FROM WAVE OPTICS TO NEGATIVE-REFRACTION LENSES: THEORETICAL REVISITATION OF IMAGING RESOLUTION LIMITS AND PEDAGOGICAL INNOVATION IN OPTICAL SCIENCE

Optical imaging, as a cornerstone of modern optical research, bears significant application value in both scientific exploration and engineering technologies. Fresnel diffraction theory reveals that when imaging a point source through an optical system, the interplay between light’s wave nature and finite lens aperture induces diffraction effects, generating an Airy disk whose spatial extent defines the Rayleigh diffraction limit. While current undergraduate curricula predominantly utilize Fresnel diffraction integrals for imaging resolution analysis, this study adopts a Fourier optics framework to rigorously derive the angular spectrum propagation of point-source radiation, thereby fundamentally unveiling the diffraction-limited nature of conventional lens systems. The first zero point of the intensity distribution in the circular aperture diffraction pattern is obtained through numerical solution based on the Fourier angular spectrum method, and the result is compared with that calculated using the Rayleigh criterion. By further integrating cutting-edge developments in negative-refraction optics, we systematically elucidate the physical principles enabling negative-index metamaterials to overcome classical diffraction constraints. This work not only establishes a novel pedagogical paradigm for optical imaging theory but also provides a critical analytical framework for super-resolution imaging research, serving as a conceptual bridge between undergraduate optics education and advanced graduate studies in photonic innovation.