374 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 3, MARCH 1999 Fig. 5. Normalized polarizabilities of an annular apertures with a floating in- ner conductor and the one with a grounded inner conductor , , , , . Fig. 6. Normalized polarizabilities versus . approximate those of open-ended coaxial lines [4]. The difference of our results from [4] may be partly due to an infinite flange width of our structure. The electric polarizability defined in [5] is (22) In Fig. 5, we illustrate the behavior of the normalized electric polarizabilities versus with inner conductor floating or grounded. Unlike the case with the inner conductor grounded, the one with the floating inner conductor has an increased polarizability due to a penetration of the electric field through the floating conductor. In Fig. 6, we plot the normalized polarizabilities versus with different ratio when . As in the magnetic polarizabilities, they reach maximum value when is around 0.6 [3]. We observe that aperture with floating inner conductor is more efficient than the one with grounded inner conductor as a coupling structure. IV. CONCLUSION The potential distribution of the annular aperture with a floating inner conductor is investigated. Unlike the case with inner conductor grounded, the series solution contains an additional term due to the induced voltage on the inner conductor. We find the voltage using the condition of charge conservation. Using the potential distribution, we calculate the capacitances of the annular aperture and electric polarizabilities of various sizes. The capacitances explain the effect due to the finite size of the inner conductor. We observe that they comprise that of the coaxial cable and those of fringing effect due to the finite length of the inner conductor. The polarizabilities seem to be insensitive to the ratio, unlike the case with the inner conductor grounded. We observe that aperture with the floating inner conductor is more efficient than the one with the grounded inner conductor as a coupling structure. REFERENCES [1] A. Zolotov and V. P. Kazantsev, “An analytic solution of the problem of the polarizability of a circular ring aperture in an unbounded planar screen of zero thickness obtained by the variational method,” Sov. J. Commun. Technol. Electron., vol. 37, no. 4, pp. 103–105, May 1992. [2] S. S. Kurennoy, “Polarizabilities of an annular cut in the wall of an arbitrary thickness,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1109–1114, July 1996. [3] H. S. Lee and H. J. Eom, “Polarizabilities of an annular aperture in a thick conducting plane,” J. Electromag. Waves Applicat., vol. 12, pp. 269–279, Feb. 1998. [4] G. B. Gajda and S. S. Stuchly, “Numerical analysis of open-ended coaxial lines,” IEEE Trans. Microwave Theory Tech., vol. MTT-31, pp. 380–384, May 1983. [5] J. D. Jackson, Classical Electrodynamics. New York: Wiley, 1962, pp. 407–411. An Anisotropic PML for Use with Biaxial Media Arnan Mitchell, James T. Aberle, David M. Kokotoff, and Michael W. Austin Abstract— This paper presents the conditions required for an anisotropic perfectly matched layer for material exhibiting a biaxial permittivity tensor. Such materials are common in optical devices. This derivation does not treat arbitrary orientations, but should be general enough for many common situations. The effectiveness of this absorbing boundary condition is considered using the finite-element method. Index Terms—Finite methods, perfectly matched layer. I. INTRODUCTION Finite methods, namely, the finite-difference (FD), and finite- element (FE) methods, have become powerful techniques for the solution of Maxwell’s equations and have found practical use in recent years. These methods are based on the differential form of Maxwell’s equations and involve discretization of the computational space. Both methods have been used to solve closed- and open- region problems. The solution of open region problems requires the use of radiation or absorbing boundary conditions (ABC’s) to Manuscript received February 5, 1998. A. Mitchell, D. M. Kokotoff, and M. W. Austin are with the Department of Communication and Electronic Engineering, Royal Melbourne Institute of Technology, Melbourne, Vic. 3001, Australia. J. T. Aberle is with the Telecommunications Research Center, Arizona State University, Tempe, AZ 85287-7206 USA. Publisher Item Identifier S 0018-9480(99)01939-0. 0018–9480/99$10.00  1999 IEEE Authorized licensed use limited to: RMIT University. Downloaded on December 20, 2009 at 20:34 from IEEE Xplore. Restrictions apply.