Numerical Study of Metal Nano-Orifices for Optical Sizing of Ultrafine Particles in Aerosols

Abstract

Optical particle sizers are widely used aerosol instruments which detect pulses of light scattered from individual airborne particles to measure their sizes. Existing optical particle sizers based on conventional optics generally cannot measure particles with diameters smaller than 100 nm, known as ultrafine particles, because optical signals are too weak due to dominant Rayleigh scattering in this particle size range. To address this challenge, we propose to harvest the nanoscale light confinement effects from nanostructures to boost the optical signals for sizing ultrafine particles. In this work, we numerically studied a nano-optical particle sizer based on a metal nano-orifice, essentially a subwavelength nano-aperture in a metal thin film with a flow-through nanofluidic channel for aerosols. When an ultrafine particle travels through the metal nano-orifice, the light transmission through the orifice gives a pulsatile optical signal, and its pulse height is correlated with the particle size. We modeled the optical responses of the metal nano-orifice using finite difference time domain simulation and the aerodynamic behaviors of ultrafine particles using finite element analysis and particle tracing technique. The numerical results suggest that ultrafine particles can be effectively sized through the metal nano-orifice. The pulse heights are found to be proportional to the third power of particle diameter and remain consistent when particle trajectories inside the orifice vary widely. This work is the first theoretical investigation of plasmonic sensors for aerosol particles. The ability of the metal nano-orifice to size ultrafine particles lays the foundation for further breakthroughs in optical-based aerosol sensing techniques.

Appendix. List of Symbols

$d_a$:

Diameter of the nano-orifice

$d_p$:

Diameter of the nanoparticle

$E_0$:

Amplitude of the electric field of the incident plane wave

$|\vec{E}(\vec{r})|$:

Amplitude of the simulated electric field at location $\vec{r}$

$\Delta T$:

Transmission increment caused by the ultrafine particle

$T_0$:

Transmission of an empty nano-orifice

$\Delta \widetilde{T}$:

Normalized transmission increment

$P_0$:

Optical power of light transmitted through empty nano-orifice

$\Delta P$:

Height of the optical pulse induced by the ultrafine particle

$P_N$:

Noise level in the optical signal

$\epsilon _{eff}$:

Effective dielectric constant

$\epsilon (\vec{r})$:

Material dielectric constant at location $\vec{r}$

$n_0$:

Refractive index of air

$\epsilon _p$:

Dielectric constant of nanoparticle material

$\epsilon _0$:

Dielectric constant of air

$n_p$:

Refractive index of nanoparticle material

$V_p$:

Volume of dielectric nanoparticle

$V_m$:

Effective mode volume

$\vec{r}_p$:

Position of dielectric nanoparticle

$\vec{r}_c$:

Position of the antinode of the resonance mode

$\rho _{air}$:

Density of air

$\mu _{air}$:

Dynamic viscosity of air

U:

Flow velocity of the fluid

L:

Characteristic width of the fluidic channel cross section

$\vec{u}$:

Fluid velocity field

$\vec{v}$:

Particle velocity

$m_p$:

Particle mass

$\tau _p$:

Particle velocity response time

$\rho _{p}$:

Density of the particle material

T:

Absolute temperature of the aerosol

$\zeta$:

Random number in normal distribution

$k_B$:

Boltzmann constant