Amplified spontaneous emission at the band edges of Ag-coated Al nanocone array

Ye Xiang; Yongping Zhai; Jiazhi Yuan; Ke Ren; Xuchao Zhao; Dongda Wu; Junqiao La; Yi Wang; Wenxin Wang

doi:10.1364/PRJ.503656

1. INTRODUCTION

The rapid development of modern information technology requires miniaturization and integration of optical devices, for instance, light pump sources advancing toward smaller sizes, faster modulation, and higher efficiency. With the maturity of the nanofabrication process, the spatial scale of these miniaturized devices enters the era of micron-scale or even nano-scale. However, resonant cavities for lasing with conventional optical feedback cannot be minimized to the half-wavelength scale because of the optical diffraction limitation. Therefore, quasi-particle surface plasmons (SPs), which are hybridized of photons and electrons, have attracted attention as they can confine the light on the nano-scale [1 –7]. SPs are in the surface electromagnetic mode formed by free electron resonance over the metal surface [8 –10], which possess small mode volume and high localized field enhancement. However, due to the large Ohmic damping of metal materials and the radiation loss of particles, SPs present broad spectral linewidth and low quality factor ( $Q$ ), which limits their practical applications.

In-plane Bloch surface waves can be induced in the lattice as plasmonic particles are periodically arranged, which can strongly suppress the radiative loss and result in resonances with ultra-sharp linewidth and high quality factor since the localized surface plasmon resonances (LSPRs) couple with Rayleigh anomalies (RAs) or the planar waveguide mode to produce surface lattice resonances (SLRs), which are collective resonant modes from coherent interactions. These SLRs exhibit obvious dispersion characteristics [11,12] and more significant electromagnetic field enhancement [13,14]. Since the periodic metal nanoparticle array presents various photonic band structures, the wavelength and efficiency of photon emissions can be controlled through band engineering [15 –17]. According to Fermi’s golden rule [18], the spontaneous emission rate of an emitter is proportional to the local density of states, and the modulation of the spontaneous emission rate in an optical cavity can be illustrated by the Purcell factor [19], $F = \frac{3}{4 π^{2}} \frac{Q}{V_{m}} {(\frac{λ}{2 n})}^{3},$ (1)where $Q$ is the quality factor of the cavity, $V_{m}$ is the mode volume, $λ$ is the resonant wavelength, and $n$ is the refractive index of the medium. $Q$ is related to the ratio of the energy stored in the cavity and energy dissipated per oscillation cycle, and it can be denoted as $Q = λ / Δ λ$ ( $λ$ is the resonant wavelength, and $Δ λ$ is the linewidth). According to Eq. (1), $V_{m} = 3 Q λ^{3} / 4 π^{2} F {(2 n)}^{3}$ , $V_{m}$ can be obtained with exact $Q$ and $F$ . On one hand, SLRs present a small $V_{m}$ and a high local density of states that originates from the SPs. The latter local density of states, on the other hand, can be further improved at the photonic band edge state in a photonic lattice since these band edge modes with low group velocity ( $d ω / d k$ , $ω$ is the angular frequency, and $k$ is the wave vector) provide an optical feedback with higher quality compared to the propagating state. Therefore, plasmonic lattices with high $Q$ SLRs are an ideal platform to investigate the intracavity light–matter interaction [20,21]. Considering the plasmonic lattice as a microcavity, the generated SLRs promote the generation of high-quality amplified spontaneous emission (ASE) with stronger emission intensity, narrower linewidth, and adjustable emission direction. The ASE, an important competitor and alternative to laser source, is a typical luminescence phenomenon without directional emission, and it can serve as a signature feature before laser threshold oscillations.

On the other hand, currently, common preparation methods for plasmonic lattices include focused ion beam lithography, laser writing, nanoimprinting, template-assisted patterning, and electron beam lithography. Among them, template-assisted patterning, in particular the anodic aluminum oxide (AAO) membrane patterning, is one of the effective methods for producing large-scale nanostructure arrays quickly and accurately. The long-range ordering AAO membranes can be achieved over a centimeter scale, and the short-range ordering membranes can reach a meter scale [22 –24]. Therefore, to combine the AAO membranes with the deposition technique, large-area plasmonic lattices with high $Q$ SLRs can be effectively prepared.

