Submicrometer perovskite plasmonic lasers at room temperature.

Plasmonic lasers attracted interest for their ability to generate coherent light in mode volume smaller than the diffraction limit of photonic lasers. While nanoscale devices in one or two dimensions were demonstrated, it has been difficult to achieve plasmonic lasing with submicrometer cavities in all three dimensions. Here, we demonstrate submicrometer-sized, plasmonic lasers using cesium-lead-bromide perovskite (CsPbBr3) crystals, as small as 0.58 μm by 0.56 μm by 0.32 μm (cuboid) and 0.79 μm by 0.66 μm by 0.18 μm (plate), on polymer-coated gold substrates at room temperature. Our experimental and simulation data obtained from more than 100 plasmonic and photonic devices showed that enhanced optical gain by the Purcell effect, large spontaneous emission factor, and high group index are key elements to efficient plasmonic lasing. The results shed light on the three-dimensional miniaturization of plasmonic lasers.

INTRODUCTION

Nanoscale lasers have received growing interest for scientific and practical applications. Various types of photonic nanolasers have been demonstrated. For example, planar photonic crystal cavities coupled with semiconductor quantum dots () or transition metal dichalcogenides () achieved lasing in the near infrared at cryogenic temperatures. Semiconductor cuboidal and disk lasers with submicrometer sizes were reported in the green () and red wavelengths (, ). While the minimum size of photonic lasers is limited to half the optical wavelength in the laser materials, incorporating metals at the perimeter is a promising route to reduce device size beyond what is possible with only semiconductors and dielectrics (). Metals can support surface plasmon polariton (SPP) modes and can also serve as reflectors for photonic modes enhancing their confinement in the cavity (). For example, metallodielectric lasers supporting high-Q photonic modes with subwavelength mode volume sizes were realized with silver-encapsulated semiconductor disks at 1550 nm ().

Among plasmonic lasers, one class known as spaser uses localized SPPs. Since its inception (), narrowband emission from dye-embedded colloidal ensembles (, ) has been observed, although lasing of single spaser nanoparticles remains to be seen (, ). Recent progress was made with an array of metallic nanopillars supporting plasmonic lattice modes. Coupling with emerging lanthanide-based upconverting emitters (), the lattice nanocavity exhibits continuous-wave laser emission at room temperature. The other class of plasmonic lasers uses propagating SPPs along the interface of a metal and gain material (–). Plasmonic lasing was demonstrated with CdS (, ) or GaN () semiconductor nanowires on top of silver substrates at cryogenic and vacuum conditions. Recently, room temperature plasmonic lasing was demonstrated with GaN nanowires () on aluminum at 375 nm and CdSe microplates () with gold at 700 nm. However, almost all the SPP-based plasmonic lasers demonstrated to date have required at least one dimension along cavity resonance to be >1 μm to restrict cavity radiative loss.

Here, we demonstrate full submicrometer plasmonic lasers operated at room temperature using lead halide perovskite (LHP) and gold. LHPs with the form of APbX3 (A = Cs+, CH3NH3+, X = Cl−, Br−, I−) are promising semiconductor materials for optoelectronic applications (, –). Among different LHPs, cesium lead bromide perovskite (CsPbBr3) is an attractive laser material owing to its long carrier diffusion length (~9 μm) () and high optical gain (~4000 cm−1) (), as well as solution processability. Using CsPbBr3 submicrometer cubes atop polymer-coated gold substrates, we achieved stable single- and multimode lasing in the air at 2.3 eV (=540 nm) with a narrow laser linewidth of 1 meV (~0.2 nm) using nanosecond optical pumping. By measuring key laser parameters including the Purcell factor, spontaneous emission factor (β), and quantum yield (η), we systematically studied the lasing action of both plasmonic lasers (test) and their photonic counterparts (control). The comparison enabled us to identify and explain a condition where efficient plasmonic lasing becomes possible.

RESULTS

Plasmonic lasing from submicrometer perovskite crystals

We synthesized CsPbBr3 micrometer- and submicrometer-sized crystals using a sonochemistry method (fig. S1) (). The crystals typically have orthorhombic shapes with aspect ratios of 0.5 to 0.9 and a corner curvature of 0.08 μm. The height-to-length ratio can be further reduced down to 0.1 in microplate shapes by adding nonionic surfactants during sonochemical synthesis (). The prepared CsPbBr3 crystals were subsequently transferred onto different substrates: gold (Au) coated with polynorepinephrine (pNE), pNE-coated silicon (Si), and bare silica (SiO2) (Fig. 1A). CsPbBr3 crystals on the gold substrate form the plasmonic laser group (test), while those on dielectric SiO2 or Si substrates are photonic counterparts (control).

Fig. 1

Plasmonic versus photonic lasers.

