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The paper analyzes the two theories of conducted light signal for Bragg fiber with high-index core, namely total internal reflection and photonic bandgap. From the perspective of the wave equation, the distribution of the electromagnetic field and the conditions for forming the guided mode when the optical signal is transmitted in the core of fiber are explained. The analysis of photonic bandgap adopts the band structure principle of natural crystals for analogy. Then, the formation process of the photonic bandgap is elaborated on.

• A differential derivation method is demonstrated to accurately calculate the refractive index curves by enhancing the mode tracking ability. • For either the incomplete or the complete coupling situations, the mode evolution can be tracked with high accuracy. • The characteristics of dispersion, birefringence, and attenuation for each mode are closely related to the refractive index curves. An accurate calculation of the fiber's refractive index will benefit the development of fiber communication and fiber sensors. The refractive index of an optical fiber is an important parameter, which is closely related to the characteristics of dispersion, birefringence, and attenuation. It is vital to accurately calculate the refractive index in designing special optical fibers. However, the refractive index curves for different transmission modes of an optical fiber may be crossed or closed at some specific wavelengths, where the calculator may easily be tricked. A differential derivation method (DDM) is demonstrated to accurately calculate the refractive index curves by enhancing the mode tracking ability. The effectiveness is verified in the calculations of the refractive index curves for the HE 11 , HE 12 , TE 01 , and EH 11 modes of a custom-designed fiber. [ABSTRACT FROM AUTHOR]