Spectral challenges of individual wavelength-scale particles: strong phonons and their distorted lineshapes

Abstract

Beyond our own interest in airborne particulate matter, the prediction of extinction and absorption spectra of single particles of mixed composition has wide use in astronomy, geology, atmospheric sciences, and nanotechnology. Single particle spectra present different challenges than traditional spectroscopic approaches. To quantify the amount of a material in a bulk sample (molecules in solution or the gas phase), one might employ the Beer-Lambert law assuming a simple slab-type assay geometry and averaging over orientation, whereas with single particles one might have a specific orientation and require a nonlinear, Mie-like particle theory. The complicating single particle issues include: strong and broad scattering at wavelengths similar to the particle size, phonon lineshape phase shifting, particle shape effects, distortion of transition lineshapes by strong vibrational bands, bi- and trirefringence, crystal orientation effects including dispersion, and composition mixtures. This work uses a combination of three-dimensional finite difference time domain (3D-FDTD) calculations and experimental infrared spectra on single, crystalline quartz particles to illustrate some of the challenges--in particular the distortion of lineshapes by strong phonons that lie within a range of strong scattering. It turns out that many mineral dust components in the inhalable size range have strong phonons. A Mie-Bruggeman model for single particle spectra is presented to isolate the effects of strong phonons on lineshapes which has utility for analysing the spectra of single, mixed-composition particles. This model will ultimately enable the determination of volume fractions of components in single particles that are mixtures of many materials with strong phonons, as are the dust particles breathed into people's lungs.

Effect of Strongly Coupled Vibration–Cavity Polaritons on the Bulk Vibrational States within a Wavelength-Scale Cavity

“…Finally, the fitted fringe polynomial was used as a transmission background, b i , for the measured vibrational transmission data, s i , to obtain an extinction vibrational lineshape, i.e., −log­( s i / b i ) as shown in Figure b with symbols. The lineshapes were all dominated by absorption and close to Lorentzian shapes, but there can also be dispersive characteristics in thin-film spectra, so each was fit to an absorption/dispersion lineshape − (solid lines in Figure b) as where φ is the phase shift, S is the linestrength, ṽ 0 is the transition position (1/λ), and Γ is the half width at half-max (HWHM). If the phase shift is zero, then only the cos φ term survives and the form is pure Lorentzian for absorption.…”

“…Finally, the fitted fringe polynomial was used as a transmission background, b i , for the measured vibrational transmission data, s i , to obtain an extinction vibrational lineshape, i.e., −log(s i /b i ) as shown in Figure 3b with symbols. The lineshapes were all dominated by absorption and close to Lorentzian shapes, but there can also be dispersive characteristics in thin-film spectra, 25 so each was fit to an absorption/dispersion lineshape 25−27 (solid lines in Figure 3b) as…”

Dust Library of Plasmonically Enhanced Infrared Spectra of Individual Respirable Particles

“…The combination of particles of comparable size to the probing wavelength and the strong vibrational spectra of common mineral components of dust 10,14 warrant the use of Mie theory, which can handle severe lineshape distortions. Mie theory 38 is a complete solution to Maxwell's equations describing the absorption and scattering of light by spherical particles given the spherical particle's complex index of refraction and radius.…”

“…Given the known symptoms of inhaling high levels of particulate matter and the risks associated with long-term exposure to elevated levels, there is a need to chemically evaluate such particles. 10 Our previous single particle work [10][11][12][13][14][15] includes the study of a spectral library of 63 individual dust particles extracted from our laboratory air 12 demonstrating chemical variability including minerals, sulfates, nitrates, and organics, as well as a model for analysis of volume fractions. 10 In this work, the study is extended to samples obtained from a home air filter and the 11 September 2001 World Trade Center (WTC) event.…”

“…Fourier transform infrared (FTIR) spectroscopy offers molecular characterization of chemical functional groups in individual dust particle samples, 12,[16][17][18][19][20] including quantitative analysis, 10 which compliments the more numerous studies characterizing atoms. 2,[21][22][23][24][25] But to quantitatively study subwavelength scale dust particles, infrared (IR) spectroscopy has challenges: 14 (1) vibrational peaks of wavelength-sized particles are dominated by Mie scattering effects that can be ten times larger; (2) vibrational lineshapes are distorted by dispersive scattering contributions, the Christiansen effect; 26,27 and (3) insignificant intensity of light is transmitted to the detector through apertures as the particle falls in the micrometer-scale size range, i.e., it is smaller than the probing wavelength and detector element. Synchrotron free electron lasers with IR microscopy adaptations 28 offer new capabilities and can overcome the latter problem (although at significantly more expense), but are still subject to scattering effects.…”