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Abstract
Near-eye displays are widely recognized as a groundbreaking technological advancement with the potential to significantly impact daily life. Within the realm of near-eye displays, micro-LEDs have emerged as a highly promising technology owing to their exceptional optical performance, compact form factor, and low power consumption. However, a notable challenge in integrating micro-LEDs into near-eye displays is the efficient light collimation across a wide spectrum range. In this paper, we propose what we believe to be a novel design of a broadband beam collimation metasurface for full-color micro-LEDs by harnessing wavefront phase modulation based on Huygens’ principle. Our results demonstrate a substantial reduction in the full width at half maximum (FWHM) angles, achieving a reduction to 1/10, 1/10, and 1/20 for red, green, and blue micro-LEDs compared to those without the metasurface, which is the best collimation result as far as we know. The central light intensity increases by 24.60, 36.49, and 42.15 times. Furthermore, the significant enhancement in the light energy within ±10° is achieved, with the respective multiplication factors of 14.16, 15.60, and 13.00. This metasurface has the potential to revolutionize the field by enabling high-performance, compact, and lightweight micro-LED displays, with applications in near-eye displays, micro-projectors, and beyond.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Near-eye display [1–4], also known as a head-mounted display, is a display system placed within the non-visual distance of the human eye [5–7]. It creates a virtual image and reproduces virtual scenes, making it crucial for immersive augmented reality (AR) and virtual reality (VR) experiences [8–10]. Since the concept of the “metaverse” was introduced in 2021, near-eye display devices have been seen as a gateway to the metaverse, leading to a significant surge in both academia and industry [11].
Near-eye display devices require higher brightness, resolution and contrast than traditional display devices such as televisions. On the one hand, AR devices need to work in natural light to ensure that images can be seen in direct sunlight, so higher brightness is required. On the other hand, due to the huge optical loss of pancake lenses in VR and the poor waveguide efficiency of AR [12,13], higher brightness is required from the image source device. Among various display technologies such as liquid crystal display (LCD), liquid crystal on silicon display (LCoS), digital light processing display (DLP), and laser beam scanning (LBS), micro-LED [14–17] offers significant advantages and is considered the ideal technology for near-eye displays. Micro-LED display technology has been used in near-eye display [18]. However, micro-LED emits light in a Lambertian distribution with a wide divergence angle higher than ± 60° [19]. In a near-eye display system, only light emitted in the near-normal direction can be effectively utilized [20], resulting in low utilization efficiency. Therefore, the common approach is to collimate the micro-LED light and couple it into the near-eye display system.
Currently, there are two primary methods for achieving beam collimation of micro-LEDs. One approach involves the use of lenses based on the principles of geometric optics [21,22]. A hemispherical lens was utilized to collimate 8-micron micro-LEDs, improving the coupling efficiency [23]. The resulting structure achieved a 62% intensity distribution within ± 20°. However, the designed hemispherical lens was much larger than the size of the micro-LEDs, making it unsuitable for near-eye display applications. In 2023, we presented a more compact structure using a miniature beam-shaping lens array [24], which had a diameter of 14.1 microns and a divergence angle of ± 20°, offering smaller size and higher collimation ability compared to the previous approach. Apart from the principles of geometric optics, the other approach involves using resonant cavities incorporated into micro-LEDs for the light collimation, reducing the divergence angle to ± 39.35° [25]. The resonant cavity structure well matched the size of the micro-LEDs, solving the problem of large pixel pitch. The material of the resonant cavity was further optimized with the reduced divergence angle to ± 28.2° [26]. However, the collimation effect of the resonant cavity is slightly inferior to that of the lens. Therefore, there still is an urgent need for a collimation scheme that offers both excellent collimation performance and a miniaturized size for full-color micro-LEDs.
Metasurfaces [27–30] are a novel type of artificial structured surface capable of precise light manipulation. Composed of periodic similar structures, metasurfaces can control the phase, amplitude, and polarization of light by adjusting the parameters of the unit structure [31–33]. With a thickness ranging from several hundred nanometers to several micrometers, metasurfaces have a flat structure and are easy to integrate, making them a promising optical element for controlling visible light [34–36]. The integration of metasurfaces into micro-LED structures maximizes their compatibility with semiconductor processes. [37,38]. As far as we know, the broadband beam collimation metasurface for full-color micro-LEDs has not been thoroughly explored.
