Mie-tronics under microscopy

Since a millennium ago, it is well known that grinding metals yields various colors, presented as the beautiful colored windows in churches or the famous Lycurgus Cup. However, the underlying physics was not elucidated until Gustav Mie developed the corresponding electromagnetic wave scattering theory in the early 20th century. The Mie theory explains how structuring metals to sizes comparable to light wavelengths, not much smaller nor much larger, creates new optical resonances, enhancing absorption/scattering of specific wavelengths, and producing vivid colors. In the 21st century, the nanoscale Mie resonance phenomenon has been extended to high-refractive-index semiconductors like silicon, which generate strong scattering in the visible spectrum.

However, the canonical studies on morphology-sensitive Mie resonances hinge on the normalized frequency, i.e. particle size over wavelength. Non-paraxial incidence symmetry by tight focusing excitation which is a typical condition of nanophotonics, dealing light-matter interactions at the subwavelength scale, is often overlooked.

Now in an international collaboration among Osaka University in Japan, Jinan University in China, National Tsing Hua University and National Taiwan University in Taiwan, our latest research discovered a new phenomenon called “displacement resonance” (Nat. Comm. 14, 7213, (2023)). Through an unique integration of confocal laser scanning microscope, mostly employed in biological studies, to examine metallic and semiconductor nanoparticles (Phys. Rev. Lett. 112, 017402 (2014); Nat. Comm. 11, 3027 (2020); Nat. Comm. 11, 4101 (2020)), the scattering point spread functions unveil distinctive spatial patterns. The team has found that when a focused light spot diameter and a silicon nanostructure are of similar sizes, not much smaller nor much larger, changing their relative positions triggers formerly unseen resonances.

The idea is illustrated in figure A. When the “relative spot size” w/FWHM is too large or too tiny, conventional plane wave excited Mie resonance or normal confocal scanning image mode is expected. Only when w/FWHM ~ 1, i.e. particle size comparable to the focal spot, typically under a tightly focused geometry when working with nanomaterials, the alignment of the beam center versus the particle, i.e. displacement d/FWHM, plays an important role in deterministic excitation of multipolar resonances.

Specifically, displacement resonance leads to a counterintuitive situation that the light-matter interactions, including scattering and absorption-induced nonlinear optical effects, are not maximal when laser focus is aligned with the particle, but become maximized when the focus spot is about 100 nanometers off-center, as manifested by figure B. This is fundamentally different from the dark-field observation, which is the standard tool for inspecting Mie resonances, shown in figure C.

The unconventional displacement resonance associated to the excitation of higher-order multipolar modes, not accessible by plane wave irradiation, may extend the century-old light scattering theory, and suggests new dimensions to tailor Mie resonances for multifarious applications. We exemplified one potential application on all-optical switching of a single nanoparticle, by leveraging displacement resonance enhanced nonlinearity. Figure D presents that with a higher excitation intensity to drive the nanoparticles into the nonlinear regime, the scattering image forms a doughnut-like pattern. Interestingly, the strongest nonlinearity is not necessarily aligned to the beam center. The complex nonlinear scattering pattern indicates that scattering nonlinearity flips sign by slightly offsetting the light spot, revealing a brand-new tuning mechanism that was never considered before.

To sum up, in physics, resonance is a fundamental concept across mechanics and electromagnetics. When considering resonance, such as a pendulum, typically the resonance condition is determined by the spatial size versus driving frequency, but not the driving source symmetry. Here we use Mie resonance as an example, to introduce a new concept of how non-paraxial excitation induces new resonance modes that are not allowed with paraxial excitation. Conceptually, our discovery opens up a new spatial dimension, revealing that when the focused light “spots diameter” and “displacement” scale are similar to the nanoparticle diameter, new resonances emerges when the focus is NOT aligned with nanostructures. Besides advancing fundamental physical concepts, we expect displacement resonance will find applications in interdisciplinary fields, including nonlinear nanophotonics, optical computing, and super-resolution microscopy.

Displacement resonance- a new degree of freedom of Mie resonance (A) The concept of displacement resonance. (B) When w/FWHM ~ 1, light-matter interaction is strongest when laser focus is NOT at the particle center. (C) Conventional Mie resonance with the same particle. (D) Higher laser intensity produces nonlinear interactions.