(A) Schematic of plasmonic (pNE-coated Au substrate) and photonic (pNE-coated Si or bare SiO2 substrates) devices. (B and C) Single-shot photoluminescence (PL) spectra of the two smallest plasmonic lasers [device i, L = 0.57 μm (B); device ii, L = 0.61 μm (C)] and their line cuts at various pump fluences. Two lasing modes in device i are denoted by M1 and M2. (D) Single-shot PL spectra from a photonic device xi (L = 1.3 μm) at pump levels below (p1) and above (p2) thresholds. Scale bars, 500 nm. a.u., arbitrary units.

We first investigated devices with cuboidal crystals fabricated with height-to-length ratios of 0.5 to 0.9. The relatively large aspect ratio is generally more favorable to photonic modes. The quantities of devices in the test and control groups are 30 (Au), 25 (Si), and 45 (SiO2), respectively. We pumped each device with nanosecond optical pulses at 480 nm (duration, 4 ns; repetition rate, 20 Hz) and recorded output emission spectra at various pump levels (fig. S2A) below and above the lasing threshold by using custom-built hyperspectral optical microscopy. We marked each device’s location on the Si substrates by pump laser irradiation at high fluence (fig. S2B). The devices were then imaged with scanning electron microscopy (SEM; resolution, 1.4 nm) for analyzing their shape and size. We calculated the effective device side length, , where S is the device area determined from top-view SEM images. The device height was determined from SEM images taken at sample tilt angles of 45° and 0° from the surface normal.

Many plasmonic devices with full submicrometer sizes demonstrated single-mode or multimode lasing. The smallest plasmonic laser (Fig. 1B, inset) had L = 0.57 μm (device i; 0.56 μm by 0.58 μm by 0.32 μm for x, y, and z directions). This device exhibited two lasing modes, M1 and M2 (Fig. 1B), above the threshold fluence. M1 reached lasing first, followed by M2. The second smallest device (device ii; 0.75 μm by 0.49 μm by 0.3 μm; L = 0.61 μm) showed single-mode lasing (Fig. 1C, inset). Below the lasing threshold, the plasmonic devices exhibited multiple fluorescence peaks in their photoluminescence (PL) spectra. Figure 2 shows the emission spectra of various other plasmonic devices with submicrometer to micrometer sizes. The 10 smallest plasmonic lasers are denoted by i to x.

Fig. 2

Shape and spectra of plasmonic laser devices.

(A) Submicrometer devices (devices iii to xi). (B) Microscale devices (L > 1 μm). For each device, (left) a representative SEM image, (middle) fluorescence spectra at pump energy E of 0.1 (black), 0.4 (dark brown), and 0.8 (brown) times the threshold Eth, respectively, and (right) lasing spectrum above threshold at E= 1.2 (dark yellow) and 2.5 (yellow) times Eth, respectively, are displayed. Scale bars, 1 μm.

By contrast, none of the photonic devices on the dielectric substrates showed lasing even at the maximum power fluence level before optical damage occurs to the gain materials. All lasing photonic devices were measured to have L > 1.2 μm, at least 10 times larger in volume than the smallest plasmonic device. Figure 1D shows a representative photonic laser with L = 1.3 μm. The shapes and output spectra of other photonic lasers are shown in fig. S3. The photonic devices below the threshold showed typical broad fluorescence spectra, with the sharp peaks observed in the plasmonic devices.

Modal analysis and finite element method simulation

The multiple emission peaks of the two submicrometer plasmonic devices, i and ii, were analyzed using Lorentzian fitting (fig. S4). A sharp reduction of the full width at half maximum (FWHM) of the PL peaks occurs above lasing threshold (Fig. 3, A and B). The smallest FWHM at the threshold is about 2.4 meV (~0.7 nm) and 2.2 meV (~0.5 nm) for M1 and M2 in device i, respectively, and 1 meV (~0.2 nm) in device ii. Both the linewidth narrowing and polarization state in the x-y plane changes (Fig. 3C) are indications of lasing. We reconstructed stimulated emission profiles of M1 and M2 by subtracting emission profiles taken just below their lasing thresholds from emission profiles taken above the thresholds (fig. S2C). From the images, M1 mode appears to be a Fabry-Perot (FP) mode, and the M2 mode is a whispering gallery mode (WGM) (Fig. 3D).

Fig. 3

Emission spectra and energy profiles.

(A and B) Measured spectral linewidth of device i (A) and device ii (B) at different pump fluences. Linewidth reduction occurs at lasing threshold (dashed lines). (C) Polar plots showing the polarization states in the x-y plane of emission below the threshold and above the threshold. (D) Measured wide-field images of the stimulated emission of device i. (E) Field (|E|) and energy (|E|2) profiles of the calculated cavity modes, revealing the FP and whispering gallery nature of the two hybrid plasmonic modes in device i. (F) Group refractive indices (solid lines) and absorption loss coefficients (dashed lines) of the M1 (cyan) and M2 (magenta) modes in device i, in comparison to an infinite-slab SPP mode (gray).

