Numerical study of the low- threshold nanolaser based on quasi-bound states in the continuum supported by resonant waveguide grating structures

Yan Meng; Sun Ke; Ning Ting-Yin; Zhao Li-Na; Ren Ying-Ying; Huo Yan-Yan

doi:10.7498/aps.72.20221894

Abstract

As a nanoscale coherent light source, semiconductor nanolaser is a key device for future optoelectronic integrated chips. The obstacle of further miniaturization of the nanolaser is that the loss increases rapidly with the decrease of cavity volume. The bound states in the continuum (BICs) can overcome the high radiative loss. Here, we propose a nanolaser based on quasi-BIC mode supported by all-dielectric resonant waveguide grating (RWG), which can effectively reduce the threshold of nanolaser. The quasi-BIC mode of the waveguide can be excited when the traditional two-part grating becomes a four-part grating. The laser behavior of the quasi-BIC is studied by finite difference-time-domain (FDTD) numerical simulation. The results show that the threshold of the naolaser based on four part-grating RWG is 20.86% lower than that of nanolaser based on two part-grating RWG when subjected to TE-polarized light irradiation. For the TM-polarized light irradiation, the threshold is 3.3 times lower than the threshold for the nanolaser based on four part-grating RWG. We also find that the threshold of the nanolaser under TE-polarized light irradiation is about one order of magnitude lower than that under TM-polarized light irradiation. Because the electric field of the structure is well confined inside the waveguide layer under TE-polarized light, which can enhance the interaction between light and gain materials and reduce the threshold of nanolasers.

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: Huo Yan-Yan, yanyanhuo2014@sdnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 91950106, 12174228), and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019MA024).

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References

[1]	Li C, Liu Z, Chen J, Gao Y, Li M L, Zhang Q 2019 Nanophotonics 8 2091 Google Scholar
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[34]	Zhao Y W, Dong Z Y, Miao S S, Deng A H, Yang J, Wang B 2006 J. Appl. Phys. 100 123519 Google Scholar

Cited By

图 1 硅衬底上四部分光栅的RWG结构单元及入射光示意图

Figure 1. Schematic diagram of the four part-grating RWG structure and incidence light on a silica substrate.

DownLoad: Full-Size Img PowerPoint

图 2 波导层中TE₀(a)和TM₀(b)导模的色散关系曲线(黑色实线), 以及在不同入射角下的k_x = k_{x, i} (i = –1, –2)色散曲线, 1° (红色虚线), 5° (绿色虚线), 10° (蓝色虚线), 15° (青色虚线).

Figure 2. Dispersion relations of the TE₀ guide mode (a) and TM₀ guide mode (b) in the waveguide layer (black solid line), and k_x = k_{x, i} (i = –1, –2) under different angle of incidence, 1° (red dashed lines), 5° (green dashed lines), 10° (blue dashed lines), 15° (cyan dashed lines), respectively.

DownLoad: Full-Size Img PowerPoint

图 3 (a)(b) θ = 5°时, 不同几何参数δ下的RWG结构在TE(a)和TM(b)偏振光照射下λ_A的反射谱; (c)在TE和TM偏振光照射下RWG结构的Q因子与δ的函数关系; (d) δ = 0.2时RWG结构分别在TE和TM偏振光照射下的共振波长与入射角的关系

Figure 3. (a)(b) Reflection spectra near λ_A of the RWG structure for different geometric parameters δ at θ = 5° under TE- (a) and TM-polarized (b) light irradiation; (c) Dependence of Q-factor of the RWG structure on δ under TE- and TM-polarized light irradiation; (d) δ = 0.2, the relation of resonance wavelength with the angle of incidence at the RWG structure under TE- and TM-polarized light irradiation.

