Article pubs.acs.org/journal/apchd5
Enhanced Directional Emission from Monolayer WSe2 Integrated onto a Multiresonant Silicon-Based Photonic Structure Haitao Chen,† Stefan Nanz,‡ Aimi Abass,¶ Jingshi Yan,† Tingge Gao,† Duk-Yong Choi,§ Yuri S. Kivshar,† Carsten Rockstuhl,*,‡,¶ and Dragomir N. Neshev*,† †
Nonlinear Physics Centre and §Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia ‡ Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany ¶ Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), P.O. Box 3640, 76021 Karlsruhe, Germany S Supporting Information *
ABSTRACT: Two-dimensional transition-metal dichalcogenides such as WSe2 show great promise as versatile atomic-scale light sources for on-chip applications due to their advanced optoelectronic properties and compatibility with a silicon photonics platform. However, the sub-nanometer thickness of such active materials limits their emission efficiency. Hence, new approaches to simultaneously enhance the emission and control its directionality are required. Here, we demonstrate enhanced and directional emission from a WSe2 monolayer integrated onto a silicon photonic structure. This is achieved by coupling of the WSe2 layer to a multiresonant silicon grating-waveguide structure. The interaction with the multiple resonant modes supported by the structure provides simultaneous excitation and emission enhancement, while the dispersion of the modes further routes the emission into specified directions. In addition, our hybrid structure offers the opportunity for ultrafast emission modulation, owing to the reduced emission lifetime of WSe2. Such a silicon-based hybrid platform is fully scalable and promising as efficient chip-integrated and spatially multiplexed light sources. KEYWORDS: 2D material, WSe2, waveguide, grating, photoluminescence, directional emission
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silicon photonic structures emerges as a new promising solution.29,30 2D materials are held together by out-of-plane van der Waals forces and can be transferred onto a silicon substrate without lattice-mismatch issues. However, the emission efficiency of a single-layer TMDC is limited by its sub-nanometer thickness (light−matter interaction length), and it is much less than for other direct-bandgap semiconductors, which prohibits monolayer TMDCs from practical applications. Coupling of 2D materials to photonic structures is a promising approach to enhance the light−matter interaction and tailor the emission radiation properties.2,3 Indeed, various plasmonic structures have been explored to enhance and engineer the photoluminescence (PL) and radiation properties from 2D TMDCs.31−37 However, the plasmonics-driven enhancement of emission is very localized to the hot-spots of the nanostructures, and the average enhancement over the entire material remains moderate.36 Furthermore, the localized hot-spots of plasmonic nanostructures make
wo-dimensional (2D) WSe2 and other transition-metal dichalcogenides (TMDCs) show great potential as atomic-scale versatile light sources, as their electronic structure forms a direct band gap when the material is reduced to a monolayer.1−4 Various important applications such as lowthreshold lasers,5−7 single-photon emitters,8−12 excitonic lightemitting diodes (LEDs),13,14 cascaded single-photon emission,15 and second-harmonic generation16−21 have been demonstrated with these 2D materials. Furthermore, the valley-based emission properties of TMDCs open a new door for information processing and novel helical light emitters.22−25 The optical properties of these emitters are also electrically tunable, which makes them suitable for on-chip circuit integration. On the other hand, enabling light sources in silicon photonics is an important requirement for on-chip optoelectronic applications.26,27 While silicon alone cannot generate the required light, integration with other direct-band-gap materials is being sought. Integration of germanium or III−V materials on silicon faces technical challenges due to a lattice-constant mismatch and different thermal properties.28 With the desire to overcome such limitations, the integration of 2D TMDCs onto © 2017 American Chemical Society
Special Issue: 2D Materials for Nanophotonics Received: May 31, 2017 Published: August 3, 2017 3031
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Figure 1. Waveguide-grating structure and its characterization. (a) Schematic side view of the structure under investigation: a monolayer WSe2 is located on top of a grating inscribed into the planar waveguide. Geometrical dimensions are not to scale. (b) Parameters of the grating-waveguide structure (i) and scanning electron microscopy image of a top view of the grating structure used in experiments (ii); part (iii) shows calculated total field profiles at guided mode resonant wavelengths of the grating-waveguide structure for normal incident plane waves. (c, d) Measured and calculated transmittance of the grating-waveguide structure for different linearly polarized light relative to the unpatterned area, respectively. The dashed line shows the measured emission spectrum of the WSe2 monolayer.
