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双凹型谐振腔结构的金属半导体纳米激光器的数值仿真

张柏富 朱康 武恒 胡海峰 沈哲 许吉

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双凹型谐振腔结构的金属半导体纳米激光器的数值仿真

张柏富, 朱康, 武恒, 胡海峰, 沈哲, 许吉

Numerical study of metallic semiconductor nanolasers with double-concave cavity structures

Zhang Bai-Fu, Zhu Kang, Wu Heng, Hu Hai-Feng, Shen Zhe, Xu Ji
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  • 近年来, 金属半导体纳米激光器作为超小尺寸的光源被广泛地研究, 其在光子集成回路、片上光互连、光通信等领域具有潜在的应用价值. 随着谐振腔体积的减小, 激光器损耗也迅速增加, 这阻碍了激光器进一步的小型化. 本文提出一种基于双凹型谐振腔的金属半导体纳米激光器结构. 该结构具有圆柱形的反射端面和内凹的弯曲侧壁, 能够使谐振模式集中于腔中心并减小辐射损耗, 从而提升品质因子和降低激光器阈值. 本文利用时域有限差分方法数值计算了三种不同曲线侧壁的双凹腔性能. 数值仿真结果表明, 相比于传统胶囊型腔结构, 本文提出的双凹腔结构的品质因子提高24.8%, 激光器阈值电流降低67.5%, 能够有效提升激光器性能. 该结构在超小型金属半导体纳米激光器领域具有重要应用价值.
    Metallic semiconductor nanolaser, as an ultra-small light source, has been increasingly attractive to researchers in last decade. It can have wide potential applications such as in photonic integrated circuits, on-chip interconnect, optical communications,etc. One obstacle to miniaturization of the laser size is that the loss increases rapidly with the cavity volume decreasing. In previous studies, a type of Fabry-Perot cavity with capsule-shaped structure was investigated and demonstrated both numerically and experimentally, showing that its cavity loss is reduced dramatically in contrast to the scenario of conventional rectangular cavities. However, when the cavity size is reduced down to nanoscale, capsule-shaped structure surfers high loss. To overcome this difficulty, in this paper, a novel type of double-concave cavity structure for metallic semiconductor nanolaser in a 1.55 μm wavelength range is proposed and numerically studied. The proposed structure consists of InGaAs/InP waveguide structure encapsulated by metallic clad, and has a cylindrical reflection end face and concave curved sidewalls. The cylindrical reflection end face can push the resonant mode into the cavity center and reduce the optical field overlap with metallic sidewalls, which can reduce the metallic loss. The curved-sidewalls topologically reduce the electric field component perpendicular to the sidewalls, and thus reducing the plasmonic loss. By optimizing the waist width of the double-concave cavity structure, the radiation loss can be effectively reduced, resulting in the improvement of cavity quality factor and the decrease of threshold current. Finite-difference time-domain simulations are conducted to investigate the properties of the proposed cavity structures such as resonant mode distribution, cavity quality factor, confinement factor, threshold gain and threshold current in this paper. The numerical results show that the double-concave cavity laser with cavity volume as small as 0.258 λ3 increases 24.8% of cavity quality factor and reduces 67.5% of threshold current, compared with the conventional capsule-shaped one, demonstrating an effective improvement of metallic nanolaser. With those advantages, the proposed structure can be used for realizing the ultra-small metallic semiconductor nanolasers and relevant applications.
      通信作者: 张柏富, zhangbf@njust.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61604073, 61805119, 11404170)和江苏省自然科学基金(批准号: BK20160839, BK20180469)资助的课题
      Corresponding author: Zhang Bai-Fu, zhangbf@njust.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61604073, 61805119, 11404170) and the Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK20160839, BK20180469)
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    Miller D A B 2017 J. Lightwave Technol. 35 346Google Scholar

    [2]

    Smit M, Tol J V D, Hill M 2012 Laser Photonics Rev. 6 1Google Scholar

    [3]

    Roelkens G, Liu L, Liang D, Jones R, Fang A, Koch B, Bowers J 2010 Laser Photonics Rev. 4 751Google Scholar

    [4]

    Huang K C Y, Seo M K, Sarmiento T, Huo Y, Harris J S, Brongersma M L 2014 Nat. Photonics 8 244Google Scholar

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    Hill M T, Gather M C 2014 Nat. Photonics 8 908Google Scholar

