Talbot Self-imaging And Superfocusing In Micro-nano Structures

The Talbot effect, also referred to lensless imaging or self imaging, is the phenomenon in which self-imaging of the periodic structure replicates periodically in the Fresnel diffraction region. Our study has expanded the field of Talbot self-imaging effect. We investigate the conditions and the imaging characteristics of Talbot effect in the two-dimensional discrete waveguide arrays. Different with continuous systems, light waves in waveguide arrays propagate through evanescently coupling between the waveguides. Unlike in one-dimensional waveguide array systems, Talbot self-imaging in two-dimensional systems has unique characteristics. Usually, it is not enough to consider the coupling only between the nearest neighbor waveguides. We observe second-harmonic Talbot effect using nonlinear crystals in experiments. Unlike traditional Talbot effect, nonlinear Talbot effect is generated by the periodic distribution of nonlinear coefficient rather than the refractive index within the crystals. And nonlinear Talbot effect has many unique features. For example, we have experimentally realized superfocusing in nonlinear Talbot effect. Also, we perform many numerical simulations of superoscillator lens (SOL). We optimize the SOL for focusing the circularly-polarized and radially-polarized beams below the diffraction limits. Finally, we discusse the diffraction characteristics of the spiral gratings illuminated with scalar or vector beams in the Fresnel field. The main results are listed as follows:1. Discrete Talbot effect in two-dimensional waveguide arrays. In the theoretical model, we consider the coupling between the nearest and the next nearest waveguides. To realize self-imaging, the period of the input field in any base vector direction is not arbitrary, but must belong to{1,2,3,4,6}. The ratio between the coupling coefficients of the nearest and the next nearest waveguides must also be rational. The period combinations of the input field can’t be (4,3) or (4,6). We further use numerical simulations by considering three different 2-D waveguide arrays (hexagonal, square, and irregular) to confirm the theoretical results.2. Fractional nonlinear Talbot effect. We demonstrate the nonlinear Talbot effect in hexagonally poled LiTaO3 (PPLT) crystals. Because the wavelength is reduced to the half of the input one in the nonlinear process, the resolution of the self-imaging is enhanced by a factor of 2. We employ both theoretical analysis (reciproacl vector theory and scalar angular spectrum theory) and experiments to study this novel Talbot effect. At 1/3 Talbot plane, we find that the classic performance of Talbot self-imaging, such as reduced period equal to (?)3/3 of the original one and pattern rotation, can be easily observed. Besides, at sepcific fractional Talbot planes, we find focal spots which are far smaller than the diffraction limit.3. Design of super-oscillatory lens (SOL) for a polarized beam. Based on the vectorial angular spectrum theory, we analyze the propagation equations of both scalar and vector light beams. In order to get a circular symmetrical superfocused spot, we optimize the SOL with circularly-polarized and radially-polarized beams. Our simulations show that the radially-polarized beam is a better choice for superfocusing through SOL becuase 1. the SOL designed with a radially-polarized beam can realize smaller hotspot than that using a circularly-polarized beam; and 2. by properly designing SOL for a radially-polarized beam, one can obtain sub-wavelength hotspots at much longer propagation distances. We also compare the amplitude-type and phase-type SOL. The simulations show that phase-type SOL have great advantages in achieving high-intensity superfocusing hotspots.4. Focusing through spiral gratings. Based on the vectorial angular spectrum theory, we analyze the Fresnel diffraction of different types of spiral gratings illuminated with circularly-polarized, radially-polarized and angularly-polarized beams by means of numerical simulations. We find that left-handed and right-handed circularly polarized lights behave very differently when they illuminate on the same amplitude spiral grating. For example, their topological charges of longitudinal electric-field component differ by two.