We numerically calculated the two eigenmodes (COMSOL Multiphysics) in device i. The spatial mode profiles agreed with the measurement (Fig. 3E). Both modes are hybrid resonances because their electric fields are concentrated inside the gap region but have considerable energy in the CsPbBr3 crystal (Fig. 3E). The fraction of modal energy inside the 5-nm-thick gap region is about 5% for M1 and 30% for M2 (Fig. 3E). Conceptually, these resonances can be understood as the surface plasmons of a planar multilayer metal-dielectric closed system restricted to specific quantized wave vectors determined by the device sizes (). The quality factors (Qm) of the modes were 61 (M1) and 41 (M2). We also simulated the plasmon dispersions of such closed systems, where the CsPbBr3 layer is infinitely extended in the x and y directions (fig. S5). From the dispersion, the group indices n of the two modes are 2.95 (M1) and 4.1 (M2), and their propagation losses α are 1800 cm−1 (M1) and 5800 cm−1 (M2) (Fig. 3F). In the simulation of a photonic device with the same size as device i but with a silicon, instead of a gold, substrate, we found two photonic modes with Q ≈ 90 and 38, respectively, and n ≈ 2.5 (fig. S5E). For this submicrometer (L = 0.57 μm) device size, the plasmonic cavity modes (M1 and M2) have similar quality factors as these photonic cavity modes. This is primarily because the higher n of the plasmonic modes results in stronger boundary reflection compensating the metallic absorptive loss. The similar quality factors indicate that the plasmonic modes are more efficient to reach the lasing threshold compared to the photonic modes at the given gain material.

Laser characteristics and analytical models

The pump fluence at the lasing threshold, Eth, was measured from each device in the three experimental groups. Figure 4A plots the result as a function of the effective device side length L. Regardless of L, the lasing thresholds were similar across all three groups. The photonic devices on both Si and SiO2 substrates have similar thresholds. This similarity is partly due to oxide layers formed on the Si substrates but mainly because the distribution of the lasing photonic modes is shifted away from the high-index substrates. In the plasmonic test group, we compared Eth at three different spacer thicknesses of 1, 5, and 10 nm, respectively (Fig. 4B). The thickness of the pNE spacer of 5 nm led to the smallest lasers, which is consistent with previous observations ().

Fig. 4

Lasing thresholds.

(A) Threshold pump fluence Eth measured from individual lasers: 30 plasmonic devices on gold (yellow), 25 photonic devices on Si (dark gray), and 45 photonic devices on SiO2 substrates (light gray). Ten submicrometer plasmonic lasers are labeled as i to x. One photonic laser xi is marked (Fig. 1D). (B) Measured threshold pump fluence of plasmonic lasers fabricated with a different pNE layer thickness of 1, 5, or 10 nm. The 5-nm thickness produces lasing with the smallest device size and lowest mean threshold energy.

We studied laser dynamics with a three-level rate equation model (). In this model, the threshold pump absorption rate Pth per volume V at frequency ω0 is given by PthV = ω0/Qβη + FtotρtrV(1 − βη)/τη (note S1), where β is the spontaneous emission factor of the lasing mode m, η is the quantum yield of the gain medium, Ftot is the total enhancement factor of emission, ρtr is the number of carriers needed to reach transparency in the gain medium, and τ is the radiative lifetime. For CsPbBr3 microcrystals, the first term relating to cavity loss is dominant to the second term, which is related to transparency or population inversion in the gain medium (note S1). Thus, the equation can be simplified as PthV ≈ ω0/Qβη. To reach the lasing threshold, three parameters in the denominator are important: quality factor Q of the lasing mode, the spontaneous emission factor β of the lasing mode, and the quantum yield η. Our finite element method (FEM) results above predicted similar Q for the plasmonic and photonic devices. Below, we show that compared to the photonic devices, the plasmonic devices actually offer higher β and η, essential for lasing at submicrometer V.

We used both laser emission and transient spectroscopy data to measure these laser parameters. First, we extracted β of the lasing mode from the PL emission spectra of the plasmonic devices at a low pump fluence at 0.2 mJ/cm2 (Fig. 5A). Using an analytical ray tracing model (, ), we calculated the number of cavity modes, N, within the gain bandwidth (Materials and Methods) to be between 3 and 6, in agreement with experimental data (fig. S6). For the plasmonic devices, we obtained β by decomposing their PL spectra into N Lorentzian peaks and a broad background fluorescence curve for uncoupled emission (fig. S4, A and D). The β values in the plasmonic devices increase from 0.05 to 0.35 as the device size decrease from 1.3 to 0.6 μm. β in the photonic devices cannot be inferred from their PL spectra because of the lack of multiple resonant peaks (fig. S4F).

Fig. 5

Laser characteristics.

(A) Extracted β-factor of the lasing modes for the plasmonic devices (yellow squares). (B) Measured fluorescence enhancement (10 to 40 times) and the associated quantum yields η of the plasmonic (yellow) and photonic (gray) devices. (C) Time-resolved PL decay (circles) of three CsPbBr3 plasmonic devices and double-exponential fits (dashed lines). The 0.4-μm-sized device exhibits enhanced fluorescence intensity and accelerated decay rates. (D) Measured (squares) light-in-light-out curves of three plasmonic devices iv (β = 0.28, η = 0.37), vii (β = 0.21, η = 0.46), and ix (β = 0.06, η = 0.38) and theoretical fits (dashed lines; see note S1B).

