Higher order mode ring resonator for trapping dielectric particulate matter in air
Résumé
Optical microcavities can be used to detect and trap nanoparticles on a chip. To overcome the challenges posed by Brownian motion of these particles in a fluid, the particles must be confined spatially. Here, we present simulation results that compare the optical trapping forces for the fundamental and first order modes by an optical ring resonator. The higher order mode design has the advantage of relaxed fabrication tolerances.
Poly aromatic hydrocarbons (specifically PM2.5) constitute one of the most significant toxic air pollutants. Due to their well-known mutagenic and carcinogenic properties, they have been extensively studied in health and environmental contexts. Monitoring such nanoparticles in in a confined space such as the interior of a car is of the utmost importance. The current state of commercialized sensors, based on the gravimetric method and light scattering, relies on several assumptions that result in unreliable and inaccurate results.
Ashkin and coworkers demonstrated optical trapping of biological particles and sub-micron Rayleigh particles in the 1970s [1]. Numerous researchers have since demonstrated manipulation of micro-particles on integrated near field optical trapping on lab-on-a-chip devices [2]. For nanoparticles, as size decreases, the trapping potential diminishes drastically, which increases the probability of particles escaping the trap due to Brownian motion. To overcome the Brownian motion, it is necessary to maintain a strong optical gradient force (> 10 KBT) [1]. Different structures such as trench waveguides [3], photonic crystal cavities with bow-tie nanoantennae has been proposed by combining photonics and plasmonic structures to increase the optical gradient potential. However, these structures pose significant fabrication challenges on an industrial platform. The optical field in ring resonators is significantly amplified due to the photons extended lifetime. For nanoparticle trapping, resonant devices such as ring resonator cavity are advantageous due to the field enhancement and spatial confinement. We purpose a higher order mode ring resonator an alternative solution to more common single mode devices as they have similar levels of evanescent field in the cladding but with relaxed fabrication tolerance. To evaluate the optical forces in our study, we used finite differences and finite element modeling to estimate the evanescent field profiles combined with the discrete dipole approximation to calculate trapping forces [4].
The time average gradient forces exerting on the Rayleigh particle is given by:
{\ \approx\pi\bullet\varepsilon_m\frac{\varepsilon_m\ -\varepsilon_p}{\varepsilon_m+{2\varepsilon}_p}\nabla|E^2|
Where \varepsilon_m and \varepsilon_p are the dilectric permittivites of the medium and particle respectively. The above equation indicates an increase in trapping as the evanescent decays more rapidly in the medium. Particle size will also increase optical forces as particle size increases. The gradient force will be stronger in the direction of maximum intensity. Compared to fundamental modes, higher-order modes have two peaks of intensity that are highly likely to trap more particles than fundamental modes. Fig 2.a shows the evanescent field profile of the higher order mode, which has the same level as the fundamental mode in the cladding, and Fig. 2.b shows the vector plot of gradient optical force in fundamental and higher order modes. The resonant cavity enhancement factor scales with Q/V (quality factor divided by mode volume) provides a quantitative comparison between different structures. It is important, further, to include perturbation theory using the modified dipole approximation model that will be presented in order to compare optical forces in the resonant structures.
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