Deviations from Plane-Wave Mie Scattering and Precise Retrieval of Refractive Index for a Single Spherical Particle in an Optical Cavity

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. (0)117 9287672 e-mail: a.orr-ewing@bristol.ac.uk AbstractThe extinction cross sections of individual, optically confined aerosol particles with radii of a micron or less can, in principle, be measured using cavity ring-down spectroscopy (CRDS). However, when the particle radius is comparable in magnitude to the wavelength of light stored in a high-finesse cavity, the phenomenological cross-section retrieved from a CRDS experiment depends on the location of the particle in the intra-cavity standing wave and differs from the Mie scattering cross section for plane-wave irradiation. Using an evaporating 1,2,6-hexanetriol particle of initial radius ~1.75 m confined within the 4.5-m diameter core of a Bessel beam, we demonstrate that the scatter in the retrieved extinction efficiency of a single particle is determined by its lateral motion, which spans a few wavelengths of the intra-cavity standing wave used for CRDS measurements. Fits of experimental measurements to Mie calculations, modified to account for the intra-cavity standing wave, allow precise retrieval of the refractive index of 1,2,6-hexanetriol particles (with relative humidity, RH < 10%) of 1.47824  0.00072.

A complete parameterisation of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles

“…By comparing the measured light scattering traces to calculations from Mie theory, n was parameterised as a function of RH for a range of inorganic aqueous solution droplets, key components of nonabsorbing atmospheric aerosol. Tang's parameterisations of n 633 for aqueous inorganic solutes have become a benchmarking standard for new techniques measuring refractive index (Cotterell et al, 2015b;Hand and Kreidenweis, 2002;Mason et al, 2012Mason et al, , 2015 and are used as reference RI data for RF calculations of aqueous inorganic aerosol (Erlick et al, 2011). However, Tang's measurements were limited to λ = 633 nm and knowledge of the optical dispersion is required to calculate spectrally weighted values of the singlescattering albedo and backscatter function.…”

Assessing the accuracy of complex refractive index retrievals from single aerosol particle cavity ring-down spectroscopy

“…However, the light of the intra-cavity ring down beam in an SP-CRDS experiment is a standing wave. As explained in our previous publications Cotterell et al 2015a;Mason et al 2015Mason et al , 2014), the measured s ext value for a particle located at a node or anti-node of the intra-cavity standing wave differs from the value predicted by Mie theory. Moreover, a particle confined in the core of a BB optical trap can move via Brownian motion along the longitudinal axis of the optical cavity over distances of micrometres, sampling several nodes and anti-nodes of the standing wave and the various phases in-between.…”

“…However, the large size range spanned by the droplet, passing through many resonances in s ext , ensures the RI retrieval accuracy remains high (0.0002). Therefore, in RI determinations for 1,2,6-hexanetriol presented in previous publications (Cotterell et al 2015a;Mason et al 2015Mason et al , 2014, the RI can be expected to be measured with an accuracy of 0.0002 (in the absence of other systematic errors such as impurities in the droplet composition). For simulations of hygroscopic response measurements, the RI is correctly retrieved (within the precision of the aforementioned step sizes of n 1 and n 2 ) when the radius is assumed to be determined perfectly.…”

“…The combination of imprecise s ext measurements with the presence of multiply charged particles of larger size can result in poor RI retrievals unless appropriately accounted for in the analysis of the E-CRDS data (Miles et al 2011b;Mason et al 2012;Zarzana et al 2014). Furthermore, analysis of E-CRDS measurements typically neglects the broadening of measured s ext values due to the effect of the CRDS standing wave Mason et al 2014). We have recently shown that a modification must be made to Mie theory to account for the intra-cavity standing wave of a two-mirror CRDS instrument in order to model correctly the s ext variations with radius Reid et al 2014;Cotterell et al 2015a;Mason et al 2015Mason et al , 2014.…”

“…Furthermore, analysis of E-CRDS measurements typically neglects the broadening of measured s ext values due to the effect of the CRDS standing wave Mason et al 2014). We have recently shown that a modification must be made to Mie theory to account for the intra-cavity standing wave of a two-mirror CRDS instrument in order to model correctly the s ext variations with radius Reid et al 2014;Cotterell et al 2015a;Mason et al 2015Mason et al , 2014.…”