Numerical study of tunable terahertz radiation from differential frequency generation in high-<i>Q</i> geometrically perturbed grating waveguide structures

LIANG Shijie; ZOU Jiaqi; WANG Wenjing; LIU Di; HUO Yanyan; NING Tingyin

doi:10.7498/aps.74.20240854

Abstract

Nonlinear difference frequency generation (DFG) is a key mechanism for realizing terahertz (THz) sources. Utilization of DFG within micro- and nano-structures can circumvent the phase-matching limitations while supporting device miniaturization and integrability, thus the DFG is made a significant area of research. Enhancing the local electric fields through resonant modes in micro- and nano-structures has become a promising approach to achieving efficient and tunable THz sources across a broad wavelength range. In this work, the mechanism of DFG in high-Q-factor grating-waveguide structures for efficiently tuning THz radiation over a wide spectral range is investigated by using numerical simulations based on the finite element method (COMSOL Multiphysics). Theoretical analysis reveals that modulating the positional perturbation of one of the adjacent gratings effectively doubles the grating period, causing Brillouin zone to fold. This folding shifts the dispersion curve of the guided mode (GM) within the waveguide layer above the light cone, forming a guided mode resonance (GMR) with an ultra-high Q-factor, thereby significantly enhancing THz generation in a broad spectral range. Taking a cadmium sulfide (CdS) grating-waveguide structure for example, numerical simulations demonstrate that the THz conversion efficiency reaches an order of 10^–8 W^–1 when both fundamental frequency beams have an intensity of 100 kW/cm², which is 10⁹ times higher than the conversion efficiency of a CdS film of the same thickness. Moreover, the fundamental frequency resonance wavelength can be widely tuned by adjusting the incident angle. High-Q-factor resonance modes enable various fundamental frequency combinations by changing the incident angles of the two fundamental frequency beams, facilitating the generation of THz waves with arbitrary frequencies. This approach ultimately enables a highly efficient and tunable THz source in a wide spectral range, providing valuable insights for generating THz sources on micro- and nanophotonic platforms.

Keywords:

Authors and contacts

Shandong Provincial Engineering and Technical Center of Light Manipulations, Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

Corresponding author: NING Tingyin, ningtingyin@sdnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12174228).

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References

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图 1 四部分光栅-波导结构和光配置示意图, 其中Λ是光栅-波导结构的周期, w_g是 CdS 的宽度, w_a和w_b是空气的宽度, h_g和h_w 分别是光栅层和波导层的高度

Figure 1. Schematic diagram of grating waveguide structure and light configuration. Λ is the periodicity of grating waveguide structure, w_g is the width of CdS, w_a and w_b are the width of air, h_g and h_w are the height of grating layer and waveguide layer, respectively.

DownLoad: Full-Size Img PowerPoint

图 2 (a) TE偏振光照射下周期为P = Λ/2的未扰动光栅-波导结构(绿点)和几何扰动δ = 0.1、周期为Λ的光栅结构-波导结构(红点和蓝点)的能带, 插图显示了箭头所示位置的GMR模式的电场(TE)分布; (b)波段A和波段B的Q因子与k_x的关系; (c)波导层中TE₀导波模式的色散关系(黑色实线), 以及k_x = k_{x, i}(i = –1, –2)在不同入射角θ下的色散关系, 分别为θ = 1° (酒红色虚线)、2° (红色虚线)、4° (绿色虚线)、6° (蓝色虚线)、8° (青色虚线)、10° (品红色虚线)

Figure 2. (a) Band structure of the unperturbated grating-waveguide nanostructure of period P = Λ/2 (green dots) and geometrical perturbated δ = 0.1 grating-waveguide nanostructure of period Λ (red and blue dots). The inset shows the electric field (TE) distribution of the GMR mode at the k_x as the arrow given. (b) Dependence of Q-factors of band A and B on k_x. (c) Dispersion relations of the TE₀ guide mode in the waveguide layer (black solid line), and k_x = k_{x, i} (i = –1, –2) under different angle of incidence θ = 1° (Wine red dashed line), 2° (red dashed lines), 4° (green dashed lines), 6° (blue dashed lines), 8° (cyan dashed lines), 10° (Magenta dashed line), respectively.

