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Modern Physics Letters B

Stokes and anti-Stokes quantum fields from a mesoscopic microparticle with cylindrical geometry: Orientation, size and angular-dependence of spectra

W. M. Edmund Loh

Published Feb 3, 2020• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984920501031

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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.
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.
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.
The mesoscopic effects on quantum correlations of photon pairs emitted by a microspherical particle composed of many quantum particles in a double Raman scheme are studied. Quantum Langevin formalism with noise operators is used to compute the nonclassical correlations between the Stokes and anti-Stokes photons, particularly the Glauber’s second-order cross- and self-correlation functions. The theory includes realistic situations of inhomogeneous field distributions of the pump and control laser fields as the result of the focusing effect of the microsphere as well as its linear dispersion. The results show that the photon correlations are affected by the size and density of the microsphere, the detection direction, and the detuning and strength of the laser fields. The self-correlation times of the quantum fields are significantly enhanced by the focusing effect of the microsphere with certain sizes.
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.
In the correlated Stokes--anti-Stokes scattering (SAS) an incident photon interacts with a Raman-active material, creating a Stokes photon and exciting a quantum vibrational mode in the medium, which is posteriorly annihilated on contact with a second incident photon, producing in turn an anti-Stokes photon. This can be accomplished by real and virtual processes. In the real process the quantum mode shared between the Stokes and anti-Stokes events is a real particle, whereas in virtual processes the pair formation is mediated by the exchange of virtual particles. Here, we introduce a Hamiltonian to describe the pair production in SAS scattering, for both types of process, when stimulated by two orthogonally polarized laser pulses in a pump-and-probe configuration. We also model the effect of the natural decay of the vibration created in the Stokes event and compute the probability of producing SAS pairs. Additionally, we follow the dynamics of the vibration by considering the Stokes and anti-Stokes fields as external reservoirs, obtaining thus a master equation for the reduced density matrix for the vibrational population. Finally, we compare our theoretical results to recently published experimental data.
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.