Analysis of cladding-mode couplings for a lensed fiber integrated with a long-period fiber grating by use of the beam-propagation method.

The beam-propagation method (BPM) is employed to analyze the coupling behavior of our scheme proposed previously, which combines a lensed fiber and a long-period fiber grating (LPFG) [Chen and Wang, Appl. Opt. 39,4490-4500 (2000)]. The influences of a core within the fiber lens are investigated. As for the fiber dependence of our coupling scheme, two typical fibers are studied: dispersion-shifted and single-mode, step-index fibers. With the BPM, the optimal coupling efficiencies for various source waists with corresponding lens radii and working distances are determined. We also compare the results with those obtained by use of the ABCD method and found that the BPM gives better agreement with experimental results.