1. Introduction

Augmented reality (AR) and virtual reality (VR) allows the overlay or superimposition of digital contents onto naked eyes [1–3]. Nowadays, AR/VR represent state-of-the-art display technology, showing vast potentials for applications in navigation [4], education [5], military [6], and entertainment [7]. AR/VR depends mainly on near-eye display via optical module, in which the use of optical waveguides is crucial. Projected light is coupled into the waveguides under a certain angle, and then is coupled out in front of the eyes after propagating in the waveguide by total internal reflection (TIR) [8]. Optical waveguides are the most promising solution for minimizing the form factor, making the designs lightweight and compact, and thus enhancing the user experience. Among the optical waveguides, geometrical optical waveguide (GOW), commercially used by companies like Lumus [9], Epson [10], and Optinven [11], offers high resolution, full-color displays, wide FOV, and large EPD, but faces challenges like bulk, ghost stray rays and double imaging [12]. Compared to GOW, diffractive optical waveguides (DOW), utilizing surface-relief gratings (SRG), can easily achieve lightweight designs, provide a larger field of view (FOV), offer more uniform optical performance, and enhance integrability, making them the mainstream solution for current AR optical modules.

DOW with SRG, replies on the micro-/nanoscale gratings which can diffract the incident light within certain angle and allow light to meet the total internal reflection (TIR) conditions, enhancing the overall optical efficiency of the DOW. Traditional SRG (e.g., binary gratings) lack coupling efficiency in the desired direction inside the waveguide, due to their non-selective dispersion between negative and positive orders. Asymmetric gratings such as blazed gratings [13] and slanted gratings [14] can suppress diffraction from undesired orders and control the deflection of incident light at specific angles, improving TIR conditions. This results in more light being transmitted to the human eye, effectively reducing stray light and improving the coupling efficiency of incident light. In addition to the special morphology of the grating for SRGs in AR, the refractive index (RI) of the grating also plays a critical role. Based on Snell's law [15], materials with higher RI can guide more light with lower loss within their structure during TIR process. In conclusion, the slanted grating with high RI can enhance light coupling efficiency by controlling diffraction and reduce losses during light propagation in TIR.

The slanted grating with high RI still poses challenge for SRGs fabrication. Chan [16] and Jonathan [17] used focused ion beam (FIB) to fabricate uniformly slanted gratings, yet difficulty in maintaining ions beam over extended periods, the patterning process limited the device area within micro-scale. Victoria [18] opted for laser direct writing to produce slanted gratings, which can only pattern on photoresist-base materials. Wu et al. utilized glancing-angle deposition to fabricate large-area metal slanted gratings [19], and Levola et al. utilized tilted etching for the fabrication of slanted gratings [20]. Yet, they encountered challenges in etching the slanted gratings of high RI materials. UV-NIL has been widely reported as a simple and reliable method for preparing slanted gratings on UV-curable resin, and it have the advantage of low cost, fast and high resolution [21].

In this research, we propose a fabrication of slanted gratings with high RI, which is comprehensive process including design, fabrication of slanted gratings from nanoimprint mold and evaluation of its optical performance. By introducing high RI UV-curable resin, we successfully fabricate centimeter-scale region of high RI slanted gratings in DOW through UV-NIL. We investigate the mechanism of slanted gratings based on the Rigorous Coupled-Wave Analysis (RCWA) model [22] and optimize the structural dimensions through simulations. The effects of etching method, etching power, and mask thickness on the morphology of the slanted gratings are thoroughly discussed. Si mold with varying tilt angles and duty cycles are fabricated successfully. Using UV-NIL, we pattern a set of high RI slanted gratings onto the substrate surface in one step. Finally, we measure the actual optical efficiency of the DOW with imprinted slanted gratings, observing a significant improvement compared to binary grating DOWs. This process strategy also provides new insights for the industrialization of slanted grating DOWs.

2. Numerical simulation

The schematic diagram of the proposed DOW with slanted grating is depicted in Fig. 1(a). This layout consists of a waveguide with an in-putting and out-putting coupler. Image bearing light from the micro-display is initially collimated, and then deflected by the in-putting coupler with slanted grating along the phase gradient. Due to total internal reflection at the waveguide/air interface, light propagates between the in-putting and out-putting gratings inside the waveguide.

