Coupling of quantum-well emission to waveguide–plasmon polaritons in rolled-up microtubes

The control and manipulation of light-emitting properties of quantum emitters represent a major challenge for both fundamental science and application-based technologies. Driven by high-potential application perspectives for photon-emission controlling, the research in tailor-made and tunable quantum emitters has gained much attention. In that sense, many studies have reported on the modification of the spontaneous emission of an emitter by designing the surrounding local optical density of states (LDOS)¹ using photonic crystals,^2,3 optical cavities,^4–6 plasmonic nanostructures,^7–11 or metamaterials.^12–14 In this article, we investigate the coupling of quantum wells (QWs) to waveguide–plasmon polaritons (WPPs),^15–18 hybrid photon–plasmon modes arising in a thin dielectric slab waveguide, which are excited and coupled into the waveguide by an adjacent periodic metal grating structure. For this purpose, we design a freestanding emitter–waveguide–plasmon structure that is composed of a 4nm GaAs QW within a 45-nm-thin InAlGaAs-based slab waveguide and a plasmonic Ag grating all embedded into the wall of a rolled-up microtube. The microtube geometry on the one hand allows measuring the photoluminescence (PL) emission of the GaAs QW from the bottom side, i.e., the side averted from the Ag grating. On the other hand, it ensures a necessary stability of the structure since it is much more rigid than bent lamellas. We investigate the coupling of GaAs QWs to a particular dielectric-waveguide/metal-grating microstructure. Since microtubes can act as optical ring resonators,^19,20 our work paves the way to investigate even more complex interactions between excitons, plasmons, and three-dimensionally confined waveguide modes. Characterizing our emitter–waveguide–plasmon structure in more detail, it is important that the grating itself consists of triangle-shaped grating bars aligned parallel to the microtube axis such that the filling factor f, i.e., the ratio of the width of the Ag bar and the grating’s unit cell, is varied along the grating bars. The design of triangle-shaped grating bars has been exploited to build a surface plasmon resonance-based integrable micro spectrometer, as reported in Ref. 21. In our case, the variable Ag grating structure adjoining the GaAs QW allows us to excite WPPs into a freestanding 45-nm-thin InAlGaAs slab. Additionally, the Ag grating bar itself represents a thin metal wire and, thus, supports localized surface plasmons (LSPs). By changing the filling factor f, we also change the width of that metal wire and, thereby, tune its LSP resonance. We observe by means of spatially, spectrally, and temporally resolved PL measurements, a coupling of the QW PL emission to the InAlGaAs–Ag structure indicated by a decrease in the PL intensity, blueshift of the PL spectrum, and reduction of the PL lifetime. Finite-element simulations show that the GaAs QW emission couples to a WPP, where at the same time, the excitation of the LSP is suppressed.