In this paper, we propose a broadband beam collimation metasurface for full-color micro-LEDs, which exhibits excellent collimation performance. The metasurface is composed of a cylindrical periodic structure array with high symmetry and minimal susceptibility to the polarization modes of the incident light. Using the FDTD method, the performance of the micro-LEDs with and without the metasurface can be thoroughly analyzed and compared. This thin planar structure offers excellent performance, making it suitable for near-eye display, micro-projectors, and other related applications.
2. Principle
The broadband beam collimation metasurface follows the Huygens-Fresnel principle [39–42] to control the phase distribution of the output light from the micro-LED. Figure 1(a) illustrates the principle of wavefront phase modulation based on Huygens’ principle for a conventional lens or a metasurface to achieve beam collimation, which considers each point of the incident light passing through as an independent secondary wave source. The unit structure of the metasurface introduces a specially designed abrupt phase change in the secondary wave source [29], resulting in the desired wavefront and altering the direction of light propagation. This allows for the achievement of beam collimation.
Fig. 1. (a) Schematic of a conventional lens or a metasurface to achieve beam collimation. (b) Traditional micro-LED light output. (c) Schematic of the beam collimation metasurface of micro-LED.
The abrupt phase φ introduced by the metasurface unit structure can be expressed as follows:
where, φ represents the abrupt phase introduced by the metasurface unit structure, k represents the wave number, d represents the period of the metasurface unit structure, and θ represents the angle between the incident light and the normal direction. Therefore, the magnitude of the abrupt phase φ introduced by the metasurface unit structure is determined by the wave number k, the period d of metasurface, and the angle θ between the incident light and the normal direction. Here, k is defined as k = 2π/λ, where λ represents the wavelength of the incident light on the metasurface.The outgoing light of traditional micro-LEDs typically exhibits a Lambertian distribution with a full width at half maximum (FWHM) angle of larger than ± 60°, as shown in Fig. 1(b). This high degree of divergence in the outgoing light is unfavorable for its application in near-eye display systems. To overcome this limitation, Fig. 1(c) illustrates a schematic diagram of utilizing a metasurface to collimate the outgoing light of a micro-LED. The locations marked as a1 to a5 represent points where the metasurface unit structure introduces abrupt phase changes. These introduced phase changes, referred to as compensating phases, are complementary to the original phase.
By passing through the metasurface, the equiphase surface becomes parallel to the outgoing light surface of the micro-LED, resulting in the beam collimation. Table 1 shows the relationship between the original phase and the compensating phase introduced by the metasurface. Corresponding original phase values are assigned to points a1 to a5, and the metasurface unit determines the corresponding structural parameters based on these values to introduce the appropriate compensating phases. As a result, the outgoing light phases become consistent, successfully achieving the collimation.
Table 1. Phase compensation correspondence tablea
The compensated phase matrix, denoted as φC, is given by:
3. Simulation
Finite difference time domain (FDTD) method was employed to simulate the unit structure of the metasurface and the micro-LED’s structure. A comparison was analyzed between the micro-LED structure with and without the designed metasurface.
3.1 Parameter optimization
The metasurface unit in this paper consists of a cylindrical structure made of TiO2 with refractive indices of 2.13, 2.16, and 2.24 in the red (λ=650 nm), green (λ=550 nm), and blue (λ=450 nm), respectively. The compensation phase can be adjusted by varying the radius of the cylinder.
As an artificial sub-wavelength structure [31], the metasurface requires a period smaller than the wavelength of the incident light. Thus, the designed unit structure is set with period parameters of 0.5λ, 0.7λ, and 0.9λ. Additionally, considering the limitations of processing technology in supporting unit structures with high depth-to-width ratios, the height parameter range is set from 100 nm to 1000 nm, and the radius parameter range is set from 0.15×period to 0.5×period. By scanning the set period, height, and radius parameters, the relationship between the metasurface unit structure and the transmittance / phase under different parameters is obtained for the three-primary-color wavebands.
Figure 2 illustrates the effects of changing the period, height, and radius on the compensation phase for the three-primary-color wavebands. Specifically, Figs. 2(a)-(c) display the variation of the compensation phase introduced by the metasurface unit structure with height and radius when the period is 0.5λ, 0.7λ, and 0.9λ, respectively, under the condition of red (λ=650 nm). Figures 2(d)-(f) and 2(g)-(i) respectively demonstrate the phase distribution for green (λ=550 nm) and blue (λ=450 nm) conditions, while varying the radius from 0.15×period to 0.5×period.