The PL intensity in the plasmonic devices was substantially higher than the photonic devices at the same effective pump fluence (~0.2 mJ/cm2) below the threshold (Fig. 5B). We calibrated the brightness with respect to the fluorescence from a batch of relatively large CsPbBr3 microcrystals (>5 μm) synthesized with the same method and placed on 5-nm-thick pNE-coated Si or SiO2 substrates. Using an objective lens with a numerical aperture (NA) of 0.5, we measured up to 40 times brighter fluorescence from submicrometer plasmonic devices compared to the reference crystals. To understand this large difference, we performed a full-wave simulation of a CsPbBr3 microcrystal with L = 0.57 μm (equivalent to device i). The ratio of total fluorescence collected by the 0.5 NA objective lens, or the collection efficiency, was 0.44, 0.31, and 0.2 for the case of Au, Si, and SiO2 substrates, respectively (fig. S5F). The relatively small difference supports that the 40-fold brightness is mostly due to an enhanced quantum yield in plasmonic devices. Resonant cavity modes, however, have more pronounced asymmetric emission patterns toward the dielectric substrates and several-fold lower collection efficiency in the vertical direction (fig. S5, G and H) (). Using an integrating sphere, we measured the intrinsic quantum yield (ηint) of the reference crystals to be ~0.015 (see Materials and Methods). The quantum yield η of the gain crystals in the plasmonic devices was enhanced by 10 to 40 times, ranging from 0.15 to 0.6. The Purcell factors (, ) calculated from the measured β and η agreed with the values obtained from a numerical simulation of the rate equation model (fig. S7).

We verified the Purcell-induced emission enhancement using time-resolved spectroscopy. Figure 5C shows representative fluorescence decays of CsPbBr3 crystals with three different sizes, placed on pNE-coated gold substrates (Fig. 5C). Table 1 summarizes various fluorescence decay parameters determined from CsPbBr3 crystals on gold or silicon substrates. The Purcell factors measured from the fluorescence decay data were greater than 20 for CsPbBr3 crystals (L < 3 μm) on gold (fig. S8). This enhancement factor is consistent with those obtained from the PL measurement in Fig. 5B.

Table 1

Measured fluorescence decay parameters.

TCSPC, time-correlated single photon counting.

	Plasmonic CsPbBr3 on pNE-gold			Photonic CsPbBr3 on pNE-Si
	L = 0.4 μm	L = 0.9 μm	L = 3.8 μm	L = 0.7 μm	L = 2.4 μm	L = 4.3 μm
τ1 from TCSPC	0.7 ns	1.2 ns	2.6 ns	4.1 ns	2.5 ns	3.2 ns
τ2 from TCSPC	–	–	18 ns	–	5.8 ns	5.6 ns
A1 from TCSPC	1	1	0.76	1	0.62	0.68
A2 from TCSPC	–	–	0.23	–	0.38	0.32
τtot measured	0.7 ns	1.2 ns	3.3 ns	4.1 ns	3.8 ns	3.7 ns
Ftot measured	50	20	1	0.5	5	1
η measured	0.4	0.1	0.015	0.007	0.075	0.015
τs computed	88 ns	240 ns	220 ns	270 ns	250 ns	250 ns
τnr computed	0.71 ns	1.2 ns	3.3 ns	4.1 ns	3.8 ns	3.7 ns

The light-in-light-out (L-L) curve is another crucial indicator of lasing. Specifically, the presence of a nonlinear kink at the threshold in an L-L curve is determined by a parameter x = βη (Fig. 5D and note S1) (). The extracted x parameters are comparable with the product of the spontaneous emission factor β and quantum yield η values that were obtained independently in Fig. 5 (A and B).

Plasmonic and photonic devices made of CsPbBr3 plates

Having analyzed the laser devices using cuboidal crystals, we investigated plate-shape CsPbBr3 crystals fabricated with height-to-side ratios of 0.1 to 0.4. Figure 6A shows measured pump threshold fluences for all three device groups (Au for plasmonic, Si and SiO2 for photonic). The smallest plasmonic device that lased had L = 0.6 μm. None of the plasmonic devices smaller than L = 0.5 μm reached lasing. By comparison, the smallest lasing photonic device had L = 1.7 μm. Figure 6B displays the output spectra from a plasmonic device (xii) with a size of 0.79 μm by 0.66 μm by 0.18 μm at various pump fluences below and above the threshold of 0.7 mJ/cm2. The numerical simulation found a few plasmonic hybrid modes in the gain bandwidth. The highest Q-factor mode had Q ≈ 26 and 15% of energy inside the gap (fig. S9). Figure 6C shows the broadband fluorescence spectra from a photonic device with L = 1.2 μm on a Si substrate, which failed to reach lasing at pump fluences close to a material damage threshold of ~2 mJ/cm2.

