In other words, the larger k x results in the stronger field confinement.įigure 2(a) compares the dispersion characteristic, which includes most propagating information of the guided wave, for different types of waveguide. From equation (3) we conclude that when the wave number k x increases, α T becomes larger, and the EM field decays faster. k 0 = ω/c is the wave number in air region, and α T represents the decay constant along the tangential direction ( y- and z- direction here). Where k x is the wave number along the propagation direction ( x- direction here). Such plasmonic waveguide supports surface mode with 2(a), including the groove depth d, groove width a, strip thickness t, and period p. Geometric parameters of the spoof SPP structure are denoted in the inset of Fig. For a decent comparison between the SPP TL and the microstrip line, we choose grounded one-side single-strip SPP structure in this paper. SPP dispersions of the plasmonic waveguideĪt microwave frequency, corrugated metallic structures are printed periodically on supporting dielectric substrate to propagate spoof SPPs. In the following sections, we will exam the SPP waveguide from these points of view. Second, in order to achieve high transmission coefficient through a small-radius bend, transmission lines with strong field confinements and high phase constant β e should be adopted. Therefore, for a specific curved open waveguide with a fixed β e, a smaller bending radius R results in more radiation loss. First, the fraction of electromagnetic wave at X > X r doesn’t propagate fast enough to catch the equiphase fronts and hence is lost to radiation. In the end, we fabricate prototypes for both transmission lines, and demonstrate our theory numerically and experimentally.Įquation (2) indicates two important properties. Next, we study the dispersion property for both SPP TL and microstrip line. We first analyze the physics behind radiation loss from curved open waveguide (SPP TL, microstrip line, et al.), as well as the solution to this issue. In this paper, we further examine the EM property of spoof SPP TL in more complicated circuit when small-radius bend is included and radiation loss inevitably increases.
Such spoof SPP TL has been proved to surpass microstrip, one of the most popular microwave TLs, in terms of low-crosstalk and flexible EM property, and hence is considered as a promising candidate to break the challenge of signal integrity in compact-size and highly-integrated communication systems 9. Advantages of spoof SPP such as high field confinement, low loss, and controllable dispersion properties can be utilized to build novel plasmonic waveguides and planar transmission lines (TLs) 7, 8. Electromagnetic energy is strongly confined in sub-wavelength-scaled unit cells and propagates in form of SPP wave, similar to what happens in nature at the interface between metal and dielectric in the optical regime. Recently, artificial surface plasmon polariton (SPP) has been realized at microwave and THz frequency bands through corrugated metallic structures, termed as the spoof (or designer) SPP 4, 5, 6. Therefore, analysis and solutions on this issue have been intensively studied 1, 2, 3. The “escaped” electromagnetic wave may depress the efficiency and accuracy of integrated system and even harm the electric circuits. One big challenge for large-scale high-integrated circuits is the crosstalk between planar transmission lines (TLs), especially when discontinuities such as bends or chamfers exist in TLs and, thereat, the radiation loss becomes significant. New physics and technology have been explored and developed continuously for integrated communication systems with low cost, limited size and high efficiency. Microwave communication may be one of the most popular applications of electromagnetic (EM) wave in the modern society.