In this paper, we investigate the light–matter interaction of a square lattice of an Ag-coated Al nanocone array (Ag-NCA) with a lattice constant of 400 nm that is packaged with Nile Red as the gain material. Under optical pumping, an obvious ASE of 15-fold is obtained from the Ag-NCA along normal emission, which is fivefold stronger than that from the Al nanocone array (Al-NCA). In addition, a strong directional ASE is observed, which illustrated the effect of the local density of states and the group velocity within the plasmonic lattice, and the ASE can be modulated by the corresponding photonic band edges. This work not only proves the plasmonic lattice offers effective optical feedback to the emitting system, and adjusts the optical parameters from intensity, direction, polarization, and so on, but also exhibits the potential applications in the coherent light source on the nanoscale for photonic information and photonic integrated circuits (PICs).

2. RESULTS AND DISCUSSION

Figure 1(a) illustrates the process of fabricating Ag-NCA with the 400 nm period using pre-imprinting and anodic oxidation processes. Briefly, the anodic oxidation method is used to guide the growth of ordered AAO membranes on the pre-embossed Al foil. The anodic oxidation conditions are 160 V and 4°C, and the oxidation solution is a mixed aqueous solution of phosphoric acid and ethylene glycol. The volume ratio is phosphoric acid:ethylene glycol:water = 1:200:400, and the oxidation time is 1.5 h. The chromic acid and phosphoric acid mix-solution is used to remove the upper-level ${Al}_{2} O_{3}$ component from the Al foil, leaving a square lattice of protruding Al-NCA. This non-lithographic process has been proven as a very effective and matured nanofabrication technique to fabricate two-dimensional photonic crystals and plasmonic lattices with various lattice arrangement and symmetries. A 100 nm layer of Ag is deposited on the surface of Al-NCA to form Ag-NCA by magnetron sputtering at a rate of 1 nm/s. Second, Nile red [1 mg Nile red dissolved in 1 mg polymethyl methacrylate (PMMA)/10 mL dichloroethane, refractive index 1.49] is packaged on the Ag/Al-NCA by the spin coating process into a homemade glove box with vacuum pump. After that, samples are taken out from the vacuum condition to do the optical measurements in the air condition. After spin-coating and curing, the Nile red/PMMA can be considered as evenly distributed on the array. Figures 1(b) and 1(c) show the scanning electron microscope (SEM) images of the Al-NCA before and after the Ag coating, respectively. The inset image shows the feature on a single cone with a diameter of 80 nm and a height of 300 nm. In the process of the Ag coating, the tip of the cone rises to a sphere with a diameter of 50 nm as shown in the inset images of Figs. 1(b) and 1(c), and the roughness decreases gradually as the thickness increase until a threshold thickness of 100 nm. The SEM images of 50 nm Ag-NCA and 150 nm Ag-NCA are shown in Fig. 4.

Figure 1.Ag-NCA packaged with Nile red. (a) Schematic of preparation of Ag-NCA. SEM images of (b) Al-NCA and (c) 100 nm Ag-NCA. The insets show the feature SEM on a single cone, and the scale bar is 400 nm.

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The nanostructure studied in this article is a periodic array composed of Ag-NCA. The collective resonance phenomenon in the two-dimensional periodic metal array, also known as SLRs, can support unique light transmission.

To study the light propagation in this plasmonic lattice, the schematic diagrams of a square lattice of Al-NCA are described in real space and reciprocal space as depicted in Figs. 2(a) and 2(b), respectively. Here, Fig. 2(a) is the lattice constant and the primitive vector of the square lattice ( $a = 400 nm$ ). According to the orthogonality relation, the corresponding reciprocal lattice vectors can be described as $| b_{1} | = | b_{2} | = 2 π / a$ . Hence, the Bragg grating vectors can be expressed as $G_{i j} = i b_{1} + j b_{2}$ , where $i$ and $j$ are integers. Based on the empty lattice approximation (ELA), the SLRs mode generated under Bragg coupling conditions can be described by the following dispersion relation [25]: $| k_{| |} + G_{i j} | = \frac{ω}{c} \sqrt{\frac{ε_{d} ε_{m}}{ε_{d} + ε_{m}}},$ (2)where $ε_{d}$ and $ε_{m}$ are the permittivity of the dielectric and the metal. $k_{| |}$ is the in-plane wave vector of the incident light, and $ω$ and $c$ are the angular frequency and velocity of light. The left side of Eq. (2) represents the magnitude of the wave vector of diffraction orders (DOs), $k_{DOs} = k_{| |} + G_{i j}$ . In the case of plasmonic lattice, radiative loss can be strongly suppressed by the Bloch surface wave, and a larger sample area will offer enough collective diffraction mode and result in high-quality resonances with narrow linewidth (low radiation loss).

