Characteristic Distance of Resonance Energy Transfer Coupled with Surface Plasmon Polaritons

Exploring plasmonic effect on exciton transport: A theoretical insight from macroscopic quantum electrodynamics

Exciton transport in extended molecular systems and how to manipulate such transport in a complex environment are essential to many energy and optical-related applications. We investigate the mechanism of plasmon-coupled exciton transport by using the Pauli master equation approach, combined with kinetic rates derived from macroscopic quantum electrodynamics. Through our theoretical framework, we demonstrate that the presence of a silver nanorod induces significant frequency dependence in the ability of transporting exciton through a molecule chain, indicated by the exciton diffusion coefficient, due to the dispersive nature of the silver dielectric response. Compared with the same system in vacuum, great enhancement (up to a factor of 103) in the diffusion coefficient can be achieved by coupling the resonance energy transfer process to localized surface plasmon polariton modes of the nanorod. Furthermore, our analysis reveals that the diffusion coefficients with the nearest-neighbor coupling approximation are ∼10 times smaller than the results obtained beyond this approximation, emphasizing the significance of long-range coupling in exciton transport influenced by plasmonic nanostructures. This study not only paves the way for exploring practical approaches to study plasmon-coupled exciton transport but also provides crucial insights for the design of innovative plasmon-assisted photovoltaic applications.

Waveguided energy transfer in pseudo-two-dimensional systems

Resonance energy transfer (RET) is an important and ubiquitous process whereby energy is transferred from a donor chromophore to an acceptor chromophore without contact via Coulombic coupling. There have been a number of recent advances exploiting the quantum electrodynamics (QED) framework for RET. Here, we extend the QED RET theory to investigate whether real photon exchange can allow for excitation transfer over very long distances if the exchanged photon is waveguided. To study this problem, we consider RET in two spatial dimensions. We derive the RET matrix element using QED in two dimensions, consider an even greater confinement by deriving the RET matrix element for a two-dimensional waveguide using ray theory, and compare the resulting RET elements in 3D and 2D and for the 2D waveguide. We see greatly enhanced RET rates over long distances for both the 2D and 2D waveguide systems and see a great preference for transverse photon mediated transfer in the 2D waveguide system.

Macroscopic quantum electrodynamics approach to multichromophoric excitation energy transfer. II. Polariton-mediated population dynamics in a dimer system

In this study, based on the theory developed in Paper I, we explore the combined effects of molecular fluorescence and excitation energy transfer in a minimal model-a pair of single-vibration-mode chromophores coupled to surface plasmon polaritons. For the chromophores with zero Huang-Rhys factors and strong couplings to surface plasmon polaritons, we find that the frequencies of Rabi oscillations (the strengths of strong light-matter couplings) are associated with the initial excitation conditions. On the other hand, for the chromophores weakly coupled to surface plasmon polaritons, our numerical calculations together with analytical analysis elaborate on the conditions for the superradiant and subradiant decay behaviors. Moreover, we show that the modified decay rate constants can be explicitly expressed in terms of generalized spectral densities (or dyadic Green's functions), revealing a relationship between photonic environments and the collective effects such as superradiance and subradiance. For the chromophores with nonzero Huang-Rhys factors and strong coupling to surface plasmon polaritons, the effects of molecular vibrations emerge. We demonstrate that the low-frequency vibrational modes do not affect the excited state population dynamics, while the high-frequency vibrational modes can modify either the period of Rabi oscillation (Franck-Condon Rabi oscillation) or the amplitude of excited state population. Our study shows that the collective effects, including superradiance and subradiance, can be controlled via dielectric environments and initial excitation conditions, providing new insights into polariton chemistry and the design of quantum optical devices.

Cavity-Free Quantum-Electrodynamic Electron Transfer Reactions

Richard Feynman stated that "The theory behind chemistry is quantum electrodynamics". However, harnessing quantum-electrodynamic (QED) effects to modify chemical reactions is a grand challenge and currently has only been reported in experiments using cavities due to the limitation of strong light-matter coupling. In this article, we demonstrate that QED effects can significantly enhance the rate of electron transfer (ET) by several orders of magnitude in the absence of cavities, which is implicitly supported by experimental reports. To understand how cavity-free QED effects are involved in ET reactions, we incorporate the effect of infinite one-photon states into Marcus theory, derive an explicit expression for the rate of radiative ET, and develop the concept of "electron transfer overlap". Moreover, QED effects may lead to a barrier-free ET reaction whose rate is dependent on the energy-gap power law. This study thus provides new insights into fundamental chemical principles, with promising prospects for QED-based chemical reactions.

