1. Introduction

III-nitride light-emitting diodes (LEDs), as efficient, energy-saving and reliable light sources, have developed various applications since discovered [1]. They now continue to capture keen interest for novel applications in smart lighting [2], displaying [3], communications [4] and biomedical fields [5], etc. Novel applications raise new demands in the modulation speed and the emission control for whether mini-, micro- or regular-sized LEDs. The requirement on the precise control of wavefront at wafer level is stated concerning future goals for miniaturized and compactly integrated displaying and communicating devices [3,4,6,7]. Controlling the emission of a LED wafer in polarization, directions and patterns is a challenging issue due to extremely low spatial coherence of light emitted from multiple quantum wells (MQWs) [8]. The extremely low coherence, which introduces blur and loss of contrast in images [9], also hinders the direct application of LEDs as partially coherent sources, such as holography [9], interferometry [10] and tomography [11]. In addition, the research on creating partially coherent light from spontaneous emission of MQWs without considerable loss in intensity is of fundamental interest. To our knowledge, the cavity structure is the only proposed configuration so far to obtain partially coherent light from LEDs at wafer level [12–14], but it requires a complicated architecture of epitaxy and negatively impacts light extraction, necessitating additional structures on surface for light extraction. The further investigations on new methods to improve coherence of LED emission is necessary.

Surface plasmons (SPs) can contribute to the creation of partially coherent light from spontaneous emission by scattering modes from photonic band structures into leaky modes in the weak coupling regime, which has been proved on sources like molecules as one of its properties [15–17]. The coherence of light emitted from the SPs and MQWs coupled system has received barely attention in reported researches on LEDs with plasmonic structures [18–21]. One recent simulation work on quantum dot LEDs has mentioned the improvement in spatial coherence through a circular patterned Ag grating [22]. There still lack experimental and theoretical investigations on optical coherence of plasmonic LEDs. Our earlier research achieved SP-MQWs coupling and an increased IQE with maintained electrical properties by a shallow-etched conic pit array covered with Ag (V-Ag) on blue LEDs [23,24]. The V-Ag array is thus utilized in this study to investigate the coherence of light emitted from a plasmonic LED wafer and evaluate its capability for emission control.

In this work, the emission and the coherence of light emitted from a plasmonic LED wafer with a hexagonally distributed V-Ag array on p-GaN have been investigated theoretically and experimentally, and compared with a plain wafer and a wafer with shallow-etched conic pit array (V-GaN). The emission of a micro area is firstly studied by micro-photoluminescence (micro-PL) tests and numerical simulations. A hexagonal pattern and a deflection in emission are observed for both the V-GaN and the V-Ag wafers. To reveal the origin of anisotropic and deflective emission of pit structures, theoretical calculations are then performed based on a slab waveguide model and Ewald constructions. The origin of anisotropic and deflective emission is diffraction of guided modes from GaN into air. The theoretical calculations meanwhile suggest an increased number of guided modes in the V-Ag wafer. The larger number of guided modes extracted and the higher spatial coherence of emitted light of the V-Ag wafer are proved by angle-resolved PL tests. Finally, we perform a macro-PL test and only the V-Ag wafer exhibits the anisotropic and deflective emission at far field. The analysis of emission spectra as the entire wafer excited shows the temporal coherence length of the V-Ag wafer is approximately 1.4 times larger than that of the plain wafer. The results evidence the enhancement in optical coherence of emitted light and the control of the emission pattern by the plasmonic structure on a LED wafer. The insights in this article provide a new perspective for the research on plasmonic LEDs and a new straightforward architecture to acquire partially coherent light from LEDs. This concept will also broaden the applications of LEDs into partially coherent sources by plasmonic structures directly integrated on wafers.