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    McCall S L, Levi A F J, Slusher R E, Pearton S J, Logan R A 1992 Appl. Phys. Lett. 60 289Google Scholar

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    Park H G, Kim S H, Kwon S H, Ju Y G, Yang J K, Baek J H, Kim S B, Lee Y H 2004 Science 305 1444Google Scholar

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    Hill M T, Oei Y S, Smalbrugge B, Zhu Y, de Vries T, van Veldhoven P J, van Otten F W M, Eijkemans T J, Turkiewicz J P, de Waardt H, Geluk E J, Kwon S H, Lee Y H, N€otzel R., Smit M K 2007 Nature Photon. 1 589Google Scholar

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    Lee J H, Khajavikhan M, Simic A, Gu Q, Bondarenko O, Slutsky B, Nezhad M P, Fainman Y 2011 Opt. Express 19 21524Google Scholar

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    Khajavikhan M, Simic A, Katz M, Lee J H, Slutsky B, Mizrahi A, Lomakin V, Fainman Y 2012 Nature 482 204Google Scholar

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    Guo C C, Xiao J L, Yang Y D, Huang Y Z 2014 J. Opt. Soc. Am. B 31 865Google Scholar

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    Kwon S H, Kang J H, Seassal C, Kim S K, Regreny P, Lee Y H, Lieber C M, Park H G 2010 Nano Lett. 10 3679Google Scholar

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    Ding K, Ning C Z 2012 Light: Sci. Appl. 1 e20Google Scholar

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    Hill M T, Marell M, Leong E S P, Smalbrugge B, Zhu Y, Sun M, van Veldhoven P J, Geluk E J, Karouta F, Oei Y S, Nötzel1 R, Ning C Z, Smit M K 2009 Opt. Express 17 11107Google Scholar

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    Ding K, Liu Z C, Yin L J, Hill M T, Marel M J H, van Veldhoven P J, Nöetzel R, Ning C Z 2012 Phys. Rev. B 85 041301

    [16]

    Ding K, Hill M T, Liu Z C, Yin L J, van Veldhoven P J, Ning C Z 2013 Opt. Express 21 4728Google Scholar

    [17]

    Zhang B, Okimoto T, Tanemura T, Nakano Y 2014 Jpn. J. Appl. Phys. 53 112703Google Scholar

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    Zhang B, Chieda K, Okimoto T, Tanemura T, Nakano Y 2016 Phys. Status Solidi A 213 965Google Scholar

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    Xiao Y, Taylor R J E, Yu C, Feng K, Tanemura T, Nakano Y 2017 Appl. Phys. Lett. 111 081107Google Scholar

    [20]

    Zhang B, Zhu K, Hao J, Wang B, Shen Z, Hu H 2018 IEEE Photon. J. 10 4502110

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    Taflove A, Hagness S C 2005 Computational Electrodynamics: The Finite-Difference Time-Domain Method (Norwood: Artech House) pp354

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    Palik E D 1985 Handbook of Optical Constants of Solids (NewYork: Academic) pp350

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    Coldren L A, Corzine S W, Masanovic M L, 2012 Diode Lasers and Photonic Integrated Circuits, ed. K. Chang (New York: Wiley) pp55-70

    [25]

    Coldren L A, Corzine S W, Masanovic M L, 2012 Diode Lasers and Photonic Integrated Circuits, ed. K. Chang (New York: Wiley) pp224

    [26]

    Zielinski E, Schweizer H, Streubel K, Eisele H, Weimann G 1986 J. Appl. Phys. 59 2196Google Scholar

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    Gu Q, Shane J, Vallini F, Wingad B, Smalley J S T, Frateschi N C, Fainman Y 2014 IEEE J. Quantum Electron. 50 499Google Scholar

    [29]

    Shane J, Gu Q, Vallini F, Wingad B, Smalley J S T, Frateschi N C, Fainman Y 2014 Proc. SPIE 8980 898027

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    Ding K, Ning C Z 2013 Semicond. Sci. Technol. 28 124002Google Scholar

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    Karouta F 2014 J. Phys. D: Appl. Phys. 47 233501Google Scholar

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    Kuttge M, Vesseur E J R, Verhoeven J, Lezec H J, Atwater H A, Polman A 2008 Appl. Phys. Lett. 93 113110Google Scholar

  • 图 1  双凹型金属半导体纳米激光器谐振腔示意图 (a)结构示意图; (b)俯视图

    Fig. 1.  Schematic of double-concave cavity of metallic semiconductor nanolaser: (a) The structure; (b) top view of the double-concave cavity.