Fig. 6

Plasmonic lasing of submicrometer CsPbBr3 microplates.

(A) Threshold pump fluence Eth measured from individual lasers: 25 plasmonic devices on gold (yellow), 24 photonic devices on Si (dark gray), and 30 photonic devices on SiO2 substrates (light gray). Nonlasing devices are also shown. (B) Single-shot PL spectra of a plasmonic laser (device xii, L = 0.72 μm, thickness of 0.18 μm) at various pump fluences. (C) Single-shot PL spectra from a nonlasing photonic device xiii (L = 1.2 μm) at low (p1 = 0.2 mJ/cm2) and high (p2 = 2 mJ/cm2) pump levels. Scale bars, 500 nm.

To investigate the spatial profiles of cavity modes, we used two-photon excitation microscopy and mapped PL emission as excitation light (920 nm, 150 fs, 80-MHz repetition) was raster-scanned in transverse cross sections at different depth positions of devices. Because the excitation photon energy (1.35 eV) is below the bandgap energy (2.38 eV) of the gain medium, charge carriers are generated at the focal plane via two-photon absorption with an axial resolution of ~2 μm given by the NA (0.9) of the excitation beam (). Since the absorption is more or less uniform in the gain medium, any difference in the output PL intensity is primarily due to the difference in the Purcell effect at the focus. Figure 7 (A to D) shows two-photon images of various devices with sizes of 2 to 5 μm. All the plasmonic devices built on 5-nm-thick pNE-coated gold substrates show the maximum intensity when the focal planes were at crystal-gold interfaces (Fig. 7E). By comparison, the maximum intensity appeared 0.5 to 1.5 μm away from crystal-gold interfaces when the thickness of the pNE coating was 20 nm instead of 5 nm (Fig. 7F). The 20-nm pNE spacer is thick enough to suppress plasmonic effects (), making these devices effectively photonic devices. Considering the same geometry except for the additional dielectric gap thickness by 15 nm, the difference in the maximum intensity plane indicates the difference in the axial mode profile (, ). For pure photonic devices built on SiO2 and Si substrates, the maximum intensity planes were also located at 0.5 to 1.5 μm above the substrate, approximately in the middle of the gain crystals (Fig. 7G). This result supports the enhanced Purcell effect in the plasmonic devices in the vicinity of the gold substrates with 5-nm dielectric layers.

Fig. 7

Two-photon excited PL intensity profiles of plasmonic and photonic devices.

(A to D) Two-photon excitation PL images at different focal plane position (Z) from the substrates for various CsPbBr3 microplates on different substrates: (A) 5-nm pNE-coated gold, (B) 20-nm pNE-coated gold, (C) SiO2, and (D) 5-nm pNE-coated Si. Scale bars, 5 μm. (E to H) Plane-integrated PL intensity measured from the images in (A) to (D). The color of the data points (circles) in (E) to (H) denotes the different devices in (A) to (D).

Polarization state and stability of laser emission

Photonic lasers with the highest Q-factors in thin microcube cavities typically have transverse-electric (TE) modes with the electric fields predominantly parallel to their substrates, but plasmonic hybrid modes are transverse-magnetic (TM) mode–like with the electric field predominantly orthogonal to the gain-metal interface. To confirm this distinct feature, we measured far-field emission images of laser devices through a linear polarizer (Fig. 8A). The sample substrates were tilted by 85° so that emission from both the side and top surfaces of the cavities is captured. For plasmonic lasing, the output emission is expected to be largely polarized along the out-of-plane (~z axis), whereas for photonic lasing, the output is supposed to be polarized along the in-plane (x axis) (Fig. 8B). Figure 8 (C and D) shows the stimulated emission images (below-threshold images subtracted from images above threshold; see fig. S2C) of four plasmonic devices on 5-nm-thick pNE-coated gold substrates and four photonic devices on Si substrates. For the plasmonic devices, out-of-plane polarization components were four to five times greater than in-plane polarizations (Fig. 8E). The opposite trend was observed for the photonic devices (Fig. 8E). Three of four photonic devices had in-plane polarization about fourfold greater than out-of-plane polarization. One device (purple circle) exhibits nearly equal intensity in both polarizations, probably because of the FP resonance in the y axis (Fig. 8B). This result evidences that the lasing modes of plasmonic devices are TM-like plasmonic hybrid modes.

Fig. 8

Polarization state and stability of laser emission.

(A) Schematic of the measurement setup. (B) Output polarization states of different cavity modes. The reference frame applies to both top and bottom panels (table). (C and D) Reconstructed stimulated emission profiles of in-plane (x) and out-of-plane (z) polarizations for various CsPbBr3 microcubes on different substrates. Scale bars, 2 μm. Images below dashed lines result from reflection from the substrates. (E) Average stimulated emission intensity of the devices (marked by colored circles) displayed in (C) and (D). *P < 0.5 and **P < 0.05 according to paired t test. (F) Stability of the lasing wavelength and (G) output intensity for three different types of devices over 10,000 pump pulses at 20-Hz repetition with pump fluence at twice the laser threshold (~1 mJ/cm2). The plotted traces are mean values of 10 samples for each type.

