Investigation of elliptical waveguides integrated with negative refractive index materials

Abstract: This paper investigates the modal characteristics of an elliptical core optical fiber embedded with negative refractive index material (NRIM). Utilizing the method of separation of variables in the elliptical coordinate system, we derive the eigenvalue equation in terms of first and second-kind Mathieu functions under the weak guidance condition. Numerical computations focus on cutoff frequencies and the behaviour of lower-order odd TM modes for different aspect ratios. The study reveals that the proposed waveguide supports only odd TM modes when highlighting a unique mode- selective feature. Additionally, the cutoff frequency exhibits a decreasing trend as the aspect ratio increases, demonstrating a direct correlation between waveguide geometry and modal dispersion. The variation of cutoff V-values is systematically analyzed and graphically represented, providing insights into optimizing waveguide design. These findings contribute to the advancement of optical waveguide technologies, offering potential applications in high- precision sensing, optical communication, and photonic integrated circuits.