2. Materials and methods

The GaN-based LED wafer used in this experiment was grown on a c-axial (0001) sapphire substrate by metal organic chemical vapor deposition (MOCVD). The epilayers consisted of a 2 µm un-doped buffer layer, a 2 µm n-GaN layer, eight pairs of InGaN/GaN multiple quantum wells (MQWs) and a 230 nm p-GaN layer. Polystyrene (PS) nanospheres with the diameter of 200 nm were self-assembled onto surface of the wafer (p-layer) and reduced by oxygen plasma etching. Evaporation of Ni followed by removal of PS spheres was conducted to form a mask with the hexagonally distributed hole array on p-GaN surface. The surface covered with Ni mask was then etched downward for about 140 nm by inductively coupled plasma (ICP) and took shape of conic pits with a taper angle around 46°. The wafer with the hexagonal array of conic pits on surface was denoted as the V-GaN wafer. The V-Ag wafer was obtained through thermal evaporation of 20 nm Ag onto the V-GaN surface and into pits [23]. The morphology of the structures was examined by the scanning electron microscope (SEM 500, Gemini). Photoluminescence (PL) was measured by optically pumping plain and V-structure wafers with a 405 nm continuous wave (CW) laser.

The emission patterns of the designed wafers were numerically simulated by a commercial software Ansys Lumerical FDTD based on finite-difference time-domain method and Yee algorithm. Three orthogonal dipoles were utilized for incoherent summation to simulate point-like sources of MQWs. Boundary conditions were all set as perfectly matched layers (PML). The emission pattern was obtained via transforming field results of near filed monitors to far field patterns based on the equivalence principle.

3. Results and discussion

The wafer with hexagonal array of conic pits on p-GaN surface is sketched in Fig. 1(a). SEM images of the fabricated conic pit array are presented in Fig. 1(b), including top view and side view (inset). The period length of pit array is 200 nm as seen in top view. The height and apex angle of cones are about 140 nm and 46°, separately, as shown in inset of Fig. 1(b). These sizes ruled the geometry of simulation models.

 

Fig. 1. (a) Sketch of the wafer with conic pit array on p-GaN (not in scale). (b) SEM images of pit array, the inset is side view of pits.

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In order to analyze the emission of the designed wafers, we firstly performed full numerical simulations based on FDTD method and equivalence principle, as described in the Materials and Methods Section. Simulation models of plain, V-GaN and V-Ag wafers are depicted in Fig. 2(a), (b) and (c) separately. All structures were simplified to infinitely thick sapphire and light was emitted to air from upper surface. For the V-Ag model in Fig. 2(c), silver in pits and on surface was set as discontinues due to the very thin film of evaporated Ag. In order to simulate incoherent and location-random point-like sources of MQWs, two averaging operations were conducted. Firstly, three orthogonal dipoles were utilized and results were incoherently summated. Secondly, three dipole positions were chosen to solve location average for V-structures, as shown on the right side of Fig. 2(b). These positions are analogous to origin point, positions along ΓM and ΓK in a unit cell. The horizontal span of simulation region included 8 × 8 periods meaning a micro area. The vertical distance from upper surface of GaN and the monitor was 200 nm decided by convergence tests. The refractive index of GaN was set as 2.5. The Johnson and Christy data set was used for Ag. The emission pattern could finally be obtained from field solutions at far field given by the software.

 

Fig. 2. Simulations for emission patterns of micro area. (a)-(c) Simulation models (not in scale) for (a) plain, (b) V-GaN and (c) V-Ag structures. Three dipole positions (right side of figure b) are chosen for average. (d)-(f) Simulated emission patterns of micro area at wavelength of 453 nm, depicted by polar diagrams for (d) plain, (e) V-GaN and (f) V-Ag structures. Intensities shown each are dealt with dividing by the incoherently summated intensity of sources and normalizing by the maximum. Color bar is on the right side.

