Three-Dimensional Simulation of Particle-Induced Mode Splitting in Large Toroidal Microresonators

Abstract

Whispering gallery mode resonators such as silica microtoroids can be used as sensitive biochemical sensors. One sensing modality is mode-splitting, where the binding of individual targets to the resonator breaks the degeneracy between clockwise and counter-clockwise resonant modes. Compared to other sensing modalities, mode-splitting is attractive because the signal shift is theoretically insensitive to the polar coordinate where the target binds. However, this theory relies on several assumptions, and previous experimental and numerical results have shown some discrepancies with analytical theory. More accurate numerical modeling techniques could help to elucidate the underlying physics, but efficient 3D electromagnetic finite-element method simulations of large microtoroid (diameter ~90 µm) and their resonance features have previously been intractable. In addition, applications of mode-splitting often involve bacteria or viruses, which are too large to be accurately described by the existing analytical dipole approximation theory. A numerical simulation approach could accurately explain mode splitting induced by these larger particles. Here, we simulate mode-splitting in a large microtoroid using a beam envelope method with periodic boundary conditions in a wedge-shaped domain. We show that particle sizing is accurate to within 11% for radii a<λ/7, where the dipole approximation is valid. Polarizability calculations need only be based on the background media and need not consider the microtoroid material. This modeling approach can be applied to other sizes and shapes of microresonators in the future.

Label-free, real-time monitoring of membrane binding events at zeptomolar concentrations using frequency-locked optical microresonators

“…They confine photons in a path circumscribing the cavity; the photons can circulate many times thus allowing small changes in the optical path, such as those caused by biomolecular binding. [18][19][20][21][22][23] Here we measure lipid membrane formation and membrane binding events by utilizing an ultra-sensitive, label-free biosensing system known as FLOWER (frequency locked optical whispering evanescent resonator). 18,19,[24][25][26][27] FLOWER is able to detect a single macromolecule; the high quality (Q)-factor and the evanescent field of WGM microtoroid resonators are exploited so that any local refractive index changes caused by analyte binding events to the resonator's surface can be measured in realtime as a shift in the cavity's resonance frequency (Fig.…”

Part-per-Trillion Trace Selective Gas Detection Using Frequency Locked Whispering-Gallery Mode Microtoroids

“…In particular, sensors based on pristine graphene and carbon nanotubes have demonstrated ultra-low limits of detection (sub-ppt) in response to nitric oxide, but lack selectivity to other gases and exhibit significant lab-to-lab variations in sensitivity 6,7 . Whispering gallery mode (WGM) microresonators stand apart from the rest of these biochemical sensors due to their long (on the order of nanoseconds) photon confinement times, [8][9][10][11][12][13][14] which causes increased interaction of light with matter and enables these devices to be ultra-sensitive sensors. 15,16 Here, we use a system previously developed in our lab known as FLOWER (frequency locked optical whispering evanescent resonator), which combines WGM technology with noise reduction techniques for sensitive detection of diisopropyl methylphosphonate (DIMP), ammonia (NH3), and formaldehyde (CH2O) 8,9,11 .…”

“…Several gas sensing technologies exist, − all with different advantages and disadvantages in terms of their sensitivity, selectivity, stability, ease of preparation, expense, and portability. In particular, sensors based on pristine graphene and carbon nanotubes have demonstrated ultra-low limits of detection (sub-ppt) in response to nitric oxide, but lack selectivity to other gases and exhibit significant lab-to-lab variations in sensitivity. , Whispering-gallery mode (WGM) microresonators stand apart from the rest of these biochemical sensors due to their long (on the order of nanoseconds) photon confinement times, − which causes increased interaction of light with matter and enables these devices to be ultra-sensitive sensors. , WGM optical resonators have previously been used to sense a wide variety of target analytes, including single molecules, , proteins, exosomes, ,, ribosomes, viruses, nanoparticles, , and nucleotide mismatches, with mechanisms that include mode shift, , mode broadening, and mode splitting . One concern with these sensors, however, is their selectivity.…”

“…In these experiments, we choose tracking the resonance position, rather than measuring mode splitting ,, or mode broadening . In theory, the mode splitting sensing mechanism requires strong scattering generated from the binding of discrete particles to split the mode.…”

“…15,16 WGM optical resonators have previously been used to sense a wide variety of target analytes, including single molecules, 8,17 proteins, 8 exosomes, 9,11,18 ribosomes, 8 viruses, 19 nanoparticles, 20,21 and nucleotide mismatches, 22 with mechanisms that include mode shift, 8,9 mode broadening, 19 and mode splitting. 13 One concern with these sensors, however, is their selectivity. Here, we apply a WGM system known as frequency locked optical whispering evanescent resonator (FLOWER), previously developed in our lab for aqueous biological sensing, 8,9,23−27 to the novel problem of gaseous chemical sensing.…”