The conversion efficiency of third harmonic generation (THG) from mid-IR (3600 nm) to near-IR (1200 nm) regions in a silicon-silicon-nanocrystal hybrid plasmonic waveguide (SSHPW) was calculated. The required modal phase-matching condition (PMC) between the 0-th mode at fundamental wave (FW) and the 2-nd mode at third harmonic (TH) is achieved by carefully designing the waveguide geometry. Benefiting from the hybridized surface plasmon polariton (SPP) nature of the two guided modes, the SSHPW is capable of achieving both high THG nonlinear coefficient $\left|I_6\right|$ and reasonable linear propagation loss, thereby resulting in large figure-of-merits (FOMs) for both FW and TH. According to our simulation, THG conversion efficiency up to 0.823% is achieved at 62.9 𝜇m SSHPW with pump power of 1 W.

We provide a comprehensive study on the efficient third harmonic generation (THG) in a lossy metal-hybrid-metal asymmetric plasmonic slot waveguide (MHM) to develop a method for efficient THG by focusing on the modal phase-matching condition (PMC), the third-order nonlinear susceptibility of the nonlinear interactive material, and the pump-harmonic modal overlap in conjunction with reasonable linear propagation loss. In addition to the PMC and the nonlinear material, the stimulated THG process can be greatly enhanced by the large pump-harmonic modal overlap. With 1 W pump power, simulation results present that THG conversion efficiency up to 2.79 × 10⁻⁴ within 4.5 𝜇m MHM can be achieved.

This paper investigates one-third harmonic generation (OTHG) by analytical methods with a nondepletion approximation and with an exact solution in continuous wave conditions. The nondepletion method shows that OTHG with a small initial power is confined in a very small range except that the overlapping integrals of the pump and signal follow a certain relation. The efficiency depends only on the initial conditions. Increasing pump power only shortens the interaction length to reach the maximum conversion. Furthermore, we exactly explore OTHG by the elliptic functions whose expressions depend on the types of roots derived from the integral and the initial power. We find that the output power level is limited by the initial conditions and the structure of the waveguide, while the pump power only determines the period. There is a constant value $\mathrm{\Gamma }$ that is determined by $U_0$, ${\theta }_0$, and the overlap integrals, where $U_0$ and ${\theta }_0$ are the initial power of the signal and the initial phase difference between pump and signal, respectively. We found that a highly efficient conversion only occurs when $\mathrm{\Gamma }$ is larger than a specific value ${\mathrm{\Gamma }}_c$, called a critical value. A ${\mathrm{\Gamma }}_c$ provides a relation between $U_0$ and ${\theta }_0$. So a set of critical conditions of $U_0$ and ${\theta }_0$ is obtained. A highly efficient conversion may be supported if $U_0$ is larger than the power in this set. We investigated some typical structure parameters and found the minimum initial power supporting high conversion efficiency. In OTHG, the variation curve has a sharp peak pattern, which means that a variation of the initial phase difference leads to a great change of the conversion. We established a way to get the smallest initial power with a large phase tolerance. Finally, we find a relation among the overlapping integrals and phase mismatching that can support a high conversion efficiency with a small initial power. This study gives valuable suggestions on the experimental design.

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.

We demonstrate an efficient third harmonic generation (THG) with the effect of nonlinear loss based on a proposed double-hybrid plasmonic slot waveguide structure. Silicon nanocrystal is integrated into the two parallel slots acting as the main interactive nonlinear material. To achieve phase matching condition, we analyze the relation between the guided mode dispersions and the waveguide geometrical parameters. The effect of nonlinear loss, which is contributed by the two-photon-absorption (TPA) effect, on the THG conversion efficiency is investigated numerically. The simulation results reveal that the THG conversion efficiency can be significantly enhanced by the field confinement and enhancement, whereas it is greatly impeded in the presence of the TPA effect (a decrement of 17.6% on the THG conversion efficiency with a pump power of 4 W). According to our calculation, the THG conversion efficiency of 0.91% without the consideration of the TPA effect and 0.75% with the TPA effect under a 4-W input pump power condition is achieved.