    图 2  CSC型谐振腔(L = 700 nm, W = 520 nm) Q值与曲率半径R的关系

    Fig. 2.  Q values of the capsule-shaped cavities (L = 700 nm, W = 520 nm) as functions of the radius of curvature R.

    图 3  三种曲线侧壁的双凹型谐振腔(L = 700 nm, W = 520 nm, L/R = 1.43)的品质因子Q、辐射品质因子Qrad和耗散品质因子QdissW0/W的关系 (a) Q; (b) Qrad; (c) Qdiss

    Fig. 3.  Quality factors Q, radiation quality factors Qrad and dissipation quality factors Qdiss of three double-concave cavities with curved sidewalls (L = 700 nm, W = 520 nm, L/R = 1.43) as functions of the W0/W: (a) Q; (b) Qrad; (c) Qdiss.

    图 4  不同谐振腔结构的谐振模式(TE模式)的归一化电场强度|E|2在穿过腔中心的xyyzxz平面的分布图 (a)— (c)为胶囊型腔; (d)— (f)为一次函数型腔; (g)— (i)为抛物线型腔; (j)—(l)为余弦函数型腔. 所有腔的几何参数详见表2

    Fig. 4.  Normalized electric field intensity distribution |E|2 of the resonant mode (TE mode) in the xy-, yz- and xz-planes crossing the cavity center: (a)–(c) The capsule-shaped cavity; (d)–(f) the linear-function-shaped cavity; (g)–(i) the parabola-shaped cavity; (j)–(l) the cosine-shaped cavity. All the geometric parameters of the cavities are listed in Table 2 in detail.

    图 5  三种曲线侧壁双凹型谐振腔(L = 700 nm, W = 520 nm, L/R = 1.43)的金属半导体纳米激光器的限制因子Γ、阈值增益gth和阈值电流IthW0/W的关系 (a) Γ; (b) gth; (c) Ith

    Fig. 5.  The confinement factor Γ, threshold gain gth and threshold current Ith of the metallic semiconductor nanolasers with three double-concave cavities with curved sidewalls (L = 700 nm, W = 520 nm, L/R = 1.43) as functions of the W0/W: (a) Γ; (b) gth; (c) Ith.

    表 1  双凹型谐振腔的侧壁曲线方程

    Table 1.  Curve equations of the sidewalls of the double-concave cavities

    侧壁曲线类型侧壁曲线方程
    一次函数型y = |a1x| + W0/2
    抛物线型y = a2x2 + W0/2
    余弦函数型y = a3cos(bx) + W/2
    下载: 导出CSV

    表 2  四种谐振腔的金属半导体纳米激光器的几何参数和数值仿真结果

    Table 2.  Geometric parameters and simulation results of the metallic semiconductor nanolasers with four types of cavities.

    参数胶囊型一次函数型抛物线型余弦函数型
    L/nm700700700700
    W/nm520520520520
    W0/W1.000.750.80.80
    L/R1.431.431.431.43
    V/λ30.2670.2580.2570.258
    λ/nm1564155215501551
    Q141174175176
    Г0.4600.4410.4400.445
    gth/cm–12190187018501830
    Ith/μA800290280260
    下载: 导出CSV
  • [1]

    Miller D A B 2017 J. Lightwave Technol. 35 346Google Scholar

    [2]

    Smit M, Tol J V D, Hill M 2012 Laser Photonics Rev. 6 1Google Scholar

    [3]

    Roelkens G, Liu L, Liang D, Jones R, Fang A, Koch B, Bowers J 2010 Laser Photonics Rev. 4 751Google Scholar

    [4]

    Huang K C Y, Seo M K, Sarmiento T, Huo Y, Harris J S, Brongersma M L 2014 Nat. Photonics 8 244Google Scholar

    [5]

    Hill M T, Gather M C 2014 Nat. Photonics 8 908Google Scholar

    [6]

    McCall S L, Levi A F J, Slusher R E, Pearton S J, Logan R A 1992 Appl. Phys. Lett. 60 289Google Scholar

    [7]

    Park H G, Kim S H, Kwon S H, Ju Y G, Yang J K, Baek J H, Kim S B, Lee Y H 2004 Science 305 1444Google Scholar

    [8]