 

Fig. 1. (a) Schematic diagram of DOW based on unidirectional polarization coupling; (b) The diagram of a binary grating describes two directions of diffraction equally, (c) is the corresponding electric field distribution, (d) is the diffraction efficiency profile; (e) The diagram of a slanted grating shows diffraction enhancement in -1st order, (f) is corresponding electric field distribution, (g) is the diffraction efficiency.

Download Full Size | PDF

Figure 1(b) and (e) illustrate the optical diffraction of a binary grating and a slanted grating, respectively. The tilted angle, width, height, and period are determined by φ_grating, w, h, and d, while the filling factor is defined by f = w/d. With a binary grating, the light is equally diffracted to two directions due to the symmetrical structure according to diffraction theory, as the Fig. 1(c) shown. In the Simulation based on Rigorous Coupled Wave Analysis (RCWA) theory, the diffraction efficiency (average value of diffraction efficiency under TM mode and TE mode) of the -1st order and 1st order for binary grating is equal as 39% (Fig. 1(d)). Oppositely, the slanted grating breaks the symmetrical diffraction related to modulate the phase of the incident light, and the light can be deflected to a certain degree, greatly improving the directional coupling efficiency (from the Fig. 1(f)). As shown in Fig. 1(g), the slanted grating (leaning to the right side) shows an enhanced diffraction efficiency of 58% at -1st order, which is 32% higher than that of the binary grating.

The -1^st diffraction efficiency of slanted grating can be expressed as [23]:

Here, E(x), Ein represent the -1st and incident electric field. E(x) can be influenced by phase change. The phase change is described by structural parameters (filling factor f, tilted angle φ, height h) and material properties (neff), and can be expressed as [24]:

Here, x represents the spatial component, ?(x) is the phase expression, k = 2π/λ is the wave number, and neff is the effective RI of the slanted grating. The electric field components are denoted by E0 for the groove and E1 for the overall structure. According to the equation above, the grating structure plays a critical role in diffraction efficiency. Detailed calculations are conducted to determine the diffraction efficiency of the grating based on refractive index (RI), period, filling factor, and tilted angle. The RI of waveguides (glass) commonly used for AR imaging is approximately 1.9. As the Fig. 2(a) shown, the diffraction efficiency is maximized when the RI of the grating closely matches that of DOW, the diffraction efficiency can reach up to 66% when their RI gradient is -0.1 ± 0.1 (RI of grating is 1.8 ± 0.1). Increasing the effective RI of the slanted grating has several effects. It lengthens the light's propagation path and optimizes the phase matching of the -1st diffraction beam. As a result, this increases the beam's intensity and ensures minimal loss for the light coupled into the waveguide. As marked in Fig. 2(b), the slanted grating with a period of 550nm∼650 nm exhibits the highest -1st diffraction efficiency in the green light band, as thus the following study selected the period as 550 nm. According to Eq. (3), adjustment in the electric field distribution, impacting the diffraction efficiency of each order. From Fig. 2(c), a smaller filling factor indicates wider groove, reducing the phase modulation, which results in a significant enhancement of electric field in the groove, allowing light diffract to the 0th order coherently. Conversely, as the filling factor increases, the groove narrow, leading to a higher effective RI and electric field. The peak -1st order diffraction efficiency reaches 78.6% when the filling factor is 0.5. However, further increasing the filling factor results in light scattering, complicating interference between diffraction orders and reducing -1st diffraction efficiency. Figure 2(d) depicts the influence of tilted angle on diffraction efficiency. As the angle increase, -1st diffraction efficiency initially increase, peaks at 82.2% at a 70° angle. This occurs because the 70° angle slanted grating optimally phase-matches with incident light, satisfying the Bragg condition [25] for the path difference of -1st order diffracted light, thereby maxing efficiency. However, after increasing the tilted angle beyond 70°, interaction distance between the gratings will be reduced, which make diffraction efficiency decline. In addition to the tilted angle, the height also affects the phase-matching and optical path. As Fig. 2(e) shown, higher slanted grating lengthens the light propagation path within the groove, cumulatively altering phase and boosting -1st diffraction efficiency. The -1st efficiency reaches approximately 85.8% at a height of 510 nm.

