Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect

An effective semianalytical method for analyzing the Cartesian multipole contributions in light transmission and reflection spectra of flat metasurfaces composed of identical nanoparticles is developed and demonstrated. The method combines numerical calculation of metasurface reflection and transmission coefficients with their multipole decompositions. The developed method is applied for the multipole analysis of reflection and transmission spectra of metasurfaces composed of silicon nanocubes or nanocones. In the case of nanocubes, we numerically demonstrate a “lattice invisibility effect,” when light goes through the metasurface almost without amplitude and phase perturbations with the simultaneous excitation of nanoparticles' multipole moments. The effect is realized due to destructive interference between the fields generated by the basic multipole moments of nanoparticles in the backward and forward directions. For metasurfaces composed of conical nanoparticles, we show that their transmission coefficient does not depend on illumination direction. In contrast, the reflection and absorption can be different for the illumination from different metasurface sides, which is associated with the excitation of different multipoles. We believe our results could be useful for analysis and understanding of the electromagnetic properties of nanoparticle arrays and pave the way for the design of novel metasurfaces for various optical applications.

Figure 1

Artistic representation of the considered silicon metasurface composed of nanocubes (infinite nanostructure illuminated with the linearly polarized plane wave).

Figure 2

Spectra of the transmission $T$, reflection $R$, and absorption $A$ coefficients of the metasurfaces composed of silicon nanocubes of height $H=250$ nm with period (a) $D=400$ nm and (c) $D=300$ nm. (b), (d) Absolute values of the multipole contributions in the electric field reflection and transmission coefficients $r$ and $t$: panel (b) corresponds to $D=400$ nm [same as (a)] and panel (d) corresponds to $D=300$ nm [same as (b)]. (e) Absolute values of the multipole contributions in the scattered electric-field amplitude [see Eq. (8)] calculated for a single silicon nanocube with size $H=250\mathrm{nm}$ in air.

Figure 3

Phases of the multipole terms in the amplitude reflection and transmission coefficients of the metasurface composed of nanocubes for (a) $D=400\mathrm{nm}$ and (b) $D=300\mathrm{nm}$. Definition of the phase is explained in the main text.

Figure 4

Phases of the electric field in the system of periodic nanocubes: the blue and red lines are for the phase difference between the incident wave and the transmitted wave for $D=400$ and 300 nm correspondingly; the green line is for the phase of the electric field in the plane of the point-multipoles positions.

Figure 5

Fragment of the spatial electric field distribution in the $zy$-plane at $\lambda =785\mathrm{nm}$ for (a) $D=400$, (left) only incident field, (right) total electric field; (b) $D=300\mathrm{nm}$, (left) only incident field, (right) total electric field. The black contours indicate the position of a nanocube in the metasurfaces.

Figure 6

The artistic representation of the considered silicon metasurface based on nanocones (infinite nanostructure illuminated by a linearly $E_x$-polarized plane wave).

Figure 7

Spectra of the transmission $T$, reflection $R$, and absorption $A$ coefficients of the metasurface composed of the silicon nanocones with $H=300\mathrm{nm}$, $D_c=300\mathrm{nm}$ with period $D=450\mathrm{nm}$ for (a) illumination from top of the nanocones, (c) illumination from the base side. (b), (d) Absolute values of the multipole contributions in the amplitude coefficients $r$ and $t$: panel (b) corresponds to the illumination from top of the nanocones [same as (a)], and panel (d) corresponds to illumination from base edge of the nanocones [same as (b)].

Figure 8

Electric field distribution inside and on the surface of one conical nanoparticle from the considered silicon metasurface ($H=300\mathrm{nm}$, $D=450\mathrm{nm}$) at the wavelength $\lambda =619\mathrm{nm}$ for the illumination (a), (b) from top of the cones (c), (d) from the base.

Figure 9

Phases of the multipole terms in the electric field reflection and transmission coefficients $r$ and $t$ of the metasurface composed of nanocones ($H=300\mathrm{nm}$, $D_c=300\mathrm{nm}$) with the period $D=450\mathrm{nm}$. (a) Illumination from the apex side of the nanocones, (b) illumination from the base edge of the nanocones. The definition of the phase is explained in the main text.