The investigated hybrid semiconductor–metal structure is prepared by rolling-up InAlGaAs-based layers and Ag nanostructures to a microtube.^22,23 The initial molecular-beam epitaxially grown semiconductor system, sketched in the right inset of Fig. 1(a), consists of a 40 nm AlAs sacrificial layer, a 15 nm In_0.2Al_0.24Ga_0.56As strained layer, and a QW heterostructure (7 nm Al_0.3Ga_0.7As, 4 nm GaAs, 16 nm Al_0.3Ga_0.7As) that is capped by a 3 nm GaAs layer. The further unprocessed GaAs QW exhibits a low-temperature PL peak energy of 1.652 eV (corresponding to a wavelength of 750 nm), which is above the bandgap of the In_0.2Al_0.24Ga_0.56As (1.615 eV at T = 6 K) strained layer. After rolling, the QW emission has redshifted to 760 nm, while the emission of the In_0.2Al_0.24Ga_0.56As layer, whose bandgap is further decreased due to strain relaxation, is strongly quenched due to non-radiative surface recombinations. A variable Ag grating with a periodicity of g = 350 nm and triangular 20-nm-thick bars is placed on top of the semiconductor layers by means of electron-beam lithography, thermal evaporation deposition, and subsequent lift-off processes. The triangle-shaped grating bars represent a variable grating coupler, and we define the filling factor f of the grating as the ratio between the width of the Ag grating bar w and that of the unit cell g, $f=wg$⁠; see the inset on the left of Fig. 1(a). Figure 1(b) shows a detailed sketch of the area framed by dashed lines in Figs. 1(a) and 1(c). The triangular grating bars are aligned such that the filling factor f is steplessly varied in y-direction, i.e., along the axial direction of the microtube, and thus, each position along that direction corresponds to a specific filling factor f. In order to prevent an asymmetrically rolled-up microtube, a 5-μm-wide Ag stripe is additionally placed at the low filling factor end of the grating (f = 0). Shallow mesa and deep mesa structures for the rolling-up process are defined via ultraviolet lithography, as reported in Ref. 24. Finally, the selective removal of the AlAs sacrificial layer by chemical wet etching in hydrofluoric acid results in the strain relaxation of the InAlGaAs layer that causes the system to bend up. Consequently, a micrometer-sized tubular geometry is constructed, as sketched in Fig. 1(c). The formation of the microtube yields a freestanding InAlGaAs-layer system with a Ag grating positioned on the inside wall of the microtube; see the inset of Fig. 1(c). We note that the location of the inner rolling edge of the microtube sketched in Fig. 1(c) and the dimensions of the Ag structures with marked filling factors f (f = 1, f = 0.5, and f = 0) of the grating in Fig. 1(b) match those of the real microtube investigated in this study. A scanning electron microscopy image of this microtube is presented in Fig. 2(a) with the tube showing a length of 85 μm and a diameter of 3.66 μm. The Ag grating positioned on the inside of the tube is visible through the InAlGaAs wall and the magnifications in Figs. 2(b) and 2(c) highlight the varying filling factor f of the prepared Ag grating.

We apply spatially, spectrally, and temporally resolved laser scanning confocal microscopy at low temperatures T ≈ 6 K to investigate the coupling of the QW emission to the hybrid semiconductor–metal system. The QW is excited above its barrier energy by pulsed laser light with a wavelength of 650 nm and a photon density of ∼10¹⁴ cm⁻². The light is generated by an optical parametric oscillator that is pumped by a pulsed Ti:sapphire laser and has a pulse duration of 130 fs, a spectral width of 5 nm, and a repetition rate of 76 MHz. For light focusing and collecting, a microscope objective (100×, NA = 0.8) is used. The emitted light is guided to a streak-camera system (f = 300 mm spectrometer with a 150 grooves/mm grating and a Hamamatsu C5680 streak camera with synchroscan module and CCD detection, temporal resolution ∼3 ps) and for each pixel scanned using the confocal microscope, a streak-camera image containing the spectral and temporal information is recorded. To rationalize on the data collection and processing utilized in this study, we show in Fig. 3, the exemplary streak-camera images of the QW emission recorded at positions on the microtube with the grating’s filling factors of (a) f = 0.33 and (b) f = 0. The white points in these false-color images represent the photon-detection events that are spectrally and temporally resolved along the horizontal axis and the vertical axis, respectively. The PL intensity of the QW emission is obtained by integrating all the photon events of the streak image. For the spectral distribution of detected photons, all the photon events in the vertical direction are summed up, as shown in the lower parts of Figs. 3(a) and 3(b). The spectral position λ_p of the maximum PL intensity is subsequently derived from a fit to a Gaussian function. The decay curves are extracted by integrating the events along the horizontal axis in a 10-nm-wide window around the fitted Gaussian center wavelength λ_p. The retrieved decay curves are plotted in the right parts of Figs. 3(a) and 3(b). A monoexponential fit to the decay curves yields the decay lifetime τ. For the position with f = 0.33 (f = 0), we obtain λ_p = 756 nm (λ_p = 759.3 nm) and τ = 9.5 ps (τ = 20.1 ps). The x- and y-coordinates given in the upper part of each panel correspond to the respective positions within Fig. 4, which is discussed below. Generally, we observe rather short PL decay times (in the range of 25 ps) of the QW emission both on the unprocessed sample and on the actual microtube. These short decay times can be explained by the particular molecular-beam epitaxially grown layer structure. The thin barrier (7 nm AlGaAs layer) is grown directly on the strained InAlGaAs layer and allows for the tunneling of excitons from the GaAs QW layer into the smaller bandgap strained layer; the thicker barrier on the other side (16 nm AlGaAs layer) of the QW prevents the tunneling of excitons into the GaAs capping layer. The tunneling represents a loss channel that decreases the PL lifetime of the QW independent from being unprocessed or rolled-up. We note that PL decay times in the range of 100 ps have been observed for different unprocessed and rolled-up GaAs QW structures without such tunneling channels.^20,25

