The Propagation Properties Of Surface Plasmon Polaritons In Metal Waveguide Arrays

With the development of the photonics, nanostructured metal waveguide arrays(MWGAs) have attracted more attention in various fields of nanooptics due to extraordinary electromagnetic properties and their potential applicatons. Nanostructured metallic waveguide arrays can provide new opportunities for manipulating light at the nanoscale, such as negative refraction subwavelength focusing, subwavelength diffraction control, plasmonic Talbot effect, and beam splitting. In this thesis, we introduce supermode theory into the propagation of surface plasmon polaritons(SPPs) in nanoscale MWGAs and investigative the discrete diffraction, deep subwavelength focusing and discrete Talbot effect in nanostructured metal waveguide arrays. The major achievements made in this thesis are summarized as follows:(1) We have studied subwavelength diffraction in a limited number of nanostructured metal waveguide arrays. Discrete diffraction in waveguide arrays has widely studied in the past years, which the number of waveguide is infinite for numerial simulation and hundreds for experiments. For finite MWGAs, the discrete diffraction has not been deeply researched. In this thesis, to explain field distributions, we introduce supermode theory into the propagation of SPPs and derive the coupling constant and show the solution of diffraction in a limited number of nanostructured metal waveguide arrays. We use a new method to derive the perturbation constants and the coupling constants. The propagation constants and the wave functions are calculated accurately for N=3, N=4, and N=5. When the input field incident from different locations of the array, it will form different diffraction field distribution. So we also discuss the incident of symmetry and asymmetry. The field distributions are studied by supermode theory. The accurate position of the maximum values and the minimum values in the diffraction field are obtained. Our theoretical results are verified by the finite-difference time-domain(FDTD) method. The numerical simulation results are consilient with the theoretical results.(2) We propose a new sheltered subwavelength focusing scheme in a limited number of MWGAs. The character is that the entrances of middle waveguides are sheltered and only both sides of the MWGAs are open. Simulation results show that this structure can transfer the plane wave into a single waveguide and realize subwavelength focusing in the middle waveguide. The full width at half-maximum(FWHM) of the focusing spot is about 54 nm. To illustrate the focusing characteristics of the MWGAs, we also analyzed the focusing without the shelter. The FWHM without shelter is about 150 nm. We find that the focus formed by the sheltered MWGA is much smaller than the focus formed by the MWGA without a shelter. We analyze the supermode propagation of SPPs in the MWGA and find that the focusing behavior can be explained by the superposition of the supermode of SPPs. The propagation constants and the wave functions are calculated by the supermode theory of SPPs. When the inputs of middle waveguides are sheltered, the incident wave can only excite the symmetric supermodes. The total field is formed by the superposition of these symmetric supermodes. Numerical simulation results show a good agreement with the theoretical predictions. We also discuss the power loss arising from the shelter and find that the shelter in middle waveguides has little effect on the energy of the focus in the waveguide. The advantage of the sheltered structure is that the incident field focused into a single waveguide and the focus size is much smaller than that if without the shelter. The peak of the focal point is sharper at the cost of a smaller loss of energy. The size of the focus is 1/12 incident wavelength.Deep subwavelength focusing is realized.(3) We have achieved the discrete Talbot effect in an array with finite metal waveguides. Usually, the waveguide arrays structures for discrete Talbot effect are quite large: the number of waveguide is infinite for numerical simulation and hundreds for experiments. How to implement the Talbot effect in the finite MWGAs has not been studied. By analyzing the propagation constant and the wave function of SPPs supermodes in MWGAs, we obtain the quantitative relationship between the factor of supermodes and the input field. We found that all levels of supermodes in MWGAs are not equivalent excitation and excited supermodes coefficient is determined by the strength distribution of the input field. According to the SPPs supermode theory, we succeeded in achieving the discrete Talbot effect in finite MWGAs by adjusting different intensity for each input field. The Talbot effect in an infinite array can also be explained by the theory of SPPs supermodes. We also validate that the period condition of the input fields in infinite MWGAs is not the same as that that with conventional dielectric waveguides. Our theoretical results are verified by the finite-difference time-domain(FDTD) method. In addition, we verify that the period condition is P= 1, 2, 3, 4, and 6, not the same as P= 1, 2, 3, 4, and 5 for the conventional dielectric waveguides.(4) We investigative the supermode excitation of SPPs nanostructured finite metal waveguide arrays. The theoretical equation for the selective excitation of SPPs supermodes is established. The SPPs supermodes can be selectively excited by adjusting the input field. We only need to substitute the levels of supermodes that we want to excite into the equation. The field amplitude can be quantitative calculated. According to the calculated field amplitude, we set the input field strength and the supermodes are excited. The superpositions of supermodes can form different intensity distributions. We excite two even supermodes at the same time and the interference patterns are formed by the two supermodes. According to the field distribution of the two supermodes, we design a power splitter based on the MWGAs.