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RESULTS AND DISCUSSION Light−matter interaction could be boosted by engineering the available photonic modes in the environment.42 Generally, the largest enhancement of the overall PL emission can be achieved when utilizing photonic structures with multiple resonances that couple to both excitation and emission radiation. We realize such a scheme through integrating a WSe2 monolayer onto a shallow multiresonant grating structure inscribed into a planar silicon waveguide, which supports multiple propagating mode resonances. The schematic of our experimental arrangement is shown in Figure 1a (side view). A WSe2 monolayer is positioned on top of a grating etched into a planar waveguide made of amorphous silicon (a-Si). The grating periodicity is selected such that both the excitation laser and the emission couple to available waveguide modes. The grating structure facilitates coupling of the pump light (from free space, as indicated by the arrow) to a waveguide mode, which increases the local field intensity at the monolayer position. Thus, the absorption of the pump light by the WSe2 monolayer is increased and translates to higher excitation efficiency. The emission of WSe2 also couples into waveguide modes supported by the high-index a-Si layer. Note that due to the amorphous structure of the silicon layer, it is nearly transparent at the emission wavelength.21 The coupling of the WSe2 layer to the silicon waveguide reduces the radiative lifetime of emission, which in turn is extracted efficiently to free space due to the grating structure. Therefore, such an experimental scheme offers boosting of the PL emission simultaneously through the excitation and emission processes.
their coupling to 2D materials highly sensitive to the distance between the emitter and structure, often requiring challenging nanometer-precision positioning. Nonmetallic nanostructures, such as photonic crystal cavities, have also been proposed for enhancing the emission from TMDC monolayers.38−40 However, these schemes rely on cavity modes with a small volume, again showing overall limited enhancement. More importantly, none of these demonstrated platforms are directly compatible to the on-chip integration in modern silicon photonics.41 A silicon photonics compatible platform to strongly enhance the collective emission of the entire 2D material and to control its directionality is highly desirable. Here we demonstrate enhanced and polarization-selective directional PL emission from monolayer WSe2 by coupling it to a multiresonant silicon grating-waveguide structure. The multiple waveguide modes supported by the structure are engineered to provide enhancement at both excitation and emission wavelengths in order to achieve an optimal PL output. The dispersion properties of these modes further offer feasibility to simultaneously control the polarization and directionality of the emission. A significant reduction in radiative emission lifetime of a WSe2 monolayer is also demonstrated by time-resolved measurements. Importantly, our approach is fully scalable, Si-based, and thus suitable for onchip integration. The demonstrated scheme could be potentially used to fabricate efficient chip-based light sources for various applications, including single-photon sources for quantum applications and ultrafast modulation emitters for visible communication. 3032
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Figure 2. PL enhancement induced by the grating-waveguide structure. (a) Left: optical image of the sample. Right: 2D PL mapping of the sample. (b) PL spectrum of WSe2 measured from on-grating and off-grating region. (c) Dependence of PL enhancement factor on the excitation wavelength. (d) Time-resolved measurements from on-grating and off-grating region.