We raster scan a sample section within an area of (4.5 × 85) μm² with a step size of 0.33 μm. This area includes the microtube. Accordingly, we obtain spatially resolved maps, as shown in Fig. 4 for (a) the PL intensity, (b) the spectral position λ_p of the maximum PL intensity, and (c) the decay lifetime τ. In these false-color plots, the microtube is located within the framed area and the Ag structures are oriented as presented in the upper sketch; gray pixels in Fig. 4 represent the values outside the plot range, as indicated by the respective color-scale bars on the left. Within Fig. 4(a), we observe a distinctively reduced PL intensity for the area corresponding to f = 0.33. This is the most important observation and will be discussed later in depth. Additionally, an increased PL intensity in the lower part (x = 1 μm–2 μm) along the tube axis can be seen. As shown in Fig. 1(c), the inner rolling edge of the microtube is located here and the microtube’s wall in that section consists of two stacked semiconductor layers. Therefore, we attribute the measured increased PL intensity to both an edge-PL emission of the rolling edge and the excitation of two QW layers. In addition, the area corresponding to the Ag stripe (y = 75 μm–80 μm) shows an increased PL intensity that can be attributed to the coupling to surface plasmons supported by the Ag film.^26,27 The metal film underlying the QW layer could as well act as a mirror for the emitted photons resulting in an additional increase in PL intensity. Similar effects should be expected for the area left of f = 1, where the Ag grating is changed into a continuous metal film. However, the initial preparation of the Ag grating is designed such that the distance between the grating bars is steplessly reduced toward the left side with high f. Due to limitations in the electron-beam lithography and lift-off processes, this results in a comparatively high surface roughness of the deposited Ag, which compensates both PL-increasing effects.

In Fig. 4(b), the spatially resolved map for λ_p is displayed. Most remarkably, a blueshift of the QW spectrum for areas with f = 0.33 and f = 0.90 is observed. This observation for f = 0.33 will be discussed in detail later. The redshift of the detected light apparent in the upper part (x = 3 μm–4.5 μm) of Fig. 4(b), which increases in strength from left (high f) to right (low f), can be explained by the flat semiconductor heterostructure layer system located underneath one side of the microtube [cf. Fig. 1(c)]. Depending on the filling factor f in the microtube, the photons of the underlying heterostructure are also recorded and these additional photons result in an apparent redshift. Besides that, a blueshifted PL emission of the QW is noticeable for the sections corresponding to the Ag stripe and for the left-most part of the grating structure with f = 1. As already argued for the increased PL intensity, the blueshift in these areas can be as well attributed to the excitation of surface plasmons in the Ag film.^28,29

Figure 4(c) shows the spatially resolved map for the PL lifetime τ. Strikingly, we observe a decrease in τ for the area with f = 0.33 that coincides with a decrease in the PL intensity [Fig. 4(a)] and the blueshift of the QW spectrum [Fig. 4(b)].

We want to highlight these features by plotting cross-sectional profiles of the PL intensity, the peak wavelength λ_p, and the PL lifetime τ taken along the y-direction and averaged from x = 1.33 μm to x = 2.67 μm as shown in Figs. 5(a)–5(c), respectively. Here, the concurrence of the decrease in the PL intensity, the blueshift of QW spectrum, and the reduction in the PL lifetime is clearly visible at y = 56 μm corresponding to the filling factor f = 0.33. The simultaneous appearance of these signatures shows that they are caused by the specific geometry of the waveguide–grating structure at f = 0.33. We note that similar signatures could not be found in different microtubes exhibiting a grating with a periodicity of 600 nm instead of 350 nm, as used here.