$Schematic of Ag-NCA in (a) real space and (b) reciprocal space. The dark blue triangle area in (b) represents the irreducible Brillouin zone. (c) Empty lattice approximation (ELA) diagram for the diffractive orders supported by a square lattice along M-Γ-X orientation. (d) Reflection dispersion spectrum of Al-NCA (left panel) and Ag-NCA (right panel, white dash lines: ELA calculations of DOs). (e) Reflection spectra of Ag-NCA are measured from 0° to 35°. The red solid line refers to the (0, ±1) SLRs, and the blue dashed line represents the (−1, 0) SLRs. The pink dashed line is the photoluminescence (PL) spectrum of Nile red, and between the two pink dashed lines is the PL range of Nile red. (f) Corresponding electric field distributions of (0, ±1) SLRs of Al-NCA (upper panel) and Ag-NCA (lower panel), respectively.$

Figure 2.Schematic of Ag-NCA in (a) real space and (b) reciprocal space. The dark blue triangle area in (b) represents the irreducible Brillouin zone. (c) Empty lattice approximation (ELA) diagram for the diffractive orders supported by a square lattice along M- $Γ$ -X orientation. (d) Reflection dispersion spectrum of Al-NCA (left panel) and Ag-NCA (right panel, white dash lines: ELA calculations of DOs). (e) Reflection spectra of Ag-NCA are measured from 0° to 35°. The red solid line refers to the (0, $\pm 1$ ) SLRs, and the blue dashed line represents the ( $- 1$ , 0) SLRs. The pink dashed line is the photoluminescence (PL) spectrum of Nile red, and between the two pink dashed lines is the PL range of Nile red. (f) Corresponding electric field distributions of (0, $\pm 1$ ) SLRs of Al-NCA (upper panel) and Ag-NCA (lower panel), respectively.

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Figure 2(c) depicts the calculated dispersion of the square lattice along $Γ$ -M and $Γ$ -X orientations by ELA. The difference between the $Γ$ -M and $Γ$ -X paths is due to the azimuth of the array relative to the incident light, which is 0° and 45°, respectively (the definitions of the incidence angle, emission angle, and azimuth angle relative to the array are shown in Fig. 5). In a square lattice of Al-NCA, all four lowest-order Bragg vectors, (1, 0), ( $- 1$ , 0), (0, 1), and (0, $- 1$ ), have the same magnitude; therefore, they degenerate at the $Γ$ point ( $k_{| |} = 0$ ) [26]. These DOs at $Γ$ point (blue circle) exhibit the densest local density of states and have the smallest group velocity, which benefits the light–matter interaction at this degenerated point. The local density of states describes the number of photon states in the system. It is mathematically distributed as a probability density function, usually the average of the space and time domains of the states occupied by the system. Normally, a high density of states can be obtained at high symmetry points and symmetry paths with low group velocity. High symmetry points normally are multiple degenerate states, and low group velocity will promise longer photon confinement time and promote the light–matter interaction probability. In this work, a band edge mode occurs at $Γ$ point with a slope approach to zero, which is designed to offer optical feedback to Nile red emission. Since the energy of the degenerated state is 2 eV, which is spectrally overlapping with the emission of Nile red, it can provide an optical feedback to the dye. In the case of oblique incidence ( $k_{| |} \neq 0$ ) along the $Γ$ -X path, the DOs of (0, 1) and (0, $- 1$ ) keep the degenerate state, but the DOs of (1, 0) and ( $- 1$ , 0) lift to a higher and a lower energy branch, respectively. In this case, the local density of states decreases, and the group velocity increases.

