A new single surface integral equation for light scattering by circular dielectric cylinders Chang-Ching Tsai * , Shin-Tson Wu College of Optics and Photonics, University of Central Florida, Orlando, FL 32816, USA Received 18 December 2006; received in revised form 4 May 2007; accepted 15 May 2007 Abstract A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the prop- erty of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown function for circular dielectric-coated cylinders. In addition, numerical simulations show that even applied to elliptic scatters our equation still gives reasonably good approximate solutions in the sub-wavelength limit. Ó 2007 Elsevier B.V. All rights reserved. For scattering problems in electrodynamics, integral approach, in contrast to differential methods, possesses the analytical characteristic of solution of Helmholtz equa- tion with point source, namely, an integration of Green function. With the use of Green identity, the scattering field is obtained by the integral of the total field and its normal derivative on the enclosed surface of the object. In scatters of perfect conductor, the integrand reduces to only one var- iable, the normal derivative of field, since the field is zero on perfect conductor. So the integral becomes with one unknown of Neumann boundary condition. In dielectric homogeneous object, because none of the two variables vanishes; one single surface Green integral indeed cannot be solved with two boundary conditions. For finding these two unknown functions on the boundary, dual surface inte- gral equations are indispensable when such integrals are numerically expressed in two sets of linear algebra equa- tions [1,2]. For three-dimensional (3D) scattering of arbi- trary-shaped body, the coupled vector integral equations require one to solve a set of unknown equivalent electric and magnetic surface currents [3–5]. The matching of boundary conditions between two media in scattering is accomplished by derivation of the fields from electric and magnetic potential via the corresponding equivalent cur- rents. In two dimensional (2D) scattering, due to the advantage of decomposition of field into TE and TM com- ponents, the respective Helmholtz equation can be treated as scalar scattering problems and discussed separately; and the equivalent surface current is essentially equivalent to the normal derivative of field. The studies of 2D electro- magnetic scattering by integral equation method are extensively found in literature [6–10]. Nevertheless, the double-loaded coupled integral equations seem unpleasant in attempting the solution by numerical scheme. The first effort to reduce these two integral equations into one in 2D problems was proposed by Maystre [9,10]. With the derivation from distribution theory, Maystre successfully expressed the boundary field and its normal derivative in terms of a single surface current function. Once the equiv- alent current is found, the fields on the boundary can be obtained through a conversion integral by substitution of the current function. Later, the same idea was applied and generalized to 3D scattering problems [11–13]. With all in common, the substitution of the real field with an equivalent surface current function is the core constituent in these formulations. 0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.05.030 * Corresponding author. E-mail address: tsaicc@creol.ucf.edu (C.-C. Tsai). www.elsevier.com/locate/optcom Optics Communications 277 (2007) 247–250