 

Fig. 2. (a) The effect of RI and wavelength on diffraction efficiency; (b) The effect of period and wavelength on diffraction efficiency; (c), (d), (e) The relationship between diffraction efficiency and fill factor, tilt angle and height, respectively; (f) Light propagation diagram of a couple slanted grating with opposing direction.

Download Full Size | PDF

The out-putting coupler of the optical module aims to efficiently couple from DOW, which also needs to modulate the light phase and ensure the diffraction efficiency. Thus, the period, filling factor, and height of the slanted grating in out-putting must align with in in-putting. Maintaining the same period, filling factor, and height of the slanted grating ensures a consistent phase relationship of the light waves passing through DOWs, and help maintain phase stability of light, avoiding unnecessary phase distortion and energy loss, thereby maximizing out-putting efficiency. However, the tilted angle directly influences out-putting direction. The tilted direction of grating determines whether the coupling is through transmission mode or reflection mode. Transmission mode ensures that incident and coupled out light are on the same side, facilitating the layout design of optical module [13]. With an optimal angle optimizing diffraction direction and enhancing efficiency in transmission mode. Remarkably, we observed that when the out-coupling grating tilt direction opposes the in-coupling grating, leading to an increase in 1^st diffraction efficiency in transmission mode, the maximum 1^st diffraction efficiency (transmission mode) reaches 86.4% (Fig. 2(f)) with 60∼70° tilted angle. Based on the simulation discussion above, we examine the morphology parameters that can impact the diffraction effect of the grating, including RI, filling factor, tilted angle, and structural height.

3. Experiment section

3.1 Preparation of master nanoimprint mold

The chromium gratings used as etching mask are fabricated by UV-NIL and lift-off process [26]. The silicon wafer with the chromium grating is placed on a homemade stage that can be tilted to a precise angle. The tilted angle of the gratings can be adjusted by changing the stage angle. This relationship can be expressed as: φ_grating = 90°- α. Ion Beam Etching (IBE) [27] or inductively coupled plasma (ICP) [28] Etching are used to fabrication the slanted grating master nanoimprint mold with various tilted angles, respectively.

3.2 Preparation of slanted polymer gratings with high RI

To achieve cost-effective and large-scale production of the high RI slanted grating, nanoimprinting lithography has been chosen as the preferred replication technology. The working mold of the slanted grating is duplicated from the master nanoimprint mold by UV-NIL. A perfluorinated working mold resin (PL-R-UPM, PRINANO) is spin-coated onto the master mold coated with an anti-adhesive layer. A special flexible PET sheet coated with an adhesive layer to PL-R-UPM is pressed on the master mold by an air cushion press imprint machine (PL-S, PRINANO). The sample is exposed to UV radiation (365-nm wavelength, 500 mJ/cm2) while being pressurized at 0.1 MPa, resulting in the working mold after being released from the silicon master mold. To fabricate high RI slanted grating, the prepared high RI UV-curable resin (PL-R-DHR, PRINANO) is spin-coated onto a RI-matched glass wafer. Specific information about the high RI UV-curable resin can be found in the Supplement 1 S1. The nanoimprinting process is consistent with the replication of the working mold.

4. Result and discussion

4.1 Preparation of master nanoimprint mold

Chromium is used as the mask to resist the etching process (The fabrication for chromium mask can be found in the Supplement 1 S2). The Si-based materials can be easily etched by IBE [27] or ICP [28,29], with Ar gas and F-based gas, eg. CF₄, SF₆. The slanted gratings produced via IBE exhibited wavy shape (refer to the Supplement 1 S3), which can be caused by physical bombardment during etching, leading to lower selectivity. Compared to IBE etching, ICP etching offers better selectivity due to its reliance on chemical reactions. As Fig. 3(a) shown, slanted gratings are effectively etched using an ICP system with a tilted etching stage. However, the processing power, including RF power and Bias power, is carefully controlled to achieve the desired etching profile, and the ratio of 2, 1, 0.5 are adjusted, respectively. As illustrated in Fig. 3(b), excessive RF power enhances plasma density, which result in significant lateral etching at the upper regions of slanted grating, leading to a reduction in etch depth. While the power ratios were equal to 1, a mismatch between plasma momentum and density occurred, causing distortion in the slanted grating structure (Fig. 3(c)). Figure 3(d) illustrates effective control over the etched structure's shape and transverse etching following matched RF power and Bias power enhancement under the ratio to 0.5. Under the optimized process power, a slanted grating mold with tilt angle of 70° is fabricated, as illustrated in Fig. 3(i), (j). The tilt angle near the edge is 70.6°, near the center is 72.4°, which is a slight deviation from the target value of 70°. This is due to the height difference between the two ends is merely 3.4 mm for a processing surface of 10 mm x 10 mm. However, the machining error are acceptable, and deviations in the tilted angle have little impact on optical performance from test.