Figure 2(d) exhibits the measured reflection dispersions of the Al-NCA (left panel) and the Ag-NCA (right panel) with an ambient refractive index of 1.49 and unpolarized incident light, and reflection intensity of scale bar is valued as $I_{ref} / I_{in}$ . The white dashed lines represent DOs (0, 1)/(0, $- 1$ ) and ( $- 1$ , 0), which interact with LSPRs to produce SLRs. The group velocity of the degenerated DOs trend to zero at $k_{| |} = 0$ (red circle), which results in band edge modes and confines the incident light with a longer interaction time. Furthermore, the reflection dip of DOs in the right panel is sharper than those in the left panel, which means the SLRs of Ag-NCA exhibit narrower full width at half-maximum (FWHM) and less damping loss than that of Al-NCA ( ${FWHM}_{Al-NCA} = 15 nm$ , ${FWHM}_{Ag-NCA} = 8 nm$ , Fig. 6). The $Q$ factors of Al-NCA and Ag-NCA can be calculated as $Q_{Al-NCA} = 38.93$ and $Q_{Ag-NCA} = 73.75$ , respectively. Combining them with the calculated $F_{Al-NCA}$ and $F_{Ag-NCA}$ by FDTD, the mode volume can be obtained as $V_{m Al-NCA} = 0.01 {μm}^{3}$ and $V_{m Ag-NCA} = 0.75 \times 10^{- 4} {μm}^{3}$ , respectively. Figure 2(e) shows the corresponding reflection spectrum of the Ag-NCA as a function of incident theta from 0° to 35°, and the reflection dips’ evolution with the DOs (0, 1)/(0, $- 1$ ) and ( $- 1$ , 0), respectively, which can spectrally overlap with the emission of Nile red (520 nm to 720 nm). Therefore, the SLRs can offer an optical feedback to the gain material because of the Purcell effect as the emission angle of $θ_{em}$ varies from 0° to 35°. In Fig. 7, the calculated dispersions of the square lattice (first row) and hexagonal lattice (second row) with different periods from 300 to 600 nm are theoretically plotted by the ELA method. It can be found that the resonant energy of dispersion decreases obviously as the period increases from 300 nm to 600 nm in both case of lattices, but the band structure is not varying very much. Furthermore, the square lattice with a period of 400 nm is a good candidate for matching well with the photoluminescence (PL) of Nile red in this work. On the other hand, the electric field distributions in Fig. 2(f) demonstrate the optical field of Ag-NCA ( $λ = 590 nm$ ), which is mainly confined at the tip, but that is distributed at the bottom in the case of Al-NCA ( $λ = 584 nm$ ). Therefore, the Ag-NCA exhibits a stronger Purcell effect by smaller $V_{m}$ and higher $Q$ factor than Al-NCA, which promotes the spontaneous emission rate of the quantum emitter. Further, the small $V_{m}$ is contributed by the plasmonic nanocone structure, and the high $Q$ factor is realized by both factors of Ag material and periodic array.

Figure 3.ASE of the Ag-NCA. (a) Angular resolution optical path diagram for the measurement of ASE. The pump source is 532 nm. (b) Schematic diagram of the energy levels transition and the energy transfer in the generation of ASE. (c) Dispersion diagram of ASE. The solid red line is the luminous peak of the Nile red in flat Ag film. (d) ASE spectra at different powers. The inset shows a power-dependent variation of the emission intensity (red) and the fitted FWHM (black) of the ASE spectra. (e) Polarization of emission light on Ag-NCA (red point) and flat Ag film (black circle). TM polarization is 90°, while TE polarization is 0°.

