Introduction

Surface plasmon resonance (SPR) in metallic nanostructures, which is the collective oscillation of electrons in a metal surface excited by incident light, offers a powerful tool for field enhancement, localization and confinement on the nanoscale1,2. In addition, SPR has spurred the development of various kinds of active and passive plasmonic nanodevices for diverse applications, such as the use in bio-sensors, chemical catalysis, super-resolution imaging and quantum information processing3,4. Especially, diverse metallic nanostructures such as films, nanowires and nanoparticles have been integrated with gain materials in the active devices to overcompensate the SPR damping and radiative losses5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, resulting in the achievement of several important milestones for plasmonic amplification and lasing21,22,23,24,25. For instance, the stimulated emission of surface plasmons has been first observed at the interface between a silver film and a dye solution with Kretschmann configurations21; surface plasmon amplification by the stimulated emission of radiation (SPASER) has been realised in gold nanoparticles coated with dye molecules22; and plasmonic nanolasers at a deep subwavelength scale have been demonstrated in a silver film supporting a CdS nanowire and a GaN nanorod, respectively23,24,25. These prominent achievements open the door for a new kind of nanophotonic source based on the coherent coupling of a surface plasmon and the gain materials.

Two-dimensional vertical metal nanorod arrays have tunable longitudinal and transverse plasmon resonances (abbreviated by L-SPRs and T-SPRs, respectively) via the free electrons near the metal surface oscillating along or perpendicular to the long axis of the nanorods. Strong coupling between the nearby metal nanorods induces the generation of standing waves in the plasmonic cavities and the formation of epsilon-near-zero plasmonic metamaterials26,27. Resonant transmission and reflection plasmon modes induced by T-SPRs are first observed in Au nanorod arrays with a far-field excitation28. The optical nanoemitters can be efficiently coupled to metal nanorods with a large Purcell factor29. In addition, they can generate subwavelength images of those nanoemitters at the opposite ends of the nanorods due to a focusing effect, while the radiative energy transfer exhibits a higher efficiency and improved directionality30,31,32. These behaviors demonstrate the advantages of metal nanorod arrays as a plasmonic cavity for both far- and near-field optical sources.

Semiconductor quantum dots (SQDs), with size tunability and strong quantum confinement, offer the potential for tunable and scalable single-photon sources as well as cooperative emission devices. Ensemble SQDs have intrinsic advantages as gain media owing to their efficient excitation energy transfer and high quantum yield33,34. Several forms of cooperative emission effects (including superradiance, amplified spontaneous emission (ASE) and stimulated emissions) from ensemble SQDs have been reported35,36,37,38,39,40,41,42,43,44,45. Experimental evidence for a long-range electromagnetic interaction of superradiance has been observed by measurements of lifetime of laterally arranged SQDs35. ASE and stimulated emissions from SQDs have been demonstrated with a variety of photonic structures, such as microspheres36,37,38, microrings39, cylindrical microcavities40, waveguides and close-packed thick films41,42,43,44,45. SQDs also have unique advantages for interacting with surface plasmons46,47,48,49,50,51 and single SQDs interacting with a silver nanowire lead to the first observations of single plasmons46. The plasmon excitation of CdSe SQDs demonstrates all-optical plasmonic modulation47. ASE processes of PbS SQDs doped in PMMA on gold film lead to an increased plasmon propagation length and narrowed output spectrum48. Spectral narrowing and shifting of the CdSe/ZnS SQDs coupled to Ag nanoisland films was also reported51. However, the cooperative emissions of ensemble SQDs assisted by plasmon cavities leaves a plenty of opportunity for investigation.

In this paper, we study the optical responses of plasmonic complex cavities consisting of a silver nanorod (AgNR) array electrochemically deposited in an anodic aluminum oxide (AAO) template nanopores and a silver nanostructured film (AgNF) deposited on the back side of the template (AgNR:AAO/AgNF). We investigate the power-dependent cooperative emission behaviors of approximately one monolayer of CdSe/ZnS SQDs coupled with AgNR:AAO/AgNF complex cavities and demonstrate the tunable spectral modulation and amplification in the nanosystems by adjusting L-SPR peak of AgNRs, thickness of AgNF and cavity-mode spacing. The corresponding physical mechanisms including power-dependent excitation energy transfer and cooperative radiances are discussed in detail by measurement and analysis of power-dependent photoluminescence (PL) lifetime.

