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Abstract
The quantum dot (QD) light-emitting diode (LED) is a robust scheme for single photon source. However, the spontaneous emission of a QD LED has arbitrary directions and polarizations, which is disadvantage for photon collection and manipulation. We propose a QD LED integrated with an Ag grating and a phase-gradient metasurface. The circular patterned Ag grating is adopted to collimate the emission beam with right phase and improve its spatial coherence, therefore a phase-gradient metasurface can work for beam manipulation. The 10°, 20°, and 30° angle deflection as well as doughnut-pattern generation are demonstrated by numerical simulation. A small metasurface with the width of 6 µm can provide a collection efficiency of 25.9% at the deflection angle of 10°. Furthermore, only one single QD can be selected from a QD assembly with a low-density.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single photon source is essential for quantum communication and computing applications. The quantum dot (QD) in semiconductor light-emitting diode (LED) structure has been suggested as a robust scheme for single photon emission [1]. Owing to the high stability, large breakdown voltage, and wide range of emission spectrum, the III-nitride materials attract much attention. Recently, electrically pumped GaN-based QD LEDs have been demonstrated from green to red spectral range [1–3].
Generally, spontaneous emission of a QD exists in all directions and, thus, only a small portion can be collected. To improve the collection efficiency, metallic gratings have been proposed to compress the emission into a small volume and collimate the beam with a small divergence angle, as well as enhance the spontaneous radiation [4–7]. By optimizing the parameters, the metallic gratings can also be used as other applications, such as beam deflectors [8], focusing lenses [9], polarization controllers [10], polarization multiplexers [11], and wavelength sorters [12]. However, the manipulation of QD emission using metallic grating is limited, while the full control of the wavefront remains elusive.
To better control the emission characteristic of the output beam, a more precise control of the wavefront is required. Metasurfaces can provide full control of the wavefront and tailored the amplitude, phase, polarization, and frequency of light beams [13,14]. Since it can be fabricated in two-dimensional within the thickness at the subwavelength scale, it has been intensively studied to replace traditional bulky optical components for beam deflection, beam collimation, polarization control, vortex beam generation, hologram, and so on [13,14]. Owing to its compatible fabrication process, metasurfaces are promising for monolithic integration with light source devices. The metasurface works well with spatially coherent light source, e.g. laser [15], but requires special design when integrated with inherent light source, e.g. QD LED.
For a single QD, its spherical phase profile was considered and compensated when the metasurface was designed [16–19]. Using this simple but effective scheme, a polarization-dependent spherical mirror [16], a collimation mirror [17], a focusing lens [18], and a spin-state separator with arbitrary directions and high collimation [19] were presented. The disadvantage is that the collection efficiency is low if the distance between the QD and the metasurface is large, unless the diameter of the metasurface is large enough [18,19]. A good solution is to embed the QD inside the metasurface [20–22]. A single photon source carrying the spin angular momentum (SAM) or orbital angular momentum (OAM) was demonstrated by placing a QD at the center of a metasurface and the collection efficiency was significantly improved [20,22]. However, a radially polarized pump light beam is required and the electrical pump is not applicable.
For a QD assembly, metal metasurfaces using surface plasmon [23–25], dielectric metasurfaces using Mie resonance [26–28], Fano resonance [29], momentum matching [30–31], or Rashba effect [32], and those integrated with resonant cavity [33–37] were demonstrated to enhance the photoluminescent signal and/or manipulate the beam wavefront. However, one single QD can not be selected from the QD assembly in these schemes. This is inconvenient for a single photon source.
