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Description
In this work we design and study a dielectric multilayer with a geometry implementing the topological Su-Schrieffer-Heeger (SSH) model1,2 supporting a strong electromagnetic field localization at the surface, which enhances linear and nonlinear optical interactions. We study second harmonic generation (SHG) from the multilayer and use it as an indirect measurement of the localized surface mode.
The studied structure consists of alternating SiO2 and Ta2O5 layers arranged following the SSH geometry, as schematically shown in Fig. 1. The multilayer is deposited on a prism in order to excite the surface modes using the Kretschmann configuration3. By selecting different truncations of the multilayer, the structure can have either a topologically non-trivial (Type 1) or trivial (Type 2) phase, which gives two structures with identical periodicity but different surface properties2.
Numerical calculations, using the transfer matrix method, reveal a highly confined surface mode in the Type 1 structure, while no localized mode is supported by the Type 2 multilayer (Fig. 1 Left). The surface mode shows strong field localization at the last layer for a wavelength of 800 nm and incident angle of 68.1º, achieving 300-fold field enhancement. In the Type 2 structure, on the other hand, there is no localization at the surface.
The increase of the confined field at the surface strengthens light-matter interactions, producing an enhancement of the nonlinear (NL) processes. In particular, since TaO2 and SiO2 are centrosymmetric materials, the expected SHG originates primarily from surface contributions and magnetic-field-induced mechanisms. In the present configuration we use the measurement of the SHG as a tool to sense the field localization on the superficial layer of the structure of Type 1. SHG measurements were performed in reflection using a tunable femtosecond laser source, with a pulse duration of 180 fs and peak intensity of 9 GW/cm2. As seen in figure 1, SHG efficiency shows a clear enhancement for the Type 1 sample compared to the Type 2 one, which has a nearly negligible signal. Moreover, Type 1 NL spectrum shows chromatic sensibility: the maximum efficiency is achieved around the resonance wavelength of the mode, 800 nm. Meanwhile, Type 2 SH signal remains flat along the measured wavelength. Experimental results show good agreement with simulations of the NL response. In addition, simulations show that the efficiencies are sensible to pulse duration, showing that the pulse bandwidth also matters.
These results show a direct link between topological field localization and enhanced harmonic generation, proving that the SHG comes only from the excitation of the surface mode in Type 1 structure.