Results

Nanostructures and optical responses of the AgNR:AAO/AgNF complex cavity

Our plasmon-exciton nanosystem consists of CdSe/ZnS SQDs coupled with an AgNR:AAO/AgNF complex cavity, as illustrated in Figure 1a, where AgNR array functions as an plasmonic cavity and AAO with a AgNF acts as a Fabry-Pérot cavity. The CdSe/ZnS SQDs are spin-coated onto the surface of the alumina barrier layer, which acts as a spacer between the SQDs and AgNRs. The thickness of the barrier layer is adjusted to be ~15 nm, within the optimal spacer distance for efficient coupling between SQDs and AgNRs and depressing fluorescence quenching. The thickness of the coated SQDs is approximately one monolayer (Figure S2). The arrayed AgNRs have an average diameter d ≈ 18 nm and a period a ≈ 50 nm (Figure 1b and 1c). The AgNF with thickness of 10 nm exhibits a porous nature with the voids less than 5 nm (Figure 1d and Figure S3).

Figure 1
figure 1

Nanostructure and optical responses of the AgNR:AAO/AgNF complex cavity.

(a) Illustration of nanostructure of the SQD/AgNR:AAO/AgNF. (b) Top-view of SEM images of the complex cavity. (c,d) Bottom view of SEM images of the complex cavity before and after deposition of AgNF. (e) Extinction spectra of the AAO cavity with and without spin-coated SQDs (incident angle θin = 0°). (f) Extinction spectra of the AgNR:AAO cavities with λL-SPR = 550, 590, 620, 650, 680 and 720 nm (θin ≈ 80°). (g) Extinction spectra of AgNR:AAO/AgNF cavities with dAgNF = 0.0, 2.1, 3.2, 4.5, 7.5 and 10.3 nm (θin = 0°).

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The extinction spectra of the empty AAO template with and without CdSe/ZnS SQDs recorded by a normal incident light source are presented in Figure 1e. The periodic oscillations in the extinction spectra are due to the interference of the incident light reflected at the two surfaces of the AAO template with a high refractive index and the minimal and maximal extinction correspond to the resonant transmittance and resonant reflection modes of these Fabry-Pérot cavities, respectively. After the spin-coating of CdSe/ZnS SQDs on the surface of the barrier layer of the empty AAO template, the extinction is increased ~0.005 in the violet region. The central PL wavelength (λSQD,0) of individual SQDs without interactions is ~588 nm and the full width at half maximum (FWHM) ΔνSQD,0 is ~31.5 nm (112 meV). The cavity-mode spacing Δνcav is adjusted in the range of 0.5–1.8ΔνSQD,0 for the purpose of observations of multimode and few-mode oscillations and amplifications by controlling the optical thickness of the cavities.

The L-SPR wavelengths of the AgNRs embedded in the AAO cavities are tuned by adjusting the electrochemical growth time of the nanorods. The tuning is confirmed by recording the extinction spectrum using a p-polarized light source with an incident angle of θin ≈ 80° (Figure 1f). The oblique incidence with p-polarization could excite the L-SPR in AgNRs. The central L-SPR peaks () of the AgNRs are tuned to being resonant, near-resonant and off-resonant with the emission peak λSQD,0 (~590 nm) of the CdSe/ZnS SQDs. Moreover, the interference oscillation amplitude and phase of the complex cavity are tuned by adjusting thickness of the sputtered AgNFs as shown in Figure 1g, where the oscillation amplitude is significantly increased and the interference phase shifts more than π when dAgNF > 7.5 nm.

Tunable spectral modulations of the ensemble SQDs coupled with the complex cavity

We first investigate the spectral modulation of the SQDs/cavity nano-systems by increasing the thickness of AgNF of the cavity and the excitation power. Figure 2a displays normalized PL spectra of the SQDs coupled to six AgNR:AAO/AgNF complex cavities with various AgNF thickness dAgNF = 0.0, 2.1, 4.5, 7.5, 10.3 and 13.5 nm. In which, the PL spectra are taken in reflective geometry and the excitation power is fixed at ~0.5 mW. As dAgNF increases to 13.5 nm, the phase of the modulated PL spectra by cavity modes is shifted and the oscillation amplitude is significantly increased as well as the extinction spectra. The reflectivity of the back surface of the cavity increases from ~0.03 to ~0.36 and the phase shift measured by extinction spectrum reaches ~3π/2 (Figure S4a and S4b). The phase shift of AgNF induces variation of PL resonance wavelength (Figure 2a), while the enhanced reflectivity leads to an increase of PL modulation factor γ = (IPL, max − IPL, min)/IPL, max from 0.26 to 0.87 (Figure 2c). The reflectivity of the back surface of the cavity could be further enhanced by increasing the thickness of AgNF.