Two bridge-particle-mediated RET between chiral molecules

The problem of resonance energy transfer between a pair of chiral molecules mediated by two electrically polarizable bridging particles is solved using molecular QED theory. In this framework a single virtual photon propagates between any two-coupled entities and is responsible for the conveyance of excitation energy from emitter to absorber. Electric dipole and quadrupole, and magnetic dipole couplings linear in the Maxwell fields are employed for donor and acceptor, while each mediator scatters two virtual photons and responds quadratically to the electric displacement field via its electric dipole polarizability. This enables fourth-order diagrammatic perturbation theory to be used to compute the probability amplitude for the process. Individual multipole moment contributions to the Fermi golden rule rate are then extracted for oriented and isotropic systems. Discriminatory transfer rates arise when either the donor or the acceptor are electric-magnetic dipole and the other has a pure multipole moment, or when both are chiral, with mixed electric dipole-quadrupole contributions vanishing in the fluid phase. The bridge-mediated transfer rate is found to be a maximum for a collinear geometry. Moreover, a multi-level model of the mediator is necessary for energy migration. Asymptotically limiting rates for arbitrary and collinear geometries are also obtained for one centre purely electric dipolar and the other purely quadrupolar, or both donor and absorber purely quadrupolar. Understanding is gained of radiationless and radiative transfer mechanisms between chiral moieties in a dielectric medium.

Molecular Polaritonics: Chemical Dynamics Under Strong Light-Matter Coupling

Chemical manifestations of strong light-matter coupling have recently been a subject of intense experimental and theoretical studies. Here we review the present status of this field. Section 1 is an introduction to molecular polaritonics and to collective response aspects of light-matter interactions. Section 2 provides an overview of the key experimental observations of these effects, while Section 3 describes our current theoretical understanding of the effect of strong light-matter coupling on chemical dynamics. A brief outline of applications to energy conversion processes is given in Section 4. Pending technical issues in the construction of theoretical approaches are briefly described in Section 5. Finally, the summary in Section 6 outlines the paths ahead in this exciting endeavor. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Simple but accurate estimation of light-matter coupling strength and optical loss for a molecular emitter coupled with photonic modes

Light-matter coupling strength and optical loss are two key physical quantities in cavity quantum electrodynamics (CQED), and their interplay determines whether light-matter hybrid states can be formed or not in chemical systems. In this study, by using macroscopic quantum electrodynamics (MQED) combined with a pseudomode approach, we present a simple but accurate method, which allows us to quickly estimate the light-matter coupling strength and optical loss without free parameters. Moreover, for a molecular emitter coupled with photonic modes (including cavity modes and plasmon polariton modes), we analytically and numerically prove that the dynamics derived from the MQED-based wavefunction approach is mathematically equivalent to the dynamics governed by the CQED-based Lindblad master equation when the Purcell factor behaves like Lorentzian functions.

Theory of molecular emission power spectra. II. Angle, frequency, and distance dependence of electromagnetic environment factor of a molecular emitter in plasmonic environments

Our previous study [S. Wang et al., J. Chem. Phys. 153, 184102 (2020)] has shown that in a complex dielectric environment, molecular emission power spectra can be expressed as the product of the lineshape function and the electromagnetic environment factor (EEF). In this work, we focus on EEFs in a vacuum-NaCl-silver system and investigate molecular emission power spectra in the strong exciton-polariton coupling regime. A numerical method based on computational electrodynamics is presented to calculate the EEFs of single-molecule emitters in a dispersive and lossy dielectric environment with arbitrary shapes. The EEFs in the far-field region depend on the detector position, emission frequency, and molecular orientation. We quantitatively analyze the asymptotic behavior of the EFFs in the far-field region and qualitatively provide a physical picture. The concept of EEF should be transferable to other types of spectra in a complex dielectric environment. Finally, our study indicates that molecular emission power spectra cannot be simply interpreted by the lineshape function (quantum dynamics of a molecular emitter), and the effect of the EEFs (photon propagation in a dielectric environment) has to be carefully considered.