In this paper, we propose a new scheme for manipulation of QD emission, which is potential for electrically pumped GaN-based QD LED that has spontaneous emission with arbitrary directions and polarizations. The QD LED is integrated with an Ag grating and a phase-gradient metasurface. The emission of the QD can excite the surface plasmon with the aid of an Ag grating, which would collimate the emission beam with right phase and improve its spatial coherence. As a result, a phase-gradient metasurface can be integrated for beam manipulation. The emission beam can be deflected at arbitrary angles and manipulated to be doughnut-pattern. To the best of our knowledge, this is the first report that a phase-gradient metasurface can fully manipulate the originally incoherent light by improving its spatial coherence with the aid of an Ag grating. Besides the powerful control ability for the beam wavefront, our proposed scheme provides a collection efficiency of 25.9% (at the deflection angle of 10°) for a small-size metasurface with the width of 6 µm. Furthermore, the scheme can select only one single QD from a QD assembly with a low-density (e.g. 2 × 109 dots/cm2).
2. Model and methods
Figure 1 (a) shows the schematic structure of our proposed GaN-based QD LED with an Ag grating and a phase-gradient metasurface. The QDs are sparsely distributed in the GaN layer. Generally, the emission direction and polarization are arbitrary in an electrically pumped GaN-based QD LED. In order to improve the spatial coherence of the QD emission, a circular patterned Ag grating is placed at the bottom of GaN layer. If the distance between the QD and Ag grating is small, such as 10 nm, the surface plasmon at the interface between the GaN layer and Ag grating can be excited. The surface plasmon spreads along the horizontal direction. With optimized geometrical parameters for Ag grating, the surface plasmon can be decoupled with right phase to produce a narrow and collimated light beam by constructive interference [4]. The collimated light beam passes through the SiO2 spacer and enters the TiO2 metasurface. The SiO2 spacer is a low refractive-index substrate for the metasurface. The TiO2 dielectric metasurface gives the phase gradient and manipulates the beam wavefront. A possible fabrication process can be described as follows. Firstly, a normal GaN-based QD LED is prepared on the sapphire substrate [1–3]. Secondly, an Ag grating is fabricated on top of the p-GaN layer, the original sapphire substrate is removed, and the n-GaN layer is polished and thinned [38]. Finally, the SiO2 spacer is deposited and the TiO2 metasurface is patterned.
Fig. 1. Schematic structure of GaN-based QD LED with an Ag grating and a TiO2 phase-gradient metasurface. (a) 3D model, (b) cross-section view, and (c) top view. The blue dots in (b) and (c) are QDs. The black dashed boxes in (b) and (c) describe the supercells in metasurface.
The model was investigated by a three-dimensional finite-difference time domain (3D FDTD) method using a commercial software (Lumerical 2019b FDTD Solver). Taking a phase-gradient metasurface with the supercell containing four unit cells as an example, Figs. 1 (b) and (c) show the cross-section view and top view, respectively, and give the structural parameters in numerical model. A QD was placed in a GaN layer with the thickness of hGaN, which was set to be 600 nm. The QD was modeled as an electric dipole with three orthogonal polarization directions (x, y, and z direction) and the working wavelength, λ, was 520 nm. The distance between the QD and the grating tooth was h, which was set to be 10 nm unless specifically stated. The Ag grating was situated on a thick Ag film which can reflect light or prevent the leaking of surface plasmon. The thickness, hAg, was set to be 120 nm, while the width, dg, and the height, hg, of the grating tooth, as well as the grating period, pg, should be optimized. The thickness of the SiO2 spacer was hSiO2, of which the initial value was set to be 450 nm and would be optimized if required. The metasurface consisted of arrayed TiO2 nanorods, in which the height and the diameter of the nanorod were L and D, respectively, as well as the period was P along x-direction and 2P along y-direction. Four nanorods with gradually changing diameter constituted a grouped supercell to produce a 2π phase gradient. A monitor was placed below the metasurface to get the input light field and power, while another one was placed above the metasurface to get the output light field and power, from which the far field distribution can be calculated. Because the electric dipole was launched three times and each time it was linearly polarized in one of the three orthogonal directions, the calculated results were averaged for final presentation. The lengths of the simulation domain in the x and y direction were 10 µm. The perfect matched layer (PML) boundary was employed along all directions to avoid boundary reflection. The refractive indices of GaN and Ag were from the database in [39] and Lumerical software, respectively, while those of SiO2 and TiO2 were fixed values of 1.47 and 2.43, respectively.
