Application of the least square method for transformation optics

In this work the least squares method is used to reduce the anisotropy in transformation optics. To apply the least squares method we added power series on the coordinate transformation functions whose coefficients were calculated to reduce the deviations in Cauchy-Riemann equations. This technique does not violate boundary conditions necessary to avoid reflections on the borders and the functionality of the obtained optical medium. A mathematical treatment for the application of transformation optics in waveguides is also presented. The technique was applied for coordinate transformation in a planar waveguide to modify electromagnetic wave trajectory. The technique was effective to reduce the anisotropy to a value close to zero.