Figure 2
figure 2

Tunable spectral modulations of the ensemble SQDs coupled with complex cavities.

(a) Normalized modulating PL spectra of the sample SQD/AgNR:AAO/AgNF with different thickness of AgNFs (P = 0.5 mW). (b) Normalized modulating PL spectra of the sample SQD/AgNR:AAO with different excitation power P. (c,d) Spectral modulating factor γ as a function of dAgNF and P. γ increases with dAgNF as well as P.

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Interestingly, the spectral modulation of the SQDs coupled to the AgNR:AAO cavity (without AgNF) is significantly enhanced by increasing the excitation power (Figure 2b). The grey dashed lines in Figure 2b label the positions of five cavity modes and the peak positions are obtained from the multi-peak fitting of experimental spectra (Figure S9b). As the excitation power increases from 0.01 to 10 mW, the modulating factor γ increases from 0.22 to 0.37 (Figure 2d). Meanwhile, the emission peak around 586 nm has a slight blue-shift (~2.2 nm) and the central wavelength of the PL envelope shifts from 586 to 596 nm (Figure S4c). The power-dependent blue-shift of the PL peak is also observed in the emissions of the cavity itself (Figure S5). The power-dependent red-shift of the PL envelope is observed in both transmittance and reflection geometry (Figure S6), this is different from the dye molecules in the thick strongly-scattering media52, where the spectra show power-dependent red- and blue-shifts in reflection and transmission geometry. These blue- and red-shifts are hardly to be observed at the SQDs on empty AAO and quartz substrates (Figure S7).

The spectral modulating factor can be approximately expressed as (see details in SI),

where r2 is reflective coefficient of the back surface of the cavity and k is coupling factor of the SQDs with the cavity. eG represents the variations of amplitude of the PL electromagnetic field travel a circle in the cavity, which includes all factors, such as gain, propagation loss and excitation energy transfer and relaxation from the higher level(s) to the lower one(s).

The observed spectral modulation shown in Figure 2 can qualitatively explained by using Equation 1. For the samples SQD/AgNR:AAO/AgNF with fixed excitation power and variable thickness of the AgNF, the increased reflective coefficient by the AgNF results in significant improvement of the modulating factor. For the samples SQD/AgNR:AAO without AgNF, the modulating factor γ is significantly improved as the excitation power increases, which indicates an equivalent nonlinear “gain” G in the nanosystem induced by the stronger excitation power.

Multi-mode oscillations and amplifications

The cavity-mode spacing Δνcav is adjusted to about 0.54ΔνSQD,0 to observe the coupling of ensemble SQDs with multi-mode of the cavity. The power-dependent PL spectra of multi-mode oscillations for the SQDs/AgNR:AAO/AgNF cavity (Δνcav = 0.54ΔνSQD,0, = 660 nm, dAgNF = 10.3 nm) is shown in Figure 3a. The energy-level structures of the broaden emission band of the individual SQDs without interaction and the multi-mode of the cavity are illustrated in the inset. One can clearly see multi-mode oscillations of the cavity from the PL spectra. Owing to large reflectivity of the AgNF, the PL spectra of the SQDs around 590 nm are highly modulated. The emissions around 500 nm from the AAO template itself are also modulated by the complex cavity itself. The spectral width (defined as the full width at half maximum) of the emission is directly extracted from the PL spectrum, which reaches as small as 11.5 nm (Figure S10a).

Figure 3
figure 3

Power-dependent multi-mode and few-mode oscillations and amplifications of the SQD/AgNR:AAO/AgNF.

(a) Power-dependent PL spectra with multi-mode oscillations (Δνcav ≈ 0.54ΔνQD,0, ≈ 660 nm and dAgNF = 10.3 nm). (b) Power-dependences of the normalized peak PL intensity of six cavity modes at the emission wavelengths of 555, 572, 588, 606, 626 and 647 nm. (c) Power-dependent emission spectra with two-mode oscillations (Δνcav ≈ 1.27ΔνSQD,0, ≈ 610 nm, dAgNF = 10.3 nm). (d) Power dependences of the emission at 575 nm and 615 nm. (e) Differential normalized PL spectrum. The emissions around 575 nm are depressed and the emissions around 615 nm are amplified.

