Cavity-modified spontaneous-emission rates in liquid microdroplets

Coherent manipulations of atoms using laser light

The internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.

Effect of adsorbed concentration on the radiative rate enhancement of photoexcited molecules embedded in single microspheres

The variation of the molecular density in a single microcavity and its influence on the radiative rate enhancement (RRE) are reported here. The quality factors of the observed morphology-dependent resonances (MDRs) of the microcavity remain unchanged in the absence of any absorbing effects. In contrast, the MDRs tend to disappear in the presence of strong absorption even due to the self-absorption by the molecule. Time-resolved fluorescence studies reveal the fact that the value of RRE decreases with an increase in the adsorbed concentration of the molecules. The results have been explained in terms of a detuning parameter, which is a function of the refractive index of the microcavity. The increased dispersing capability of the microsphere upon increasing its molecular density has been found to be responsible for the observed decrease in RRE.

Enhancement of Förster Energy Transfer within a Microspherical Cavity

Energy transfer from pyrene to perylene molecules co-doped within a poly(methyl methacrylate) latex microsphere was drastically accelerated relative to free space. Fluorescence spectra of the microspheres showed that the relative emission intensities of pyrene and perylene changed with the sphere diameter. Analyses of emission decay profiles clarified that Förster-type energy-transfer processes were induced and that the transfer rates increased within the microspherical cavity. This enhancement can be ascribed not only to the quantum electrodynamic effects on the pyrene emission rate, but also the cavity effect of increasing the overlapping factor between donor emission and acceptor absorption spectra.

Microcavity-Controlled Single-Molecule Fluorescence

We present for the first time cavity-controlled fluorescence spectra and decay curves of single dipole emitters interacting at room temperature with the first longitudinal mode of a Fabry-Perot microcavity offering a lambda/2-spacing between its silver mirrors. The spontaneous emission rate of individual dye molecules was found to be enhanced by the Purcell effect by up to three times compared to the rate in free space, in agreement with theoretical predictions. Moreover, our new microcavity design was found to provide long-term stability and single-molecule sensitivity under ambient conditions for several months without noticeable reduction of the cavity-Q value. We consider this as a significant advance for single-photon sources operating at room temperature.

Spontaneous emission of europium ions embedded in dielectric nanospheres

We measure fluorescence lifetimes of emitters embedded in isolated single dielectric nanospheres. By varying the diameters of the spheres from 100 nm to 2 microm and by modifying their dielectric surrounding, we demonstrate a systematic change of paradigm in the spontaneous emission rate, as we cross the border from the superwavelength regime of Mie resonances to the nanoscopic realm of Rayleigh scattering. Our data show inhibition of the spontaneous emission up to 3 times and are in excellent agreement with the results of analytical calculations.

Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity

We measured fluorescence from spherical water droplets containing tryptophan and from aggregates of bacterial cells and compared these measurements with calculations of fluorescence of dielectric spheres. The measured dependence of fluorescence on size, from both droplets and dry-particle aggregates of bacteria, is proportional to the absorption cross section calculated for homogeneous spheres containing the appropriate percentage of tryptophan. However, as the tryptophan concentration of the water droplets is increased, the measured fluorescence from droplets increases less than predicted, probably because of concentration quenching. We model the dependence of the fluorescence on input intensity by assuming that the average time between fluorescence emission events is the sum of the fluorescence lifetime and the excitation lifetime (the average time it takes for an illuminated molecule to be excited), which we calculated assuming that the intensity inside the particle is uniform. Even though the intensity inside the particles spatially varies, this assumption of uniform intensity still leads to results consistent with the measured intensity dependence.

Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities

We show that the artificial resonances of dielectric optical cavities can be used to enhance the detection sensitivity of evanescent-wave optical fluorescence biosensors to the binding of a labeled analyte with a biospecific monolayer. Resonant coupling of power into the optical cavity allows for efficient use of the long photon lifetimes (or equivalently, the high internal power) of the high-Q whispering gallery modes to increase the probability of photon absorption into the fluorophore, thereby enhancing fluorescence emission. A method to compare the intrinsic sensitivity between resonant cavity and waveguide formats is also developed. Using realistic estimates for dielectric cylindrical cavities in both bulk and integrated configurations, we can expect sensitivity enhancement by at least an order of magnitude over standard waveguide evanescent sensors of equivalent sensing geometries. In addition, the required sample volume can be reduced significantly. The cylindrical cavity format is compatible with a large variety of sensing modalities such as immunoassay and molecular diagnostic assay.

Theory of microcavity-enhanced Raman gain

We present a method for obtaining a simple relation between bulk and cavity-modified Raman gains for microcavities with arbitrary geometric shapes. The analytical expression for the microcavity-enhanced Raman gain quantitatively accounts quite well for all the main features of the related experiments.