 

Fig. 3. (a) Diagram of the etching process using the titled stage; (b), (c) and (d) SEM image of the etching behavior under different power ratio; (e), (f) SEM image of the slanted grating with 70° tilted angle near the edge and the center of master nanoimprint mold, respectively.

Download Full Size | PDF

As shown in Fig. 4(a), thickness of chrome mask also can influence the etching profile duo to it blocks some accelerating plasma, leading to a reduction in the line-spacing of the slanted grating. This relationship can be described as:

 

Fig. 4. (a) Diagram of the relationship between mask layer thickness and slanted grating spacing; (b), (c) SEM image of slanted grating with 30 nm, 60 nm chromium layers (d), (e) and (f) SEM image of slanted grating with different tilt angles.

Download Full Size | PDF

4.2 Preparation of slanted polymer gratings with high RI

Once we obtained the slanted grating mold and the high RI UV-curable resin suitable, we proceed with the replication process using nanoimprinting technology. Figure 5(a) depicts the preparation process for the high RI slanted grating. The slanted grating mold undergoes anti-adhesion treatment with a standard vapor-phase method after cleaning and drying. Next, a layer of 800-nm thick Perfluorinated UV resin (PL-R-UPM, PRINANO) is spin-coated onto the mold surface. The PET with the adhesive layer is overlaid onto the prepared master nanoimprint mold, and the sample is exposed to UV radiation (365 nm wavelength, 500 mJ/cm2) while being pressurized at 0.1 MPa, resulting in the PET/UPM working mold after being released from the master nanoimprint mold, as shown in Fig. 5(b). A layer of 200-nm high RI UV-curable resin is spin-coated onto a high RI glass. The one-step fabrication process involved producing two opposite slanted gratings in a single operation. A dual PET/UPM working mold replication strategy is employed, subsequently inverting the orientation of one mold. These molds are concurrently positioned on opposing sides of the substrate, followed by pressurization at 0.6 MPa and UV exposure for 60 seconds. Finally, a couple of high RI slanted gratings identical to the master nanoimprint mold is obtained after the mold release. It is noteworthy that, while the demolding direction of binary gratings is parallel to the grating lines, the demolding direction of slanted gratings is oriented perpendicularly to the grating lines and aligned with the inclined direction of the grating, as demonstrated in Fig. 5(d). F1 and F2 denote the forces exerted on the two slanted teeth during the demolding process, respectively, with the forces operating in these directions facilitating the effortless separation of the slanted grating lines from the mold.

 

Fig. 5. (a) Process flowchart for one-Step imprint of high refractive index slanted gratings; (b) is the PET/UPM mold with slanted gratings; (c), (c-i) and (c-ii) is the couple of high refractive index polymer slanted gratings; (d) The diagram of demolding.

Download Full Size | PDF

Figure 5(c-i) and (c-ii) are the high RI slanted gratings with the same structure as the master nanoimprint mold. The very regular edges of the grating structure and the orderly array configuration indicate that we have successfully replicated the slanted grating. Furthermore, high RI slanted gratings have been effectively reproduced onto rigid substrates (Including but not limited to high RI glass, Si wafer, etc.) via a simple imprinting process. Additionally, the residual layer can be controlled to a very-thin level by calculating the amount of UV-curable resin required for the UV-NIL process, which conduces to reduce the negative effect caused by excessive thickness of the residual layer in optical applications. Moreover, in order to validate the universality of our fabrication approach, we have also successfully prepared slanted gratings with varying degrees (refer to the Supplement 1 S5).

