Phase matching via plasmonic modal dispersion for third harmonic generation

The overall effectiveness of nonlinear optical processes along extended nonlinear media highly depends on the fulfillment of the phase-matching condition for pump and generated fields. This is traditionally accomplished by exploiting the birefringence of nonlinear crystals requiring long interaction lengths (cm-scale). For nonbirefringent media and integrated photonic devices, modal phase matching can compensate the index mismatch. Here, the various interacting waves propagate in transverse modes with appropriate phase velocities, but they suffer from a low refractive index contrast and cm-scale interaction lengths. This work harnesses modal phase matching for third-harmonic generation (THG) in plasmonic waveguides using an organic polymer (poly[3-hexylthiophene-2,5-diyl]) as the nonlinear medium. One demonstrates experimentally an effective interaction area as small as ≈ 0.11 µm2 and the phase-matched modal dispersion results in THG efficiency as high as ≈ 10–3 W-2 within an effective length scale of ≈ 4.3 µm. THG also shows a strong correlation with the polarization of the incident laser beam, corresponding to the excitation of the antisymmetric plasmonic modes, corroborating that plasmonic modal phase matching is achieved. This large reduction in device area of orders of magnitude is interesting for various applications where space is critical (e.g., device integration or on-chip applications). Z.W., Z.W., V.K., and Y.W.H. contributed equally to this work. Z.W., V.K., T.X.H., H.-S.C., Y.G., C.A.N. acknowledge the support from the National Research Foundation (NRF), under the Prime Minister's Office, Singapore, under the Medium Sized Centre Programme and the Competitive Research Programme (CRP) (NRF-CRP17-2017-08). Z.W., Z.W., Y.W.H., J.C.V.-G., and G.E. acknowledge the support from the Ministry of Education (MOE), Singapore, under AcRF Tier 3 (MOE2018-T3-1-005). J.C.V.-G. acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT), Portugal 2020 and Compete2020 through the project PTDC/NAN-OPT/29265/2017.