In this paper, we propose a reflectionless design of an optical waveguide coupler that is nonmagnetic and homogeneous. The coupler is designed using the linear coordinate transformation of triangles from virtual space to physical space. The common problem of reflections from the boundaries of a nonmagnetic coupler is remedied by analytically specifying the common vertex of triangles in such a way that the Jacobian matrix determinant becomes equal for all transformed triangles. The device performs ideal transmission without distorting the beam profile. We employ the effective medium theory to demonstrate the realizability of the device by using consecutive dielectric layers. We present a procedure to specify the dielectric constants of the layers from common existing optical materials. Numerical finite-element simulations confirm the functionality and the reflectionless property of the proposed designs.

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