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More interestingly, the SQDs populations coupled to the six modes of the complex cavity have different power dependences as shown in Figure 3b. The SQDs population on the cavity modes with wavelengths shorter and longer than λSQD,0 is sublinearly and superlinearly dependent on the excitation power, respectively. The power dependence of the populations is qualitatively described by the slope index ζ = logI/logP. As the excitation power increases, the slope index ζ decreases to 0.85, 0.65 and 0.78 for the three modes with wavelengths of 555, 572 and 588 nm, but increases to 1.25, 1.42 and 1.36 near threshold excitation power Pc for the three modes with wavelengths of 606, 626 and 647 nm (Figure S10b). This indicates that the emissions of the SQDs coupled to the three cavity modes with wavelengths longer than λSQD,0 are nonlinearly amplified.

Few-mode oscillations and amplifications

Then, the cavity-mode spacing Δνcav is increased to be comparable or larger than the spectral width ΔνSQD,0 of the bare SQDs and the central L-SPR peak of the AgNRs is tuned to closed to λSQD,0, which lead to oscillations and amplifications of a few modes. Figure 3c displays two-mode oscillations of SQD/AgNR:AAO/AgNF (Δνcav ≈ 1.27ΔνSQD,0, ≈ 610 nm, dAgNF = 10.3 nm), where only a single mode at 615 nm is amplified. Two emissions (centered at 575 nm and 615 nm) are well separated owing to large feedback field induced by AgNF on the back surface of the cavity. It's very interesting to compare the different power-dependence of these two emissions. (1) The PL intensity at 615 nm is amplified with slope index ζ = 1.26, while the 575 nm emission becomes saturated and then decreases with the excitation power (Figure 3d). (2) The spectral width of the emissions at 615 nm decreases to 21.1 nm (69.2 meV) and the one at 575 nm increases to 24.7 nm (92.7 meV) as the excitation power increases (Figure 3c). The spectral width of 615 nm emission is 25.4% smaller than that of 575 nm emission at P = 5.5 mW. (3) The differential normalized PL intensity ΔIPL,nor(λ) = IPL(P + ΔP,λ)/(P + ΔP) − IPL(P,λ)/P is positive around 615 nm owing to nonlinear amplifications (Figure 3e), but it is negative around 575 nm owing to nonlinear energy transfer and saturation. Notice that the nonlinear PL of the SQD/AAO:AgNR/AgNF sample with ≈ 610 nm has stronger saturable effect for the higher level and prominent spectral narrowing effect for the lower level comparing to those of the sample with ≈ 660 nm. The spectral narrowing and amplification at higher excitation power are not observed in the controlled samples without AgNRs (see Figure S8).

ΔIPL,nor(λ) is approximately proportional to the differential “gain” ΔG = G(P + ΔP,λ) − G(P,λ) (see Equations S4–S7 in SI). Therefore, a positive peak of ΔIPL,nor(λ) around 615 nm indicates an increment of the “gain” ΔG at the stronger excitation, which is the origination of the emission amplifying as well as a power-dependent spectral narrowing. The peak position of this singly amplified emission is also tunable (in the range 605 ~ 620 nm) by adjusting mode-spacing and phase shift of the complex cavity.

Power-dependent emission dynamics

To reveal dynamic processes and physical mechanism of the nonlinear emissions of the ensemble SQDs coupled with a complex cavity, the PL lifetimes at different emission wavelength are measured with a weak and a strong excitation power by using time-resolved PL (TRPL) (Figure 4). The control sample SQD/quartz has a single PL decay process (dashed lines), which is almost independent on power. On the contrary, the TRPL decay trace of the sample SQD/Ag:AAO/AgNF (Δνcav ≈ 1.5ΔνSQD,0, ≈ 610 nm, dAgNF = 10 nm) is power-dependent and contains a fast and a slow process (solid lines), which is approximately reproduced by a two-component exponential function,

where τf (τs) and Af (As) represent lifetime and weight factor of the fast (slow) process. As shown in Figure 4a–c, the TRPL recorded at three emission wavelengths (λemi = 570, 590 and 615 nm) has different power-dependent behaviors.