In order to investigate the specific optical properties of our plasmonic microtube structure, we perform finite-element simulations with COMSOL Multiphysics in which we ignore the QW emitter and regard the structure as a passive dielectric layer with a metallic grating attached. We carry out two-dimensional electromagnetic calculations using the unit cell geometry as depicted in the inset of Fig. 6(a). A complex permittivity for Ag is regarded³⁰ and the whole semiconductor structure is approximated as a homogeneous GaAs layer with a permittivity of ϵ = 13.9. We do not define any further GaAs heterostructure, i.e., no GaAs QW is specified within the simulation, and therefore, any plasmonic mode arising in the structure is independent of the QW structure. The curvature of the microtube is neglected to reduce the simulation complexity, which is reasonable because (i) we compare the theoretical results to the data measured on the two-dimensional projection of the central part of the microtube, for which the effect of the curvature is minimal, and (ii) it is known from earlier investigations that for the waveguiding properties, the curvature of microtube walls plays only a minor role.^19,20 Floquet periodic boundary conditions are applied to the edges of the unit cell (marked with dashed lines) in order to construct the Ag grating.

First, we calculate the reflectance R of an unpolarized plane wave with normal incidence to the structure for which the filling factor is varied from f = 0.1 to f = 0.6; the resulting reflectance spectra are plotted in false-color in Fig. 6(a). Here, two sets of branches with a reduced reflectance can be seen, i.e., two branches (I and II) that shift to shorter wavelengths λ and three branches (III, IV, and V) that shift to longer wavelengths λ with an increase in f. Surprisingly, for branches I and IV, a non-crossing behavior is present around f = 0.33. More precisely, the reflectance dip corresponding to branch IV is suppressed while approaching the branch I. However, we can still assign a non-crossing point of branches I and IV, if we anticipate the progression of branch IV by ignoring the reflectance suppression.

In Fig. 6(b), vertical cross sections in the 700 nm–800 nm wavelength range for filling factors f = 0.2, f = 0.33, and f = 0.45 as indicated by the black frame and the dashed lines in Fig. 6(a) are plotted. Here, the position at the full width at half maximum of the QW emission for the InAlGaAs–Ag structure with f = 0 [see Fig. 3(b)] is highlighted in blue. The QW emission is centered at around 760 nm. From Figs. 6(a) and 6(b), it becomes obvious that from all calculated branches only branch I and IV can in principle interact with the QW emission. Interestingly, the interaction would take place for both branches around f = 0.33, i.e., close to the non-crossing point of both branches, and this is exactly the filling factor for which the spectral blueshift and the decrease in the PL lifetime τ have been measured. If the QW would only couple to one of the different branches, the spectral shifts would be expected in both directions for increasing filling factors: first a redshift then a blueshift for branch I [because of its negative slope in Fig. 6(a)] and vice-versa for branch IV (because of its positive slope). If the branches were independent of each other, a coupling of the QW emission would also lead to a complex blueshift and redshift. The fact that the branches show a non-crossing behavior and the observation of only a blueshift of the PL emission strongly suggests that the QW couples to a plasmonic mode that is composed of both branches but is dominated by the plasmonic nature of branch I.

In order to get insight into the type of plasmonic resonances that are present in the QW’s emission regime, we additionally determine the distribution of the absolute electric field $|E→|$ at the dip wavelengths λ₀ of branches I and IV for the filling factors f = 0.2, f = 0.33, and f = 0.45, as identified in Fig. 6(b). These field distributions are depicted in Fig. 6(c). For f = 0.2 and λ₀ = 736 nm, the electric-field distribution is localized at the edges of the metal slab and, thus, corresponds to a localized surface plasmon (LSP). On the other hand, the excitation with λ₀ = 776 nm leads to a field distribution within the whole thickness of the dielectric waveguide, which is characteristic for a waveguide–plasmon polariton (WPP).^16,31 Applying this discrimination to all reflectance branches in Fig. 6(a), we assign branches I and II to WPPs, while branches III, IV, and V correspond to LSPs. Except for the crossing of branch I and branch IV, all other crossings of WPP and LSP branches appear to be the simple superposition of the individual branches without any mutual change in reflectance within each branch, as one would expect for non-interacting modes. However, for the WPP branch I and the LSP branch IV, there is a non-crossing point for f = 0.33 and λ₀ = 756 nm. The electric-field distribution for this configuration, depicted in the center panel of Fig. 6(c), resembles the one of a WPP, while the LSP character of the mode is strongly suppressed. For this point, the reflectance of branch IV is suppressed and we argue that both modes are coupled to each other with the WPP-like mode being strongly dominant compared to the LSP-like mode. With respect to the experimental results, we argue that the QW emission can in principle couple to both plasmon modes, WPP and LSP. However, while reaching the filling factor of f = 0.33, the calculations reveal that it is particularly the coupling to a dominant WPP-like mode at f = 0.33 that is responsible for the measured interaction, i.e., the spectral blueshift and the decrease in the PL lifetime τ.

