Morphology-dependent Resonances Research Articles

Double-resonance stimulated Raman scattering in micrometer-sized droplets

Programmed size ramping of an aerosol stream permits a Q-switched mode-locked 532-nm laser to satisfy periodically the input resonance condition of various low-order (l = 2 to l = 4) TE and TM morphology-dependent resonances in 23.0–23.7-μm-diameter ethanol droplets. The resulting size-versus-amplitude spectra of stimulated Raman scattered light revealed high-Q modes that are not normally observed in elastic scattering. Simultaneous elastic scattering measurements permit unambiguous identification of these input resonances. The relative output intensities of stimulated Raman scattering and time histories imply that the Q of the l = 2 modes is degraded to a value of 107 by the departure of the droplet from an ideal homogeneous sphere.

Simulation of stimulated Raman scattering in droplets

Recent experiments in stimulated Raman scattering in droplets suggest that the enhancement of the nonlinear gain can be phenomenologically modelled by considering the pumped active path to be greatly enhanced. Total internal reflection traps the signal in the droplet at morphology-dependent resonances. A simulation of this and a number of other new aspects of the process that result from considering a variable pumped gain within the droplet are described.

Droplet sizing in fuel injections by stimulated Raman scattering

It is often difficult to distinguish between morphology-dependent resonance and Raman intensity features in nonlinear Raman spectra of organic fuel droplets. In theory the morphology-dependent resonances can be deconvoluted from single-shot spectra, but in practice this is difficult because of shot-to-shot parameter variation. Frequency-analysis methods have been applied to spectra obtained from fuel sprays, and correlation analysis is found to be quick and easily interpreted.

Stimulated raman scattering of fuel droplets

The strong stimulated Raman scattering (SRS) from diesel fuel droplets has the potential of providing the relative concentration of multicomponent fuel and the absolute size of individual droplets. The morphology-dependent resonances (MDRs) of a sphere cause the droplet to act as an optical resonator which greatly lowers the SRS threshold. The number density, quality factor, and frequency shift of several MDRs are calculated as a function of the ratio of the index of refraction of the liquid and the surrounding gas, which approaches unity at the thermodynamic critical condition for the fuel spray. The SRS spectra of monodispersed droplets of toluene, pentane, Exxon-Aromatic-150, and Mobil D-2 are presented. The exponential growth region of the SRS intensity I 1S as a function of the input laser intensity I input is investigated for the toluene carbon ring breathing mode v 2 and the pentane C-H stretching region. The I 1S ratio of toluene and pentane is measured as a function of the ratio of the toluene and pentane concentration for monodispersed droplets. The reduced fluctuation in I 1S when I input is changed from multimode to single-mode is displayed as a histogram of the I 1S of the v 2 mode of toluene droplets.

Identification of morphology dependent resonances in stimulated Raman scattering from microdroplets

Orders l = 2 and 3 TM and TE morphology dependent resonances were identified in stimulated Raman scattering spectra from 23 μm diameter ethanol droplets. These assignments are made possible through use of an improved stabilized vibrating orifice droplet generator and a novel variational size spectroscopy that permits sufficiently precise estimates of index of refraction and droplet radius to be obtained.

Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets.

Laser cavities are open systems, in that energy can leak to the outside via output coupling. The ``normal modes'' are therefore quasinormal modes, with eigenvalues that are complex and eigenfunctions that extend outside the cavity, such that any normalization integral is dominated by the region outside; in short, such systems are non-Hermitian. This paper addresses the question: How is the complex eigenvalue (i.e., the mode frequency) changed when the cavity is perturbed by a small change of dielectric constant? The usual time-independent perturbation theory fails because of non-Hermiticity. By generalizing the work of Zeldovich [Sov. Phys.---JETP 12, 542 (1961)] for scalar fields in one dimension, we express the change of frequency in terms of matrix elements involving the unperturbed eigenfunctions, so that the problem is reduced to quadrature. We then apply the formalism to shape perturbations of a dielectric microdroplet, and give analytic formulas for the frequency shifts of the morphology-dependent resonances. These results are, surprisingly, independent of the radial wave function, so that all integrals can be performed and explicit algebraic expressions are given for axially symmetric perturbations.

