Anisotropy minimization via least squares method for transformation optics

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Materials Science

Background:

• Transformation optics enables novel electromagnetic device design by manipulating spacetime.
• Anisotropy in transformation optics can lead to performance limitations and fabrication challenges.
• Existing methods for reducing anisotropy are often complex or limited in scope.

Purpose of the Study:

• To develop a straightforward and effective method for reducing anisotropy in transformation optics.
• To apply the least squares method to coordinate transformation functions for isotropic media.
• To demonstrate the technique's efficacy in designing practical optical devices like waveguides.

Main Methods:

• Incorporation of a power series into coordinate transformation functions.
• Calculation of series coefficients to minimize deviations from Cauchy-Riemann equations.
• Application to the design of a bent waveguide with varying output width.

Main Results:

• The least squares method successfully reduced transformation anisotropy to near zero.
• The designed waveguide exhibited reduced anisotropy, validating the technique's effectiveness.
• The method proved to be straightforward to implement.

Conclusions:

• The proposed least squares method offers a simple yet powerful approach to mitigate anisotropy in transformation optics.
• This technique facilitates the design of high-performance optical devices with improved isotropic properties.
• The findings pave the way for more efficient and practical transformation optics applications.