3. Function demonstration
3.1 Beam deflection
The phase-gradient metasurface was designed as follows. Firstly, the phase shift and transmittance of a unit cell, in which a TiO2 nanorod with the height of L and the diameter of D was placed on a SiO2 substrate with the width of P along x-direction and the length of 2P along y-direction, were investigated. The L and P were fixed to be 800 nm and 260 nm, respectively, while the D was varied to adjust the phase shift. A large value of L was to guarantee the variation of D can cover a 2π phase shift, while the P was set to be λ / 2. The simulation results show that the variation of D within the range from 50 to 185 nm can cover a 2π phase shift and possess a high transmittance. Secondly, the appropriate unit cells were selected to get a beam deflecting metasurface. According to the generalized Snell’s law, the light beam passed through a metasurface can be deflected at an arbitrary angle, θ, which is described as [40]
Fig. 2. (a) Schematic structures of phase-gradient metasurface with SiO2 and GaN layer. (b) Far field patterns of the output beam when the light source is a Gaussian beam with two orthogonal polarization directions. (I), (II), and (III) are the cases for 10°, 20°, and 30° angle deflection, respectively. The black dashed boxes in (a) describe the supercells in metasurface.
However, if the Gaussian beam is replaced by a QD, the output beam can not be deflected by the metasurface. Figure 3 (a-I) gives the schematic structure of a GaN-based QD LED with the phase-gradient metasurface designed in Fig. 2 (a-II). The electric dipole located at the center of the GaN layer in x and y directions, while the distance between the electric dipole and the bottom boundary of the GaN layer was 10 nm. Figures 3 (b-I) and (c-I) present the far field pattern and its polar plot, respectively. It is shown that the light intensity distribution is chaotic and does not follow the function of 20° angle deflection as shown in Fig. 2 (b-II). For comparison, a normal GaN-based QD LED without metasurface was also investigated. Figure 3 (a-II) gives its schematic structure and Figs. 3 (b-II) and (c-II) present the far field patterns. It is demonstrated that the output beam follows the Lambertian distribution, which is the typical far field pattern of random light sources. The ripple in the envelope of Lambertian distribution comes from the interference between forward lights and reflected lights. Furthermore, a GaN-based QD LED with the designed phase-gradient metasurface and an Ag film was also investigated for comparison. As shown in Fig. 3 (a-III), the interface between the Ag film and GaN layer is smooth. Figures 3 (b-III) and (c-III) present the far field patterns, which show that the light intensity distribution is chaotic. This implies the Fabry-Perot resonance between the metasurface and Ag film can not make the output beam to be deflected.
Fig. 3. (a) Schematic structure of GaN-based QD LEDs. (b) Far field patterns and (c) their polar plots when the light source is an electric dipole with three orthogonal polarization directions. (I), (II), and (III) are GaN-based QD LED (I) with metasurface, (II) without metasurface, and (III) with metasurface and Ag film, respectively. The white dashed lines in (b) describe the position for polar plots.
