Fig. 1. Schematic diagram of the output optical beam from (a) a normal fiber facet, (b) the fiber facet with concave cavity, and (c) the FECL with UV adhesive.

Fig. 2. Schematic of the FECL fabrication process.

Fig. 3. Measured microscope images and sectional height profiles of the etched fiber facet: (a) NMF facet, (b) NMF height profile, (c) OM4 multimode fiber facet, (d) OM4 multimode fiber height profile.

Fig. 4. (a) Measured cavity depths of NMF under etching time varying from 8 to 30 min. (b) and (c) are height profiles with paraboloid fitting after 12 min and 28 min etching, respectively.

Fig. 5. Simulated optical beam field of the output fundamental mode: (a) NMF without etching, (b) facet cavity without filling the UV adhesive, and (c) FECL with UV adhesive.

Fig. 6. Simulated fundamental mode optical beams: (a) K=0.09, (b) K=0.11, (c) K=0.13, (d) K=0.15 with fixed N_UV value at 1.6; (e) N_UV=1.56, (f) N_UV=1.6, (g) N_UV=1.64, (h) N_UV=1.68 with fixed K value at 0.12.

Fig. 7. Simulated reduction of the effective area of fundamental mode. The inset figures: (1) fundamental mode in the NMF; (2)–(5) shrunken mode fields of different FECLs.

Fig. 8. Simulated longitudinal displacement tolerance of fundamental mode spot effective area at different K.

Fig. 9. Simulated LP11 mode optical field simulation: (a) K=0.09, (b) K=0.11, (c) K=0.13, (d) K=0.15, (e) N_UV=1.56, (f) N_UV=1.6, (g) N_UV=1.64, and (h) N_UV=1.68. The N_UV value is fixed at 1.6 in (a)–(d) and the K value at 0.12 in (e)–(h), respectively.

Fig. 10. Simulated reduction of the effective area of the LP11 mode. The inset figures: (1) LP11 mode in the NMF; (2)–(5) shrunken mode fields after different FECLs.

Fig. 11. Simulated longitudinal displacement tolerance of the LP11 mode spot effective area after different FECLs. Displacement from the minimum spot area from plus to minus 12 µm.

Fig. 12. Schematic diagram of two kinds of inverse tapers: (a), (b) the top view and sectional view of the inverse taper and (c) top view of the Y-junction inverse taper waveguide.

Fig. 13. Simulated coupling efficiency of the fundamental mode from the FECL to the inverse taper under different cavity coefficient K: (a) longitudinal coupling tolerance along with longitudinal displacement and (b) lateral coupling tolerance along with horizontal alignment.

Fig. 14. Simulated coupling efficiency of the LP11 mode coupling from the fiber to the Y-junction inverse taper with different K: (a) coupling tolerance at the optimal coupling point in the longitudinal direction and (b) lateral coupling tolerance of the coupling efficiency.

Fig. 15. Simulated transmission spectrum of the FECL coupling to inverse taper for (a) the fundamental mode and (b) the LP11 mode.