image: Figure 1 | Schematic diagram of Lorentz-term-driven SHG induced by the magnetic dipole (MD) resonance in a dimer-on-film nanocavity: the plasmon-enhanced, spatially overlapping electromagnetic field at the fundamental frequency amplifies the Lorentz contribution at the harmonic frequency. a Schematic of the nanocavity, consisting of two 100 nm-diameter Au nanoparticles coated with 2 nm silica shells, placed on a smooth Au film. The silica shells form three stable nanoscale gaps, creating a ternary LC resonant circuit that excites the MD resonance. b Dark-field scattering spectrum measured with a custom-built angularly tunable and polarization-controlled single-particle dark-field scattering microscope, showing the MD resonance peak at ~950 nm with a linewidth of ~50 nm (Q ≈ 19, significantly larger than the Q of the electric resonance). c Surface charge distributions, d electric field enhancement maps, and e, magnetic field enhancement maps of magnetic dipole. f Coulomb, g Lorentz, and h Convective contribution to the second-order charge distributions, clearly showing the dominant contribution of the Lorentz term in the hotspot region.
Credit: Wang, Y., Razdolski, I. et al.
Plasmonic resonances have opened new opportunities to manipulate nanoscale light–matter interactions, allowing to overcome the inherent limitations of natural materials. This field was pioneered by Sir John Pendry of Imperial College London, who proposed that split-ring resonators (SRRs) can generate magnetic fields at optical frequencies and predicted that placing a weakly nonlinear material in an SRR gap could significantly enhance the material’s nonlinear response (IEEE Trans. Microw. Theory Tech. 1999, 47.11, 2075). His prediction has since been experimentally validated in various metal-dielectric hybrid systems.
However, realizing magnetic-driven nonlinear effects in pure metallic nanostructures has long been challenging. Nineteen years ago, a study published in Science reported Lorentz-force-driven second-harmonic generation (SHG) based on SRRs (Science 2006, 313, 502). The same research team’s subsequent study, however, demonstrated that the observed SHG was mainly due to the convective contribution associated with electric-field gradients (Opt. Lett. 2008, 33, 1975), which means that inhomogeneous free-electron flow produces strong nonlinear currents. The D. R. Smith group at Duke University further showed that the SHG emission from an SRR structure originates from the coupling between surface charges induced by polarization gradients and the electric field of an incident light (Phys. Rev. B 2012, 85, 201403). These studies underscore the complexity of magnetic-driven nonlinear plasmonic processes. In conventional plasmonic resonators, electric and magnetic field enhancement regions are spatially separated (for example, in SRRs), rendering the Lorentz contribution negligible in second-order nonlinear processes. Moreover, the coupling of higher-order multipolar resonances further complicates the underlying physics of magnetic-driven nonlinear effects, highlighting the requirement for innovative designs to achieve breakthroughs.
Most subsequent studies remained phenomenological and did not fully explore the mechanisms of magnetic-driven SHG. Notably, Reuven Gordon and colleagues designed T-shaped apertures in a gold thin film to realize spatial overlapping between electric and magnetic fields within the T-shape bridge, thereby increasing the Lorentz contribution to SHG (Nano Lett. 2018, 18, 8030). Yet, they did not provide detailed experimental and theoretical analyses on the SHG behaviors (such as radiation patterns) arising from convective, Coulomb, and Lorentz contributions under different excitation conditions, which left the proposed mechanism unclear and also prevented systematic optimization of each contribution. Thus, the core mechanism of magnetic-driven SHG remained elusive and demanded novel design strategies.
In a recent paper published in Light: Science & Applications, a team of scientists, led by Professor Dangyuan Lei from Department of Materials Science and Engineering, City University of Hong Kong, building on their earlier study of magnetic-resonant plasmonic nanocavities (Laser Photon. Rev. 2020, 14.9, 2000068), employed a bottom-up nanoparticle assembly approach to fabricate subwavelength dimer-on-film nanocavities. By judiciously selecting the incident direction and polarization of light, they were able to effectively excite the cavity’s magnetic dipole (MD) resonance and precisely control the spatial distribution of electromagnetic fields in the cavity. This enabled a pronounced Lorentz-term-dominated SHG, providing a new platform and strategy for exploring magnetic-resonant nonlinear optics.
The team summarize that they successfully realized Lorentz-force-driven SHG in an ultra-compact subwavelength plasmonic nanocavity. Experimental results confirm that the MD resonance achieves an SHG conversion efficiency of 6 × 10-8 W-1. By optimizing the spatial overlap of electromagnetic fields and introducing symmetry-broken dimer designs, they quantitatively reveal the Lorentz-term-dominated second-order nonlinear mechanism, breaking the conventional design paradigms that focus predominantly on electric-field enhancements. This approach is highly versatile, applicable to various plasmonic nanocavity configurations, and can be extended by tuning operating wavelengths or coupling to other optical modes to realize richer optical control. Notably, MD-enhanced two-photon photoluminescence from single high-refractive-index dielectric resonators have shown potential in probing unknown optical magnetic fields of arbitrary electromagnetic structures (Nano Lett. 2021, 21, 2453). The manipulation of nonlinear optical responses via magnetic modes shows remarkable richness and offers a new framework and paradigm for future studies of magnetic field related nonlinear optical processes.
Journal
Light Science & Applications
Article Title
Enhanced magnetic second-harmonic generation in an ultra-compact plasmonic nanocavity