normal incident plane waves were done to confirm the nature of the observed resonances, and the results are shown in Figure 1d. To account for the focusing effect introduced by the objectives used in the experiments, we assume that the incoming pump light has an angular distribution that follows a Gaussian shape centered around normal incidence with a standard deviation of 2 degrees. The three resonances can indeed be attributed to TE0, TM0, and TE1 modes supported by the underneath waveguide as labeled, which is discussed in detail below. As shown in the figures, the emission spectrum of the WSe2 overlaps with both TE0 and TM0 resonances. The excitation wavelength could be chosen such that the pump laser couples to the TE1 waveguide resonance; thereby we could enhance excitation and emission at the same time. The emission out-coupled from TE0 and TM0 modes will go into different defined directions due to their respective dispersive nature and sharp resonance line widths. Thus, control the emission directionality can be accomplished by tailoring either the periodicity or polarization. A relation of the leaky waveguide modes’ dispersion is given in the Supporting Information (Figure S3) in order to provide further clarity on the dispersive nature of the modes. One can observe discrepancies in terms of magnitude and line shapes when comparing the numerical and experimental results. We associate these discrepancies to fabrication and measurement uncertainties. However, we wish to note that the simulation still well reproduces the resonant wavelengths and line widths of the waveguide mode resonances, which is of main importance in the work. The general trend of the relative transmittance spectrum is also captured well. A monolayer of WSe2 exfoliated from a bulk crystal was dryly transferred onto the grating. Figure 2a shows the optical microscope (left) and 2D PL mapping images (right) of the
Furthermore, as the emission couples into different leaky modes supported by the grating-waveguide structure, the emission can be highly directional. In experiments, a 200 nm layer of hydrogenated a-Si was deposited on a glass substrate by plasma-enhanced vapor deposition as the waveguiding layer. Compared to crystalline Si, whose absorption starts to increase sharply below 1100 nm, hydrogenated a-Si is transparent up to 700 nm owing to a high optical band gap of 1.73 eV.43 Hence a-Si was chosen in this work because of its low optical loss at the emission peak of WSe2 around 750 nm. The refractive index and extinction coefficient of the waveguide layer were measured by ellipsometry methods afterward (given in Figure S1 in the Supporting Information). In the next step, a binary grating with periodicity of 214 nm and depth of 50 nm designed to facilitate coupling of waveguide modes to radiation and excitation was etched into the a-Si layer. Part (i) of Figure 1b shows the designed parameters of the grating-waveguide structure (side view), and part (ii) shows a scanning electron microscopy image of the top view of the fabricated grating. The calculated TE0, TM0, and TE1 mode profiles confined by this structure are also shown in part (iii). By examining the simulated extinction (1 − T0) spectra for normal incident light (Figure S2 of the Supporting Information), we can expect a high coupling efficiency between the free-space radiation and the waveguide modes, reaching >80% for the resonances of interest. Figure 1c shows measured transmittances for different linear light polarizations of the patterned grating relative to the unpatterned area for almost normal incidence. Multiple resonances arising from the excitation of waveguide modes are visible. The black dashed line shows the measured PL emission spectrum of the WSe2 monolayer overlapping with the resonances. Finite-element light-scattering simulations for 3033
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sample, respectively, where we could observe obvious PL enhancement induced by the grating. Here, we define the PL enhancement factor (PLef) as the average on-grating PL intensity divided by the off-grating value as shown in the formula under Figure 2a. By exciting the sample with a 633 nm (around the TE1 resonance) He−Ne continuous-wave (CW) laser, we observed up to 8 times enhancement of the PL from the on-grating area compared to the off-grating one. The spectra measured from two different positions (on-grating and off-grating region) are shown in Figure 2b. To confirm and distinguish the enhancement effects coming from excitation and emission, we also measured the dependence of the enhancement factor on the excitation wavelength, as shown in Figure 2c. In these measurements we used a supercontinuum laser (Fianium), where a 10 nm spectral band has been selected using an acousto-optic filter, under the same average power. The strongest enhancement happens when the sample is excited by a laser wavelength of around 630 nm, which corresponds to the TE1 resonance of our sample and fulfills our expectation. The overall enhancement factor is slightly weaker than that in our CW experiments, which is due to a broader spectral and pulsed (a few picosecond) excitation. This experiment also shows the feasibility of tuning the enhancement factor by varying the excitation wavelength. In addition, we conducted time-resolved measurements with resolution down to 2 ps to check the emission enhancement as shown in Figure 2c. For better comparison, here we normalized the emission intensity to its respective maximum and plotted the decay behavior in a logarithmic scale. We also fitted the decay curve into a biexponential function44 shown as solid lines. We could observe that the radiative behavior of WSe2 for the on-grating region is around twice faster than the off-grating one, which proves that we harvested emission enhancement from our samples too. Note that the decay curves are not straight lines (on a logarithmic scale), which is likely because there are multiple recombination processes involved in the emission.44 However, the detailed study of the dynamics of carriers is beyond the scope of this work. Also, we found that the decay lifetimes of the delays were in the range of tens of picoseconds, which offers the opportunity for ultrafast modulation with speeds up to 50 Gbps. Thus, we conclude that our multiresonant Si grating-waveguide structure could effectively enhance PL of a WSe2 monolayer on average up to 8 times by combing both the excitation and emission enhancements. To further explore the coupling between the monolayer WSe2 and grating-waveguide structure, we investigated the farfield angular emission from our system. Near- and far-field analyses are done using the finite element solver JCMsuite (JCMwave, Germany).45 The in-plane momentum (kx, ky) distribution of the emission was obtained through back-focalplane imaging, where each point in the image plane maps to a specified angle of the emission.46 The in-plane momentum is related to the emission polar angle θ through the relation sin(θ) = k∥/k0, where k∥ = |kx + ky|, and k0 = 2π/λ is the wave vector amplitude at wavelength λ. We observed quite different emission patterns from the on-grating and off-grating regions. Figure 3a shows the back-focal-plane image of the total emission from the on-grating regions, where we observe that the emission goes preferentially into four distinct angular regions. In contrast, the back-focal-plane image of emission from unpatterned regions, shown in Figure 3d, displays a typical pattern with intensity decaying from the center. Furthermore, we mapped the back-focal-plane imaging of the
Figure 3. Experimental back-focal-plane images of emission from monolayer WSe2. A notch filter with a half-maximum bandwidth of 10 nm centered at 750 nm was used to filter out the spectrum. (a) Overall emission from on-grating WSe2. (b, c) Back-focal plane images of the emission component polarized perpendicular (Iy) and parallel (Ix) to the grating ridge from the on-grating WSe2 structure, respectively. (d) Back-focal plane image of the total emission from off-grating WSe2 structure.
