發展有限元素特徵模態分析方法以研究存在於介電質與金屬介電質多層結構之表面電磁波

Development of Finite-Element Based Eigenvalue Algorithm for Analyzing Electromagnetic Surface Waves at the Interface between a Dielectric and a Metal-Dielectric Multilayered Structure

石璧魁(Pi-Kuei Shih)

指導教授 ： 張宏鈞

國立臺灣大學/電機資訊學院/光電工程學研究所/博士(2018年)

https://doi.org/10.6342/NTU201803967

摘要

無資料

關鍵字

全向量式有限元素分析法 ； 週期性結構 ； 金屬介電質多層結構 ； Dyakonov表面波 ； 洩漏波 ； 傳播損耗

並列摘要

A full-vectorial finite element method is developed to analyze the surface waves propagating at the interface between two media which could be dissipative particularly. The dissipative wave possessing a complex-valued propagation constant can be determined precisely for any given propagation direction and thus the property of losses could be thoroughly analyzed. Besides, by applying a special characteristic of the implicit circular block matrix, we can greatly reduce the computational consumptions in the analysis.
By utilizing this method, the Dyakonov-like surface wave (DLSW) at the interface between a dielectric and a metal-dielectric multilayered (MDM) structure is discussed. At first, we consider the case when the involved MDM structure serves as an elliptic medium according to the effective medium approximation (EMA). Different from the conventional Dyakonov surface waves, we find that this kind of DLSW possesses an unexpected leaky property due to an additional hyperbolic-like wave in the MDM structure, resulting in a significant increase of propagation loss compared to the results estimated by a simple effective model based on the EMA. Moreover, such leaky property is found to be sensitive to the period of the MDM structure. Thus, to diminish this non-negligible leaky loss, one can suppress the amplitude of the leaky component by designing the MDM structure with a shorter period.
As to the case when MDM structure serves as a hyperbolic medium, we find the calculated results for the DLSW with a small period of the MDM structure will show a great inaccuracy if we ignore the metallic absorption. However, for cases of longer periods, the influence of the metallic absorption for the DLSW becomes slight. In addition, for this DLSW, we find a trade-off between its propagation loss and the field confinement. Its propagation loss is smaller for the longer period of the MDM structure but the field becomes less confined to the propagating interface of the DLSW. Furthermore, as this hyperbolic-like MDM structure with serious nonlocal effect sometimes can support an additional elliptic-like isofrequency contour, we also discuss the DLSW based on this contour. For such DLSW, an apparent leaky property is observed similarly to the case when the MDM structure serves as an elliptic medium. This DLSW propagates with a wider range of propagation direction but suffers from a poor field confinement to the interface it is propagating along.

並列關鍵字

full-vectorial finite element method ； periodic structure ； metal-dielectric multilayered structure ； Dyakonov surface wave ； leaky wave ； propagation loss

參考文獻

Ardakani, A. G., M. Naserpour, and C. J. Zapata-Rodr´ıguez, “Dyakonov-like surface waves in the THz regime,” Photon Nanostruct: Fundam. Appl., vol. 20, pp. 1–6, 2016.

Arnoldi,W. E., “The principle of minimized iterations in the solution of the matrix eigenvalue problem,” Quart. Appl. Math., vol. 9, pp. 17–29, 1951.

Artigas, D., and L. Torner, “Dyakonov surface waves in photonic metamaterials,” Phys. Rev. Lett., vol. 94, 013901, 2005.

Averkiev, N. S., and M. I. Dyakonov, “Electromagnetic waves localized at the interface of transparent anisotropic media,” Opt. Spectrosc., vol. 68, pp. 653–655, 1990.

Baken, N. H., M. B. J. Diemeer, J. M. V. Splunter, and H. Blok, “Computational modeling of diffused channel waveguides using a domain integral equation,” J. Lightwave Technol., vol. 8, pp. 576–586, 1990.