Surface plasmon coupling effects on the förster resonance energy transfer from quantum dot into rhodamine 6G

Rhodamine 6G (R6G) molecules linked CdZnSeS/ZnS green-emitting quantum dots (QDs) are self-assembled onto Ag nanoparticles (NPs) for studying the surface plasmon (SP) coupling effect on the Förster resonance energy transfer (FRET) process from QD into R6G. SP coupling can enhance the emission efficiency of QD such that FRET has to compete with QD emission for transferring energy into R6G. It is found that FRET efficiency is reduced under the SP coupling condition. Although R6G emission efficiency can also be enhanced through SP coupling when it is directly linked onto Ag NP, the enhancement decreases when R6G is linked onto QD and then the QD-R6G complex is self-assembled onto Ag NP. In particular, R6G emission efficiency can be reduced through SP coupling when the number of R6G molecules linked onto a QD is high. A rate-equation model is built for resembling the measured photoluminescence decay profiles and providing us with more detailed explanations for the observed FRET and SP coupling behaviors.

Theory of molecular emission power spectra. I. Macroscopic quantum electrodynamics formalism

We study the emission power spectrum of a molecular emitter with multiple vibrational modes in the framework of macroscopic quantum electrodynamics. The theory we present is general for a molecular spontaneous emission spectrum in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. Moreover, the theory shows that the molecular emission power spectra can be decomposed into the electromagnetic environment factor and lineshape function. In order to demonstrate the validity of the theory, we investigate the lineshape function in two limits. In the incoherent limit (single molecules in a vacuum), the lineshape function exactly corresponds to the Franck-Condon principle. In the coherent limit (single molecules strongly coupled with single polaritons or photons) together with the condition of high vibrational frequency, the lineshape function exhibits a Rabi splitting, the spacing of which is exactly the same as the magnitude of exciton-photon coupling estimated by our previous theory [S. Wang et al., J. Chem. Phys. 151, 014105 (2019)]. Finally, we explore the influence of exciton-photon and electron-phonon interactions on the lineshape function of a single molecule in a cavity. The theory shows that the vibronic structure of the lineshape function does not always disappear as the exciton-photon coupling increases, and it is related to the loss of a dielectric environment.

Controllable Frequency Dependence of Resonance Energy Transfer Coupled with Localized Surface Plasmon Polaritons

We investigate the intrinsic characteristics of resonance energy transfer (RET) coupled with localized surface plasmon polaritons (LSPPs) from the perspective of macroscopic quantum electrodynamics. To quantify the effect of LSPPs, we propose a numerical scheme that allows us to accurately calculate the rate of RET between a donor-acceptor pair near a nanoparticle. Our study shows that LSPPs can be used to enhance the RET rate significantly and control its frequency dependence by modifying a core/shell structure, which indicates the possibility of RET rate optimization. Moreover, we systematically explore the angle (distance) dependence of the RET rate and analyze its origin. According to different frequency regimes, the angle dependence of RET is dominated by different mechanisms, such as LSPPs, surface plasmon polaritons (SPPs), and anti-resonance. For the proposed core/shell structure, the characteristic distance of RET coupled with LSPPs (approximately 0.05 emission wavelength) is shorter than that of RET coupled with SPPs (approximately 0.1 emission wavelength), which may provide promising applications in energy science.

Coherent-to-Incoherent Transition of Molecular Fluorescence Controlled by Surface Plasmon Polaritons

We investigate the coherent-to-incoherent transition of molecular fluorescence of a chromophore above a silver surface (including bulk and thin-film systems) and explore the distance dependence of fluorescence rate enhancement. In the framework of macroscopic quantum electrodynamics, we generalize our previous theory to include multiple vibrational modes. The present theory can accurately describe quantum dynamics from the coherent limit to the incoherent limit. Moreover, we introduce a new concept Incoherent Index to quantify the degree of quantum coherence and demonstrate that the coherent-to-incoherent transition can be controlled by the dielectric environment and the molecule-silver distance. In addition, our theory indicates that strong molecule-photon (polariton) coupling can be achieved by virtue of small Huang-Rhys factors, large transition dipole moments, and appropriate dielectric material design. The present study provides a new direction for engineering light-matter interactions in polaritonic chemistry.