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The simulated emission patterns of micro area at wavelength of 453 nm are shown in Fig. 2(d)-(f). The results are given by polar diagrams with azimuthal angle (φ) of 0-360° and zenith angle (θ) of 0-90°. The light intensity of each individual structure is divided by the incoherently summed intensity of the dipoles and normalized by its respective maximum value. The uniform color bar is on the right side. In Fig. 2(d), the emission pattern of the plain wafer is homogenously distributed in azimuth angle and Lambertian distributed at zenith angle. The normalized intensities at θ = 0°, θ = 30° and θ = 60° are 1, 0.81 and 0.3 respectively. The emission patterns of V-GaN and V-Ag are shown in Fig. 2(e) and 2(f) separately. They exhibit significant differences from that of the plain wafer. The emission direction is deflected and the strongest shifts to around 28° rather than 0° of the Lambertian angular distribution. The distribution on φ is a hexagonal pattern. Two sets of hexagonally distributed bright spots can be observed at (i) θ₁, φ₁ and (ii) θ₂, φ₂, here (i) θ₁ = 28.5° ± 1°, φ₁ = 30°, 90°, 150°, 210°, 270°, 330° and (ii) θ₂ = 60° ± 1°, φ₂ = 0°, 60°, 120°, 180°, 240°, 300°. The strongest intensity (equaling 1 after normalization) is at (i). For normalized intensity distributions of V-GaN in Fig. 2(e), the intensities at θ = 0° and (ii) are 0.85 and 0.3 separately. For V-Ag in Fig. 2(f), the intensities at θ = 0° and (ii) are 0.75 and 0.47 separately. As comparing the emission patterns of two V-structures, V-Ag exhibits higher contrast than V-GaN in deflection and hexagonal distributions. The hexagonal distribution is analogous to a rotation of the real pit arrangement on surface, which suggests diffraction happens in light extraction process, so spatial coherence of emission from V-Ag might be enhanced. This will be discussed later.

The emission pattern of the designed wafers was also studied by micro-PL, as illustrated in Fig. 3. Figure 3(a) gives a schematic of the optical system. A 405 nm CW laser was focused and normally incident into the back side (sapphire) of the sample. The sample was optically pumped and excited 452.7 nm light. The emission collected by an object lens formed an image on a charge-coupled device (CCD) which was then recorded with a digital camera in the form of light and dark for qualitative intensity distributions. A 20× visible object lens (O.) was used for focusing the incident laser. The reason for pumping the back side is to avoid the initial anisotropy of exciting energy on MQWs when laser incidents on the pitted surface of p-GaN. To collect the emission of the sample, a 50× visible object lens with numerical aperture (NA) of 0.5 and field number (FN) of 26.5 mm was introduced. The light was set to pass through a 450 ± 10 nm filter to eliminate laser and a plane-convex lens to focus on CCD before finally recording the emission pattern.

 

Fig. 3. Experiments. (a) Sketch of micro-PL for CCD imaging. The sample is optically pumped backward by focusing 405 nm CW laser on MQWs via a 20× object lens (O. 20×). The emission of micro area is amplified by a 50× object lens (O. 50×) and focused on CCD by a plane-convex lens (L). A band-pass filter (450 ± 10 nm) is inserted before L to ensure the pumping laser is eliminated. (b)-(d) Emission images of micro-PL for (b) plain, (c) V-GaN and (d) V-Ag wafers.

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Figure 3(b), (c) and (d) list the emission images recorded by CCD camera of micro-PL for plain, V-GaN and V-Ag wafers, separately. These patterns are almost consistent with simulated ones in Fig. 2(d)-(f). The plain wafer shows a homogenous distribution in azimuthal rotation as seen in Fig. 3(b). The emission pattern of V-GaN and V-Ag wafers exhibit a hexagonal form in azimuthal distribution and V-Ag is the more obvious one between these two, consistent with simulated results. Notably, the differences in emission images among plain, V-GaN and V-Ag wafers arise from structural variations due to the same excitation energy and recording setups. The central area of images is overexposed for higher visibility of hexagonal distribution around, considering the strong to weak energy distribution from center to edge of pumping laser.

The anisotropic and deflective emission of V-structures shown in Fig. 2 and Fig. 3 can be quantitatively analyzed by Ewald construction [25,26]. As mentioned in references, this anisotropy through shallow-etched surface mainly arises from diffraction of guided modes in GaN to air. We therefore conducted a theoretical calculation for waveguide modes in V-structures in advance.