To make the phase-gradient metasurface works for QD, an optimized Ag grating was proposed to improve the spatial coherence, namely, to collimate the beam with right phase before entering the metasurface. Figure 4 (a) gives the schematic structures of GaN-based QD LED with an Ag grating and a phase-gradient metasurface for 10°, 20°, and 30° angle deflection. Note that an independent design of the Ag grating could collimate the beam in the GaN layer without a metasurface but would loss its ability after integrating with the phase-gradient metasurface designed in Fig. 2. The reason may be ascribed to the reflected lights from the GaN/SiO2 interface and the metasurface [34]. Therefore, the optimization of the Ag grating must be carried out based on the Ag/GaN/SiO2/metasurface structure shown in Fig. 4 (a). After optimization, the width and height of the grating tooth were set to be dg = 50 nm and hg = 120 nm, respectively, and the grating period was set to be pg = 330 nm. Figure 4 (b) presents the far field patterns of the input beam before entering the metasurface. It is demonstrated that most part of the input beam is well collimated. As a result, the output beam can be manipulated by the phase-gradient metasurface. The far field patterns of the output beam are presented in Figs. 4 (c) and (d). It is shown that the output beam can be deflected at pre-designed angles and the deflection efficiencies are 26.5%, 20.6%, and 17.4% for 10°, 20°, and 30° angle deflection, respectively. The deflection efficiency is defined as the fraction of optical power collected within the angle of θ ± 10° with respect to the total transmitted optical power, where θ is the deflection angle.
Fig. 4. (a) Schematic structures of GaN-based QD LED with an Ag grating and a phase-gradient metasurface. (b, c) Far field patterns and (d) their polar plots for (b, d) the input beam and (c, d) output beam of the metasurface, when the light source is an electric dipole with three orthogonal polarization directions. (I), (II), and (III) are the cases for 10°, 20°, and 30° angle deflection, respectively. The black dashed boxes in (a) describe the supercells in metasurface. The white dashed lines in (b) and (c) describe the position for polar plots.
3.2 Doughnut-pattern beam generation
To further demonstrate the manipulating ability of the QD emission using the proposed scheme with an Ag grating and a phase-gradient metasurface, a doughnut-pattern beam was generated. The same Ag grating designed in Fig. 4 was used and the phase-gradient metasurface was redesigned, which is shown in Fig. 5 (a). From the top view, the metasurface was divided into six sectors along the azimuth direction. The diameters of the TiO2 nanorod within a sector were the same, but gradually decreased in different sectors along the counter-clockwise direction to cover a 2π phase shift. To make the phase gradient linear, the diameters of the TiO2 nanorod in the six sectors were set to be [180, 150, 140, 135, 85, 50] nm. All TiO2 nanorods were distributed on concentric circles, in which the diameter of these circles was set to be 2P, 4P, 6P, …, and so on. Figures 5 (b) and (c) present the far field patterns when the light source is a Gaussian beam and an electric dipole, respectively. It is demonstrated that the output beam can be manipulated to be doughnut-pattern. The nonuniformity of the doughnut-pattern may be ascribed to the different transmittance of the unit cells [34]. Following [41], the mode purities of the doughnut pattern are calculated as 94.0% and 82.0% for the Gaussian source and electric dipole source, respectively.
Fig. 5. (a) Top-view of the phase-gradient metasurface for doughnut-pattern beam generation. Far field patterns when the light source is (b) a Gaussian beam with two orthogonal polarization directions or (c) an electric dipole with three orthogonal polarization directions.
4. Discussion
4.1 Collection efficiency
The collection efficiency is defined as the fraction of optical power collected within the angle of θ ± 10° with respect to the source power, where θ is the deflection angle. Thus, the collection efficiency is the product of the deflection efficiency and the transmittance. Figure 6 gives the deflection efficiency, transmittance, and collection efficiency of the QD LEDs with the phase-gradient metasurface for 10°, 20°, and 30° angle deflection. It is shown that the peak wavelengths are around 520 nm, which is the designed working wavelength. The transmittance of the three QD LEDs at 520 nm are around 90%. This is a significant enhancement, compared to the low transmittance of 4% in the normal QD LED shown in Fig. 3 (a-II). The reason can be explained by the enhancement of the light extraction efficiency, which comes from the beam collimation, and by the enhancement of the spontaneous radiation, which comes from the Purcell effect [4–6]. As a result, the values of the collection efficiency are almost the same as those of the deflection efficiency. The collection efficiencies at 520 nm are 24.2%, 18.7%, and 15.2% for 10°, 20°, and 30° angle deflection, respectively.
