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Physical Review A

Quantum plasmonics of finite-size particles with coherent anti-Stokes Raman scattering

C. H. Raymond Ooi, Chan Hin Kam

Published May 30, 2019• 3 citations
Publisher

Abstract

We have developed a semianalytical theory to study a quantum plasmonic system composed of a quantum particle and a metallic particle with finite size. The quantum particle is composed of molecules driven by three laser fields and produces a coherent anti-Stokes Raman scattering (CARS) signal which is enhanced by plasmonic resonance of the metallic particle. The enhanced CARS field and the control laser form a $\mathrm{\ensuremath{\Lambda}}$ scheme that gives highly nonlinear and spatially nonlocal effects. We obtain absorption spectra that show periodic oscillations with radius of the spherical quantum particle, the whispering gallery effect. Plasmonic resonance gives very large and narrow absorption peaks as well as vanishing absorption or Fano dip at specific values of frequency and interparticle distance. The space between the two particles provides a resonant cavity effect which explains the oscillations of absorption power spectra with interparticle distance.

DOI
10.1103/physreva.99.053849

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We have developed a semianalytical theory to study a quantum plasmonic system composed of a quantum particle and a metallic particle with finite size. The quantum particle is composed of molecules driven by three laser fields and produces a coherent anti-Stokes Raman scattering (CARS) signal which is enhanced by plasmonic resonance of the metallic particle. The enhanced CARS field and the control laser form a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ scheme that gives highly nonlinear and spatially nonlocal effects. We obtain absorption spectra that show periodic oscillations with radius of the spherical quantum particle, the whispering gallery effect. Plasmonic resonance gives very large and narrow absorption peaks as well as vanishing absorption or Fano dip at specific values of frequency and interparticle distance. The space between the two particles provides a resonant cavity effect which explains the oscillations of absorption power spectra with interparticle distance.
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.
Quantum Langevin formalism with noise operators is used to provide quantum descriptions of photon pairs (the Stokes and anti-Stokes fields) emitted by a mesoscopic spherical particle composed of quantum particles in a double Raman configuration. The spectra of the fields obtained are sensitive to the dimension of the microsphere and can be controlled by pump and control laser fields. Spectral peaks due to quantum coherence are Stark shifted by the laser fields experiencing autofocusing inside the spherical particle, causing broadening of peaks as the size of the microsphere increases. The antinormal-order spectrum is found to be identical to the normal-order spectrum. The anti-Stokes spectrum is identical to the Stokes spectrum when the linear dispersion is neglected. Frequency-dependent dielectric functions of the Stokes and anti-Stokes spectra corresponding to the linear dispersions of the particle yield narrow morphology-dependent resonance gain peaks at certain frequencies of the Stokes and anti-Stokes spectra that depend not only on the particle size but also on the angle of observation.
We present a semi-analytical theory to describe the nonlinear scattering of Raman photon pairs from a cylindrical microparticle comprising of quantum particles in double Raman configuration. The normally ordered Stokes and anti-Stokes spectra are computed to gain insights into the quantum optical properties of the system and the variation of the spectra with microparticle’s size, orientation as well as observation angles are also analyzed and compared with the results obtained in our previous work involving mesoscopic spherical particle. Our results show several features in the spectra that are unique to the case of cylindrical microparticle and not found in the spherical particle case, such as the shifting of the side peaks originally formed due to ac Stark shifts towards the center at certain range of particle radius values, occurrence of side peaks with magnitudes comparable to that of the central peak, formation of additional peaks at certain observation angles and strong dependence of the spectra on the microparticle’s cylinder axis orientation. Most of these effects are either caused by the inhomogeneity of the incident pump and control laser fields within the volume of the cylindrical microparticle or simply due to the lack of three-dimensional symmetry of cylindrical geometry.
The optical response used in studies of coherent anti-Stokes Raman scattering (CARS) microscopy can be enhanced or suppressed by means of electromagnetic confinement. In this paper, an approach based on planar mirrors is presented. Because of the classical origin of such a nonlinear optical effect, the theory is developed within a fully classical framework and it turns out that the CARS signal can be modified in a fashion similar to what has been extensively investigated for equivalent alterations of incoherent signals understood in terms of cavity quantum electrodynamics.
The optical mixing of sufficiently coherent radiations of frequency (omega) 1 and (omega) 2 inside a suitable molecular medium can result coherent radiation at new frequency (omega) 3 equals [(omega) 1 + ((omega) 1 - (omega) 2)]. If (omega) 1 is kept fixed and (omega) 2 is varied so that a condition (omega) 1 - (omega) 2 equals (omega) is reached where (omega) is a molecular frequency of the medium, then (omega) 3 equals (omega) 1 + (omega) equals 2(omega) 1 - (omega) 2. In this case (omega) 3 coincides with the anti- Stokes Raman frequency associated with the molecular frequency (omega) . This process of coherent anti-Stokes Raman Scattering (CARS) is an important nonlinear optical process which provides intense collimated signal beams and is also an excellent spectroscopic tool. CARS being a four-wave mixing process, it is of interest to study the process in multi-level system to obtain a better insight into the problem. In the current paper we investigate the different quantum statistical properties of CARS in a inhomogeneously broadened three-level system based on density-matrix formalism where both the atomic system and the radiation fields are quantised. The photon-statistics, coherence characteristics and the occurrence of anti-bunching of the CARS field, in the steady state, are investigated.
The non-classical effects of squeezing of light in coherent anti-Stokes Raman scattering (CARS) and coherent anti-Stokes hyper-Raman scattering (CAHRS) are investigated under the short-time approximation based on a fully quantum mechanical approach. In an idealized model CARS, the interaction is looked upon as a process involving absorption of a pump photon and emission of a Stokes photon, which is followed by absorption of a pump photon and subsequently emission of an anti-Stokes photon at a different frequency, whereas CAHRS is looked upon as a process involving absorption of two pump photons and emission of a Stokes photon, which is followed by absorption of two more pump photons and subsequent emission of an anti-Stokes photon at a different frequency. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. It is shown that squeezing in the Stokes and anti-Stokes mode in CARS is found to be dependent on amplitude-squared squeezing of the initial pump field while, in CAHRS, it is dependent on the fourth-order amplitude squeezing of the initial pump field. Higher-order squeezing can be converted to linear squeezing through these processes. It is also shown that squeezing is greater in CAHRS than the corresponding squeezing in CARS.