Analysis on the Gaussian approximation of LP 01 mode

Abstract

A new method that the equivalent mode field radius can be acquired according to the equivalent matching efficiency method is presented and the equation of the equivalent mode field radius, which is based on the core layer radius, the normalized standing wave parameter and the normalized evanescent wave parameter, is given. Moreover, adopted computer numerical simulation, a mathematical modeling between the equivalent mode field radius and the normalized frequency of fiber is established. Based on this, the equation between the equivalent mode field radius and the normalized frequency is introduced by curve fitting method. The numerical calculation indicates that it has a higher precision. As for weakly guiding optical fiber, referred to the characteristic of the beam propagation factor of diffractive beam of LP 01 mode from its end surface, it was illuminated that the Gaussian approximation for the mode field distribution of LP 01 mode is rational. The characteristic of the field of the Gaussian approximation, which is based on the equivalent mode field radius, is analyzed. The difference between the eigen mode field of LP 01 mode and the field of its Gaussian approximation is discussed. From that, we can draw the conclusion that it is relatively accurate to adopt the equivalent matching efficiency method to obtain the equivalent mode field radius.

Analysis on divergence half-angle of Gaussian approximation for the far-field of planar waveguide

“…This leads to a new definition of divergence half-angle, that is, it is redefined based on the maximal matching efficiency method. Due to the speciality of normalized frequency itself, it is so important that relationship between beam parameters and normalized frequency is widely researched and some approximate formulas are presented [7,8] . Thus, we also provide a simple series expansions based on the normalized frequency for computing divergence half-angle with a pocket calculator.…”

Analysis on the Gaussian approximation for the far-field of optical fiber

“…Moreover, as relation between beam parameters and normalized frequency is often studied and some approximate formulas are presented and used widely [7][8][9][10] , a formula of the maximal matching efficiency divergence half-angle as function of normalized frequency is given too according to a mathematical model and solving linear equations.…”