In the V-GaN case, conic pits on p-GaN surface can be treated as embedded air so that there forms a layer of lower effective refractive index on the surface of the wafer [27], denoted as a pit layer from now on. The pit layer and the sapphire substrate serve as two low-index layers in which GaN of high refractive index is sandwiched. This three-layer system was treated as a waveguide and guided modes of a slab waveguide were solved (see Supplement 1). According to calculations, a set of 15 discrete guided modes is supported in GaN between sapphire and pit layer. For the V-Ag case, the pit layer was regarded as Ag embedded in GaN and dielectric constants instead of refractive index were employed in calculations. Results show a set of 23 discrete guided modes is supported in GaN between sapphire and Ag/GaN pit layer (see Supplement 1). The calculated dispersion relations of these modes, namely in-plane wave vector ${k_\parallel }$ corresponding to wavelength λ, are shown in Fig. S1 and Fig. S2 for V-GaN and V-Ag wafers separately.

The guided modes in plain wafer can barely emit into air without specific treatments for light extraction [26,28]. Here in V-structures, shallow-etched pit array diffracts guided modes as ${{\mathbf{k}}_{{\parallel} ,\ell }} = {{\mathbf{k}}_\parallel } + \ell {\mathbf{G}}$, where ${\mathbf{G}}$ is the reciprocal vector of pit array and $\ell $ is an integer. The modes can emit if modified into the air cone, i.e., $|{{{\mathbf{k}}_{{\parallel} ,\ell }}} |< {k_0}$, where ${k_0} = 2\mathrm{\pi }/\lambda $ is wave vector of light in air. The emission direction is defined by angle (θ) with c-axis, ${\mathrm{\theta }_\ell } = \textrm{arcsin}({|{{{\mathbf{k}}_{{\parallel} ,\ell }}} |/{k_0}} )$. This diffraction process is simply described in Fig. 4(a).

 

Fig. 4. Theoretical calculations for light extraction of V-structures. (a) Sketch in side view (not in scale). Pits are embedded with air or Ag. Guided modes (briefly depicted in green) in GaN with ${{\mathbf{k}}_\parallel }$ can be diffracted by reciprocal vector ${\mathbf{G}}$ and emit (blue line) to air. (b), (c) Projections of the Ewald sphere in plane for guided modes propagating along the ΓM and ΓM + ΓK directions, respectively. Guided modes are diffracted by ΓM and diffraction vectors are ${{\mathbf{k}}_1}$ and ${{\mathbf{k}}_2}$, separately. Grey dots are the reciprocal lattice of hexagonally distributed pits at surface of GaN. Green circles are projections of the Ewald sphere, and blue ones are of the air cone. (d), (e) Calculated dispersion relations of guided modes which are diffracted into the air cone (light blue, k₀) for (d) V-GaN and (e) V-Ag. k₁ and k₂ denotes diffraction in (b) and (c), separately.

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Now we analyze the diffraction by Ewald constructions. Figure 4(b) and (c) schematically interpret two cases that guided modes can be diffracted into air. Blue and green circles are the projections of air cone and Ewald sphere, separately. Grey dots in a hexagonal arrangement are reciprocal lattice of the pit array. In Fig. 4(b), the guided mode propagating along ΓM direction is diffracted by reciprocal vector ΓM and goes to diffracting vector ${{\mathbf{k}}_1}$. The vector ${{\mathbf{k}}_1}$ falls in the air cone so it will emit to air. Similarly in Fig. 4(c), the guided mode propagating along ΓM + ΓK direction is diffracted by reciprocal vector ΓM and goes to diffracting vector ${{\mathbf{k}}_2}$ and emits. Vectors ${{\mathbf{k}}_1}$ and ${{\mathbf{k}}_2}$ are in fact ${{\mathbf{k}}_{{\parallel} , - 1}}$ and ${{\mathbf{k}}_{{\parallel} ,1}}$, separately. It is these two diffracting cases which lead to reciprocal lattice-like and hexagonal distribution of emission in Fig. 2 and Fig. 3.

