Reflection, transmission, and absorption are several forms of interactions between light and matter. The reflected light caused by the refractive index difference between different media results in low energy conversion efficiency and signal interference. Therefore, reducing broadband reflection to improve transmission or absorption is crucial for improving the performances of optical components and optoelectronic devices. Currently, the main methods to achieve antireflection are the thin-film and micro-nano structure methods. However, a single-layer antireflection film can only act at a specific wavelength, whereas the material selection of a multilayer antireflection film is difficult. Simultaneously, the film thickness is strictly controlled, and there are certain thermal mismatch and mechanical stability problems among the multiple layers. Research on the micro-nano structure methods concentrates on the subwavelength antireflection structure, which is an ordered micro-nano periodic structure that can be equivalent to a dielectric layer with a gradual refractive index to eliminate refractive index mismatch. At present, research on subwavelength antireflection structures mostly focuses on adjusting the size parameters and distribution forms of existing geometric structures, such as cylinder, cone, and moth-eye structures. The optimal value is a special case for such structures. Alternatively, an improved structure is directly proposed based on the original structure, and its antireflection ability is compared with that of the original structure to prove its superiority. Both methods are based on the analysis of specific situations; therefore, proposing a general design method is useful for expanding the potential application of subwavelength antireflection structures.
The antireflection ability of different subwavelength structures is related to the forms of their equivalent refractive indices . In contrast to the above two methods, this study investigates the relationship between the equivalent refractive index of the subwavelength structure and antireflection performance. An equivalent refractive index expression with optimal antireflection performance is obtained. The equivalent refractive index can satisfy the expected expression when combined with geometric modeling, and the design requirements of a new structure with optimal antireflection performance in broadband can be achieved. In this study, the equivalent refractive indices of the cylinder, cone, and moth-eye structures are obtained using the equivalent medium theory. The reflectance curves of the three structures are obtained using the finite-difference time-domain (FDTD) method. According to the simulation results, the performance of antireflection is best when the equivalent refractive index curve is closest to the linear transition and there is no abrupt change at the top and substrate. To further improve the broadband antireflection of the subwavelength structure, a design method for the geometric structure and distribution form of a subwavelength structure that meets the ideal equivalent refractive index curve is investigated. The relationship between the equivalent refractive index and filling factor of the subwavelength structure is studied using a graphic method, and a single subwavelength structure whose equivalent refractive index is closest to the linear change is established by structural parameter control through three-dimensional modeling. Subsequently, a subwavelength array structure with no abrupt refractive index change at the top and substrate is obtained by adjusting its distribution form. Based on this, a cone-like structure design method with an ideal equivalent refractive index curve that meets the above two requirements is proposed.
The triangular, tetragonal, and hexagonal pyramid structures that meet the design requirements are selected and compared with the moth-eye structure to verify the antireflection ability. The reflectances of four structures with the same size are compared using the FDTD method in the wavelength range of 300-1100 nm. Specifically, the diameters of the inscribed circles at the bottom of the microstructure are 200, 300, and 500 nm, and the aspect ratios are 1.0, 1.5, 2.0, and 2.5. The reflectances of the three structures are lower than that of the moth-eye structure when the aspect ratios are 1.5, 2.0, and 2.5, respectively (Figs. 9 and 11). All four structures achieve the lowest average reflectance when the aspect ratio is 2.5. Among these structures, the hexagonal pyramid structure exhibits the best antireflection performance (Figs. 9 and 11). When the diameter of the inscribed circle at the bottom of the microstructure is 500 nm and the aspect ratio is 2.5, the optimal average reflectance of the hexagonal pyramid structure (0.029%) is 22.5% of that of the moth-eye structure (0.129%) (Fig. 11). Under other conditions, compared with the optimal reflectance of the moth-eye structure, the average reflectance can still be reduced by nearly 70% (Figs. 9 and 11). Subsequently, two characteristic wavelengths (500 nm and 850 nm) are selected to further investigate the wide-angle antireflection performance of the cone-like and moth-eye structures. Overall, the three cone-like structures have an advantage over the moth-eye structure, among which the average reflectance of the tetragonal pyramid structure is reduced by 62% and 40% under two characteristic wavelengths, respectively (Fig. 12). According to the above results, the cone-like structure has the better antireflection performance.
In this study, based on the equivalent medium theory and finite difference time domain method, the equivalent refractive index curve and transition form when the subwavelength structure has the best antireflection performance are proposed. A design method for a series of cone-like structures based on this equivalent refractive index curve is proposed. The average reflectance of the cone-like structure in the wavelength range of 300-1100 nm is reduced by approximately 70% compared with that of the traditional moth-eye structure, with excellent antireflection performance. Meanwhile, the wide-angle antireflection ability of the cone-like structure is better than that of the moth-eye structure at the two selected characteristic wavelengths. The results demonstrate that the cone-like structures designed using this method have better antireflection performance than traditional subwavelength structures. In addition, when combined with advanced manufacturing technology, this design method has potential applications in the fields of ultra-precision optical chips, on-chip optical integration, and optical interconnections.