Both plasmonic and photonic lasers were stable over 10,000 pump pulses (20-Hz pulse rate) (Fig. 8, F and G). Pulse-to-pulse wavelength fluctuations were measured to be 0.12 nm for plasmonic devices, better than 0.28 nm for photonic devices on silicon substrates and 0.40 nm for glass substrates. The reason for these differences is not fully understood but may be due to reduced charge accumulation (). We expect that the heating of CsPbBr3 microcrystals during laser oscillation is nearly the same regardless of substrate materials. The thermal conductivity of CsPbBr3 is about 0.4 mm2/s () and that of bulk gold is 127 mm2/s. During 4 ns, the heat diffusion distance is only 40 nm in CsPbBr3 and 710 nm in gold. Therefore, the temperature of CsPbBr3 microcrystals during laser buildup and oscillation is nearly the same for both plasmonic and photonic devices (fig. S10).

DISCUSSION

Our systematic study of the lasing actions in both plasmonic and photonic devices allowed us to identify a regime where efficient plasmonic lasing becomes possible. Figure 9 illustrates the regime from the perspective of gain, in which the threshold carrier density ρth is plotted for the three experimental groups. The theoretically calculated curves (solid and dashed lines) are based on ρthV ≈ ω0τ/Qβtot (note S1). The experimental ρth data (squares) were drawn from measured Eth values (fig. S11 and Materials and Methods). The benefit of high group indices and Purcell factors in the plasmonic devices outweighs the metallic absorptive loss, resulting in a net decrease of the lasing threshold. The regime for efficient plasmonic lasing is indicated by a shaded yellow region in Fig. 9.

Fig. 9

Efficient plasmonic lasing.

As the laser device size decreases, a regime (yellow region) that makes plasmonic lasing more efficient than photonic lasing emerges. The solid curves indicate the calculated threshold carrier density for our plasmonic (brown solid line) and photonic (gray solid line) lasers, respectively. Our experimental data are plotted (squares; calculated from Fig. 4A for microcubes and Fig. 6A for microplates). The metallic loss (magenta upward arrow) increases the lasing threshold (pink dashed curve), which is compensated by the Purcell effect (cyan downward arrow). The higher group index of plasmonic modes reduces the radiative loss for a given device size (purple leftward arrow). Inset: Device schematic illustrating the migration of charge carriers in the strongly pumped EHP state above the Mott transition density (ρMott; horizontal dashed green line) of optically pumped CsPbBr3.

Experimentally realizing this regime for submicrometer plasmonic lasing, however, should not be taken for granted because the gain medium must be able to produce the threshold carrier density. Two properties of the CsPbBr3 seemed to have played a critical role, which are a low carrier loss at high density and a long carrier diffusion length. From the material’s perspective, the maximal attainable ρ (proportional to optical gain) is limited by various loss mechanisms, such as Auger recombination and heat-induced material damage. In CsPbBr3 near the lasing threshold, carrier density ρ exceeds the Mott transition density ρMott (dashed green line in Fig. 9) and reaches 1018 to 1019 cm−3, forming electron-hole plasma (EHP) (note S2) (). At ρ = 1019 cm−3, a high gain coefficient of 4000 cm−1 has previously been reported (). Gain coefficients under strong pumping conditions can be much greater than absorption coefficients at the same wavelength without pumping (, , ). This is because the gain and absorption spectra are altered at the high concentration of charge carriers in the EHP state (note S3) via various nonlinear processes, such as the EHP plasmon-coupled stimulated emission (), bandgap renormalization in the EHP state (, ), suppressed cooling bottleneck under the resonant pumping (), and slow large polaron formation (, ). The gain coefficients of CsPbBr3 are comparable to those of the state-of-the-art III-V semiconductors, such as InGaN quantum wells in the green wavelength range (), and II-VI semiconductors, such as CdSe in the far-red wavelength range (). The diffusion length of charge carriers in CsPbBr3 exceeds 9 μm (, ). This large diffusivity allows the charge carriers created over the entire device volume to migrate in the gain medium and increase the chance of interaction with plasmonic lasing modes (), undergoing Purcell-enhanced radiative recombination (Fig. 9, inset).

The CsPbBr3-on-gold lasers that we demonstrated are operated in the efficient plasmonic lasing regime. Compared to previously reported visible plasmonic lasers (table S1), the largest dimension of 580 nm of device i represents about 2-fold reduction over II-VI lasers (, ) and 20-fold reduction over organic-inorganic hybrid perovskites (). The pump fluence and pulse energy are comparable to those of state-of-the-art plasmonic devices (fig. S12) (, , ). In a recent paper, CsPbBr3 submicrometer cubes formed on sapphire substrates using a spin-coating method showed an eightfold higher quantum yield than those formed on glass substrates and were used to achieve lasing in Mie-resonant photonic devices as small as 310 nm in size, twofold smaller than our devices (). Our work shows that, for given gain materials, plasmonic modes could lead to further miniaturization. Although the specific fabrication method does not render a simple path to form plasmonic devices on gold substrates, efforts to use the ongoing innovations in dielectric cavities (, ) and gain materials () in the plasmonic configuration would be worthwhile. These improvements may further miniaturize plasmonic nanolasers toward the deep subdiffraction limit.