Frequency pulling of stimulated Raman scattering in microdroplets

Spectral features observed in stimulated Raman scattering from 20-microm methanol droplets at 1-GW/cm(2) pumping levels appeared locked in wavelength at the center of their respective gain profiles. Typically, a feature's wavelength remained constant while the droplet size varied by as much as 0.3%. This is attributed to frequency-pulling effects caused by the presence of Raman gain. Wavelength shifts of up to +/-0.5 nm in the positions of morphologydependent resonances would explain the observations and are consistent with calculations.

Vibrating orifice droplet generator for precision optical studies

A special purpose vibrating orifice droplet generator is described possessing improved short-term monodispersity (instantaneous diameter fluctuations of 2×10−5 and a differential drift of 10−5/min.). We demonstrate that this is sufficient to allow cw laser excitation of specific morphology-dependent resonances (MDRs). Improved performance results from (1) the liquid sample being direct pressure fed to the vibrating orifice from a closed pressure reservoir rather than by a conventional gear driven syringe pump, and (2) the vibrating orifice is driven by a periodic square wave voltage source having a frequency which is four orders of magnitude more constant (1 part in 108 per day) than sources normally used. A novel variational size spectroscopy is also described that is made possible by programmed frequency ramping of the voltage source driving the vibrating orifice. By monitoring elastic scattering during ramped size changes we have been able to infer precise values of droplet index of refraction (to ±0.001) and size (to ±3 parts in 104) at any orifice operating frequency by comparison of the resulting experimental pattern to Lorentz–Mie calculations. This aerosol source permits the next generation of optical experiments (e.g., double resonance, fluorescence rate inhibition and enhancement, cw nonlinear optical, accurate chemical speciation, etc.) to be performed on droplets with diameters of 10–80 μm.

Pumping of stimulated Raman scattering by stimulated Brillouin scattering within a single liquid droplet: input laser linewidth effects

The intensity threshold for stimulated Raman scattering (SRS) with a single-mode laser beam is noted to be ≈3 times lower than that with a multimode beam. The intensity threshold for stimulated Brillouin scattering (SBS) from droplets is lower than that for SRS. The temporal profiles of the laser pulse, SRS, and SBS are simultaneously measured with a streak camera (100-psec resolution). The first SBS pulse always occurs earlier than the first SRS pulse. In addition, the subsequent series of SBS and SRS pulses is temporally correlated; i.e., the minimum of the (n + 1)th SBS pulse occurs when the nth SRS pulse reaches a maximum. The second-harmonic beam of a single-mode or multimode Q-switched Nd:YAG laser is tightly focused at the center of the droplet’s illuminated face in order to avoid excitation of any morphology-dependent resonances of a droplet. We conclude that, for single-mode laser excitation of droplets, the internal SBS pumps the SRS.

Some novel features of morphology dependent resonances of bispheres

On aggregation, two identical spheres produce split resonant structures so broadened as to be observable even if their (single) progenitor resonances are narrow beyond detectability.

Remark on the morphology-dependent resonance in the decay rate spectrum for molecules near a spherical surface

It is known that in the decay rate spectrum for molecules near a spherical surface, an extra morphology-dependent resonance structure appears in addition to the usual surface plasmon resonance (ω sp≈ω p bulk/√3). Here an alternative but more physical interpretation of these peaks is given, where it is seen that the morphology-dependent peak can be described only in a dynamic retarded theory.

Multimode stimulated raman scattering in fuel droplets

Stimulated Raman scattering inn liquid droplets gives rise not only to morphology-dependent resonances determined by droplet size, but also to a number of subsidiary molecular peaks. This contrasts with the bulk liquid where only one peak is observed. The subsidiary molecular peaks are related to maxima observed in the spontaneous Raman cross section. Using this technique chemical and physical effects can be decoupled in the signal to give separate information on droplet size and composition.