The calculated dispersion relations of extracted guided modes are demonstrated in Fig. 4(d) and 4(e), for V-GaN and V-Ag respectively. The line of air cone is in light blue. The extracted modes are drawn in dark blue and green, corresponding to diffraction as in Fig. 4(b) and 4(c), separately. Comparing over V-GaN, V-Ag supports lager number of guided modes propagating in GaN, which are all extracted by diffraction. The extracted modes of V-Ag emit at 0.6° < θ < 30° and 56° < θ < 70° as for the cases of ${{\mathbf{k}}_1}$ and ${{\mathbf{k}}_2}$ separately. This result is matched with the emission directions of simulated results in Fig. 2.

The anisotropic and deflective emission of V-structures is now confirmed to be caused by diffraction. The higher contrast in the emission distribution of the V-Ag wafer compared to the V-GaN wafer suggests the stronger spatial coherence of light emitted from the V-Ag wafer. In order to confirm whether SPs can improve the spatial coherence of LED emission, further investigations on spatial coherence were conducted on V-structures.

The measurement of spatial coherence is based on angle-resolved PL and Young’s double slit experiment [16,29]. The sample was optically pumped and the Fourier image (FI) was recorded on CCD in spectrometer. The experiment setup is sketched in Fig. 5(a). The excitation part was the same as micro-PL described in Fig. 3(a). The 50× O. with NA = 0.5 and FN = 26.5 mm was introduced to collect the emission of the sample and to turn the illumination into parallel light. The filter (450 ± 10 nm) was inserted in this parallel light to eliminate the pumping laser. Two plane-convex lens L1 and L2 were utilized to invert the FI at back focal plane (BFP) of the 50× O. into a real image (RI) (by L1) and to Fourier transform again into FI (by L2) for recording in spectrometer. The FI recorded in spectrometer contains the intensity distribution of (λ, f₂tanθ), where f₂ is the focal length of L2 and θ is zenith angle of emission. Here 0° ≤ θ ≤ 30° with NA = 0.5. As for measuring spatial coherence, a double slit (DS) with interslit spacer of 450 µm and slit width of 50 µm was inserted in the RI plane between L1 and L2. Due to a magnification around 28×, the equivalent interslit spacer and slit width were about 16 µm and 1.8 µm on the sample surface separately. The DS at RI plane enables a direct detection on the spatial coherence of emission on the wafer surface in the far field. The criterion of the spatial coherence is that a fringe pattern appears at FI plane in spectrometer only when the spatial coherence length of the mode is greater than the interslit distance [16].

 

Fig. 5. Experiments. (a) The measurement set up for angle-resolved spectra. The focused 405 nm CW laser is used to optically pump the sample. A double slit (DS) is placed at real image (RI) plane when measuring spatial coherence. O. and f. are object lens and filter (450 ± 10 nm); L1 and L2 are two plane-convex lens; FI, Fourier image. (b), (d), (f) Angle-resolved spectra of (b) plain, (d) V-GaN, (f) V-Ag wafers along the ΓM direction, respectively. (c), (e), (g) Spectra for measuring spatial coherence of (c) plain, (e) V-GaN, (g) V-Ag wafers, measured by placing DS at RI plane of (b), (d), (f) respectively.

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Figure 5(b), 5(d) and 5(f) list the angle-resolved spectra of the plain, V-GaN and V-Ag wafers separately. The measured spectrum of the plain wafer shows a pattern of direct emission. In Fig. 5(d) and 5(f), each spectrum comprises direct emission and a series of bright oblique lines representing the extracted guided modes from GaN to air. The spectrum of V-Ag exhibits a larger mode number and therefore a more pronounced deflection angle compared to that of V-GaN. These measured results are matched with the calculated ones in Fig. 4(d) and 4(e).

