硅透镜在双向梯度负折射率光子晶体中的亚波长聚焦研究

Subwavelength Focusing Study of Silicon Lenses in Bidirectional Gradient Negative Refractive Index Photonic Crystals

摘要: 梯度负折射率光子晶体以其折射率的非均匀性结构赋予了光子晶体独特的光学特性，利用梯度负折射率光子晶体的特殊性质，可以改善光学通信系统中的传输效率和信号质量。但大多的研究仅仅是从一个方向上设计梯度折射率，本文提出了一种利用双向梯度负折射率光子晶体和单个硅透镜相结合的亚波长聚焦系统，实现了在远场的亚波长分辨率超聚焦，突破了传统衍射极限。实验中采用硅介质制备光子晶体基底和微球透镜，其折射率为3.45，并用FDTD算法对其进行仿真模拟。通过空气孔直径的横向变化和纵向变化相结合调整光子晶体中折射率的分布模式，显著提升了聚焦效果，使焦点的半峰全宽值降至0.341 λ。再通过改变硅透镜曲率与位置，建立了一种动态调焦系统，使得最终图像的像点半峰宽度和位置发生变化。在硅透镜特定的空间位置条件下，实现了亚波长成像条件下0.13 λ~0.76 λ的焦点调谐范围，且焦点半峰全宽值最低为0.288 λ，实现了良好的超分辨聚焦效果。

Abstract: Gradient-negative refractive index photonic crystals have unique optical properties due to the non-uniform structure of their refractive indices, and the special properties of gradient-negative refractive index photonic crystals can be utilized to improve the transmission efficiency and signal quality of optical communication systems. However, most of the researches only design the gradient refractive index from one direction. In this paper, a subwavelength focusing system combining a bidirectional gradient-negative refractive index photonic crystal and a single silicon lens is proposed to realize far-field subwavelength-resolved hyper focusing, which breaks through the traditional diffraction limit. A photonic crystal substrate with a refractive index of 3.45 and a microsphere lens were prepared using a silicon medium and simulated using the FDTD algorithm. The refractive index distribution pattern in the photonic crystal is adjusted by the combination of lateral and vertical variations of the pore diameter, which significantly improves the focusing effect and reduces the half-peak full width of the focal point to 0.317 λ. Under the specific spatial position of the silicon lens, a focusing range of 0.13 λ to 0.76 λ is achieved under the sub-wavelength imaging condition, and the half-peak full width of the focal point is as low as 0.288 λ, which realizes a good super-resolution focusing effect.