emission of different polarizations. Figure 3b and c show the emission patterns when a polarizer oriented across and along the grating ridge was applied in the detection path, respectively. These two images show clearly that the emission direction is polarization-dependent. Therefore, the emission directionality and intensity in the grating region can be tailored with a polarizer to a great degree. The details of the back-focal-plane imaging is presented in Methods. To investigate further the physical mechanism behind the measured PL characteristics, we performed numerical simulations of the emission of a WSe2 monolayer coupled to the grating-waveguide structure. The WSe2 monolayer emission is modeled as a superposition of different electric dipole emitters, placed 1 nm above the grating, for three different lateral positions: in the center of the unit cell (this corresponds to the position above the center of the ridge), above the edge of the ridge (this corresponds to the position at 58.5 nm from the center), and close to the boundary of the unit cell (corresponding to the position that is almost above the center of the trench). As the WSe2 monolayer does not support outof-plane-oriented dipole moments,46 we only simulated inplane-oriented electrical dipoles, oriented across (y-direction) and along (x-direction) the grating ridge. Typically, simulating a single dipole emission in a periodic system requires one to consider a large amount of unit cells, which in a full three dimensions is computationally time-consuming. To handle this, we utilize a supercell algorithm that allows us to deduce the singular dipole emission response in a periodic system by combining single unit-cell simulations with varying phase relations along the periodic boundaries.47 3034
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(Figure 4b), we reproduce the main features in Figure 3b, in which there is high peak intensity around ky ≈ ±0.3k0. Conversely, considering only the intensity component parallel to the grating ridges (Figure 4c) allows us to reproduce the features of Figure 3c. This observed polarization-selective directional emission property is linked to the waveguide modes the emitters couple to. To demonstrate this, we calculated the dispersion relation of TE0 and TM0 waveguide modes for a flat slab waveguide system (air/175 nm a-Si/SiO2) folded into the first Brillouin zone with a grating vector G = 2π/214 nm (Figure 3d). The folded kspace cross-section of the waveguide mode dispersion leads to four curves related to ±1 diffraction coupling of radiation to the TE0 and TM0 waveguide modes. These four curves match well with what was observed in the experiments and far-field simulations, which indicates that these are indeed the modes that the monolayer is coupling to. In addition to the folded dispersion curves, we show intensity plots obtained from 2D finite element simulations of a line dipole emission above the grating-waveguide and the flat multilayer structure (Figure 5a and b). As a-Si is not absorbing in the emission wavelength, the waveguide modes in the grating-waveguide region have a long propagation range. Due to this, one would have to account for the contribution of many unit cells of the periodic system. Here, we show simulations assuming 100 unit cells with the line dipole source placed in the center of the central unit cell. Figure 5a shows the intensity profiles when the dipole line source is polarized along the grating ridges, which thereby excites TE waves. As can be seen in the intensity plots, a major portion of the emission couples to the waveguide modes for the cases both with and without grating. Efficient coupling of the emission to the waveguide modes can also occur when the dipole line source is polarized along the y-direction, which excites TM waves (Figure 5b). Since efficient coupling of the emission to the waveguide modes occurs, one can expect that the radiation properties would be dictated by the waveguide modes’ radiative nature if their outcoupling is facilitated. Without the grating structure, however, a large portion of the emission that couples
The simulated far-field distribution in momentum space, averaged over the positions and orientations, is shown in Figure 4a. Good matching of the singular dipole far-field calculations
Figure 4. Simulated momentum space distribution of the emission’s far field averaged over the considered position and orientation. (a) Total far-field intensity. (b, c) Far-field intensity component perpendicular (Iy) and parallel (Ix) to the grating ridge, respectively. (d) Folded dispersion relation of the TE0 and TM0 waveguide modes at a wavelength of 750 nm for a flat slab waveguide system assuming a period of 214 nm in the y-direction.
