硅酸盐学报

基于超表面人工基元序构协同的太赫兹涡旋二次谐波产生

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李林涛 ¹^,² , 王陈 ¹ , 文永正 ¹^,⁴ , 于凯新 ¹ , 谭永 ¹ , 张任飞 ³ , 姚佳栋 ³ , 孙竞博 ¹ , 李勃 ²^,⁴ , 周济 ¹

硅酸盐学报 | 研究论文 2026,54(7): 2184-2194

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硅酸盐学报 |研究论文 2026 , 54 (7) : 2184 -2194

基于超表面人工基元序构协同的太赫兹涡旋二次谐波产生

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李林涛¹^,², 王陈¹, 文永正¹^,⁴, 于凯新¹, 谭永¹, 张任飞³, 姚佳栋³, 孙竞博¹, 李勃²^,⁴, 周济¹

作者信息

^1．清华大学材料学院，新型陶瓷材料全国重点实验室，北京 100084

^2．清华大学深圳国际研究生院，材料研究院，广东深圳 518055

^3．乌镇实验室，超材料研究中心，浙江嘉兴 314500

^4．苏州实验室，江苏苏州 215000

通讯作者:

文永正（1987—），男，博士，副研究员；

李勃（1976—），男，博士，研究员；

周济（1962—），男，博士，教授。

作者简介:

李林涛（1998—），男，博士研究生；

王陈（1996—），女，博士。

Terahertz Second-Harmonic Vortex Generation Based on the Synergistic Design of Metasurface Meta-Atoms and Spatial Arrangement

Lintao LI¹^,², Chen WANG¹, Yongzheng WEN¹^,⁴, Kaixin YU¹, Yong TAN¹, Renfei ZHANG³, Jiadong YAO³, Jingbo SUN¹, Bo LI²^,⁴, Ji ZHOU¹

Affiliations

^1.School of Materials Science and Engineering, State Key Laboratory of New Ceramic Materials, Tsinghua University, Beijing 100084, China

^2.Institute of Materials Research, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, Guangdong, China

^3.Research Center for Metamaterials, Wuzhen Laboratory, Jiaxing 314500, Zhejiang, China

^4.Suzhou Laboratory, Suzhou 215000, Jiangsu, China

Corresponding Author:

WEN Yongzheng (1987-), male, Ph.D., Associate Professor. E-mail: wenyzheng@tsinghua.edu.cn;

LI Bo (1976-) male, Ph.D., Professor. boli@mail.tsinghua.edu.cn;

ZHOU Ji (1962-) male, Ph.D., Professor. zhouji@tsinghua.edu.cn

LI Lintao (1998-), male, Doctoral candidate. E-mail: llt24@mails.tsinghua.edu.cn;

WANG Chen (1996-), female, Ph.D. wang-chen@mail.tsinghua.edu.cn

出版时间: 2026-06-23 doi: 10.14062/j.issn.0454-5648.20260149

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摘要

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太赫兹（THz）频段非线性超表面在实现片上频率转换与波前调控一体化方面具有重要应用前景。然而，现有人工非线性结构多集中于增强非线性辐射强度，在频率转换过程中难以实现相位的独立调控。本工作基于洛伦兹力诱导的太赫兹非线性机理，提出一种通过超表面人工基元谐振模态操控，实现二次谐波相位和波前涡旋按需设计的方法。仿真分析表明，在单一基元谐振模主导且工作频点固定的条件下，结构几何参数可改变局域场相位关系，从而调控二次谐波相位。在此基础上设计并制备8种离散相位基元，实验测量结果显示，各基元在基频附近具有一致的谐振特性，其二次谐波相位在0~2π范围内形成离散等相位差分布。进一步利用实验标定的各超表面二次谐波响应，通过螺旋梯度序构排布实现阵列的空间相位编码，基于等效源模型对阵列远场进行重构计算，结果表明该离散相位基元可实现具有螺旋相位分布特征的二次谐波涡旋光，且涡旋光的拓扑荷数可控。本工作验证了人工非线性超表面中通过谐振相位实现频率转换和波前调控的可行性，为太赫兹片上非线性功能器件的波前设计提供了新的技术路径。

关键词

太赫兹二次谐波 / 非线性超表面 / 谐振相位调控 / 涡旋光产生

Abstract

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Introduction

Terahertz (THz) waves, typically spanning the frequency range from 0.1 to 10 THz, possess unique characteristics such as low photon energy, broad bandwidth, and strong penetration through nonpolar materials, enabling important applications in wireless communication, biomedical sensing, and nondestructive evaluation. Efficient manipulation of the amplitude, frequency, and phase of THz radiation is essential for the development of high-performance functional devices. Metasurfaces composed of subwavelength artificial meta-atoms provide a versatile platform for THz wavefront engineering through tailored electromagnetic responses. However, most reported THz metasurfaces operate in the linear regime and rely on propagation or geometric phase, which limits their functionality to the fundamental frequency and prevents the integration of frequency conversion and wavefront control. Second-harmonic generation (SHG) offers an effective approach for extending the accessible THz spectral range. Conventional nonlinear crystals, however, suffer from low nonlinear efficiency and stringent phase-matching requirements in this frequency region, which restrict device miniaturization and integration. Resonant artificial microstructures in semiconductors provide an alternative nonlinear mechanism through strong local electromagnetic field enhancement, where the Lorentz-force-driven nonlinear current gives rise to an effective second-order response. Nevertheless, the phase of nonlinear radiation remains difficult to control independently of the radiation amplitude. Therefore, establishing a deterministic relationship between the resonance phase and the nonlinear radiation phase is critical for nonlinear wavefront engineering. In this work, a GaAs-based metasurface is designed to correlate the resonance phase at the fundamental frequency with the phase of the second-harmonic radiation, enabling phase-engineered nonlinear wavefront construction.

