Objective Terahertz (THz) wireless communication is considered a strong candidate for 6G networks. Currently,the rapid development of terahertz science and technology faces significant bottlenecks. One of the main reasons is that traditional electronic devices used for generating radio waves can no longer meet the demands for low-noise terahertz wave generation and high-speed modulation. This challenge impedes the widespread deployment and commercialization of terahertz technology across various application fields. Among the many nonlinear optical materials for generating terahertz waves,lithium niobate stands out due to its excellent electro-optic,acousto-optic,and nonlinear properties,as well as its ultra-wide transparent window and relatively high refractive index. These attributes have made it one of the most versatile and attractive photonic materials. Furthermore,metamaterials,which feature sub-wavelength artificially designed microstructures,exhibit extraordinary physical properties not found in natural materials. This provides unprecedented flexibility in the manipulation of optical materials. We aim to apply the design philosophy of metamaterials to develop a terahertz source on a lithium niobate platform that can meet the demands of 6G communication.Methods Starting from the theory of nonlinear optical difference frequency generation and the derivation of coupled-wave equations,we employ COMSOL Multiphysics software for simulation and numerical calculations to design a hybrid waveguide that integrates optical and terahertz waves. For the first time,we integrate an annealed proton-exchanged lithium niobate optical waveguide with a metallic superlattice terahertz waveguide for difference frequency generation of terahertz waves. The signal light and pump light in the near-infrared communication band propagate through the lithium niobate waveguide,inducing a nonlinear difference frequency process to generate THz waves. The waveguide structure is designed to compress the mode field. By optimizing the structural parameters of the metallic superlattice terahertz waveguide,we not only guide the propagation of the generated THz waves but also compress the THz optical field to sub-wavelength dimensions,thereby enhancing the spatial overlap with the electric field distribution of the lithium niobate optical waveguide. Additionally,we control the propagation and dispersion of the terahertz waves. This theoretically achieves quasi-phase matching,enhances the group refractive index of the THz waves,and further amplifies the nonlinear effects through the slow light effect. The difference frequency-generated THz waves are ultimately radiated into free space at the end of the waveguide.Results and Discussions Based on a hybrid integrated waveguide that combines an annealed proton-exchanged lithium niobate waveguide with a metallic superlattice terahertz waveguide,nonlinear difference frequency generation produces 0.379 THz terahertz waves. The theoretical nonlinear conversion efficiency reaches up to 3.6×10-7 W-1. The mode field distribution and dispersion of the near-infrared light transmitted through the annealed proton-exchanged lithium niobate waveguide are presented (Fig. 2). The mode field distribution and dispersion of the metallic superlattice terahertz waveguide are also provided (Fig. 3). The near-infrared and terahertz waves meet the first-order quasi-phase matching condition for difference frequency generation. The variation of the real and imaginary parts of the nonlinear coupling coefficient within one period with length is shown in the Fig. 4(a). The variation of nonlinear conversion efficiency with length is depicted as well[Fig. 4(c)]. Theoretically,this leads to a room-temperature,continuous,efficient,integrated,low-noise,and easily modulated coherent terahertz source. Notably,the fabrication process for our proposed nonlinear hybrid waveguide is mature and simple,eliminating the need for electron beam lithography (EBL) or polarization.Conclusions In this paper,we begin with the theory and formulas of nonlinear optical difference frequency generation to design an efficient nonlinear difference frequency terahertz source. This design integrates annealed proton exchange lithium niobate waveguides with metallic superlattice terahertz waveguides. By designing the waveguide structure and leveraging the unique characteristics of edge slow-light effects,we theoretically address challenges related to phase mismatch and weak nonlinear interactions between optical and terahertz waves under quasi-phase-matching conditions. Theoretically,this approach presents a room-temperature,continuous,high-efficiency,integrated,low-noise,and easily modulated coherent terahertz source. The metallic superlattice structure is not confined to a specific functional form. Various methods,including machine learning and optimization,can be employed to identify the most suitable field distribution. Additionally,by coating the ends of the waveguide to create a microcavity,the nonlinear conversion efficiency can be further enhanced. This hybrid integration method is not only applicable to optical difference frequency generation but also to other nonlinear optical processes. Moreover,it is not restricted to lithium niobate but can be used in photonic chips of other systems.
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