Figure 4
figure 4

Power-dependent emission dynamics of the ensemble SQDs coupled with a AgNR:AAO/AgNF complex cavity (Δνcav ≈ 1.5ΔνSQD,0, ≈ 610 nm, dAgNF = 10.3 nm).

Time-resolved PL decay traces recorded at λemi = 570 nm (a), 590 nm (b) and 615 nm (c). The blue and red lines represent the results recorded with a weak and a strong excitation power (P = 0.3 and 9.0 mW). With weak excitation (P = 0.3 mW), τf = 2.55, 2.62 and 2.21 ns, τs = 15.0, 16.0 and 16.7 ns at λemi = 570, 590 and 615 nm. With strong excitation (P = 9.0 mW), τf = 1.94, 2.24 and 1.78 ns, τs = 11.5, 20.8 and 11.6 ns at λemi = 570, 590 and 615 nm.

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i) For the emissions at the lower level (λemi = 615 nm > λSQD,0), the fast decay rate (1/τf) increases from 1/2.21 to 1/1.78 ns−1 as the excitation power increases from 0.3 to 9.0 mW and the slow decay rate (1/τf) also slightly increases. The rate increase of this level at strong excitation is larger than those of two other levels and is mainly attributed to power-enhanced radiative processes since the PL intensity is nonlinearly increases with the excitation power. ii) For the emissions at the higher level (λemi = 570 nm < λSQD,0), both fast and slow decay rates increase with the excitation power, but the PL intensity shows saturated-like behaviors, which indicates that the increase of decay rate of this level is mainly caused by power-enhanced nonradiative processes. iii) For the emissions around λSQD,0 (λemi = 590 nm), the fast decay rate 1/τf slightly increases from 1/2.62 to 1/2.24 ns−1 but the slow decay rate decreases from 1/16.0 to 1/20.8 ns−1 as the excitation power increases from 0.3 to 9.0 mW. This puzzled power-dependent dynamic behavior has also been observed in other SQD/Ag:AAO/AgNF samples with few-mode and implies a more complicated interaction processes in the nanosystem.

FDTD simulations for cooperative radiances

To further investigate enhancement of the radiative rate of the ensemble SQDs couple with an AgNRs complex cavity, we have performed the 3D-FDTD simulations of one and two radiative dipole sources on the top of AgNRs (Figure 5). Two-configurations of the two diploes used in the FDTD calculations are shown in Figure 5a and 5e, respectively.

Figure 5
figure 5

Superradiance and subradiance of two dipole sources coupled with AgNRs.

(a) and (e) Illustration of the positions and polarizations of two dipoles. (b–d) Local fields (|E|2) of one and two dipoles coupled with AgNRs (LAgNR = 30 nm, λ = 600 nm) by configuration shown in (a). (f–h) Local fields of one and two dipoles coupled with AgNRs (LAgNR = 32 nm, λ = 600 nm) by configuration shown in (e). Enhanced radiances of two dipoles are demonstrated in (c) and (g) and the depressed radiances are demonstrated in (d) and (h).

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The radiative rate of two dipole sources (separated by 5 nm) in the middle of two AgNRs (Figure 5a) with a polarization along the short axis of the nanorods and with the same phase (Δϕ = 0) are increased about 95% comparing to that of a single dipole coupled with the AgNRs and the corresponding local fields of the two nanorods are significantly enhanced (Figure 5c and Figure S13). On the other hand, the radiance of the local field of two nanords is almost totally depressed when the two dipoles are out of phase Δϕ = π (Figure 5d). These enhanced and depressed emissions are the superradiance and subradiance of two dipoles induced by surface plasmon of the AgNRs.

Similar superradiance and subradiance are also demonstrated when the two dipoles located at the two sides of an AgNR (Figure 5e). The distance of two dipoles is as large as 40 nm, the local field around the central AgNR is enhanced ~100% by supperradiance (when Δϕ = π, Figure 5g) and almost totally depressed by subradiance (when Δϕ = 0, Figure 5h). The probability of these cooperative emissions of the ensemble SQDs is larger than that of two SQDs and will increases with excitation power. Here it should be noted that, we use symmetric finite size rod arrays to calculate the cooperative behaviors. Although the structures are not periodic as that used in experiments, they are quite equivalent to investigate the cooperative effects between to QDs near a rod. Because the rods that are far away from the two QDs do not affect the coherent couplings. The near field distribution is also affected by the array parameters such as the rod distance, plasmon resonance of rods and the distance between QD and rods.