Fig. 6. (a) Deflection efficiency, (b) transmittance, and (c) collection efficiency of GaN-based QD LEDs for 10°, 20°, and 30° angle deflection, when the light source is an electric dipole with three orthogonal polarization directions.
Although the Purcell factor is large, the transmittance shown in Fig. 6 (b) is still less than 1. This is because a large amount of power is lost. In the present configuration, the QD decay channel contains four parts: direct photon emission, surface plasmon, waveguide mode, and nonradiative decay; besides, the surface plasmon dissipation has three parts: scattering to photons, absorption to heat, and residual surface plasmon [22,42]. Following [22,42], the coupling efficiency of different decay channels in the QD LEDs for 10°, 20°, and 30° angle deflection were estimated and listed in Table 1. It is shown that less than a quarter of the total power generated from QD would contribute the photon emission; more specially, the contribution is less than 8% for the z-polarized electric dipole. Note that, for all the photon emission, only those from surface plasmon scattering can be manipulated by our designed metasurfaces, while those from direct emission can not.
Table 1. The coupling efficiency of different decay channels in our GaN-based QD LEDsa
As mentioned before, an advantage of the metallic grating is to compress the emission into a small volume. This implies that the size of the GaN-based QD LED can be reduced, which is beneficial for high-density integration. Figure 7 (a) shows the simulation model of a small QD LED with an Ag grating and a phase-gradient metasurface, of which the lengths in the x and y direction are 6 µm. Taking the case for 10° angle deflection as an example, the far filed patterns for the input beam and output beam of the metasurface are presented in Figs. 7 (b) and (c), respectively. Compared with those in Figs. 4 (b-I) and (c-I), the patterns in Figs. 7 (b) and (c) have less stray lights. This may be because the light that does not meet the collimation condition has a larger possibility to escape the smaller QD LED from the side wall. Therefore, more portion of the input beam are collimated in the center and more portion of the output beam are deflected at desired angles. The deflection efficiency for the three small QD LEDs at 520 nm can be improved to be 31.0%, 23.9%, and 20.6%, respectively. However, for the same reason, the transmittances decrease when the size of the QD LEDs become small. As a result, the collection efficiency for the three small QD LEDs at 520 nm are 25.9%, 18.0%, and 15.5% for 10°, 20°, and 30° angle deflection, respectively, which are almost the same as those in Fig. 6 for the larger QD LEDs.
Fig. 7. Small GaN-based QD LED with an Ag grating and a phase-gradient metasurface, of which the lengths in the x and y direction are 6 µm. (a) Simulation model. (b, c) Far filed patterns for (b) the input beam and (c) output beam of the metasurface for 10° angle deflection. (d) Deflection efficiency, (e) transmittance, and (f) collection efficiency of the small LEDs for 10°, 20°, and 30° angle deflection. The light source is an electric dipole with three orthogonal polarization directions.
The collection efficiency can be further improved by optimizing the thickness of SiO2 spacer. Taking the case for 20° angle deflection as an example, the thickness of SiO2 spacer was set to be hSiO2 = i • λ / nSiO2 / 4, where nSiO2 was the refractive index of SiO2 material and i was [0, 1, 2, …, 12]. As shown in Fig. 8, the collection efficiency oscillates when hSiO2 varies. The maximum efficiency appears when i is an odd number, while the minimum efficiency appears when i is an even number. This demonstrates again that the reflected lights from the GaN/SiO2 interface and the metasurface can alter the performance. With the increase of hSiO2, the maximum efficiency first increases and then decreases. The highest collection efficiency located at hSiO2 = 265 nm is 24.8%, which gets 32.6% improvement compared to the initial thickness of hSiO2 = 450 nm shown in Fig. 6 (c).