Methods

The metasurface consists of gold split-ring resonators patterned on a silicon-doped n-type GaAs epitaxial layer grown on a semi-insulating GaAs substrate. Under normal incidence of an x-polarized THz wave, the resonant current in the metallic ring generates a localized magnetic field perpendicular to the surface and a strongly enhanced electric field in the split gap. The electric field drives free carriers in the n-GaAs layer, while the localized magnetic field exerts a Lorentz force on the moving carriers, resulting in a nonlinear current oscillating at twice the fundamental frequency. Three-dimensional full-wave simulations based on the finite-element method were carried out to optimize the structural parameters and analyze both the linear resonance and nonlinear time-domain response. An anisotropic conductivity tensor was introduced to describe the magneto-electric coupling induced by the Lorentz force. Four meta-atoms with equally spaced resonance phases were designed, and an additional π phase shift was obtained by rotating the structures by 180°, resulting in eight discrete nonlinear phase states covering the full 0-2π range. The samples were fabricated using metal-organic chemical vapor deposition, photolithography, magnetron sputtering, and lift-off processes. The nonlinear response was characterized using a home-built strong-field terahertz time-domain spectroscopy (THz-TDS) system, in which the second-harmonic signal was extracted by spectral filtering and detected via electro-optic sampling.

Results and discussion

Frequency-domain simulations show that all metasurface structures exhibit pronounced resonances near 0.8 THz, ensuring that the nonlinear phase comparison is performed under nearly identical linear response conditions. At the resonance frequency, strong local electric and magnetic field enhancements are observed, providing the physical origin for the Lorentz-force-driven nonlinear current. Time-domain simulations and experimental measurements confirm the generation of a cross-polarized second-harmonic signal at 1.6 THz. The four designed meta-atoms provide a phase interval of 0.25π, and the corresponding rotated structures introduce an additional π phase shift, resulting in eight discrete nonlinear phase states with nearly uniform spacing over the entire 0-2π range. Although slight amplitude variations exist among different unit cells, the measured phase evolution follows the designed linear dependence, indicating that the nonlinear phase can be effectively modulated through the resonance phase. Based on the experimentally extracted complex responses of the meta-atoms, an equivalent surface current model was employed to reconstruct the far-field radiation. By arranging the discrete phase elements according to the helical phase distribution, the reconstructed far-field exhibits a doughnut-shaped intensity profile and a continuous azimuthal phase variation of 2πl, which are the characteristic features of vortex beams. These results confirm that the experimentally obtained nonlinear phase library enables nonlinear helical wavefront construction through ordered spatial arrangement of the meta-atoms.

Conclusions

A nonlinear metasurface capable of phase-engineered terahertz second-harmonic radiation has been designed and experimentally demonstrated. By correlating the resonance phase at the fundamental frequency with the phase of nonlinear radiation, eight discrete nonlinear phase states covering the full 0-2π range were achieved through meta-atom design and structural rotation. Based on the experimentally extracted complex responses, nonlinear helical wavefronts were reconstructed through ordered spatial arrangement of the phase elements. The results verify that nonlinear wavefront engineering can be achieved through the cooperative strategy of meta-atom design and ordered arrangement. This approach enables the integration of frequency conversion and wavefront shaping within a planar artificial structure and provides a feasible route for phase engineering in nonlinear THz metasurfaces as well as for integrated structured-light sources in THz communication, imaging, and information processing.

Key words

terahertz metasurface / second-harmonic generation / nonlinear phase control / vortex beam

引用本文

李林涛, 王陈, 文永正, 于凯新, 谭永, 张任飞, 姚佳栋, 孙竞博, 李勃, 周济. 基于超表面人工基元序构协同的太赫兹涡旋二次谐波产生. 硅酸盐学报, 2026 , 54 (7) : 2184 -2194 . DOI: 10.14062/j.issn.0454-5648.20260149

Lintao LI, Chen WANG, Yongzheng WEN, Kaixin YU, Yong TAN, Renfei ZHANG, Jiadong YAO, Jingbo SUN, Bo LI, Ji ZHOU. Terahertz Second-Harmonic Vortex Generation Based on the Synergistic Design of Metasurface Meta-Atoms and Spatial Arrangement[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (7) : 2184 -2194 . DOI: 10.14062/j.issn.0454-5648.20260149

基金

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国家重点研发计划(2023YFB3811400)
国家自然科学基金基础科学中心项目(52388201)
国家自然科学基金(52332006; 12504387; 52573329)
北京市自然科学基金(Z240008)
中国博士后科学基金会(BX20250299; 2025M773396)

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2026年第54卷第7期

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文章信息

doi: 10.14062/j.issn.0454-5648.20260149

接收时间：2026-03-13
首发时间：2026-10-22
出版时间：2026-06-23

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出版历史

收稿日期：2026-03-13
修回日期：2026-05-09

基金

国家重点研发计划(2023YFB3811400)

国家自然科学基金基础科学中心项目(52388201)

国家自然科学基金(52332006; 12504387; 52573329)

北京市自然科学基金(Z240008)

中国博士后科学基金会(BX20250299; 2025M773396)

作者信息

^1．清华大学材料学院，新型陶瓷材料全国重点实验室，北京 100084

^2．清华大学深圳国际研究生院，材料研究院，广东深圳 518055

^3．乌镇实验室，超材料研究中心，浙江嘉兴 314500

^4．苏州实验室，江苏苏州 215000

通讯作者:

文永正（1987—），男，博士，副研究员；

李勃（1976—），男，博士，研究员；

周济（1962—），男，博士，教授。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20260149

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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