DownLoad: Full-Size Img PowerPoint

图 3 (a)不同参数δ的光栅-波导结构在入射角θ = 6°时的透射光谱, 插图分别显示了 δ = 0.2和1.0 结构中共振模式处的E_z分布; (b) δ = 0.1 的光栅-波导结构的透射率与入射角的关系, 插图显示了θ = 6°结构中共振模式处的电场E_z分布; (c) 在TE偏振光照射下, 光栅-波导结构的Q因子与δ的关系, 插图显示了Q因子与δ^–2之间的线性关系, 虚线为线性拟合; (d) δ = 0.1 时, 共振波长(黑色实线)和品质因数(黑色虚线)与入射角的关系

Figure 3. (a) Transmittance spectra of grating waveguide structure of different parameter δ at the incidence angle θ = 6°. The inset shows the electric field E_z distribution at the resonance modes in the structure of δ = 0.2 and 1.0, respectively. (b) The dependence of transmittance of grating waveguide structure of δ = 0.1 on the incidence angle. The inset shows the electric field E_z distribution at the resonance modes in the structure of θ = 6°. (c) Dependence of Q-factor of the grating waveguide structure on δ under TE-polarized light irradiation. The inset shows the linear relationship between Q-factor and δ^–2, and the dash line is a linear fitting. (d) The relation of resonance wavelength (solid black line) and quality factor (black dashed line) with the angle of incidence at the grating waveguide structure of δ = 0.1.

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图 4 不同入射角下DFG产生的THz转换效率与入射波长的关系, 其中入射角分别为(a) 1°和2°, (b) 3°和4°, (c) 5°和6°及(d) 7°和8°

Figure 4. Generated THz conversion efficiency (CE) from DFG as a function of incident wavelength for different incidence angles. The incident angles are (a) 1° and 2°, (b) 3° and 4°, (c) 5° and 6°, and (d) 7° and 8°.

DownLoad: Full-Size Img PowerPoint

图 5 DFG产生THz波功率与入射强度 I₁ 和 I₂ 的关系

Figure 5. Relationship of THz power via DFG with the incident intensities I₁ and I₂.

