Analysis of Nano-Wires at Terahertz and Optical Frequencies Using Surface Impedance Models

Document Type : Research Article


School of Electrical Engineering, University of Shahid Beheshti, Tehran, Iran


Different surface impedance models are applied to circular nano-wires at terahertz and optical frequencies and the accuracy of these surface impedance boundary conditions (SIBCs) is studied. The simplest form of SIBC defines a local relation between the tangential electric and magnetic equivalent surface currents at each point on the boundary. This definition is very dependent on the constituent material of the wire and its radius. The generalized IBC (GIBC) improves the accuracy of the local definition by considering the curvature of the surface at each observation point. On the other hand, the operator definition of the surface impedance presented in the SIGO method (surface impedance generating operator), is an exact field theoretical approach that determines the relation between equivalent electric and magnetic surface currents. Moreover, this method is suitable for parallel processing. For the special case of circular wires, the SIGO operator is derived. To validate the SIBC models, the results are compared with the SIGO. In spite of its extreme simplicity, it is observed that the accuracy of SIBC models is limited at optical and terahertz frequencies. It is also shown that some forms of SIBCs presented in the literature for nano-wires can be considered as special cases of SIGO formulation.


Main Subjects

 [1] Simon Ramo, John R. Whinnery and Theodore Van Duzer, Fields and Waves in Communication Electronics, Wiley, 1994.
[2] Rautio, James C., and Veysel Demir. "Microstrip conductor loss models for electromagnetic analysis." IEEE transactions on microwave theory and techniques 51, no. 3 (2003): 915-921.
[3] T. B. A. Senior, J. L. Volakis, Aproximate boundary conditions in electromagnetic, The Institution of Electrical Engineering, 1995.
[4] Gholipour, Alireza, Reza Faraji-Dana, Guy AE Vandenbosch, and Safieddin Safavi-Naeini. "Surface impedance modeling of plasmonic circuits at optical communication wavelengths." Journal of lightwave technology 31, no. 20 (2013): 3315-3322.
[5] Gholipour, Alireza, and Shokrollah Karimian. "Rectangular Nano-Wire Analysis at Terahertz and Optical Frequencies Using Interior-Exterior Method and Surface Impedance Model." In 2019 2nd West Asian Colloquium on Optical Wireless Communications (WACOWC), pp. 143-146. IEEE, 2019.
[6] T. B. a. Senior and J. L. Volakis, “Generalized impedance boundary conditions in scattering,” Proc. IEEE, vol. 79, no. 10, pp. 1413–1420, 1991.
[7] K. Coperich and A. C. Cangellaris, “Enhanced skin effect for partial-element equivalent-circuit (PEEC) models,” Microw. Theory Tech. IEEE Trans., vol. 48, no. 9, pp. 1435–1442, 2000.
[8] Shiquan He; Sha, W.E.I.; Lijun Jiang; Choy, W.C.H.; Weng Cho Chew; Zaiping Nie; “Finite-Element-Based Generalized Impedance Boundary Condition for Modeling Plasmonic Nanostructures,” Nanotechnology, IEEE Trans., vol. 11, no. 2, pp. 336–345, 2012.
[9] Gholipour, Alireza, Reza Faraji-Dana, and Guy AE Vandenbosch. "High performance analysis of layered nanolithography masks by a surface impedance generating operator." JOSA A 34, no. 4 (2017): 464-471.
[10] G. Hanson, “On the applicability of the surface impedance integral equation for optical and near infrared copper dipole antennas,” Antennas Propagation, IEEE Trans., vol. 54, no. 12, pp. 3677–3685, 2006.
[11] K. Wang and D. Mittleman, “Dispersion of surface plasmon polaritons on metal wires in the terahertz frequency range,” Phys. Rev. Lett., vol. 157401, no. April, pp. 1–4, 2006.
[12] J. Yang, Q. Cao, C. Zhou1, "Analytical Recurrence Formula for the Zeroth-order Metal Wire Plasmon of Terahertz Waves," J. Opt. Soc. Am. A, Vol. 27, No.7, July 2010.
[13] L. Knockaert, P. Van den Abeele, and D. De Zutter, “Surface impedance of cylinders and wedges: A Neumann approach,” Int. J. Electron. Commun., vol. 53, no. 1, pp. 11–17, 1999.
[14] L. Knockaert and D. De Zutter, “Integral equation for the fields inside a dielectric cylinder immersed in an incident E-wave,” Antennas Propagation, IEEE Trans., vol. 34, no. 8, pp. 1065–1067, 1986.
[15] Gholipour, A. "Analysis of optical nanostructures using the surface impedance generating operator." JOSA B 37, no. 2 (2020): 295-303.
[16] Weng Cho Chew, Mei Song Tong and Bin Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan, 2009.
[17] A. D. Rakić, A. B. Djurišic, J. M. Elazar, and M. L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices, Appl. Opt. 37, 5271-5283 (1998)