In above considerations, we proved the coupling of the QW emission to a WPP-like mode by measuring distinct changes in the PL intensity, wavelength, and lifetime for a special grating configuration and by simulating the electromagnetic modes in the waveguide–plasmon structure by finite-element calculations. These considerations are independent of the exact nature of the QW emission, on which we want to speculate in the following.

The QWs incorporated in rolled-up microtubes are not optimized for being of extraordinary high-quality. We assume that the monolayer and alloy fluctuations in our QW induced by the strained quaternary InAlGaAs layer only 7 nm below the QW result in potential variations in the QW, which lead to exciton localization. Consequently, the QW emission resembles the emission of an ensemble of quantum dots. These localization effects manifest themselves in a rather broad PL emission, which has been utilized to probe optical modes in microtube ring resonators over a broad energy range³² and to achieve lasing in a microtube bottle resonator with an embedded GaAs QW as a gain material.²⁵ Such localized excitons behave like molecular dipolar emitters, for which a spectral shift with an associated lifetime decrease is a distinct indicator for a resonant coupling to a close-by plasmonic or dielectric cavity.^33,34 In our case, the observed spectral shift would be a consequence of a transition-rate modification of the blue spectral part of the QW emission induced by a plasmonic resonance of the InAlGaAs–Ag structure with f = 0.33. If the incorporated QW was of very high quality and if very small excitation densities were used in the experiments, the coupling of delocalized excitons and the changes in their intrinsic radiative lifetimes³⁵ to the waveguide–plasmon system could have been investigated. The coupling of delocalized excitons is interesting because the electric dipole fluctuations have a short wave-vector and intraband excitations in the Ag Fermi sea connected with surface plasmon interactions are momentum disallowed.²⁸ In our experiments, we used a photon density of 10¹⁴ cm⁻² for the excitation, which yields an exciton density of 10¹¹ cm⁻² if we assume an absorption efficiency of ∼0.1% for the thin GaAs QW structure. This exciton density is on the threshold to the Mott transition for GaAs QWs³⁶ at which an electron–hole plasma is formed in addition to the excitons. As reported in Ref. 37 for an InGaAs QW, an electron–hole plasma also exhibits a PL spectrum that is, however, broadened with an exponential high-energy tail compared to the spectrum with a solely excitonic character. In order to specifically investigate the coupling of an electron–hole plasma to waveguide–plasmon modes, a higher excitation power could be used.

In conclusion, we designed and investigated a rolled-up emitter–waveguide–plasmon structure composed of a GaAs quantum well, an InAlGaAs-based slab waveguide, and a plasmonic Ag grating. We exploited the strain-induced formation of semiconductor layers to prepare a hybrid semiconductor–metal microtube that consists of a freestanding light-emitting InAlGaAs layer and a tunable plasmonic Ag grating. By varying the grating’s filling factor, we were able to tune its plasmonic resonances to match the photoluminescence emission of the embedded quantum well. By means of spatially, spectrally, and temporally resolved photoluminescence measurements, we observed a coupling of the quantum-well emission indicated by a decrease in the photoluminescence intensity, spectral blueshift, and reduction in the lifetime. Finite-element simulations revealed that the GaAs quantum-well emission couples to a waveguide–plasmon polariton while suppressing the excitation of a localized surface plasmon.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft via Grant No. ME 3600/1-1. T.K. also acknowledges funding from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska–Curie Grant Agreement No. 656598.