Fig. 8. The collection efficiency of GaN-based QD LEDs with different thickness of SiO2 spacer for 20° angle deflection. For circle markers, hSiO2 = i • λ / nSiO2 / 4, where nSiO2 is the refractive index of SiO2 material and i is [0, 1, 2, …, 12]. For the square marker, hSiO2 = 450 nm. The light source is an electric dipole with three orthogonal polarization directions.
4.2 Selection for only one single QD
The manipulation performance is sensitive to the QD location, which implies one single QD can be precisely selected and manipulated. Taking the case for 20° angle deflection as an example, the location shift in x, y, and z direction were set to be l = [0, 10, 25, 40, 55, 70, 80, 90, 100, 330] nm, w = [0,10, 25, 40, 55, 70, 80, 90, 100, 330] nm, and h = [5, 10, 20, 50, 75, 90, 100] nm. Note that the value of (l, w, h) = (0, 0, 10) nm is the initial location for QD in Section 3. The polar plots of far field pattern as well as their maximum intensities are presented in Fig. 9.
Fig. 9. (a) Schematic diagrams of location shift in (I) x, (II) y, and (III) z directions. (b) The polar plot of far field patterns and (c) their maximum intensities for the case of 20° angle deflection. The light source is an electric dipole with three orthogonal polarization directions.
In the horizontal plane, the deflection function keeps working when the l (or w) is no larger than 70 nm. When the l (or w) is 80 nm or larger, there is a large amount of scattered light. In the case of l (or w) = 330 nm, in which the electric dipole is right above a grating tooth, the deflection function still loses its ability. This means that the reason for the failure of the deflection function is the deviation of QD from the center of Ag grating, which implies the failure of the constructive interference of the surface plasmon modes, rather than the long distance between the QD and the Ag grating, which implies the weakened surface plasmon effect. With the increasing of l or w, the light intensity drops quickly. As shown in Figs. 9 (c-I) and (c-II), the full-width at half-maxima (FWHM) of the maximum intensity in x or y direction is estimated to be about 25 nm. This make sure that only one single QD can be selected and manipulated in a low-density (e.g. 2 × 109 dots/cm2 [1]) QD assembly. It is convenient for a single photon source. On the other hand, this is a sufficient fabrication tolerance based on fluorescence images and standard electro-beam lithography [20,22].
Besides, in the vertical direction, the h should be no larger than 90 nm. When the h is 100 nm, there is a large amount of scattered light although the deflection still occurs. This means that the weakened surface plasmon would reduce the deflection. With the increasing of h, the light intensity decreases. As shown in Figs. 9 (c-III), the FWHM of the maximum intensity in z direction is estimated to be about 75 nm.
5. Conclusion
To fully manipulate the beam wavefront of a QD emission with arbitrary directions and polarizations, a circular patterned Ag grating was adopted to collimate the emission beam with right phase and improve its spatial coherence, therefore a phase-gradient metasurface can work for beam manipulation. The GaN-based QD LEDs with an Ag grating and a phase-gradient metasurface for 10°, 20°, and 30° angle deflection as well as doughnut-pattern generation were demonstrated by 3D FDTD simulation. Owing to the advantage of the metallic grating that can compress the emission into a small volume, small GaN-based QD LEDs with the width of 6 µm can provide the collection efficiency of 25.9%, 18.0%, and 15.5% for 10°, 20°, and 30° angle deflection, respectively. The collection efficiency can be further improved by optimizing the thickness of SiO2 spacer. Owing to the sensitivity of the QD location, only one single QD can be selected from a QD assembly with a low-density for beam wavefront manipulation. Our proposed scheme is a potential solution for single photon source from electrically pumped GaN-based QD LED that has spontaneous emission with arbitrary directions and polarizations.
Funding
Natural Science Foundation of Guangdong Province (2018A030310373); open foundation of Guangxi Key Laboratory of Processing for Non-ferrous Metals and Featured Materials, Guangxi University (2021GXYSOF08).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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