Fourier Analysis And Simulations Of Optical Invisibility, Nanopatterns Recognition,and Super-resolution Imaging

Optical invisibility has become a hot topic in recent years for the important scientific values and the challenges of process technology. On the other hand, pattern recognition has been successfully applied into wide fields of military, civil, science, and technology such as fingerprint identification, target recognition, remote sensing etc. Super-resolution imaging system can theoretically and technically break the diffraction limit to achieve non-destructive imaging of samples makes it have great application values in biology, chemistry, and medicine. In this dissertation, we give a Fourier analysis method to elucidate the invisibility cloaks and extend this method into time domain to design temporal cloaks. We also use Fourier analysis method to achieve recognition of nanostructures and to design quasi-periodic grating for far-field super-resolution imaging. The main works included in this dissertation are:1. Fourier analysis method is used to give analytical insight into the physical mechanism behind the invisibility cloaks from the perspective of optical imaging. By introducing transfer functions to elucidate the roles of the invisibility cloaks played on angular spectrum of the objects, the Fourier analysis method can not only get the electromagnetic parameters of invisibility cloaks but also unify both Pendry’s cloaks and complementary medium-based invisibility cloaks mathematically. The results are strictly of consistence with that obtained from transformation optics, confirming the validity of our method. On the other hand, this method can even deal with lossy invisibility cloaks, which is hard to treat by transformation optics.2. A carpet filter is proposed to hide objects and creating illusions above the filter based on the Fourier analysis method. Instead of using the transformation optics, we get the electromagnetic parameters of the filter by the optical transfer functions which play the roles of modulating the propagation of the scattering angular spectrum directly from an object upon the filter to make the object invisible. By constructing an additive function layer into the carpet filter, we can even camouflage the object appeared as completely another different object. We further analytically show and numerically demonstrate two filters for realizing another invisible way:optically camouflaging an object at one place to appear at another place with parallel displacement or orientation changeable displacement, respectively. The cloaks are simply the spatial filters with different transfer functions and play the role of actively modulating the propagation optical field to make the position of object changeable.3. A Fourier analysis method is introduced to design temporal cloaks for hiding events in time domain. The cloaks are constructed with two linear time-invariant filters with different transfer functions, which can create a temporal gap and then closed it orderly, making any events occurring during the gap not detectable outside. Furthermore, we reveal that even a no-gap temporal cloak can also hide events outside the cloak.4. Combining the Fourier analysis method, a complementary medium-based matched filter is synthesized through transformation optics for the recognition of nanopatterns. The recognition is independent of the spatial position of the nanopatterns and is irrelative to the existence of other noise structures. Our results may inspire new interesting applications in biology, medicine, and chemistry for nondestructive and label-free discrimination imaging of biological cells, protein macromolecules, and organic tissues.5. One-dimensional Fibonacci gratings are designed to transform evanescent waves into propagation waves for far-field super-resolution imaging. By detecting far-field intensity distributions of light through objects in front of the Fibonacci grating in free space, we can observe the objects with nearly λ/9spatial resolution. We also discuss the effects of sampling error and the inhomogeneity between the objects and grating on imaging resolution of the system.