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Abstract
In the case of two-dimensional gradient index cavities designed by the conformal transformation optics, we propose a boundary integral equation method for the calculation of resonant mode functions by employing a fictitious space which is reciprocally equivalent to the physical space. Using the Green’s function of the interior region of the uniform index cavity in the fictitious space, resonant mode functions and their far-field distributions in the physical space can be obtained. As a verification, resonant modes in limaçon-shaped transformation cavities were calculated and mode patterns and far-field intensity distributions were compared with those of the same modes obtained from the finite element method.
Highlights
In the case of two-dimensional gradient index cavities designed by the conformal transformation optics, we propose a boundary integral equation method for the calculation of resonant mode functions by employing a fictitious space which is reciprocally equivalent to the physical space
We show that conventional boundary element method (BEM) can still be used to calculate resonant modes of transformation cavity (TC) with a spatially-varying refractive index profile determined by an optical conformal mapping
In order to build the boundary integral equation (BIE) for the interior region of cavity, we introduce the reciprocal virtual (RV) space which is obtained from the physical space by the inverse conformal mapping, η = f −1(ζ), as shown in Fig. 1(c, d)
Summary
Jung-Wan Ryu[1,5], Jinhang Cho[2,5], Soo-Young Lee[3,6], Yushin Kim[4], Sang-Jun Park[3], Sunghwan Rim[2], Muhan Choi2,3* & Inbo Kim2*. Many studies in TO have mainly been focused on devices enabling the control of light path, such as invisibility cloaks, flat Luneburg lenses[11,12], and waveguide bends[13], to name a few In addition to these applications of TO, recently Kim et al have suggested that TO can be exploited to the design of two-dimensional (2D) optical dielectric cavities[14]. Boundary-only methods such as the dual reciprocity method (DRM)[15] and analog equation method (AEM)[16] which have been developed from the pure BEM can be used for this kind of problems with inhomogeneous material properties These boundary-only formalism commonly uses internal nodes (collocation points) in the inhomogeneous potential region and convert domain integrals into boundary integrals, which is a rather complicated and cumbersome procedure and there is no report, as far as we know, that these methods have been employed for the optical resonant mode calculation of the 2D GRIN dielectric cavities. We demonstrate the validity of our BEM with examples of limaçon-shaped TCs
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