4.3 Optical performance detection

The slanted gratings, optimized with specific structural parameters, are fabricated using high RI UV-curable resin on 5 mm thick high RI glass. For comparison purposes, a binary grating is also prepared on the same substrate. The assessment and comparison of diffraction efficiencies are conducted through two methodologies: firstly, by quantifying the light coupling achieved by slanted grating, and secondly, by evaluating the overall throughput of both gratings. The experimental setup, depicted in Fig. 6(a), involves illuminating the laser light source (MLL-U-532), with a spectrometer and a detector connected to a power meter. In Fig. 6(b), compelling visual evidence show the formation of a concentrated spot with high light intensity resulting from the coupling of light within the slanted grating. The detected light incident power is 0.72 mW. The observed spot exhibits a remarkable intensity of approximately 0.51 mW, which accounts for 70.8% of the incident light intensity, signifying a significant enhancement compared to the meager 0.134 mW achieved by binary gratings. An essential aspect of this research is the strategic utilization of a high RI UV-curable resin, carefully selected to match the high RI glass, which allows for clear visualization of the optical path characterized by total internal reflection (Fig. 6(c)). Additionally, if the substrate surface consists of a set of diffraction gratings, as shown in Fig. 6(d), the incident light is decoupled and focused to a bright point. To quantify the diffraction efficiency, two 45° faces are polished on the high RI glass. For the optimized slanted grating, 73.1% of the incident light is coupled out at -1^st order, while 8.2% is coupled into 1^st order. 8.2% of the light is recorded in the 0^th diffraction order. As for the binary grating, 27.6% and 25.3% are coupled out at -1^st order and 1^st order, with 44.2% transmitted to the 0^th diffraction order. The green laser is vertically incident on the input coupler, and the more light is coupled into the high RI glass, propagating by total internal reflection until it is coupled out by the output coupler. The throughput is measured, which is the ratio between the intensity of the light coupled out and the intensity of the light coupled in. The throughput of the slanted grating is 62.8%, while it is only 3.23% when the light follows the 0^th order path. For the binary grating, throughputs of 2.74% and 4.19% are measured. The adjacent throughputs in both directions, as well as the power coupled into the 0^th diffraction order, are measured and summarized in Table 1. Simulation results demonstrate that when light is incident on the slanted grating, its diffraction efficiency for the first order is significantly higher than that for the other orders, which has been confirmed by experimental measurements. It is worth noting that although the experiment detected diffraction efficiencies that followed the same general trend as the simulation results, the actual numerical values were significantly smaller than the simulated ones. The primary reason for this discrepancy lies in the occurrence of substantial optical losses and experimental errors in the optical setup, leading to significant light attenuation during the experiments.

 

Fig. 6. (a) Schematic diagram and image of optical detection platform; (b) The spot is diffracted by binary grating and slanted grating, respectively; (c) The picture of optical path characterized by total internal reflection; (d) The light spots diffracted by a set of slanted gratings.

Download Full Size | PDF

The processed slanted gratings are utilized as optical modules for AR imaging, and static imaging experiments are conducted. The actual results demonstrate that the AR images perceived through the coupling of slanted gratings are remarkably clear and sharp, with virtually imperceptible stitching errors within the patterns. For specific imaging videos, please refer to the Figure S6 and Visualization 1.

5. Conclusion

We proposed a nanoimprinting-based fabrication strategy for slanted gratings and conducted a comprehensive study from master mold preparation to optical experiments. First, we simulated and optimized various parameters of the slanted gratings using the rigorous coupled-wave analysis (RCWA) model, achieving an optimized diffraction efficiency of up to 86.4%.

Regarding the fabrication process, we specifically discussed the impact of different etching methods, and etching parameters on the morphology of slanted gratings. By optimizing the etching scheme, we achieved large-area, well-defined master nanoimprint mold with multi-angle slanted grating. Using the high RI UV curable resin and a novel PET/UPM flexible working mold, we replicated the slanted gratings by nanoimprinting technology. This approach is versatile for various target substrates and allows for the replication of slanted gratings on high RI glass. Furthermore, we effectively controlled the residual layer of UV-curable resin to a very thin state, expanding the design space and application range of slanted gratings.

Finally, we conducted optical experiments on the optical modules with fabricated slanted gratings. The results showed that the high RI slanted gratings facilitated more incident light coupling into the glass for total internal reflection. Comparing to the binary gratings, the highest diffraction efficiency reached 73.1%, and the overall efficiency of the optical module reached 62.8%. Imaging experiments demonstrated clear and sharply defined edges.