Figure 5(c), 5(e) and 5(g) illustrate the spectra for investigating spatial coherence of the plain, V-GaN and V-Ag wafers by inserting DS at RI plane of the setup as measuring Fig. 5(b), 5(d) and 5(f) separately. There appears a visible fringe pattern in the spectrum of V-Ag. The fringes are analogous to replicas of original dispersions in Fig. 5(f), which are the interference pattern of original extracted modes from GaN to air. On the contrary, the spectrum of the plain and V-GaN wafer in Fig. 5(c) and 5(e) exhibits no fringe pattern and only a weaker pattern of original spectra in Fig. 5(b) and 5(d) respectively. The difference indicates the spatial coherence length of extracted modes from V-Ag wafer exceeds the interslit distance (16 µm), which is longer than that of the plain and V-GaN wafer. According to near-filed field intensity distributions of V-GaN and V-Ag (in Supplement 1, Fig. S3), there occurs localized field around Ag in pits of V-Ag under illumination of a point-like source, which indicates SPs are involved in the emitting process of V-Ag. Therefore, it is evidenced that SP-assisted diffraction increase the spatial coherence length of extracted modes, so the spatial coherence of light emitted by the V-Ag wafer is enhanced compared to both plain and V-GaN wafers.

For now, clearer diffraction and higher spatial coherence of emitted light from V-Ag compared to V-GaN have been observed and proven to be the main reason for the strongly anisotropic and deflective emission of a micro area. Next we will investigate the far-field emission and reveal the effects of enhanced spatial coherence on macroscopic light distributions.

The macroscopic emission of plain, V-GaN and V-Ag wafers were studied by a far-field angle-resolved PL test, as sketched in Fig. 6(a). The expanded laser beam illuminated on the entire wafer placed at the center of a stage and pumped it. The sizes of three-configuration wafers were fixed as 1 cm × 1 cm to ensure the consistent laser energy pumped on the wafers. A collecting arm connecting a visible multi-mode fiber of which probe was 15 cm away from the sample was used to collect the emission into spectrometer. The stage and the collecting arm were rotatable for acquiring emission spectra at various (θ, φ). The light emission spectra were taken in between -90° ≤ θ ≤ 90° and 0° ≤ φ ≤ 360° for every 10° as resolution. The spectra were integrated at each (θ, φ) and the integrated intensities were drawn as pixels on polar diagrams.

 

Fig. 6. Experiments. (a) Sketch of far-field angle-resolved PL test. The 405 nm CW laser is used to excite the entire 1 cm × 1 cm wafer. The rotatable stage and collecting arm connecting the fiber are used for acquiring PL intensities at various (θ, φ). (b)-(d) The far-field distributions of integrated intensities for (b) plain, (c) V-GaN and (d) V-Ag wafers.

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The measured emission distributions at far field of plain, V-GaN and V-Ag wafers are illustrated in Fig. 6(b), (c) and (d) separately. The plain wafer has a homogeneous emission in azimuth angle (φ) so a half (0° ≤ φ ≤ 180°) is given in Fig. 6(b) for simplicity. The Lambertian distribution of emission direction is demonstrated again in this result. The intensities at θ = 30° and θ = 60° decrease to around 88% and 75% of the maximum at θ = 0° respectively. In Fig. 6(c), the far-field emission distribution of V-GaN exhibits deflections and a little indication of anisotropy only, being different from the emission of micro area in Fig. 3(c). The intensities at θ = 0° and θ = 60° are around 0.76 and 0.65 times of the maximum at θ = 30° respectively. Unlike plain and V-GaN wafers, V-Ag exhibits a clear anisotropic and deflective emission at far field as shown in Fig. 6(d). The hexagonally distributed intensity of φ and deflective emission direction can still be seen in the emission distributions at far field of the V-Ag wafer. Every extreme spot occurs at a 60° interval for the azimuthal distribution. The emission direction is deflected and the strongest shifts to around 30°. We concentrate on intensity values at θ = 0°, (i) θ₁ = 30°, φ₁ = 30°, 90°, 150°, 210°, 270°, 330° and (ii) θ₂ = 60°, φ₂ = 0°, 60°, 120°, 180°, 240°, 300° as discussing Fig. 2(f). The measured intensity at θ = 0° is 8.10 × 10^5. The averaged intensities at (i) and (ii) are (1.23 ± 0.19) × 10⁶ and (7.34 ± 0.44) × 10⁵ separately, where the artificial errors in measurements lead to not exactly equal values at each φ₁ or φ₂. The strongest intensity occurs at (i) of which the intensities at θ = 0° and (ii) are around 0.66 and 0.59 times separately. The distinguishing performance of V-Ag is granted based on discussions above, which is achieved by the SP-assisted diffraction in light extraction and enhanced spatial coherence of emitted light. It is worth noticing that here the anisotropic emission at macroscopy is realized by a highly isotropic distribution of nanostructures. This result exhibits the ability to control the LED emission by designing plasmonic structures on wafers.

