Rethinking photonic nanojets: a new definition and design paradigm

TL;DR

This work addresses the lack of a rigorous PNJ definition by introducing an energy-density localization measure based on optimal transport, yielding a relative concentration coefficient and a boundary-compensated PNJ metric. Using this framework, the authors develop a phase-only illumination strategy and a KAN-based optimization to steer PNJs without any opto-mechanical intervention. They demonstrate 2D PNJ steering via comprehensive FEM simulations and transport-based optimization, showing PNJ placement at targeted coordinates with convergent results. The approach provides a robust, dimension-agnostic method for designing and dynamically controlling PNJs, with potential implications for super-resolution microscopy and label-free photonics.

Abstract

We propose a rigorous, physically interpretable, and quantifiable definition of the photonic nanojet (PNJ). This framework resolves longstanding ambiguities in measuring PNJ dimensions and leverages an optimal mass transport-based metric to quantify PNJ quality. Building on this metric, we develop a PNJ steering methodology that requires no opto-mechanical intervention, relying solely on phase-only illumination modulation.

Figures (8)

• Figure 1: Artistic rendering of a photonic nanojet created by a dielectric micro-element.
• Figure 2: The commonly used PNJ measures of waist width and decay length are intuitive and useful, but the underlying choice of the field intensity level curve is not rigorously justified. Left: a PNJ with FHWM measures. Right: the same PNJ with $e^{-1}$ measures.
• Figure 3: A highly localized and a delocalized field produced by two different illuminations (computed structured illumination in the left column and a uniform plane wave illumination in the right column) of the same micro-element. The $L^{\infty}$ normalization is performed over the shown domain.
• Figure 4: Diagram of the setup. The shaded area is a micro-element with refractive index $n_{\rm e} > n_{\rm air}=1$. The incident field propagates in the negative $y$-direction. The three curvy lines illustrate the phase modulation $\varphi(x)$ of the incident wave. Near the bottom of the micro-element, the PNJ is depicted as the concentrated field.
• Figure 5: An optimized, 20-component phase modulation $\varphi(x)$, and the resulting $|\bm{E}^{\rm tot}|$. The PNJ position is 3.67 $\mu m$ along the negative $y$-axis from the micro-element boundary and at $x=-2.67\,\mu$m. The phase is embodied with a resolution given by $\lambda / (2 N_A)$, with $N_A$ the numerical aperture.