Fig. 2. The compensation phase varying with radius and height under different wavelength period conditions. (Radius range: 0.15×period to 0.5×period)
To effectively adjust the outgoing light field distribution of the micro-LED, it is essential for the compensation phase introduced by the metasurface unit structure to cover the range of 0∼2π [39]. Hence, from the aforementioned data, the structural parameters that satisfy this requirement are identified. Specifically, the period and height parameters that result in a compensation phase covering 0∼2π are determined, and the average transmittance is calculated for different radii under these conditions. The average transmittance represents the mean transmittance of the metasurface unit structure, which has varying radius parameters ranging from 0.15×period to 0.5×period.
From the data where the compensated phase covers 0∼2π, structural parameters with the highest average transmittance are selected, as presented in Table 2. For the red (R, λ=650 nm) wavelength band, the selected period is 585 nm (0.9λ) with a corresponding height of 800 nm. For the green (G, λ=550 nm) wavelength band, the chosen period is 495 nm (0.9λ) with a height of 700 nm. For the blue (B, λ=450 nm) wavelength band, the selected period is 405 nm (0.9λ) with a height of 400 nm. The spectra of the three-primary-color micro-LEDs are shown in Fig. 3(a). Under these selected structure parameters, the compensation phase curve with respect to the radius is depicted in Fig. 3(b).
Fig. 3. (a) The spectra of the three-primary-color micro-LEDs, and (b) the change of the compensation phase with the radius. (Radius range: 0.15×period to 0.5×period)
Table 2. The structure parameters at three-primary-color wavebands.
3.2 Model establishment
Figure 4(a) and 4(b) illustrates the comparison between the traditional micro-LED structure on the left side and the micro-LED structure with the designed metasurface on the right side. The traditional micro-LED [43] structure comprises a 200 nm metal reflection layer (Ag) at the bottom, followed by a 200 nm P-GaN layer, a 200 nm multiple quantum wells (MQWs) layer, and a 3 µm N-GaN layer. In addition, the chip geometry of the three-primary-color micro-LEDs is a square with side length of 11.7 µm for red, 9.9 µm for green and 8.1 µm for blue, respectively. Figure 4(c) shows the schematic diagram of the micro-LED structure for FDTD simulation. The original phase of the light at corresponding points is measured to obtain the original phase matrix φO. Based on this, the compensating phase for the corresponding points is determined, resulting in the corresponding compensating phase matrix φC. This allows us to determine the radius value for the unit structure of the cylindrical metasurface. To represent the light source generated by electron-hole recombination, an electric dipole source is placed in the MQW layer [44].
Fig. 4. (a)(b) The schematic diagram of the traditional micro-LED structure and the micro-LED structure with the designed metasurface. (c) Schematic diagram of the micro-LED structure for FDTD simulation.
3.3 Results and discussion
The comparison between the micro-LEDs with and without the metasurface involves the analysis of three key aspects: the phase distribution, the far-field energy distribution, and the angular distribution. Figure 5 shows the phase distributions, where Figs. 5(a)-(c) is for traditional three-primary-color micro-LEDs without metasurface, while Figs. 5(d)-(f) represent the micro-LEDs with the designed metasurface. In traditional micro-LEDs, the phase distribution gradually changes from the center to both sides in the range of 0 to 2π. This change is cyclic and repeated, resulting in equiphase surface showing a semi-elliptical shape overall. Consequently, the emitted light exhibits a Lambertian distribution after propagating from the vertical equiphase surface. However, the addition of the metasurface structure for phase compensation leads to significant changes in the phase distribution of micro-LEDs. In most regions, the phase distribution shows a horizontal distribution state. As a result, the emitted light experiences vertical emission from the emitting surface in the direction perpendicular to the vertical equiphase surface propagation, achieving collimated emission for micro-LEDs.
Fig. 5. The phase distribution of the three-primary-color micro-LEDs. (a)-(c) Without the metasurface, (d)-(f) With the metasurface.