DownLoad: Full-Size Img PowerPoint

[1]	Tonouchi M 2007 Nat. Photonics 1 97 Google Scholar
[2]	Huang Y, Shen Y C, Wang J Y 2023 Engineering 22 106 Google Scholar
[3]	Koch M, Mittleman D M, Ornik J, Castro-Camus E 2023 Nat. Rev. Methods Primers 3 48 Google Scholar
[4]	Rubano A, Mou S, Marrucci L, Paparo D 2019 ACS Photonics 6 1515 Google Scholar
[5]	Li X R, Li J X, Li Y H, Ozcan A, Jarrahi M 2023 Light Sci. Appl. 12 233 Google Scholar
[6]	Lewis R A 2014 J. Phys. D: Appl. Phys. 47 374001 Google Scholar
[7]	Li H T, Lu Y L, He Z G, Jia Q K, Wang L 2016 J. Infrared, Millimeter, Terahertz Waves 37 649 Google Scholar
[8]	Li Q, Li Y D, Ding S H, Wang Q 2012 J. Infrared Millim. Te. 33 548 Google Scholar
[9]	曹俊诚, 韩英军 2024 中国激光 51 0114001 Google Scholar Cao J C, Han Y J 2024 Chin. J. Lasers 51 0114001 Google Scholar
[10]	Lai R K, Hwang J R, Norris T B, Whitaker J F 1998 Appl. Phys. Lett. 72 3100 Google Scholar
[11]	Upadhya P C, Fan W H, Burnett A, Cunningham J, Davies A G, Linfield E H, Lloyd-Hughes J, Castro-Camus E, Johnston M B, Beere H 2007 Opt. Lett. 32 2297 Google Scholar
[12]	Fan W H 2011 Chin. Opt. Lett. 9 110008 Google Scholar
[13]	Bakunov M I, Bodrov S B 2014 J. Opt. Soc. Am. B 31 2549 Google Scholar
[14]	柴路, 牛跃, 栗岩锋, 胡明列, 王清月 2016 物理学报 65 070702 Google Scholar Chai L, Niu Y, Li Y F, Hu M L, Wang Q Y 2016 Acta Phys. Sin. 65 070702 Google Scholar
[15]	黄敬国, 陆金星, 周炜, 童劲超, 黄志明, 褚君浩 2013 物理学报 62 120704 Google Scholar Huang J G, Lu J X, Zhou W, Tong J C, Huang Z, Chu J H 2013 Acta Phys. Sin. 62 120704 Google Scholar
[16]	刘欢, 徐德刚, 姚建铨 2008 物理学报 57 5662 Google Scholar Liu H, Xu D G, Yao J Q 2008 Acta Phys. Sin. 57 5662 Google Scholar
[17]	钟凯, 姚建铨, 徐德刚, 张会云, 王鹏 2011 物理学报 60 034210 Google Scholar Zhong K, Yao J Q, Xu D G, Zhang H Y, Wang P 2011 Acta Phys. Sin. 60 034210 Google Scholar
[18]	Bakunov M I, Efimenko E S, Gorelov S D, Abramovsky N A, Bodrov S B 2020 Opt. Lett. 45 3533 Google Scholar
[19]	Lu Y, Wang X, Miao L, Zuo D, Cheng Z 2011 Appl. Phys. B 103 387 Google Scholar
[20]	Tochitsky S Y, Ralph J E, Sung C, Joshi C 2005 J. Appl. Phys. 98 026101 Google Scholar
[21]	Zhong K, Yao J Q, Xu D G, Wang Z, Li Z Y, Zhang H Y, Wang P 2010 Opt. Commun. 283 3520 Google Scholar
[22]	Jiang Y, Ding Y J 2007 Appl. Phys. Lett. 91 091108 Google Scholar
[23]	Shi W, Ding Y J 2005 Opt. Lett. 30 1861 Google Scholar
[24]	Brenier A 2018 Appl. Phys. B 124 194 Google Scholar
[25]	Liu P X, Xu D G, Li J Q, Yan C, Li Z X, Wang Y Y, Yao J Q 2014 IEEE Photonics Technol. Lett. 26 494 Google Scholar
[26]	Wu F, Wu J J, Guo Z W, Jiang H T, Sun Y, Li Y H, Ren J, Chen H 2019 Phys. Rev. Appl. 12 014028 Google Scholar
[27]	Ning T Y, Li X, Zhao Y, Yin L Y, Huo Y Y, Zhao L N, Yue Q Y 2020 Opt. Express 28 34024 Google Scholar
[28]	Wu F, Qin M B, Xiao S Y 2022 J. Appl. Phys. 132 193101 Google Scholar
[29]	Wu F, Liu T T, Long Y, Xiao S Y, Chen G Y 2023 Phys. Rev. B 107 165428 Google Scholar
[30]	Wu F, Qi X, Luo M, Liu T T, Xiao S Y 2023 Phys. Rev. B 108 165404 Google Scholar
[31]	Wu F, Qi X, Qin M B, Luo M, Long Y, Wu J J, Sun Y, Jiang H T, Liu T T, Xiao S Y, Chen H 2024 Phys. Rev. B 109 085436 Google Scholar
[32]	闫梦, 孙珂, 宁廷银, 赵丽娜, 任莹莹, 霍燕燕 2023 物理学报 72 044202 Google Scholar Yan M, Sun K, Ning T Y, Zhao L N, Ren Y Y, Huo Y Y 2023 Acta Phys. Sin. 72 044202 Google Scholar
[33]	Sun K L, Wei H, Chen W J, Chen Y, Cai Y J, Qiu C W, Han Z H 2023 Phys. Rev. B 107 115415 Google Scholar
[34]	Boyd R W 2020 Nonlinear Optics (London: Academic Press
[35]	Jiang H, Han Z H 2022 J. Phys. D: Appl. Phys. 55 385106 Google Scholar
[36]	Sutherland R L 2003 Handbook of Nonlinear Optics (New York: Marcel Dekker
[37]	Amnon Yariv, Yeh P 1984 Optical Waves in Crystals (New York: Wiley
[38]	Lu J, Ding B Y, Huo Y Y, Ning T Y 2018 Opt. Commun. 415 146 Google Scholar
[39]	Liu W X, Li Y H, Jiang H T, Lai Z Q, Chen H 2013 Opt. Lett. 38 163 Google Scholar

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Numerical study of tunable terahertz radiation from differential frequency generation in high-Q geometrically perturbed grating waveguide structures

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Corresponding author: NING Tingyin, ningtingyin@sdnu.edu.cn

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Numerical study of tunable terahertz radiation from differential frequency generation in high-Q geometrically perturbed grating waveguide structures

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Corresponding author: NING Tingyin, ningtingyin@sdnu.edu.cn

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