Finally, we compare macro-PL spectra of all the structures and evaluate the temporal coherence. The wafers were pumped as sketched in Fig. 6(a) and the emission was collected right above the wafers. The acquired spectra of plain, V-GaN and V-Ag wafers using Gauss fit are listed in Fig. 7. Each spectrum is normalized to its maximum for clarity. The raw spectra are listed in Supplement 1, Fig. S4. The spectra of three structures give almost the same shape with barely shift in peak centered at 452.7 nm. The difference of the spectra lies in full width at half maximum (FWHM), which are 23.3 nm, 22.6 nm and 16.8 nm for plain, V-GaN and V-Ag wafers separately. The temporal coherence length of a Gauss beam is ${l_c} = {({2\textrm{ln}2/\mathrm{\pi }} )^{1/2}} \times {\lambda ^2}/\Delta \lambda $, where λ and Δλ are the peak wavelength and FWHM of the spectrum separately [30]. The temporal coherence lengths of plain, V-GaN and V-Ag wafers thus are 5.8 µm, 6.0 µm and 8.1 µm respectively. The ${l_c}$ of the V-Ag wafer at far field is about 1.4 and 1.35 times larger than that of the plain and the V-GaN wafer respectively.

 

Fig. 7. Experimental macro-PL spectra for plain (grey), V-GaN (red) and V-Ag (blue) wafers using Gauss fit. Each PL spectrum is normalized to its maximum.

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4. Conclusions

In summary, we have investigated the improved coherence of light emitted from a blue LED wafer, achieved through a conic plasmonic structure on p-GaN. The emission of plain, V-GaN and V-Ag wafers in micro area and at far field has been experimentally investigated. The hexagonal pattern and deflection in emission direction are observed in micro-PL of both V-GaN and V-Ag wafers, while in macro-PL such features are observed in the V-Ag wafer only. Numerical simulations and theoretical calculations reveal the origin of anisotropic and deflective emission, i.e., extraction of guided modes in GaN into air by diffraction. The higher contrast of anisotropy and deflection in emission from V-Ag compared to V-GaN indicates higher spatial coherence of emitted light, which have been proved in examinations of the spatial coherence length with angle-resolved PL. In addition, the temporal coherence of emission has been evaluated by analyzing macroscopic emitting spectra of three wafers. The results suggest that temporal coherence length of the V-Ag wafer is 8.1 µm, which is 1.4 times larger than that of the plain wafer.

The investigations in this article demonstrate the improvement in both spatial and temporal coherence of LED emission by SPs for the first time, and exhibit its capacity for manipulating the emission. The higher degree of coherence and controlling efficiency can be acquired by a stronger coupling between SPs and MQWs, which requires embedding plasmonic structures in close proximity to MQWs, in case where electrical performance is not of importance. The plasmonic nanostructures can be readily applied on micro-LEDs though here on regular-sized wafers. The concept can broaden the applications of LEDs into partially-coherent sources by plasmonic structures directly integrated on wafers, enabling more complex functionalities such as beam focusing, holography and many more.