Discussion

Finally, we discuss relationships and underlying physical mechanisms for the nonlinear spectral shifting, narrowing, modulating and amplification of the emissions from the ensemble SQDs coupled with plasmonic complex cavities based on the above observations and calculations. Three optical processes are probably involved in our nanosystem.

Nonradiative energy transfer to the lower-level mode(s)

The observed saturated-like PL intensity and increased decay rate at the stronger excitation power at the higher level(s) (570 nm) are the strong evidence of the excitation energy transfer process from the higher to the lower level(s). Usually, the distance of efficient nonradiative energy transfer between SQDs is only few nanometers, but the surface plasmon of AgNRs largely extends this energy transfer distance to several tens nanometers via exciton-plasmon-exciton resonant coupling53,54.

Radiative energy transfer to the lower-level mode(s)

The radiative emissions from AAO cavity itself and other SQDs with larger spatial distance are reabsorbed by the SQDs via radiative energy transfer process. The arrayed AgNRs strongly focus radiative field at the tops of the nanorods30,31,32, therefore, the focused radiative energy are efficiently transferred to the SQDs nearby. This energy transfer process indicates that appropriate radiative emissions from the complex cavity itself increase the equivalent “gain” of the radiance at the lower level(s), but extremely strong PL of AgNRs around 590 nm will lead to spectral broadening of the SQDs55,56,57.

Enhanced radiance of the lower-level mode(s)

Both peak PL intensity and decay rate of the lower level(s) are increased and the corresponding spectral width is narrowed at stronger excitation, which indicates that the pumped population at the lower level radiates more efficient at stronger excitation power. The origin of these three spectral behaviors of nonlinear emissions has independently attributed to superradiance, stimulating emission and ASE and we believe that the dominated process in our nanosystem is stimulating emission and superradiance enhanced by a vertical complex cavity rather than ASE assisted by a lateral waveguidance. The plasmon-enhanced superradiance of the ensemble SQDs could not be neglected since the threshold effect is very weak. The radiative rate of two or more SQDs (radiative dipoles) coupled with AgNRs with appropriate phase could be increased or depressed. The possibility of this cooperative processes is increased when more excitonic populations in the SQDs are pumped near the threshold regime. Additionally, a fast followed by a slow PL decay processes observed at stronger excitation is also coincided with the theoretical predictions of these cooperative emissions58.

It is hard to distinguish the superradiance of the ensemble SQDs from the stimulated emissions with a soft-threshold and the stimulating process increases the probability of in phase for two SQDs, which will then increase superradiance. Experimental studied on the super- and sub-radiances of the ensemble SQDs are relatively difficult than the cooperative emissions of rare-earth ions, where the cooperative energy transfer and radiation between two ion-dipoles with well-separated energy levels are relatively easy to be manipulated and observed by spectroscopy via efficient up- or down-converted luminescence59,60. The multiexciton processes in SQDs could also lead to power-dependent nonlinear PL and emission dynamics61,62. However, the lifetime of multiexciton processes is determined by the nonradiative Auger interaction and in picosecond scale. The experimental data with PL integrate time at microsecond scale and lifetime at nanosecond scale in this paper cannot be assigned to the multiexciton process. More experimental evidences (such as lifetime and photon-statistics) about the cooperative emissions of ensemble SQDs remain to be further studied.

In summary, we have demonstrated power-dependent spectral shifting, narrowing, modulation and amplification of ensemble SQDs coupled to AgNR:AAO/AgNF complex cavities by tuning L-SPR of AgNRs, thickness of AgNF and mode-spacing of the cavity. Amplified emissions of one, two and three cavity-modes with narrowed spectrum and soft threshold of the ensemble SQDs are demonstrated. The nonlinear “gain” of the amplified emissions is analyzed from spectral modulation factor and differential PL spectrum. Power-dependent enhancements of radiative and nonradiative rates are also observed at the lower and higher level(s). Superradiance and subradiance of two SQDs coupled to the AgNR array are demonstrated by FDTD simulations. Based on these measurements and analysis, we conclude that the observed nonlinear spectral behaviors are mainly attributed to stimulated emissions with a soft-threshold and superradiance of ensemble SQDs enhanced by the plasmonic complex cavity. Our findings offer a new strategy to design active plasmonic complex cavities and a powerful tool to manipulate cooperative emissions of the ensemble of optical radiative dipoles, leading to augmented properties of light emission diode devices or nanolasers.

