The Improved Definitions for Mode-Field Radius and Divergence Half-Angle of Optical Fiber

The improved definitions for mode-field radius and divergence half-angle of optical fiber with an arbitrary index profile are proposed in this paper, and their simple relationship as well as their relations to the second moment and differential operator definitions are derived. Analytical expressions of these definitions are obtained for the LP
₀₁
mode in step-index optical fiber; furthermore, relations between the mode-field radius, divergence half-angle, and normalized frequency are presented. Numerical data show that they are more suitable as the beam spot size of the Gaussian approximation for the near-field and far-field, respectively.