Nano-optics refers to the study of the remarkable properties and phenomena associated with nano-scale materials or devices when interacting with optical light. It is a vigorously growing discipline that has opened up a broad range of possibilities for modern science and technology. With the advent of innovative patterning techniques allowing for the sculpting of materials with nanometer precision, it is presently promising to fabricate optical devices that can perform tasks at scales unattainable with conventional optics, and with great speed and efficiency. This project is devoted to the optical scattering and imaging of nano-structures. The outcome of the theoretical work will provide advances in the understanding of new types of light-matter interactions in subwavelength nano-structures. In addition, the computational frameworks will provide inexpensive, fast, and accurate modeling of optical wave propagation in such tiny structures and enhance near-field optical imaging techniques. Furthermore, the fast implementations of forward modeling and inverse imaging tools will also provide realistic guidance for the design of nano devices with the desired properties in their interactions with the optical light.
The project focuses on examining fundamental mathematical issues and developing computational methods for new and important classes of problems arising from the optical wave scattering and imaging of nano-structures. This consists of mathematical studies of extraordinary field enhancement in metallic nano-structures and their super-resolution imaging via inverse scattering. The technical focus of the model problems is on Maxwell's equations in complicated and multi-scale media. New analytical tools based upon a combination of the boundary integral equation approach and asymptotic analysis techniques will be developed for rigorous studies of the tightly confined optical wave fields in nano apertures/holes. Computationally, in order to address the significant challenges brought by the extreme scale difference between the aperture size and the wavelength of radiation, fast and high-order horizontal and vertical mode matching numerical schemes will be designed for the simulation of wave propagations in nano-structures. Finally, efficient numerical algorithms based on the inverse scattering theory will be applied for imaging multi-scale subwavelength structures and for breaking the diffraction limit.
