Extreme light confinement mediated by the transverse Kerker effect

Abstract

Dielectric nanoparticles can be engineered to scatter light predominantly in the transverse direction, a phenomenon known as the transverse Kerker effect. Although complete cancelation of forward scattering from a single object is forbidden by the optical theorem, we show that a single photonic mode can nonetheless realize an ideal transverse Kerker effect. The mode remains dark under normal incidence but evolves into an accidental bound state in the continuum when the nanoparticles are arranged in metasurfaces. This enables a new route to polarization-independent quasi-bound states in the continuum whose quality factors are tunable without symmetry breaking. We experimentally demonstrate our concept in the visible, achieving the first polarization-independent bound state in the continuum without the need for Brillouin-zone folding. Furthermore, we show that our modes maintain large quality factors over a substantially broader region of momentum space than conventional bound states in the continuum. Our results establish a platform for realizing ultranarrow resonances free of the constraints for designs with standard bound states in the continuum.

Figures (4)

• Figure 1: (a) Formation mechanism of the transverse Kerker effectTKE in terms of multipole moments. (b) A square lattice of dielectric cylinders. Parameters: refractive index $n=3.85$, period [id = SG]$p$$P$ = 235.8 nm. (c) Transmittance map as a function of height [id = SG]$h$$H$ and diameter [id = SG]$d$$D$ of the cylinder at normal incidence of a plane wave, calculated at wavelength $\lambda$ = 645 nm. (d)Magnitude of electric and magnetic fields for the transverse-Kerker bound states in the continuum 1 and 2 (see panel c), displayed on planes through the center of the unit cell.The distribution of absolute value of electric and magnetic fields for two different modes supporting TK BIC.
• Figure 2: Transverse Kerker effect (TKE) in a single dielectric cylinder and in a square array of dielectric cylinders. The nanoparticle height is [id = SG]$h = 230$$H = 230$ nm, the array period is [id = SG]$p = 235.8$$P = 235.8$ nm, and the refractive index of the cylinder is $n = 3.85$. The surrounding material is air. (a) Electric field magnitude of eigenmodes in a single cylinder at the TKE ([id = SG]AI) and at the supercavity ([id = SG]BII) conditions. (b) Left: Dispersion of two eigenmodes (complex-valued resonance wavelength $\lambda_\nu$) with low and high quality factors $Q_\nu=|\text{Re}\lambda_\nu/2\text{Im}\lambda_\nu|$ (displayed by color). Right: $\mathrm{ED}/\mathrm{MQ}$ ratio of the multipole coefficients for these modes. (c) Normalized scattering cross section (SCS) of a single cylinder with [id = SG]$d = 250$$D = 250$ nm (supercavity mode) and [id = SG]$d = 218$$D = 218$ nm (TKE). (d),(e) Same as in panel a but for an array of cylinders for the TKE condition ([id = SG]CIII) and a quasi-BIC ([id = SG]DIV). (f) Spectra of the array: Transmittance for normally incident plane waves for [id = SG]$d = 213$$D = 213$ nm ([id = SG]CIII) and [id = SG]$d = 200$$D = 200$ nm ([id = SG]DIV).
• Figure 3: Observation of the transverse Kerker bound state in the continuum (TK BIC) at optical wavelengths and its polarization robustness. (a) SEM image of the fabricated silicon nanodisk metasurface on a sapphire substrate (disk diameter [id = SG]$d=275~\mathrm{nm}$$D=275~\mathrm{nm}$, height [id = SG]$h=300~\mathrm{nm}$$H=300~\mathrm{nm}$). (b) Simulated and (c) measured normal incidence transmittance spectra versus wavelength and lattice period. (d) Unit-cell geometries[id=SG], adapted from Fig. 2, supporting two different BIC mechanisms: TK BIC (left)—a square array of dielectric cylinders with refractive index $n=3.85$—and a quasi-BIC (right) realized by introducing a symmetry-breaking defect, i.e., a hole aligned along the $y$ axis with radius $r=10~\mathrm{nm}$. Cylinder diameter [id = SG]$d=200~\mathrm{nm}$$D=200~\mathrm{nm}$, height [id = SG]$h=230~\mathrm{nm}$$H=230~\mathrm{nm}$, period [id = SG]$p=235.8~\mathrm{nm}$$P=235.8~\mathrm{nm}$, refractive index $n= 3.85$. (e) Simulated normal incidence transmission spectra plotted versus wavelength detuning from the resonance for $x$- and $y$-polarized illumination: the TK BIC resonance position is identical for both polarizations, whereas the SP BIC resonance is present only for $y$ polarization. (f) Experimental transmission map as a function of linear-polarization angle $\alpha$ and wavelength for a metasurface of silicon cylinders on sapphire at fixed period [id = SG]$p=400~\mathrm{nm}$$P=400~\mathrm{nm}$, confirming that the quasi TK BIC resonance is preserved under rotation of the incident polarization.
• Figure 4: [id=SG]TK BICs in momentum SpaceMomentum-space robustness of TK BICs near the $\Gamma$ point. (a) Numerical analysis of the stability of Transverse-Kerker bound states in the continuum (TK BICs) around the $\Gamma$ point, benchmarked against a conventional symmetry-protected (SP) BIC supported by a vertical electric-dipole-like mode. Dispersion (resonance wavelength versus in-plane Bloch wavevector) in the vicinity of $\Gamma$ along the $\Gamma$X and $\Gamma$M directions. [id=SG]Q factorQ-factor maps around $\Gamma$, showing that the two degenerate TK BIC modes (TK BIC [ id=SG]1U1 and TK BIC [ id=SG]1B2) exhibit a substantially slower radiative-Q degradation with increasing $|{\bf k}_\text{b}|$ than the SP BIC. Simulated structure: square array of dielectric cylinders with refractive index $n=3.85$, height [id=SG]$h=230~\mathrm{nm}$$H=230~\mathrm{nm}$, period [id=SG]$p=235.8~\mathrm{nm}$$P=235.8~\mathrm{nm}$, and diameter [id=SG]$d=213~\mathrm{nm}$$D=213~\mathrm{nm}$. (b) Experimental angle-resolved reflection of a silicon-nanodisk metasurface on a sapphire substrate, presented as a reflection map [id=SG]scanned along $X-\Gamma-X$ (varying the in-plane wavevector $k_x$ through $\Gamma$ at $k_y=0$)versus Bloch wavevector $k_\text{b}$ scanned along $\Gamma$X and $-X$$\Gamma$. Two dispersive branches are resolved, corresponding to the two modes that are degenerate at $\Gamma$ and constitute the quasi-BIC at normal incidence. Schematic of the angle-resolved reflection setup: a halogen lamp provides collimated white light, linearly polarized by a linear polarizer and focused onto the sample through a $60\times$ (NA$=0.95$) objective via a $50:50$ beamsplitter. The reflected beam is collected by the same objective; a Fourier lens images the backfocal plane, and a 4f relay projects it onto the spectrometer entrance slit. The dispersed signal is recorded on a CCD (M, mirror).