Chains of nanoparticles for flat-band emission and lasing

Abstract

Controlling light-matter interactions is central to photonic technologies ranging from lasers to optical information processing. Suitably designed photonic structures give rise to flat (dispersionless) bands, where the density of states diverges, and group velocity goes to zero, allowing light localization. These properties make flat bands attractive for lasing; however, designing photonic structures supporting flat bands suitable for lasing is challenging. Here, we introduce nanoparticle chain lattices. These chain geometries provide long-range coupled systems that support, at predictable wavelengths, bands that are totally flat and extend over the full angular range. We demonstrate lasing in the transverse-magnetic (TM) mode of single chains of nanoparticles and explain the transition from flat band lasing to the single-mode normal-incidence (Gamma-point) lasing as the number of chains is increased. Moreover, we show partially coherent emission from square and triangular two-dimensional chain lattices. The excited modes depend on the pump power and polarization. Our results establish chain lattices as a versatile platform for exploring flat band lasing and suggest new routes toward narrowband, linearly polarized, and bright light sources with tailored coherence.

Figures (4)

• Figure 1: Experimental measurement of the extinction. (a) Scheme of a number ($L$) of parallel chains. The case $L=3$ is depicted in the schematic, while the inset shows a scanning electron microscope image of a single chain ($L=1$). Measured extinction [panels (b)--(f)] and band structure calculated using the empty lattice approximation [panels (g)--(k)] of $L = \text{1, 2, 5, 10, and 40}$ lines of square lattice with a periodicity of 580 nm. Particles were gold nanocylinders with a diameter of 120 nm and height of 50 nm in an index-symmetric background with $n = 1.52$, and no polarization filters were used in the measurement. The first Brillouin zone (for an $L \rightarrow \infty$ system) extends between $k_y \approx \pm 5.4\per µm$.
• Figure 2: Lasing emission from single chain systems. (a) Scheme of the single chain. (b) Momentum-space-resolved spectrum of single-chain system lasing emission at a pump fluence of 0.05 mJ/cm$^{2}$. (c) Emission intensity and linewidth dependencies on pump fluence for a single-chain system at a pump fluence of 0.07 mJ/cm$^{2}$. (d) and (e) real and momentum-space emission patterns of single-chain lasing. (f) Momentum-space-resolved spectrum of an $L=40$ chain system lasing emission at a pump fluence of 0.09 mJ/cm$^{2}$. (g) Lasing emission dependence on $k_y$ for systems of different numbers of chains. The pump fluences were as follows: 0.05 mJ/cm$^{2}$ for $L=1$, 0.07 mJ/cm$^{2}$ for $L=5$, 0.1 mJ/cm$^{2}$ for $L=10$, and 0.09 mJ/cm$^{2}$ for $L=40$ (h) Background-free Michelson interference pattern of single-chain lasing emission at a pump fluence of 0.1 mJ/cm$^{2}$.
• Figure 3: Emission from square 2D chain arrays. (a) SEM image and scheme of the square 2D chain array. (b) Emission intensity dependence on pump fluence. (c) Momentum-space-resolved spectrum of square 2D array emission at a pump fluence of 0.13 mJ/cm$^{2}$. (d) and (e) Real and momentum-space pattern of square 2D chain array emission at a pump fluence of 0.14 mJ/cm$^{2}$. (f) Background-free interference pattern of the square 2D chain array emission, showing fringes along the x-direction but fading features in y. The pump fluence was 0.25 mJ/cm$^{2}$. The arrays consisted of cylindrical gold nanoparticles with a diameter of 110 nm and a height of 50 nm. The period of the array was 580 nm, and the distance between the chains was 40 particles.
• Figure 4: Emission from triangular 2D chain arrays. (a) SEM image and scheme of the triangular 2D chain array. (b) Momentum-resolved spectrum of the triangular array emission at a pump fluence of 0.18 $\mathrm{mJ/cm^2}$. (c) Emission intensity dependence on the pump fluence, the red dots denote pump fluence values used for momentum and real-space pattern collection. (d)--(g) Momentum [(d) and (f)] and real [(e) and (g)] space emission patterns of triangular 2D chain arrays for the fluence values of 0.18 $\mathrm{mJ/cm^2}$ [(d) and (e)] and 1 $\mathrm{mJ/cm^2}$ [(f) and (g)]. (h) Background-free interference pattern of triangular 2D chain array emission under the fluence value of 1 $\mathrm{mJ/cm^2}$. The arrays consisted of cylindrical gold nanoparticles with a diameter of 120 nm and a height of 50 nm. The period of the chains was 580 nm, and the distance between the chains was 33 particles.