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Photonic nanojets as emergent free-space power flux funnels

Mirza Karamehmedović, Cristian Placinta, Tobias Abilock Mikkelsen, Jesper Glückstad

Abstract

A reduced local field model derived from full-wave electromagnetic simulations shows that photonic nanojet formation corresponds to an emergent mesoscopic funnel of propagating power flux sustained by an effective free-space transverse mode structure. This interpretation moves beyond purely geometric-optics or interference-based explanations by identifying a self-consistent redistribution of phase gradients and effective longitudinal wavenumber near the nanojet waist. The model quantitatively captures characteristic nanojet morphology, including the formation and local structure of the jet waist. It also yields a geometry-independent lower bound on the nanojet waist, linking transverse confinement to the effective axial wavenumber through an explicit trade-off. The model establishes a direct connection between full-wave Maxwell fields and a reduced free-space oscillator description, yielding new physical insight into nanojet confinement and suggesting design principles for nanojet-assisted imaging, lithography, and subwavelength field localization.

Photonic nanojets as emergent free-space power flux funnels

Abstract

A reduced local field model derived from full-wave electromagnetic simulations shows that photonic nanojet formation corresponds to an emergent mesoscopic funnel of propagating power flux sustained by an effective free-space transverse mode structure. This interpretation moves beyond purely geometric-optics or interference-based explanations by identifying a self-consistent redistribution of phase gradients and effective longitudinal wavenumber near the nanojet waist. The model quantitatively captures characteristic nanojet morphology, including the formation and local structure of the jet waist. It also yields a geometry-independent lower bound on the nanojet waist, linking transverse confinement to the effective axial wavenumber through an explicit trade-off. The model establishes a direct connection between full-wave Maxwell fields and a reduced free-space oscillator description, yielding new physical insight into nanojet confinement and suggesting design principles for nanojet-assisted imaging, lithography, and subwavelength field localization.
Paper Structure (11 sections, 36 equations, 10 figures, 1 table)

This paper contains 11 sections, 36 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. The PNJ phase as a power flux funnel
  3. 2D case
  4. 3D case
  5. PNJs as free-space oscillators
  6. 3D axisymmetric reduction and Laguerre–Gaussian transverse modes.
  7. 2D Cartesian reduction and Hermite--Gaussian transverse modes.
  8. Numerical investigation of the free-space oscillator PNJ model
  9. 2D TM$^x$ case.
  10. 3D case.
  11. Conclusion

Figures (10)

  • Figure 1: Top: Amplitude (V/m) and phase (rad) of a TM$^x$-polarized, $-z$-directed 2D PNJ field produced by a square cross-section micro-element illuminated by structured light 2022-PNJ1. Bottom: Unwrapped phase (rad) of the PNJ field showing the hourglass structure, and with the PNJ position indicated by a yellow dot; next, the relative error of our PNJ phase funnel model \ref{['eqn:phi']}. Mean relative error over the domain shown at bottom right is 1.5%.
  • Figure 2: Top: Amplitude and phase of a TE$^x$-polarized, $-z$-directed 2D PNJ field produced by a square cross-section micro-element illuminated by structured light PNJ_CriTob. Bottom: Unwrapped phase (rad) of the PNJ field (with visible hourglass shape, and with the PNJ position and propagation direction indicated by a yellow arrow) and the wrapped phase (rad) over a small tilted strip near the PNJ neck.
  • Figure 3: Top: Wrapped phase (rad) of PNJ field for the TE$^x$ case, together with an hourglass-shaped domain for phase fitting; unwrapped phase (rad) over the hourglass domain. Bottom: Phase funnel fit and related relative error. Mean relative error over the shown hourglass domain is 4.6%.
  • Figure 4: Unwrapped phase and normalized time-average power flow in the PNJ field. Left: 2D TM$^x$ case, right: 2D TE$^x$ case. There is no significant outward transverse ($y$-directed) component of the time-average power flow at the PNJ neck.
  • Figure 5: A Lorentz-Mie series computation of the amplitude (V/m) and phase (rad) of a TM$^x$-polarized, $-z$-directed 3D PNJ field produced by a spherical micro-element illuminated by a Gaussian beam.
  • ...and 5 more figures