Laser beam-splitting diffractive elements are highly demanded in fields such as laser radar, optical time-of-flight depth sensing, and three-dimensional structured light sensing due to their miniaturization and high diffraction efficiency. With advancements in lithography nanostructure resolution, it is now feasible to produce diffractive elements with small feature sizes and large diffraction angles. However, as the diffraction angle increases, designs based on scalar diffraction theory no longer satisfy the paraxial approximation, leading to significant errors in the uniformity of far-field diffraction spot energy distribution. This makes it difficult to meet the design requirements for large-angle diffraction elements. Furthermore, the pixel-based structure of two-dimensional laser beam-splitting elements often involves hundreds of thousands of design variables, making it challenging for traditional optimization algorithms to achieve uniform beam-splitting. In this paper, we propose a method that combines vector diffraction theory with the adjoint method to optimize the design of large-angle beam splitters. This approach requires only two electromagnetic simulations per iteration to compute the gradient of the evaluation function relative to all design variables, significantly improving design efficiency. Our research aims to enhance the uniformity of large-angle laser beam-splitting diffractive structures.

In this paper, we propose a design method based on vector diffraction theory and an adjoint method for optimizing large-angle beam-splitting diffractive elements. First, we calculate the initial phase distribution using a non-paraxial scalar iterative Fourier transform algorithm to achieve the desired diffraction angle. Next, we design the dielectric constant distribution by relating the phase to the depth of the beam-splitting diffractive element, allowing for a continuous dielectric constant distribution within the structural region. Finally, the gradient descent direction is calculated using the finite-difference time-domain (FDTD) method and the adjoint method, and the structural parameters are updated accordingly. Using this approach, we design a 7×3 beam-splitting diffractive structure with a wavelength of 632.8 nm, a period size of 2.8 µm×6 µm, and a full diffraction angle of 78°×12°. The design is fabricated using conventional semiconductor processing techniques on UV-curing resin, involving coating, homogenizing, exposure, development, etching, and imprinting.

The variation curve of the evaluation function F and the dielectric constant distribution of the designed two-dimensional laser beam-splitting diffractive element are shown in Fig. 2. The change in the evaluation function with the number of iterations during the process is shown in Fig. 2(a). The total number of iterations is only 75, and the convergence speed is rapid. In addition, increasing the projection intensity β drives the diffraction structure to gradually become binary discrete during the iteration. Comparing the starting point unit structure in Fig. 2(c) with the unit structure after the iteration in Fig. 2(d), it can be seen that as β value continues to increase, the diffraction structure completely transforms into a binary step diffraction structure, which can be directly used for subsequent processing and preparation. The final beam-splitting uniformity error is 21.3%. The fabrication results of the diffraction beam splitter are shown in Fig. 4. A comparison between the fabricated structure in Fig. 4(c) and the theoretical structure in Fig. 2(f) confirms that the experimental results are consistent with the theoretical design. The scanning electron microscope (SEM) image of the cross-section is shown in Fig. 4(d), demonstrating good verticality of the structure. By measuring the depth at 25 different etching points, the average etching depth is found to be 590 nm, which is close to the theoretical depth of 580 nm. The experimental test results of the beam-splitting effect are shown in Fig. 5. The uniformity error of the experimental test data is 29.14 %, which is consistent with the theoretical result. These results confirm the effectiveness of the proposed vector adjoint optimization method for designing beam-splitting laser diffractive elements.

In this paper, we propose a vector optimization method for the design of large-angle laser diffractive elements. By requiring only two vector calculations to obtain the gradient of the evaluation function for all design variables, this method significantly simplifies the optimization process for large-angle diffractive elements. The number of iterations required for optimization is reduced and diffraction uniformity is improved. Using this method, we design a laser beam-splitting diffractive element with a wavelength of 632.8 nm and a full diffraction angle of 78°×12°. The structure is fabricated using conventional refractive index materials (with a refractive index of 1.53) with a uniformity error of 29.14%. This work provides a valuable technical reference for the fabrication of high-uniformity, large-angle diffractive elements using conventional materials.