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The ASE system is prepared by packaging Nile red (dissolved in PMMA/dichloromethane with $n = 1.49$ ) on the Ag-NCA. Figure 3(a) is the schematic diagram of the angle-resolved spectroscope setup for ASE measurement. Under an excitation of a 60° incident $θ_{in}$ of a 532 nm pump light source from a semiconductor laser, the emission is measured by the spectrometer from 0° to 50°, and the signals go through the optical path collimation, reflection mirrors, polarizers, and optical fibers. The azimuth angle $φ$ of the array relative to the incident laser is 0°. The $θ_{in}$ and $θ_{em}$ denote the incidence angle and emission angle, respectively. Since the incidence angle for ASE excitation does not affect the emission (Fig. 8), it is set as $θ_{in} = 60 °$ in this work. Figure 3(b) is the diagram of energy transfer between the emission from the dye and the SLR mode from Ag-NCA. On the left side is a simplified schematic of the energy level of the Nile red with a typical four-level system. Electrons in the ground state $S_{0}$ are excited to the state of $S_{3}$ by a 532 nm laser, and then they transit from state $S_{3}$ to $S_{2}$ by non-radiative decay. The electron transition from $S_{2}$ to $S_{1}$ results in a spontaneous emission with a broad linewidth. The ASE of 590 nm is mainly due to the fact that the band edge SLR higher exhibits higher local density of states than other SLRs modes and can boost the photon emission from $S_{2}$ to $S_{1}$ . The enhancement of the electric field of SLRs results in effective resonance feedback and light amplification. An orange emission (590 nm) from the Nile red is obtained under an external driving source with 532 nm. This 590 nm emission serves as the driving light to excite the SLR mode, which offers an optical feedback and results in an amplification to such emission.

Figure 3(c) shows the emission dispersion of Nile red packaged Ag-NCA as a function of the emission angle, and the pumping power and incidence angle of driving light are 1.75 W and 60°, respectively. The strongest emission signal is captured along normal emission ( $θ_{em}$ is 0°) as a result of the advantages of the band edge state with lower group speed and stronger local density of states, which is 15-fold stronger than that from Nile red packaged on Ag film and 5-fold stronger than that from Nile red packaged on Al-NCA (Fig. 9). Figure 3(d) shows the emission of the system at $Γ$ point, and the inset curves show the FWHM and emission intensity as a function of pumping power from 1.55 to 1.90 W. The threshold of ASE can be obtained at 1.65 W, where the slope of the intensity has a significant change. The FWHM of the emission gradually decreases as pumping power exceeds the threshold and then stabilizes at about 30 nm. Figure 3(e) is the polar diagram of Nile red packaged Ag-NCA as a function of polarization and emission intensity. The pumping power is 1.75 W (1.08 $P_{th}$ ), and the central wavelength of emission is 590 nm. The ASE of Ag-NCA exhibits stronger emission intensity with an elliptical coherence pattern at polarization angles of 0° and 90°, which is related to the symmetry of the square lattice. According to the group theory, there are four eigenstates ( $A_{1}$ , $A_{2}$ , $B_{1}$ , $B_{2}$ ) in the square lattice with different symmetries. Therefore, the regulation of Nile red emission can be realized by coupling with different eigenstates or the degenerated states of them. For instance, the doublet degenerated SLR (0, $\pm 1$ ) is designed to couple with the emission in this work, and the generated ASE will exhibit the symmetry features of $A_{1}$ and $B_{1}$ in both direction and polarization. Additionally, the maximum intensity is observed at $Γ$ point, which is a degenerated state of (0, $\pm 1$ ) and ( $- 1$ , 0) mode, and it can be expressed as a linear combination of these eigenfunctions. Therefore, the polarization property in Fig. 3(e) is from the hybrid states of $A_{1}$ and $B_{1}$ and exhibits a normal emission ( $k_{| |} = 0$ ), while the luminescence on the Ag film exhibits a lower intensity with circularly polarized coherence. This result proves the plasmonic lattice not only boosts the intensity of ASE but also regulates the directionality and polarization of ASE.

3. CONCLUSION

In conclusion, this work presents a square lattice of Ag-NCA compounded with Nile red to realize the directional emission of ASE with obvious polarization. The band edge states of the plasmonic lattice possess high local density of states and less damping loss at $Γ$ point, which offers a strong optical feedback to gain materials. A 15-fold stronger ASE is obtained along the normal emission at a threshold of 1.65 W under the optical pumping of 532 nm laser. Additionally, the polarization is manipulated by the symmetry of the lattice. This work not only explores the coupling mechanism of the interaction between SLRs and gain medium but also extends the application of the minimized light source for photonic information and quantum optics.

Category: Surface Optics and Plasmonics

Received: Sep. 12, 2023

Accepted: Oct. 19, 2023

Published Online: Nov. 29, 2023

The Author Email: Wenxin Wang (wenxin.wang@hrbeu.edu.cn)

DOI:10.1364/PRJ.503656