and the measured momentum space of the emission is obtained, when compared with Figure 3a. By considering only the far-field component perpendicular to the grating ridges
Figure 5. Calculated intensity profiles of singular line dipole emissions in a 2D system for multilayer structures with and without gratings for 100 unit cells. When the line dipoles are polarized parallel (a) and perpendicular (b) to the grating ridge, they are normalized to their respective maximum for both cases. (i) and (ii) correspond to the on-grating and off-grating region, respectively. The line dipoles are placed 1 nm above the grating ridge (or the a-Si slab layer for the flat reference case). The line source is laterally placed at the middle of the center unit cell (middle of the ridge) in both cases. (c) Angle-averaged intensity enhancement for the grating case relative to the flat case as a function of the excitation wavelength. We consider TE incoming polarization and assume the same Gaussian distribution of the incoming plane waves’ inclination angles as done for Figure 1d. The inset gives the total field profile for normal incidence at the peak resonant wavelength (640 nm). 3035
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provides opportunities for ultrafast modulation up to 50 Gbps. In addition, our numerical simulations have revealed how different modes contribute to the emission enhancement and directionality, and the numerical results explain experimental data well. These findings, demonstrated on a fully scalable Sibased platform, are important for chip-integrated optoelectronic applications of 2D materials.
to the waveguide mode remains guided and does not affect the angular distribution of the detected PL signal. Having discussed the origin of the polarization-dependent directionality, we proceed to examine the photonic effects that provide enhancement at the emission wavelength. We calculate the average ratio of total emitted power by point dipoles in the grating-waveguide system relative to the flat case with the flat grat expression Pgrat tot /Ptot , where Ptot indicates the total emitted power in the grating structure and Pflat tot the total emitted power of the flat structure with a thickness of the a-Si layer of 200 nm. For the dipoles polarized across the grating, we obtained a ratio of 1.5, which is comparable to the measured lifetime enhancement, indicating that the emission process is dominated by spontaneous emission, and thus contributions of different dipoles to the PL can be summed up in an incoherent manner. For the dipoles polarized along the grating, we get a ratio of only 1.01, which suggests that they have a longer lifetime in the grating system than the dipoles polarized across the grating. To calculate the outcoupling enhancement, we compare the total dipole emission power Ptot with the power radiated into air, Prad, for both the grating structure and the flat structure. grat flat flat From our simulations, we get Pgrat rad /Ptot = 0.26 and Prad/Ptot = 0.11. This means that the portion of power outcoupled into air in the grating system is by a factor of 0.26/0.11 = 2.36 larger than in the flat system. Even when this outcoupling enhancement factor is multiplied by the calculated lifetime enhancement factor (×1.5), the result does not match the PL enhancement factor obtained in the measurement. This enhancement factor mismatch indicates that the grating structure does not only enhance the emission. To further confirm the absorption enhancement of the pump light, which can contribute to the PL enhancement, we calculate the intensity enhancement 1 nm above the grating ridge for TE-polarized light for different excitation wavelengths relative to a flat unpatterned multilayer slab. We consider plane waves incoming to the structure from air at different inclination angles as done in Figure 1d. The angle-averaged intensity enhancement for the wavelength range 500 to 700 nm is plotted in Figure 5c. An intensity enhancement peak around the wavelength of 640 nm is visible in agreement with the measurement in Figure 2c. The intensity enhancement peak is due to the excitation of a TE1 mode as shown by the inset figure, which shows the calculated field intensity for a normal incident plane wave. Our simulations further show that one can obtain a peak intensity enhancement reaching 6 times around 640 nm due to the TE1 mode excitation, which can be expected due to a also roughly 6 times maximum increase of absorption by the WSe2 monolayer. Further engineering of the mode profile by the grating shape or the placement of the emitter can potentially increase this even more.