Figures 6(a)-(c) represent the normalized far-field energy distribution of the three-primary-color micro-LEDs without metasurface, while Figs. 6(d)-(f) is the result after incorporating the metasurface structure. It is clear that without the metasurface, the far-field energy distribution of the micro-LEDs exhibits a relatively uniform pattern across all angles, with a significant amount of light emitting at large angles. This results in low energy utilization in the near-normal direction and also causes pixel crosstalk. However, upon adding the metasurface, the emitting light energy becomes predominantly concentrated within a small angle range with a rotational angle of 10° from the normal direction.
Fig. 6. Normalized far-field energy distribution of the three-primary-color micro-LEDs, (a)-(c) without the metasurface, (d)-(f) with the metasurface. (g)-(i) Intensity distribution of the vertical cross section of the three-primary-color micro-LEDs with and without the metasurface.
Table 3 provides further insight by showing the proportion of far-field energy distribution for the three-primary-color micro-LEDs within different angles. Without the metasurface structure, the proportion of energy distribution is relatively low within the rotational angles of 10°, 20°, and 30° from the normal direction. However, the addition of the metasurface brings a significant improvement, indicating enhanced control and confinement of light within the desired angles.
Table 3. The proportion of far-field energy distribution for the three-primary-color micro-LEDs within different angles.
Figures 6(g)-(i) illustrate the intensity distribution of the vertical cross section of the three-primary-color micro-LEDs with and without the metasurface. The red curves represent the results without the metasurface, while the blue curves are after integrating the metasurface. It is evident that the angular distribution of light intensity for the conventional micro-LEDs exhibits a Lambertian radiation pattern. Here, the FWHM angle is introduced to define the angular range over which the intensity of light is at the half of its maximum value. Upon adding the metasurface, a notable reduction in the FWHM angle is observed. Additionally, the central light intensity of the three-primary-color micro-LEDs is significantly enhanced after incorporating the metasurface, thereby further boosting the normal brightness of the micro-LEDs. Table 4 reflects the collimation effect of the three-primary-color micro-LEDs with the metasurface, where the “Multiplication factor of the central light intensity (Normal direction)” refers to the ratio of the central light intensity after adding the metasurface to the central light intensity of a micro-LED without the metasurface. The micro-LEDs, equipped with the designed metasurface, demonstrate the capability to achieve collimated emission over a broad wavelength range. This highlights outstanding collimation effects and a substantial improvement in brightness in the normal direction of the micro-LEDs.
Table 4. The collimation effect of the three-primary-color micro-LEDs with the metasurface.
3.4 Multidipole simulation and metasurface partitioning
A single electric dipole is used to analyze the emission characteristics of the MQWs layer of a micro-LED with a small size. However, as the size of the micro-LED increases, the electron-hole distribution within the MQWs layer becomes more dispersed and complex. In such cases, using multiple electric dipoles can effectively capture this dispersed distribution and provide a more accurate simulation for the emission behavior [44,45]. This realizes a more comprehensive representation of the optical properties of the micro-LEDs at larger sizes.
Multidipoles are used to simulate electron-hole pair recombination in MQWs layer. Figure 7(a) shows a schematic of a micro-LED model with a 4 × 4 electric dipole arrangement. The simulation process is modeled using a single dipole at a time, and finally the simulation results of the dipoles placed in different positions are superimposed together. The three-primary-color micro-LEDs are simulated from 1 × 1 dipole to 16 × 16 dipoles, that is, 1 to 256 dipoles in total. The variation curves of FWHM angle and far-field energy of the three-primary-color micro-LEDs with dipoles are shown in Fig. 7(b) and 7(c). Notably, the FWHM angle slightly fluctuates with multiple electric dipoles, and the far-field energy remains relatively constant when the number of electric dipoles is equal to or greater than 4. Therefore, the 4 × 4 arrangement of electric dipoles with a total number of 16 dipoles is used for further simulation. Figures 7(d)-(f) depicts the normalized far-field energy distribution of these micro-LEDs. The far-field distribution achieved through the multi-electric dipole simulation more closely resembles a Lambertian distribution. Figure 7(h) shows the normalized vertical cross-section angle distribution of the three-primary-color micro-LEDs. In addition, the angular color shift caused by the mismatch of spatial light distribution of three-primary-color micro-LEDs is considered [46]. Under CIE 1976, 10 color points are used, and their serial numbers and positions are shown in Fig. 7(i). Figure 7(j) shows the angular color shift of the three-primary-color micro-LEDs with 10° step size when the observation angle changes from 10° to 80° and the normal direction is 0°. Our previous work has provided a potential solution for this kind of angular color shift [19].