Theory of enhanced energy tranfer in an aerosol particle

The enhanced tranfer of energy between donor and acceptor molecules in a micrometer size aerosol particle due to the presence of sharp morphology dependent resonances is discussed quantum mechanically. By making use of density of states and quasimode concepts, it is shown that the enhancement factor depends only on the quality factor Q of the resonances, but not on the mode functions, therefore yielding results valid for any microparticle geometry (for which the mode functions are, in general, unknown). Emphasis is also placed on the absorption dominated limit (easily reached in practice), in which the result is particularly simple.

Multiple scattering by two parallel dielectric cylinders

The solution of the multiple-scattering problem for two parallel infinite dielectric cylinders is considered for plane wave illumination perpendicular to the cylinder axes. Numerical results show the coupling effect with respect to cylinder size, separation, and orientation of the cylinder axes with respect to the incident wave. The coupling effect is illustrated by calculations of the internal and near-field intensity for end-on and broadside incidence. Results for circular cylinders with a size/wavelength ratio corresponding to a particular morphology-dependent resonance (size parameter = 45.329) show that the local effect of the resonance is completely damped when the two cylinders touch.

Light scattering by two parallel glass fibers

Angular- and spectral-light-scattering measurements have been made for a glass fiber parallel to and at varying distances from a mirror. Scattering calculations have been made for two parallel fibers. The multiple-scattering effects between a fiber and its mirror image or between two fibers are shown to be quite similar, even for an imperfectly conducting mirror. The multiple scattering becomes less important when one fiber is not in the shadow of the other and when the separation is large. Also, the morphology-dependent resonances shift, and the line shapes change as the separation decreases. In the fiber–mirror configuration, the evanescent fields of the fiber couple to propagating surface plasmons of the metal mirror for TE polarization, greatly damping the scattered intensity.

Morphology-dependent resonances associated with stimulated processes in microspheres

The density of morphology-dependent resonances (MDR’s) of microspheres is shown to be larger than the density that is observed in typical resonance spectra and is large enough to be consistent with observations [ S.-X. Qian R. K. Chang , Phys. Rev. Lett.56, 926 ( 1986)] of multiorder Stokes emission in the stimulated Raman scattering from CCl4 microspheres. Many of the MDR’s have computed linewidths far too narrow to be observed in elastic scattering spectra. Evidence that these very-narrow-linewidth MDR’s may provide significant optical feedback for stimulated processes in microspheres is discussed. The integrated area under resonances in the internal field coefficients does not decrease as the linewidth decreases.

Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets

The coherent Raman mixing spectra from individual micrometer-sized droplets of ethanol and of water consist of regularly spaced peaks that correspond to the morphology-dependent resonances of a spherical droplet. In contrast, the coherent anti-Stokes Raman scattering spectra from droplets exhibit no morphology-dependent peaks. Both results are explained by the spatial overlap of the matching conditions associated with the droplet.

Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra

Low-energy laser irradiation (~0.15 microJ) on a Rhodamine 6G ethanol droplet (radius, 21.1 microm) flowing in a linear stream has been shown to induce damped oscillations in the wavelengths at which the morphology-dependent resonances (MDR's) in the fluorescence are located. Such oscillatory behavior of the MDR's is consistent with those calculated for the elastic scattering from a large sphere that oscillates with small amplitudes (5 parts in 10(4)) from a sphere to a prolate spheroid and then to an oblate spheroid. The observed damped oscillations provide information on the surface tension and viscosity of an ethanol droplet.

Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances

Stimulated Raman scattering (SRS) from an individual liquid droplet (~30-microm radius) has been observed for H(2)O, D(2)O, and ethanol. The occurrence of a series of spectrally narrow peaks that are regularly spaced in wavelength is consistent with morphology-dependent resonances of the droplet, which acts as an optical resonator. The input intensity required to achieve the SRS threshold for the droplet is considerably less than that for the liquid in an optical cell.

Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances

Inelastic emission characteristics from individual ethanol droplets (60-microm diameter) containing Rhodamine 6G dye and pumped by a cw laser (514.5 nm) were investigated. Laser emission was confirmed by noting the spectral, temporal, and output-versus-input intensity behavior. The liquid-air boundary of the droplets provides the optical feedback at selected wavelengths corresponding to the morphology-dependent resonances of a spherical droplet.