Tunable plasmonic bound states in the continuum in the visible range

Bound states in the continuum (BICs) have been observed in a variety of systems. A plasmonic BIC offers interesting opportunities, since a surface plasmon is known to confine light to the nanometer scale. However, the observation and manipulation of plasmonic BICs is a challenge due to the intrinsic loss of metals. Here, we study plasmonic BICs in the visible range in a one-dimensional all-metallic grating. First, by tuning the resonances of localized and propagating surface plasmon modes to resonance, we successfully observe symmetry-protected plasmonic BICs in an all-metallic system. Next, by continuously tuning the localized mode, we demonstrate topological band inversion characterized by a Zak phase transition. In addition, we engineer off-Γ-point BICs and confirm their formation mechanism. Finally, we experimentally determine that the quality ($Q$) factor of a 10-groove structure can exceed 60, about one order of magnitude greater than conventional metallic structures. The simulations reveal that, with more grooves, the $Q$ factor can be over 200. The plasmonic BICs in the visible range demonstrated in this paper pave the way to promising applications in lasers, sensors, light-matter interactions, nonlinear optics, and quantum optics.

Figure 1

Illustration of Type I bound states in the continuum (BICs) in an all-plasmonic system. (a) and (b) Without strong coupling, only one mode is bright at the Γ point, hindering the observation of the dark mode (BIC) in the visible range. (c) and (d) With the addition of the localized surface plasmon resonant (LSPR), the single bright mode is split into two modes, making the dark BIC uncovered.

Figure 2

Experimental optical path diagram. (a) Schematic of the optical setup of angle-resolved spectroscopy. A white light beam (halogen lamp) was projected on the sample by a microscope objective (Olympus,100 ×, $\mathrm{NA}=0.9$). Parallel light reflected from the sample was focused at the back focal plane (Fourier plane) of the objective and a lens assembly (Lens1 and Lens2) was used to project the Fourier plane onto the entrance slit of a spectrometer. An image of the sample was project on the camera after Lens1 and BS2. BS: beam splitter, Lens: tube lens. (b) Schematic of the optical setup of diffractive angle-resolved spectroscopy. Here, we only show the incident part; the other part is the same as (a). White light is incident on the sample with a very large incident angle using a dark-field objective. The diffractive light is collected by the objective and sent to the angle-resolved spectrometer.

Figure 3

Angle-resolved reflection spectra of a one-dimensional (1D) silver grating with a fixed pitch (670 nm) with different groove depths of 335, 411, 446, 501, and 550 nm. (a)–(e) The two localized surface plasmon resonant (LSPR) modes are tuned from blue to red by increasing the groove depth. The black-dashed ellipses mark the positions of the Type I bound state in the continuum (BIC). The yellow ellipse denotes the 1D Dirac point, which will be discussed in Fig. 5. The blue rectangle represents the Type II BICs, which will be discussed in Fig. 6. The top of each spectrum shows the dark-field and bright-field images of the corresponding grating. The size of each grating is ∼10 μm. The fitting curves based on CMT can be found in Fig. S2, which indicates that $g_{\mathrm{bg}}=0.02\mathrm{eV}$ and $g_{\mathrm{str}}=0.15\mathrm{eV}$.

Figure 4

Full wave simulation of the angle-resolved reflection spectra corresponding to Fig. 3. (a)–(e) The groove depth change from (a) 180 nm to (e) 270 nm. The pitch is the same as in the experiment 670 nm. The black-dashed ellipses correspond to the Type I bound states in the continuum (BICs).

Figure 5

Zak phase transition of the hybrid band. (a)–(d) Zak phase evolution corresponding to Figs. 3–3. The band inversion occurs in (b), where the Zak phase cannot be defined. The center of the unit cell is chosen to be its inversion center located at the middle of the groove to calculate the Zak phase. Therefore, the Type I BIC is always in the band with ${\theta }_n^{\mathrm{Zak}}=\pi$. (e) The field distribution at $k_{//}=0$ (top panel) and $k_{//}=\pm \pi /p$ (lower panel).

Figure 6

Observation and characterization of Type II bound states in the continuum (BICs). (a) Angle-resolved reflection spectrum of another sample with different pitch and groove depths, showing several clear BIC features. Black-dashed ellipse: Type I BIC. Blue rectangle: Type II BIC. (b) Angle-resolved diffraction spectrum of the same sample, showing a consistent result with (a). White rectangle: Type II BIC. (c) Coefficient analysis of the band indicated by the blue arrow in (a), including both the magnitude and sign. The normalized fraction can be obtained by the square of the magnitude of the coefficient. (d) Same as (c) but a sum of the lattice surface plasmon polariton (LSPP) and localized surface plasmon resonant (LSPR) components. (e) and (f) Measured $Q$ factors of Type I BIC (e, 62) and Type II BIC (f, 51.4) in (a) by tuning $k_{//}$.

Figure 7

The typical $Q$ factors of Type I bound states in the continuum (BICs) extracted from experimental and simulation results. (a) Experimental results of a 10-groove sample (62). (b) Simulation results (105.8) corresponding to (a). (c) Simulation results (216) with optimized groove shape. The simulation results correspond to infinite groove numbers.