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METHODS Fabrication of Samples. The hydrogenated a-Si layer was deposited on a SiO2/Si wafer by plasma-enhanced vapor deposition at 250 °C. The refractive index and extinction coefficient of the material were measured by ellipsometry afterward. Then, the grating structure was patterned by electron beam lithography at 20 kV using the positive resist ZEP-520A. The development was performed by inserting the sample into n-amyl acetate. The resulting resist pattern was used as an etch mask for a-Si etching in CHF3/SF6 plasma. The residual resist was removed by oxygen plasma. Then, a single layer of WSe2 sample was mechanically exfoliated from the bulk crystal and dry-transferred onto the sample. PL Characterization. PL Spectrum and Back-Focal-Plane Characterization. An in-house microscopy system using a 100× objective with a numerical aperture of 0.7 was used for excitation and collection of emission in reflection configuration. A 633 nm He−Ne CW laser was used as an excitation source. An Ocean Optics spectrometer was used to measure the spectra. A pair of lenses was used to translate the back focal plane of the imaging objective to a CCD camera. A polarizer was used in the detection path to distinguish different components of the emission. 2D PL Mapping and Wavelength-Dependent Measurements. The micro-PL spatial mappings were performed on a commercial WiTec alpha300S system in confocal microscope configuration. A Fianium WhiteLase supercontinuum laser was used as excitation source, where a 10 nm spectral band was selected using an acousto-optic filter. Time-Resolved Measurements. An Optronis SC-10 streak camera triggered by a Coherent Chameleon Ultra II femtosecond laser with resolution down to 2 ps was used. The sample was also excited by the femtosecond laser at a central wavelength of 680 nm, with a repetition rate of 80 MHz and a pulse duration of 140 fs. Numerical Simulations. For the far-field calculation of a singular dipole emission near the grating-waveguide structure, we utilized unit cells consisting of a 200 nm thick substrate of SiO2 and an a-Si grating with a 150 nm thick guiding layer and a 50 nm thick ridge on top. Above the grating was air (refractive index n = 1). As upper and lower boundaries of the unit cell, we placed perfectly matched layers that attenuate the field to suppress reflections at the computational domain boundaries. The horizontal width of the unit cell was 214 nm and the width of the ridge was 107 nm. Periodic boundary conditions were used in the x- and y-direction. Each simulation of a unit cell with periodic boundary conditions implied that an infinite number of periodically arranged dipole sources with a certain phase relation between them were considered. By performing inverse Floquet transformation, which superposes the solutions for different periodic phase relations of the single unit cell results, we reconstructed the field of a singular dipole in a periodic system.47 A total of 128 supercells were used as a compromise between accuracy and computational time.
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CONCLUSION We have demonstrated enhanced and polarization-selective directional emission from monolayer WSe2 integrated onto a Si grating-waveguide structure. The PL enhancement and directionality have been realized by simultaneously coupling the emission and the excitation fields into the resonant modes supported by the structure. By tailoring the resonant frequencies and dispersion of the waveguide modes, we have shown great flexibility in controlling the WSe2 monolayer emission in both intensity and directionality. Furthermore, our time-resolved measurements show that our structure could effectively reduce the lifetime of the radiation decay, which 3036
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b00550. Measured refraction data of the a-Si we used in experiments; calculated extinction profiles of the grating-waveguide structure and planar waveguide reference; further details of the dispersion of the modes sustained by the grating-waveguide structure (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. ORCID
Haitao Chen: 0000-0002-0272-2264 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge useful discussions with M. Noginov. We acknowledge the financial support by the Australian Research Council through Discovery projects, Group of Eight AustraliaGermany Joint Research Cooperation Scheme, and the use of the Australian National Fabrication Facility (ANFF), the ACT Node. H.C. acknowledges financial support of the China Scholarship Council for Ph.D. scholarship no. 201206110047. We further acknowledge financial support by the Karlsruhe School of Optics and Photonics and by the DFG Priority Programm 1839 Tailored Disorder. We are also grateful to the company JCMwave for their free provision of the FEM Maxwell solver JCMsuite, with which the simulations in this work have been performed.
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