Methods

Preparation of AgNR:AAO/AgNF complex cavities

The anodic aluminum oxide (AAO) templates were prepared by a two-step anodisation process. The polished aluminum sheets were exposed to a 0.3 M H2SO4 solution under constant voltage of 19 V in an electrochemical cell at a temperature of approximately 4°C. The alumina layer produced by the first anodization process was removed by wet chemical etching in a mixture of phosphoric acid (0.15 M) and chromic acid (0.60 M) at ~60°C, in order to obtain a fresh Al surface which is advantageous to achieve uniform AAO nanopore arrays. The AAO templates were anodized with a stepwise reduced potential from 19 V down to 13 V in H2SO4 solution to decrease the thickness of the AAO barrier layer. The AgNRs were grown in the nano-pores of AAO templates by alternating-current electrolysis (50 Hz, 7 V, AC) in an electrolyte containing AgNO3 (0.03 M) and H2SO4 (0.03 M) with the underlying Al layer as an electrode and a Pt counter electrode. After dissolving the underlying Al substrate by using the mixture of HCl (1.2 M) and CuCl2 (0.44 M) solution, the AgNR:AAO cavity was obtained. Then, the AgNFs were deposited onto the surface with nanopores of the AgNRs:AAO by using a magnetron sputtering (Quorum-K575X), forming an air gap between the AgNRs and the AgNF. The thickness of the deposited films was monitored by a quartz crystal.

Spin-coating CdSe/ZnS SQDs

Commercial carboxyl CdSe/ZnS core–shell quantum dots with central emission wavelengths of ~590 nm were purchased from Invitrogen Corporation. A 10 μL SQD suspensions was diluted by 490 μL purified water. A 13 μL droplet of the diluted QD suspensions was dropped onto the surface of the alumina barrier layer of the AgNR:AAO/AgNF cavity and rotated for 30 s at 1500 rpm.

Characterization of samples

The scanning electron microscopy (SEM) was performed using a FEG SEM Sirion 200 operated at an accelerating voltage of 25.0 kV. The transmission electron microscopy (TEM) was performed using a JEOL 2010HT operated at 100 kV. The TEM samples were prepared by dissolving the AAO template containing AgNRs in NaOH solution. The morphology of the back surface of the AAO templates with and without QDs was investigated by using atomic force microscopy (AFM, SPM-9500J3, Shimadzu). The absorption spectra were recorded by a UV-VIS-NIR spectrophotometer (Varian Cary 5000) by using a p-polarized source with an incident angle 80°, as shown in Figure S1a.

Optical experiments

The optical excitation source was a mode-locked Ti:sapphire laser (Mira 900, Coherent) with a pulse width of ~3 ps and a repetition rate of 76 MHz and the excitation wavelength was tuned to 400 nm by using a second-harmonic generation system (HarmoniXX, APE GmbH). As shown in Figure S1b, a lens with a 150 mm focal length was used to focus the laser beam onto the sample, where the incident angle of the laser beam was ~80° and the area of the focus spot on the sample was approximately 6.7 × 10–4 mm2. The PL signal from the samples was collected by a reflection measurement, filtered with two filters and recorded through a spectrometer (Spectrapro 2500i, Acton) with a liquid-nitrogen-cooled charge-coupled device (SPEC-10, Princeton). The time-resolved PL emission decay traces were recorded using a time-correlated single-photon counting system (PicoQuant GmbH).

Numerical simulations

The simulations were carried out by using the software FDTD Solutions 7.5. In the simulations, the refractive index of Ag rods is taken from Palik (Handbook of Optical Constants of Solids; Academic Press: New York, 1985). The index of the hole under each Ag rod is taken as 1 and the height of the holes is 500 nm. The Ag rod array has a period a = 50 nm and rod diameter d = 20 nm. The Ag rods with holes are placed in an AAO with refractive index 1.6. The quantum dots are taken as dipole emitters and the layer height is 6 nm with index 2.5. The whole structure is placed in air with refractive index 1. Perfectly matched layer boundary conditions are used in the simulations.