Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures.With this conventional difficulty still puzzling us and the prosperous development of wave dynamics o...Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures.With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years,how spatial curvature affects the diffraction limit is an attractive and important question.Here we investigate the issue of the diffraction limit and optical resolution on two-dimensional curved space—surfaces of revolution(SORs)with constant or variable spatial curvature.We show that the diffraction limit decreases and the resolution is improved on SORs with positive Gaussian curvature,opening a new avenue to super-resolution.The diffraction limit is also influenced by the propagation direction,as well as the propagation distance in curved space with variable spatial curvature.These results provide a possible method to control the optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of the nonuniform strong gravitational effect by probing locally the optical resolution.展开更多
As an analog model of general relativity,optics on some two-dimensional(2 D)curved surfaces has received increasing attention in the past decade.Here,in light of the Huygens-Fresnel principle,we propose a theoretical ...As an analog model of general relativity,optics on some two-dimensional(2 D)curved surfaces has received increasing attention in the past decade.Here,in light of the Huygens-Fresnel principle,we propose a theoretical frame to study light propagation along arbitrary geodesics on any 2 D curved surfaces.This theory not only enables us to solve the enigma of"infinite intensity"that existed previously at artificial singularities on surfaces of revolution but also makes it possible to study light propagation on arbitrary 2 D curved surfaces.Based on this theory,we investigate the effects of light propagation on a typical surface of revolution,Flamm’s paraboloid,as an example,from which one can understand the behavior of light in the curved geometry of Schwarzschild black holes.Our theory provides a convenient and powerful tool for investigations of radiation in curved space.展开更多
基金National Natural Science Foundation of China(11974309,62375241)Israel Science Foundation(1871/15,2074/15,2630/20)United States-Israel Binational Science Foundation(2015694)。
文摘Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures.With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years,how spatial curvature affects the diffraction limit is an attractive and important question.Here we investigate the issue of the diffraction limit and optical resolution on two-dimensional curved space—surfaces of revolution(SORs)with constant or variable spatial curvature.We show that the diffraction limit decreases and the resolution is improved on SORs with positive Gaussian curvature,opening a new avenue to super-resolution.The diffraction limit is also influenced by the propagation direction,as well as the propagation distance in curved space with variable spatial curvature.These results provide a possible method to control the optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of the nonuniform strong gravitational effect by probing locally the optical resolution.
基金Natural Science Foundation of Zhejiang Province,China(LD18A040001)National Natural Science Foundation of China(11974309,11674284)National Key Research and Development Program of China(2017YFA0304202)。
文摘As an analog model of general relativity,optics on some two-dimensional(2 D)curved surfaces has received increasing attention in the past decade.Here,in light of the Huygens-Fresnel principle,we propose a theoretical frame to study light propagation along arbitrary geodesics on any 2 D curved surfaces.This theory not only enables us to solve the enigma of"infinite intensity"that existed previously at artificial singularities on surfaces of revolution but also makes it possible to study light propagation on arbitrary 2 D curved surfaces.Based on this theory,we investigate the effects of light propagation on a typical surface of revolution,Flamm’s paraboloid,as an example,from which one can understand the behavior of light in the curved geometry of Schwarzschild black holes.Our theory provides a convenient and powerful tool for investigations of radiation in curved space.
