Study On Propagation And Focusing Of Terahertz Surface Plasmon Polaritons

Terahertz(THz) wave refers to the electromagnetic wave with a frequency of about 1012 Hz. It has many excellent characteristics and has been applied in the fields of bioscience, material science, high-speed wireless communication technology and security technology, etc. It is one of the hottest research topics in recent years. Transmission problem, is an emphasis and a challenge of the THz technology. As one of THz waveguide candidates, a single metal wire waveguide, which has been presented experimently in 2004, can be used to guide terahertz radiation with low loss and dispersion. The experimental results by Mittleman’s team were published in Nature in that year. It is quickly followed by a theoretical explanation given by Qing Cao and Jürgen Jahns. They pointed out that the efficient single metal wire waveguiding comes from the surface plasmon polariton(SPP). Since then, a variety of other types of terahertz metallic surface plasmon polaritons, or terahertz metallic waveguides, are studied for the use of efficient conduction of terahertz wave. For these researches, the effective index is very important, whose imaginary part can be used to calculate the loss, while the real part can be used to calculate the dispersion. Therefore, one can evaluate the transmission properties of terahertz surface plasmon polaritons through the effective index values in corresponding metallic structures.This dissertation is based on the analysis of existing terahertz metallic surface plasmon polaritons, and pays its emphasis on the study of two kinds of terahertz metallic surface plasmon polaritons, in which we get some valuable results: 1. An approximate explicit expression for two-wire terahertz metallic surface plasmon polariton with different radii is established.We introduce the technique of perturbation of boundary condition to the problem of two-wire terahertz metallic surface plasmon polariton with different radii. Based on the quasi-TEM analytical mode field in the cross-section, an approximate explicit expression for the complex effective index is obtained. This work has the following innovations:a) Previous studies focus on the symmetric two-wire metallic structure with two identical radii. Our results can be applied to its general form, the two-wire metallic structure with different radii. This result could help researchers to design two-wire metallic structures with more shapes. In the study on the two-wire metallic surface plamon polariton with different radii, A problem was encountered that how to figure out the electric field distribution in the cross-section of such a complex structure. We solved this problem successfully by use of M?bius transformation.b) For the symmetric two-wire metallic structure, the solution of the effective index of terahertz surface plasmon polariton is very difficult to be obtained. In fact, it is very hard to solve the Helmholtz equations of the longitudinal electric and longitudinal magnetic fields in the cross-section. Therefore, it is almost impossible to establish a strict eigenvalue equation. Researchers often relied on numerical simulations to solve this problem before. Although having the advantage of high accuracy, the numerical method has low efficiency and can hardly give a clear physical picture. In recent years, researchers turn to establishing approximate analytic expression of the effective index and have got some encouraging results. By use of energy conservation, the approximate expression of attenuation of dual metal wire has been obtained. It means that the imaginary part of the effective index can be explicitly and approximately expressed. The approximate expression of the whole complex effective index, however, has not been established before the publication of our work. In this work, we give this expression and apply it to the more common case of the symmetric two-wire metallic structure, which is the dual metal wire with different radii. The expression is in good agreement with the result of numerical simulation, and can be easily extended to evaluate the dispersion and the loss of the two metal wire terahertz surface plasmon polariton.c) In the study of the dispersion of the terahertz surface plamon plarition in the two-wire metallic waveguide, we take the advantage of the approximate expression, and find a zero value point of the group velocity dispersion around 1.268 THz when the metal is copper. This result can be used to help researchers to choose the appropriate frequency of the guided wave. 2. A tapered hyperbolic metallic surface plasmon polariton is suggested for the nanofocusing of terahertz waves.A hyperbolic metallic surface plasmon polariton is a waveguide, whose metal-air boundary consist of the two branches of a hyperbola in the cross-section. We found that this waveguide has very small loss when the vertex distant is in the nanoscale. Base on this feature, we designed a tapered hyperbolic metallic surface plasmon polariton to focus the terahertz wave with a wavelength in the millimeter range to a spot of about 5 nm. This work has the following innovations:a) Previous studies on the tapered metal plate waveguide and coaxial waveguide showed that the limit of the terahertz wave focal spot with tapered structures is the skin depth of the metal in the frequency. At 1 THz, it is about 60 nm. Neither of the two waveguides is able to reach this limit. However, the low loss tapered hyperbolic metallic surface plasmon polariton can break this limit, and can focus the terahertz radiation at 1 THz into a spot of about 5 nm. It is smaller than that of the tapered metal plate waveguide by about 2 orders of magnitude under the same condition.b) While the 5 nm focal spot can be achieved, the energy flux density(Strength of the Poynting’s vector in the center), by use of the tapered hyperbolic metallic surface plasmon polarition, can be enhanced by 10,000 folds. The enhancement is stronger than that of the tapered metal plate waveguide by about 3 orders of magnitude under the same condition.c) We gave the expression of the electric field in the cross-section of the tapered hyperbolic metallic surface plasmon polarition. The expression agrees well with the result of the numerical simulation.This dissertation includes our studies on the properties of terahertz metallic surface plasmon polaritons, focuses on the transmission properties of the two structures. The sizes of the structures are from microscale to nanoscale. These results may lead to potential applications in terahertz communication, circuits, super-resolution imaging, nanolasers, etc.