Fig. 7. (a) Schematic diagram of a multiple electric dipole model for micro-LEDs with different sizes. (b)(c) Variation curve of FWHM angle and far-field energy with the number of dipoles. (d)-(f) Normalized far-field energy distribution and (h) intensity distribution of the vertical cross section of the RGB micro-LEDs. (i)(j) the chromaticity diagram under CIE 1976.
When metasurface are not optimized, the far-field energy intensity distribution of the normalized three-primary-color micro-LEDs after simulation with 4 × 4 dipoles is shown in Figs. 8(a)-(c) and the vertical sectional angle distribution is shown in Fig. 8(d). Obviously, the metasurface no longer has the function of collimation. That is the reason why we further introduce metasurface partitioning to achieve the collimation. Figure 8(e) illustrates the micro-LED with 4 × 4 metasurface partitions. In the following simulations, the number of dipoles is 4 × 4 dipoles. Figure 8(f) represents the change of FWHM angle with the number of metasurface partitions, and Fig. 8(g) represents the change curve of multiplication coefficient of central light intensity between three-primary-color micro-LEDs with different metasurface partitions and those without the original metasurface. The results shown in Fig. 8(f) and 8(g) indicate that the collimation effect of the micro-LED with 4 × 4 metasurface partitions. When the metasurface partitions are 4 × 4, the far-field energy distribution after the normalization are shown in Figs. 8(h)-(j), and the vertical sectional angle distribution is shown in Fig. 8(k). The FWHM angle of the three-primary-color micro-LEDs is reduced to ±6.06°, ± 6.06°, and ±6.64° respectively, and the center light intensity is increased by 10.47,12.85, and 3.75 times, respectively. The angular color shift can be greatly reduced because the light is mostly focused within a narrow angle range.
Fig. 8. (a)-(c) Normalized far-field energy distribution and (d) intensity distribution of the vertical cross section of the RGB micro-LEDs. (e) Schematic diagram of the micro-LED with different metasurface partitions. (f)(g) Variation curve of FWHM angle and multiplication factor of the central light intensity with the number of metasurface partitions. (h)-(j) Normalized far-field energy distribution and (k) intensity distribution of the vertical cross section of the RGB micro-LEDs.
4. Conclusions
Conventional micro-LEDs with Lambertian intensity distribution pose challenges for near-eye displays due to low collection efficiency and high crosstalk. This paper presents a full-color micro-LED structure incorporating a broadband beam collimation metasurface. Through harnessing wavefront phase manipulation, the metasurface effectively compensates the phase of the output light from traditional micro-LEDs, resulting in significantly improved collimation. The designed metasurface reduces the FWHM angles in the 650 nm, 550 nm, and 450 nm wavelength bands from ±65.44°, ± 66.87°, ± 65.44° to ±6.64°, ± 6.64°, ± 3.17°, respectively, corresponding to a reduction of 1/10, 1/10, and 1/20 compared to the original values. After collimation, the light intensity in the normal direction is enhanced by 24.60, 36.49, and 42.15 times for the three-primary-color micro-LEDs. Additionally, the proportion of light concentration within a 10° angle from the normal direction increases from the original values of 2.93%, 2.45%, and 2.45% to 41.48%, 38.21%, and 31.86%, representing improvements with the respective multiplication factors of 14.16, 15.60, and 13.00. The proposed multiple electric dipole model and the metasurface partition approach facilitates improved collimation for larger micro-LEDs. For the case of metasurface partition, the FWHM angles of the three-primary-color micro-LEDs are reduced to ±6.06°, ± 6.06°, and ±6.64° respectively, and the center light intensity are increased by 10.47, 12.85, and 3.75 times, respectively. The innovative method simplifies the device structure, minimizes crosstalk, and optimizes light utilization for near-eye display applications. These promising features position the innovative micro-LED structure as a catalyst for advanced near-eye display technology.
Funding
National Key Research and Development Program of China (2022YFB3603503); National Natural Science Foundation of China (62005111, 62175032); The Natural Science Foundation of Fujian (2022J011124); Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2020ZZ111, 2021ZZ122).
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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