Optimal design for antireflective tapered two-dimensional subwavelength grating structures

Techniques for the design of continuously tapered two-dimensional (2D) subwavelength surface-relief grating structures for broadband antireflection surfaces are investigated. It has been determined that the Klopfenstein taper [ Proc. IRE44, 31 ( 1956)] produces the optimum graded-index profile with the smallest depth for any specified minimum reflectance. A technique is developed to design the equivalent tapered subwavelength surface-relief grating structure by use of 2D effective-medium theory. An optimal Klopfenstein tapered 2D subwavelength grating is designed to reduce the Fresnel reflections by 20 dB over a broad band from an air–substrate (ns = 3.0) interface. The performance is verified by use of both a 2D effective-medium-theory simulation algorithm and rigorous coupled-wave analysis. These structures are also shown to achieve this low reflectance over a wide field of view (θFOV > 110°). The pyramidal spatial profile, which has generally been assumed to produce the optimal broadband antireflection grating structure, is shown to require a significantly larger depth to achieve the same performance as a Klopfenstein-designed tapered antireflection grating structure.