Last, both the gain medium and dielectric gap material in our devices were fabricated entirely using solution-based chemistry in room temperature, instead of conventional epitaxial or sputtering processes in a high-temperature vacuum. This unique fabrication method holds promise for adding functional organic molecules () and tuning the laser wavelength by postsynthetic anionic exchange of the material compositions ().

MATERIALS AND METHODS

Fabrication of laser devices

For producing CsPbBr3, CsBr and PbBr2 were dispersed at an equal saturating concentration (typically 75 mM each) in N,N-dimethylformamide (DMF) in a vial. The vial was sonicated at 20 to 80 kHz in a bath-type ultrasonicator or a tip ultrasonicator in room temperature. After 2 to 3 min of ultrasonication, single-phase CsPbBr3 micrometer- and submicrometer-sized crystals in cuboidal shapes are spontaneously formed. For the synthesis of microplates, polysorbate 80 (0.1%, v/v) was added before sonication. For pNE coating, 2 mg of dl-norepinephrine hydrochloride was mixed with tris-HCl buffer (pH 8.5). A polycrystalline Au film–coated substrate (Platypus) was placed in this solution at room temperature. An incubation time of 2.5 hours produces a 5-nm-thick pNE layer on the gold. The coated film was cleaned and dried under a stream of N2 flow. Last, the prepared CsPbBr3 crystals were drop-casted on pNE-coated Au substrates. For photonic devices, pNE-coated Si substrates or uncoated SiO2 substrates were used.

Material characterization

The complex refractive index was measured from variable angle spectroscopic ellipsometry data measured over 55° to 75°C in steps of 5°C (J.A. Woollam V-VASE32). The spectral range was from 300 to 620 nm. The data fitting was initiated with the Cauchy model at the transparent region and completed by the Gaussian oscillator model. For powder x-ray diffraction, data over 2θ angles from 10° to 60° were collected using a PANalytical X'Pert PRO high-resolution x-ray diffraction system with a CuKα irradiation source. For SEM and energy-dispersive x-ray (EDX), samples were transferred onto a chipped Si wafer by drop-casting and imaged using a Zeiss Merlin high-resolution SEM equipped with an EDX detector operated at 15 kV. For TEM, samples were drop-casted onto a grid (Ted Pella), and images were acquired using a FEI Tecnai Multipurpose TEM at 120 kV. The illumination beam was expanded to avoid sample damage. Atomic force microscopy images were acquired using the NanoScope IV Scanning Probe Microscope (Veeco Metrology Group) in a tapping mode. Spectroscopic ellipsometry was demonstrated at the Harvard Center for Nanoscale Systems. All other measurements were performed at the Massachusetts Institute of Technology (MIT) Center for Material Science and Engineering.

Laser characterization

The samples are placed in a homebuilt epifluorescence microscopy setup (fig. S2A). The pump light source was an optical parametric oscillator (Opotek HE 355 LD) tuned to 480 nm with a repetition rate of 20 kHz and a pulse duration of 4 ns. The pump light in a circular polarization state was focused to a single device via a 0.5 NA, 50× air objective lens (Nikon) with an FWHM beam width of ~25 μm. The output emission from the device is collected by the objective lens, passed through a dichroic mirror and a dichroic filter, and split to an electron multiplication charge coupled device (EMCCD) camera (Luca, Andor) for wide-field imaging and to a grating-based EMCCD spectrometer (Shamrock, Andor) with a spectral resolution of ~0.1 nm. For absolute quantum yield measurement, we used a continuous-wave laser at 491 nm (Cobolt Calypso) for excitation. For time-resolved PL measurements, we used a picosecond laser (VisIR-765, PicoQuant), which was frequency-doubled to 382 nm for excitation, a single-photon avalanche photodiode (Micro Photonics Devices) with a response time of 50 ps, and a time-correlated single-photon counting board (TimeHarp 260, PicoQuant) with a resolution of 25 ps. For polarization measurement, the linear polarizer was placed on the detection path in the setup (fig. S2A), and the polarizer angle was rotated by using a motorized rotation mount. For two photon-excited PL imaging, a laser scanning intravital microscope (IVIM Technology) with femtosecond excitation laser (920 nm, 150 fs, 80-MHz repetition) was used. All optical measurements were conducted at room temperature.

FEM simulation

The eigenmodes and field profiles of the submicrometer lasers were numerically simulated with a commercial finite-element solver COMSOL Multiphysics with geometries as close to the shapes found by SEM as possible. The Purcell factors were obtained by calculating the spontaneous emission rates of vertical-oriented dipoles inside the gap region.