DownLoad: Full-Size Img PowerPoint

图 4 (a)TE偏振光照射时, RWG结构在不同几何参数δ下反射峰处对应的电场(E/E₀)分布; (b)(c) TM偏振光照射时, RWG结构在不同几何参数δ下反射峰处对应的磁场(H/H₀) (b)和电场(E/E₀) (c)分布

Figure 4. (a) The electric field (E/E₀) distribution corresponding to the reflectance peaks of the RWG structure with different $\textit{δ}$ under TE-polarized light irradiation; (b)(c) The magnetic field (H/H₀) (b) and the electric field (E/E₀) (c) distributions corresponding to the reflectance peaks of the RWG structure with different $\textit{δ}$ when under TM-polarized light irradiation.

DownLoad: Full-Size Img PowerPoint

图 5 δ = 0.1时RWG结构分别在TE(a)和TM(b)偏振光照射下所支持的BIC/准BIC模式的能带结构. 黑色圆圈处为准BIC模式, 插图为该处的电场(TE)和磁场(TM)分布

Figure 5. δ = 0.1, the band structure of the BIC/quasi-BIC mode supported by the RWG structure under TE-(a) and TM-polarized (b) light irradiation.The black circle corresponds to the quasi-BIC mode. The insets show the electric field (TE) and magnetic field (TM) distribution of the quasi-BIC modes.

DownLoad: Full-Size Img PowerPoint

图 6 半导体增益介质InP的能级图

Figure 6. The energy level diagram of the semiconductor gain medium InP.

DownLoad: Full-Size Img PowerPoint

图 7 TE (a)(b)和TM (c)(d)偏振光照射时, 基于四部分光栅的RWG结构的纳米激光器的激射行为; (a)和(c) 归一化发射光谱随泵浦光功率密度的变化; (b)和(d) 归一化的最大发射强度和共振峰线宽随泵浦功率密度的变化. 插图为阈值处的电场和磁场分布

Figure 7. Lasing actions of the four part-grating RWG structure under TE (a)(b) and TM-polarized (c)(d) light irradiation; (a)(c) Evolution of the normalized emission spectra as a function of pump optical power density; (b)(d)Evolution of the normalized maximum emission intensity and emission spectra line-width as a function of pump fluence. The insets show the electric field and magnetic field distributions at threshold.

DownLoad: Full-Size Img PowerPoint

图 8 TE(a)和TM(b)偏振光照射下, 不同几何参数δ的RWG结构的归一化最大发射强度随泵浦光功率密度的变化

Figure 8. The normalized maximum emission intensity of RWG structure with different geometric parameters δ under TE-(a) and TM-polarized (b) light irradiation as a function of the input pump fluence.

