}*]

^{1/2},

_{s}represents the radius containing a valence electron. Charles Enz has derived a similar confinement length L for the electromagnetic field and he has also quantized the corresponding electromagnetic field [52]. Therefore, L can be viewed as the inverse of an effective mass of the photon in the system. Effective massive photons in a medium have also been recently discussed by Arbab [53,54]. Here, the length L can lead to a large mass and a strong confinement. If we assume that r

_{s}about 1 nm, then L becomes of the order of a tenth of nanometer. Thus, SERS can be transformed into a single molecule spectroscopic probe, that can compress the electromagnetic field at the molecular scale [9].

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Model of CdSe quantum dot resonantly coupled to Bacteriorhodopsin from [28].

**Figure 2.**Absorption power of the metal nanoparticles (MNPs) for a SQD/MNP dimer case [R = 13 nm is the SQD-MNP distance; a = 3 nm is the MNP radius and the light intensity is 10

^{3}W/cm

^{2}]; the solid line presents a Fano shape for an SQD electric dipole μ = 0.25 e nm, and the dashed line shows excitation induced transparency and a modified Fano shape, for an SQD electric dipole μ = 2 e nm.

**Figure 3.**Results from the semiconductor quantum dot (SQD)/ bacteriorhodopsin (bR) model of [28]. Upper panel: Efficiency as function of distance. Lower panel: time evolution of the donor exciton occupation displaying a coherent oscillation.

**Figure 4.**Schematics of the Auger mediated sticking (AMS) effect: The dotted line indicates the vacuum level. Copper is a typical example with work function of about $\mathsf{\varphi}$ = 4.5 eV and a positron bound state E

_{2}= −2.8 eV. E

_{AMS}is the kinetic energy of the emitted electron.

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**MDPI and ACS Style**

Barbiellini, B.; Das, S.; Renugopalakrishnan, V.; Somasundaran, P.
Electromagnetic Field in Hybrid Quantum Plasmonic-Photonic Systems. *Condens. Matter* **2018**, *3*, 10.
https://doi.org/10.3390/condmat3020010

**AMA Style**

Barbiellini B, Das S, Renugopalakrishnan V, Somasundaran P.
Electromagnetic Field in Hybrid Quantum Plasmonic-Photonic Systems. *Condensed Matter*. 2018; 3(2):10.
https://doi.org/10.3390/condmat3020010

**Chicago/Turabian Style**

Barbiellini, Bernardo, Subhabrata Das, Venkatesan Renugopalakrishnan, and Ponniseril Somasundaran.
2018. "Electromagnetic Field in Hybrid Quantum Plasmonic-Photonic Systems" *Condensed Matter* 3, no. 2: 10.
https://doi.org/10.3390/condmat3020010