The number of resonance modes

The resonance condition for cavity modes is given by , where m and m are integers, N = m + m, n is the effective refractive index of the modes in the crystal, and θ is a beam angle to the surface normal within a range between θ and π/2 − θ, where θ = sin−1(1/n) is the critical angle for total internal reflection (). The circles in fig. S6 (A and C) were generated for several different aspect ratios (a/L = 1, 1.05, 1.1, 1.15, and 1.2). From the spread of these simulation data, the variability observed in the experimental data may be attributed to small differences in the aspect ratio and shape of the gain crystals in the devices. An approximation solution of the cavity resonance condition has been derived (): , where n is group refractive index, and v and δv are the center frequency and FWHM of the optical gain spectrum, respectively. This formula was used to plot the dashed curves in fig. S6, with reasonably good correspondence to the simulation and experimental results.

βm, η, and Fm

We used theoretical models to calculate , and , where Q was calculated for WGM in spherical cavities with a diameter L and V = f is mode volume. The fractional volume factor f was the fitting parameter. For plasmonic devices (assuming F = 5), we found f ≈ 0.006, corresponding to a modal height of 3 to 10 nm. For photonic devices (F = 1), f = 0.9 produced the best fit. The fitting values for β, η, and F are in reasonable agreement with the experimental data considering the simple assumptions made, such as same V and Q for all modes. To determine the internal quantum efficiency ηint (=τ/τ) of CsPbBr3, we used as-made CsPbBr3 microcrystals (dominantly with L > 4 μm) in DMF solution. The samples were excited by using a picosecond frequency doubled laser (λ = 382 nm) at low pumping (ρ = ~1016 cm−3). The total magnitude of output fluorescence was measured. This apparatus was calibrated with respect to 10 μM of fluorescein dye in 0.1 N NaOH aqueous solution (), which has a known η of 0.92. The measured intrinsic η of the CsPbBr3 samples was 0.015. Using time-correlated single-photon counting, fluorescence lifetime was measured. Total lifetime constant was extracted from the exponential fit to the fluorescence decay curves using τtot = A1τ1+Α2τ2. The radiative decay time constant τ of the sample is related to τtot and ηint by using τ = τtotηint.

Threshold carrier density

The density of absorbed pump photons, ρ, at threshold can be expressed as ρ = ζEth/(Lω), where L is the height of the gain medium, ℏω (=4 × 10−19 J) is the energy of single pump photon, and ζ is a conversion factor related to the reflection and absorption of the pump light. The conversion factor is shown to be (): ζ = (1 − R1) − [R2(1 − R1)e− + (1 − R2)](1 − R1)e−/(1 − R1R2e−2), where R1 and R2 are reflectivities and k is the absorption coefficient of CsPbBr3 for the pump wavelength (104 cm−1 at 293 K) (). For a CsPbBr3 cube with a height of 1 μm, a total of 52 and 55% of the pump light is absorbed in plasmonic and photonic devices, respectively. The total absorbed pump photons can be converted to the rate of absorption of photon pumps per volume, Pth. In our experiments, the pump light is nanosecond pulses with a pulse duration of τ. Then, the time-averaged absorption rate is given by Pth = ρ/τ. For example, for a 1-μm-high plasmonic laser device that reaches its lasing threshold at Eth = 0.46 mJ/cm2, we get ρ = 6 × 1018 cm−3 and Pth = 1.2 × 1018 cm−3 ns−1. Last, threshold carrier density can be estimated by using ρth = Pthτη/Ftot.

Theoretical curves in Fig. 9

The total Q-factor, Qtot, of a cavity consists of radiative Q-factor, Qrad, and absorptive Q-factor Qabs: 1/Qtot = 1/Qrad + 1/Qabs. The radiative Q-factor of WGM in a spherical cavity using the analytic equation was calculated using an approximate formula (). The large group index and stronger surface reflection of plasmonic modes in the device boundary makes Qrad for plasmonic lasers much higher than Qrad in photonic devices. On the contrary, high metallic absorption (with a coefficient of α) in plasmonic devices makes Qabs in photonic devices much lower than Qabs in photonic devices. In submicrometer devices, these effects approximately cancel each other: Qtot in plasmonic and photonic devices are about the same, according to experiments and FEM calculations, within a factor of 2. To calculate Qrad, we used the well-known WGM mode theory using a core group index of 3.8, a clad index of 1.65, and absorption coefficient α = 5800 cm−1 for plasmonic cuboidal lasers; a core group index of 4.0, a clad index of 1.95, and absorption coefficient α = 9000 cm−1 for plasmonic microplate lasers; a core index of 2.0, a clad index of 1, and an absorption coefficient α = 600 cm−1 for photonic cuboidal lasers; and a core index of 1.8, a clad index of 1, and an absorption coefficient α = 600 cm−1 for photonic microplate lasers. The absorption coefficient of photonic lasers was adapted from the measured absorption spectra of CsPbBr3 microcrystals presented in fig. S11B.