DownLoad: Full-Size Img PowerPoint

[1]	Li C, Liu Z, Chen J, Gao Y, Li M L, Zhang Q 2019 Nanophotonics 8 2091 Google Scholar
[2]	Du W, Li C H, Sun J C, Xu H, Yu P, Ren A B, Wu J, Wang Z M 2020 Laser Photonics Rev. 14 2000271 Google Scholar
[3]	Ma R M, Oulton R F 2019 Nat. Nanotechnol. 14 12 Google Scholar
[4]	Saxena D, Mokkapati S, Jagadish C 2012 IEEE Photon. J. 4 582 Google Scholar
[5]	Moitra P, Slovick B A, Li W, Kraychencko II, Briggs D P, Krishnamurthy S, Valentine J 2015 ACS Photonics 2 692 Google Scholar
[6]	Bi K, Wang Q M, Xu J C, Chen L H, Lan C W, Lei M 2021 Adv. Opt. Mater. 9 2001474 Google Scholar
[7]	Qiu J L, Liu X Y, Liang Z Z, Zhu J F 2021 Opt. Lett. 46 849 Google Scholar
[8]	Jahani S, Jacob Z 2016 Nat. Nanotechnol. 11 23 Google Scholar
[9]	Ma Z J, Hanham S M, Albella P, Ng B H, Lu H T, Gong Y D, Maier S A, Hong M H 2016 ACS Photonics 3 1010 Google Scholar
[10]	Tian J Y, Li Q, Belov P A, Sinha R K, Qian W P, Qiu M 2020 ACS Photonics 7 1436 Google Scholar
[11]	Neuman J V, Wigner E 1929 Phys. Z 30 467 Google Scholar
[12]	Friedrich H, Wintgen D 1985 Phys. Rev. A 32 3231 Google Scholar
[13]	Bogdanov A A, Koshelev K L, Kapitanova P V, Rybin M V, Gladyshev S A, Sadrieva Z F, Samusev K B, Kicshar Y S, Limonov M F 2019 Adv. Photonics 1 016001 Google Scholar
[14]	Joseph S, Pandey S, Sarkar S, Joseph J 2021 Nanophotonics 10 4175 Google Scholar
[15]	Zhang Y B, Liu W W, Li Z C, Li Z, Cheng H, Chen S Q, Tian J G 2018 Opt. Lett. 43 1842 Google Scholar
[16]	Huo Y Y, Zhang X, Yan M, Sun K, Jiang S Z, Ning T Y, Zhao L N 2022 Opt. Express 30 19030 Google Scholar
[17]	Foley J M, Young S M, Phillips J D 2014 Phys. Rev. B 89 165111 Google Scholar
[18]	Zhang M D, Zhang X D 2015 Sci. Rep. 5 8266 Google Scholar
[19]	杜芊, 陈溢杭 2021 物理学报 70 154206 Google Scholar Du Q, Chen Y H 2021 Acta Phys. Sin. 70 154206 Google Scholar
[20]	Yang J H, Huang Z T, Maksimov D N, Pankin P S, Timofeev I V, Hong K B, Li H, Chen J W, Hsu C Y, Liu Y Y, Lu T C, Lin T R, Yang C S, Chen K P 2021 Laser Photonics Rev. 15 2100118 Google Scholar
[21]	Kodigala A, Lepetit T, Gu Q, Bahari B, Fainman Y, Kante B 2017 Nature 541 196 Google Scholar
[22]	Hwang M S, Lee H C, Kim K H, Jeong K Y, Kwon S H, Koshelev K, Kivshar Y, Park H G 2021 Nat. Commun. 12 4135 Google Scholar
[23]	Azzam S I, Chaudhuri K, Lagutchev A, Jacob Z, Kim Y L, Shalaev V M, Boltasseva A, Kildishev A V 2021 Laser Photonics Rev. 15 2000411 Google Scholar
[24]	Bi W L, Zhang X, Yan M, Zhao L N, Ning T Y, Huo Y Y 2021 Opt. Express 29 12634 Google Scholar
[25]	Zhang H R, Wang T, Tian J Y, Sun J C, Li S X, De Leon I, Zaccaria R P, Peng L, Gao F, Lin X, Chen H S, Wang G F 2022 Nanophotonics 11 297 Google Scholar
[26]	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
[27]	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
[28]	Liu W X, Li Y H, Jiang H T, Lai Z Q, Chen H 2013 Opt. Lett. 38 163 Google Scholar
[29]	Quaranta G, Basset G, Martin O J F, Gallinet B 2018 Laser Photonics Rev. 12 1800017 Google Scholar
[30]	Adachi S 1989 J. Appl. Phys. 66 6030 Google Scholar
[31]	Yariv A, Yeh P 1984 Optical Waves in Crystals ( New York: Wiley)
[32]	Sun K L, Jiang H, Bykov D A, Van V, Levy U, Cai Y J, Han Z H 2022 Photonics Res. 10 1575 Google Scholar
[33]	Chang S H, Taflove A 2004 Opt. Express 12 3827 Google Scholar
[34]	Zhao Y W, Dong Z Y, Miao S S, Deng A H, Yang J, Wang B 2006 J. Appl. Phys. 100 123519 Google Scholar

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