The performance of a volume holographic grating as an incoupling/outcoupling element seriously affects the field of view (FOV) of a waveguide system. Many studies try to extend the incident angle response bandwidth of the volume holographic gratings to increase FOV. Most volume holographic gratings are designed based on the center ray. However, in a waveguide system, the collimation system converts the position information on the image source into angular information, which makes the beam incident to the volume holographic grating within a certain angle range (Δθ). Based on the Kogelnik theory, the angular range of the diffracted beam Δθ' is much larger than Δθ. Since the diffracted beam of the incoupling grating is the incident beam of the outcoupling grating, the mismatch between Δθ and Δθ' will make the outcoupling grating cannot fully receive all the angular information in the diffracted beam, causing insufficient transmitted image information. We propose a design method of multiplexed volume holographic gratings. The response bandwidth of the outcoupling grating is increased through multi-time multiplexing, while the diffraction angle offset range of the incoupling grating is reduced to match its bandwidth as much as possible, which can guarantee that enough image information can be received to increase the FOV of a waveguide system.

The analysis reveals that the factors limiting the FOV of the waveguide system include not only the response bandwidth of the volume holographic grating itself but also the bandwidth mismatch between incoupling grating and outcoupling grating. Therefore, a design method of multiplexed volume holographic gratings is proposed. The object and reference light preparation angles of a single grating are determined according to the total reflection condition of the waveguide. The diffraction efficiency corresponding to each of its angles is calculated, as well as the response bandwidth of the incoupling grating, the diffracted light angle of the incoupling grating, and the response bandwidth of the outcoupling grating. The diffracted light angle range of the incoupling grating is revealed to be much larger than the response bandwidth of the outcoupling grating, with a bandwidth mismatch. According to the multiplexed coupled wave theory, the bandwidth extension of the multiplexed gratings can be compounded together in a similar way as superposition. Based on the angular range of the bandwidth mismatch occurrence, the response bandwidth of the outcoupling grating is expanded by the multiplexed method, and the diffracted light angle of the incoupling grating is contracted at the same time. This makes the incoupling/outcoupling grating bandwidths match as much as possible, compensating for the lack of some image information when the waveguide system is imaged.

Firstly, the diffraction efficiency corresponding to each of its angles is calculated based on the parameters of the designed single grating (Fig. 3). Meanwhile, image simulation is performed by simulation software (Fig. 6) and the diagonal FOV of the waveguide system is 16.1°. The horizontal FOV is too small, resulting in the inability to fully couple out the image coupled into the waveguide. Therefore, the multiplexed grating angle is designed (Fig. 4) to match the incoupling/outcoupling grating response bandwidths. The FOV is further extended to 18.7° (Fig. 7). The angular information of the coupled-in waveguide should be increased to further increase the FOV. Triple multiplexing is performed based on the secondary multiplexing, and the response bandwidth of the incoupling grating is extended simultaneously (Fig. 8). The simulation results show that the diagonal FOV can reach 22.9° (Fig. 9). The multiplexed volume holographic grating designed by this method is simple to prepare and can expand the FOV of the waveguide system.

We first analyze the bandwidth mismatch in the incoupling/outcoupling gratings of the waveguide system. The factors limiting the FOV of the holographic waveguide system are not only the response bandwidth of the volume holographic grating itself but also the bandwidth mismatch between the incoupling grating and outcoupling grating. Therefore, a design method of multiplexed volume holographic grating is proposed to control its diffraction angle and the response bandwidth of the outcoupling grating. Based on the multiplexed coupled wave theory, the secondary multiplexed grating is first designed. Additionally, the response bandwidth of the outcoupling grating is expanded and the contraction of its diffraction angle is realized at the same time. The image simulation and the optimized design of triple multiplexing are further carried out, whose diagonal FOV of the holographic waveguide system is improved to 22.9°. The FOV of the waveguide system can be further enlarged by more times of multiplexed design. The designed multiplexed holographic grating is simple to prepare and can extend the FOV of the waveguide system with limited refractive index modulation.