Abstract: This paper investigates the modal characteristics of an elliptical core optical fiber embedded with negative refrac-tive 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 graph-ically represented, providing insights into optimizing waveguide design. These findings contribute to the advancement of op-tical waveguide technologies, offering potential applications in high- precision sensing, optical communication, and photonic integrated circuits.

| DOI: 10.17148/IJIREEICE.2025.13108