We investigate the one-third harmonic generation (OTHG) in optical microfibers with power attenuation considered by analytically analyzing and numerically solving the coupled mode equations (CMEs). Both the strength and effective length of signal power growing in nonlinear media, which are extremely sensitive to the relative phase between the interaction waves, contribute to the final conversion efficiency. The relative phase and its evolution along the propagating direction play crucial roles in highly efficient OTHG. In order to obtain high conversion efficiency, the general expressions of optical threshold conditions are derived and discussed for choosing proper initial parameters. Numerically simulations are performed with both partial and absolute phase matching, which are corresponding to the microfibers with uniform and non-uniform diameters, respectively. Optimizations of relative phase and phase compensation are suggested by the simulations and provide significant enhancement of conversion efficiencies.
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