Abstract. We present a theoretical investigation of the process of phase matched direct third harmonic (TH) generation in single quadratic crystal with periodical change of the sign of the second-order nonlinearity. The phase matching is achieved with quasi phase matching by appropriate choice of the period of the periodical change of the sign of the crystal second-order nonlinearity. The peculiarity in our case is that the phase matched direct TH radiation is generated as a result of the cascading of two non phase matched second-order processes: (i) second harmonic generation and (ii) frequency mixing of the second harmonic field and the fundamental field. In contrast to the process of TH generation in bulk birefringence second-order nonlinear crystals, where the phase matched TH wave is a sum of the contributions of both intrinsic cubic nonlinearity and cascaded [χ⁽²⁾ : χ⁽²⁾] cubic nonlinearity, in the case considered here only the cascaded [χ⁽²⁾ : χ⁽²⁾] cubic nonlinearity contributes to the phase matched TH signal. The developed model enables the optimization of the design parameters (period, duty factor) of periodically poled quadratic crystals for efficient TH generation at a given laser wavelength. As an example we analyzed the direct frequency tripling of 1500 nm radiation in periodically poled LiNbO₃ crystal with period 18 μm and found that conversion efficiency up to 25% could be achieved with moderate pump intensities.

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