Spatial photoselection of single molecules on the surface of spherical microcavities

We show that ultrasensitive microdroplet-stream fluorescence techniques combined with surfactant forms of Rhodamine dyes can be used to probe single molecules on the surfaces of spherical microcavities. Individual octadecyl Rhodamine B molecules, shown previously by ensemble measurements to be localized and oriented at the surfaces of liquid microspheres, were spatially photoselected primarily along great circles lying perpendicular or parallel to the detection axis by use of polarized laser excitation. A polarization dependence is observed in the distribution of single-molecule fluorescence amplitudes that can be interpreted qualitatively in terms of position-dependent fluorescence-collection efficiencies.

Collection of emission from an oscillating dipole inside a sphere: analytical integration over a circular aperture

We describe a method for integrating analytically, over a circular aperture, the emission from an oscillating dipole inside a dielectric sphere. The model is useful for investigating fluorescence, Raman, or other emission from molecules inside of spherical particles or droplets. The analysis is performed for two cases: (a) the dipole emits from a fixed orientation, and (b) the dipole emits from all orientations and the collected energy is summed. This second case models the collection of emission from a molecule that is excited repeatedly; after each excitation it rotates to a random orientation before emitting. These results are applicable to single-molecule detection techniques employing microdroplets and to other techniques for characterizing microparticles with luminescence or inelastic scattering.

Collection of fluorescence from single molecules in microspheres: effects of illumination geometry

The collection of fluorescence from a molecule inside a sphere illuminated with single or counterpropagating plane waves is modeled. The results are applicable to microdroplet-based single molecule detection techniques and to some microparticle characterization techniques using inelastic emission. The large position-dependent variations in the fluorescence collection rate are primarily attributable to variations in the excitation intensity. With plane-wave illumination the collection from shadow regions is low because the incident energy is refracted by the droplet surface away from these regions. The average collection rate from molecules in shadow regions can be increased by illuminating with counterpropagating beams.

Effect of optical resonances on photochemical reactions in microdroplets

We have examined photochemical reactions in microdroplets under optical resonances for situations in which photoreactive molecules dissolve from a surrounding gas phase. The link among photochemical reaction, droplet-phase diffusion, and gas-phase mass transfer rate processes produces numerous concentration distributions of reactive molecules between two limiting distributions that are characterized by the absence of reactive molecules and by the saturation concentration level. Each distribution yields a unique intensity field. The analysis shows that the reaction rate is dependent on five dimensionless parameters and is significantly enhanced by a number of combinations of parameter values.

Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency

We present calculations of fluorescence from single molecules (modeled as damped oscillating dipoles) inside a dielectric sphere. For an excited molecule at an arbitrary position within the sphere we calculate the fluorescence intensity collected by an objective in some well-defined detection geometry. We find that, for the cases we model, integration over the emission linewidth of the molecule is essential for obtaining representative results. Effects such as dipole position and orientation, numerical aperture of the collection objective, sphere size, emission wavelength, and linewidth are examined. These results are applicable to single-molecule detection techniques employing microdroplets.

Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering, and evaporation characteristics

Single optically levitated microparticles were investigated by Raman spectroscopy. The particles were composed of di-octyl-phthalate (DOP) and glycerol; these substances are not mixable and form a two-phase droplet. Measurements of the Raman spectrum confirm the formation of droplets containing both chemical species. The spectra show strong input and output structural resonances as expected. If the particle is in resonance, the field inside the particle is enhanced, and most of the inelastically scattered light is emitted from molecules close to the droplet rim. If the particle does not fulfill the resonance condition, the contribution of an individual molecule to the Raman scattering does not depend strongly on the radial position of this molecule. On this basis, the radial distribution of the two components inside the evaporating droplet was determined by time-dependent measurements of the Raman spectrum. Furthermore, elastic-light scattering and the evaporation characteristics of the particles were investigated.

Aerosol-fluorescence spectrum analyzer: real-time measurement of emission spectra of airborne biological particles

We have assembled an aerosol-fluorescence spectrum analyzer (AFS), which can measure the fluorescence spectra and elastic scattering of airborne particles as they flow through a laser beam. The aerosols traverse a scattering cell where they are illuminated with intense (50 kW/cm(2)) light inside the cavity of an argon-ion laser operating at 488 nm. This AFS can obtain fluorescence spectra of individual dye-doped polystyrene microspheres as small as 0.5 µm in diameter. The spectra obtained from microspheres doped with pink and green-yellow dyes are clearly different. We have also detected the fluorescence spectra of airborne particles (although not single particles) made from various biological materials, e.g., Bacillus subtilis spores, B. anthrasis spores, riboflavin, and tree leaves. The AFS may be useful in detecting and characterizing airborne bacteria and other airborne particles of biological origin.