In this paper, a theoretical analysis of quasi-phase-matched (QPM) one-third harmonic generation (OTHG) in waveguides with different modal dispersion modulation schemes is presented. According to the different relative phase evolutions along the propagating path within the decay length, the QPM scheme falls into two categories: modal phase-mismatch switching (MPMS) and modal phase-mismatch compensating (MPMC). The enhancements of OTHG conversion efficiency in these two different modulation schemes with the same modulation depth, as compared to the unmodulated traditional modal phase-matching condition, are calculated and compared. It turns out that a higher conversion efficiency of OTHG can be achieved in a MPMC scheme than in a MPMS scheme. The dependence of OTHG conversion efficiency on the parameter of modulation depth in each modulation scheme is also analyzed. It is demonstrated that the maximal conversion efficiency of OTHG increases with the modulation depth in a MPMS scheme, which is insensitive to the modulation depth in a MPMC scheme. Based on the analysis, an improved proposal for a MPMC scheme that makes full use of the evolution of nonlinear dispersion along the propagating path is proposed and demonstrated in waveguide with optimally designed constant modal dispersion, which supports the most efficient OTHG conversion of all the discussed modal dispersion modulation schemes.
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