Long-Range Single-Molecule Förster Resonance Energy Transfer between Alexa Dyes in Zero-Mode Waveguides

Zero-mode waveguide (ZMW) nano-apertures milled in metal films were proposed to improve the Förster resonance energy transfer (FRET) efficiency and enable single-molecule FRET detection beyond the 10 nm barrier, overcoming the restrictions of diffraction-limited detection in a homogeneous medium. However, the earlier ZMW demonstrations were limited to the Atto 550-Atto 647N fluorophore pair, asking the question whether the FRET enhancement observation was an artifact related to this specific set of fluorescent dyes. Here, we use Alexa Fluor 546 and Alexa Fluor 647 to investigate single-molecule FRET at large donor-acceptor separations exceeding 10 nm inside ZMWs. These Alexa fluorescent dyes feature a markedly different chemical structure, surface charge, and hydrophobicity as compared to their Atto counterparts. Our single molecule data on Alexa 546-Alexa 647 demonstrate enhanced FRET efficiencies at large separations exceeding 10 nm, extending the spatial range available for FRET and confirming the earlier conclusions. By showing that the FRET enhancement inside a ZMW does not depend on the set of fluorescent dyes, this report is an important step to establish the relevance of ZMWs to extend the sensitivity and detection range of FRET, while preserving its ability to work on regular fluorescent dye pairs.

Off-Resonance Control and All-Optical Switching: Expanded Dimensions in Nonlinear Optics

The theory of non-resonant optical processes with intrinsic optical nonlinearity, such as harmonic generation, has been widely understood since the advent of the laser. In general, such effects involve multiphoton interactions that change the population of each input optical mode or modes. However, nonlinear effects can also arise through the input of an off-resonant laser beam that itself emerges unchanged. Many such effects have been largely overlooked. Using a quantum electrodynamical framework, this review provides detail on such optically nonlinear mechanisms that allow for a controlled increase or decrease in the intensity of linear absorption and fluorescence and in the efficiency of resonance energy transfer. The rate modifications responsible for these effects were achieved by the simultaneous application of an off-resonant beam with a moderate intensity, acting in a sense as an optical catalyst, conferring a new dimension of optical nonlinearity upon photoactive materials. It is shown that, in certain configurations, these mechanisms provide the basis for all-optical switching, i.e., the control of light-by-light, including an optical transistor scheme. The conclusion outlines other recently proposed all-optical switching systems.

Extending Single-Molecule Förster Resonance Energy Transfer (FRET) Range beyond 10 Nanometers in Zero-Mode Waveguides

Single-molecule Förster resonance energy transfer (smFRET) is widely used to monitor conformations and interaction dynamics at the molecular level. However, conventional smFRET measurements are ineffective at donor-acceptor distances exceeding 10 nm, impeding the studies on biomolecules of larger size. Here, we show that zero-mode waveguide (ZMW) apertures can be used to overcome the 10 nm barrier in smFRET. Using an optimized ZMW structure, we demonstrate smFRET between standard commercial fluorophores up to 13.6 nm distance with a significantly improved FRET efficiency. To further break into the classical FRET range limit, ZMWs are combined with molecular constructs featuring multiple acceptor dyes to achieve high FRET efficiencies together with high fluorescence count rates. As we discuss general guidelines for quantitative smFRET measurements inside ZMWs, the technique can be readily applied for monitoring conformations and interactions on large molecular complexes with enhanced brightness.

Effects of Intrinsic Local Fields on Molecular Fluorescence and Energy Transfer: Dipole Mechanisms and Surface Potentials

A general theory is developed to identify the influence of local dipole fields on fluorescence and intermolecular electronic excitation transfer. The analysis, based on electrodynamical principles, identifies the fundamental quantum mechanisms and delivers full analytical results. The aim is to afford new physical insights, assisting the interpretation of measurements on the specific effects of local molecular dipoles on direct fluorescence and on fluorescence resonance energy transfer. Dipole field effects, which include those originating from intrinsically polar chromophores and surface field gradients, also prove to be manifest in electronic transitions of quadrupole symmetry character. The results have particular significance for fluorescence studies of cell membrane biophysics.