    Hill M T, Oei Y S, Smalbrugge B, Zhu Y, de Vries T, van Veldhoven P J, van Otten F W M, Eijkemans T J, Turkiewicz J P, de Waardt H, Geluk E J, Kwon S H, Lee Y H, N€otzel R., Smit M K 2007 Nature Photon. 1 589Google Scholar

    [9]

    Lee J H, Khajavikhan M, Simic A, Gu Q, Bondarenko O, Slutsky B, Nezhad M P, Fainman Y 2011 Opt. Express 19 21524Google Scholar

    [10]

    Khajavikhan M, Simic A, Katz M, Lee J H, Slutsky B, Mizrahi A, Lomakin V, Fainman Y 2012 Nature 482 204Google Scholar

    [11]

    Guo C C, Xiao J L, Yang Y D, Huang Y Z 2014 J. Opt. Soc. Am. B 31 865Google Scholar

    [12]

    Kwon S H, Kang J H, Seassal C, Kim S K, Regreny P, Lee Y H, Lieber C M, Park H G 2010 Nano Lett. 10 3679Google Scholar

    [13]

    Ding K, Ning C Z 2012 Light: Sci. Appl. 1 e20Google Scholar

    [14]

    Hill M T, Marell M, Leong E S P, Smalbrugge B, Zhu Y, Sun M, van Veldhoven P J, Geluk E J, Karouta F, Oei Y S, Nötzel1 R, Ning C Z, Smit M K 2009 Opt. Express 17 11107Google Scholar

    [15]

    Ding K, Liu Z C, Yin L J, Hill M T, Marel M J H, van Veldhoven P J, Nöetzel R, Ning C Z 2012 Phys. Rev. B 85 041301

    [16]

    Ding K, Hill M T, Liu Z C, Yin L J, van Veldhoven P J, Ning C Z 2013 Opt. Express 21 4728Google Scholar

    [17]

    Zhang B, Okimoto T, Tanemura T, Nakano Y 2014 Jpn. J. Appl. Phys. 53 112703Google Scholar

    [18]

    Zhang B, Chieda K, Okimoto T, Tanemura T, Nakano Y 2016 Phys. Status Solidi A 213 965Google Scholar

    [19]

    Xiao Y, Taylor R J E, Yu C, Feng K, Tanemura T, Nakano Y 2017 Appl. Phys. Lett. 111 081107Google Scholar

    [20]

    Zhang B, Zhu K, Hao J, Wang B, Shen Z, Hu H 2018 IEEE Photon. J. 10 4502110

    [21]

    Taflove A, Hagness S C 2005 Computational Electrodynamics: The Finite-Difference Time-Domain Method (Norwood: Artech House) pp354

    [22]

    Palik E D 1985 Handbook of Optical Constants of Solids (NewYork: Academic) pp350

    [23]

    Long H, Huang Y Z, Zou L X, Yang Y D, Lv X M, Ma X W, Xiao J L 2014 J. Lightwave Technol. 32 3192Google Scholar

    [24]

    Coldren L A, Corzine S W, Masanovic M L, 2012 Diode Lasers and Photonic Integrated Circuits, ed. K. Chang (New York: Wiley) pp55-70

    [25]

    Coldren L A, Corzine S W, Masanovic M L, 2012 Diode Lasers and Photonic Integrated Circuits, ed. K. Chang (New York: Wiley) pp224

    [26]

    Zielinski E, Schweizer H, Streubel K, Eisele H, Weimann G 1986 J. Appl. Phys. 59 2196Google Scholar

    [27]

    Zou Y, Osinski J S, Grodzinski P, Dapkus P D, Rideout W C, Shadin W F, Schlafer J, Crawford F D 1993 IEEE J. Quantum Electron. 29 1565

    [28]

    Gu Q, Shane J, Vallini F, Wingad B, Smalley J S T, Frateschi N C, Fainman Y 2014 IEEE J. Quantum Electron. 50 499Google Scholar

    [29]

    Shane J, Gu Q, Vallini F, Wingad B, Smalley J S T, Frateschi N C, Fainman Y 2014 Proc. SPIE 8980 898027

    [30]

    Ding K, Ning C Z 2013 Semicond. Sci. Technol. 28 124002Google Scholar

    [31]

    Karouta F 2014 J. Phys. D: Appl. Phys. 47 233501Google Scholar

    [32]

    Kuttge M, Vesseur E J R, Verhoeven J, Lezec H J, Atwater H A, Polman A 2008 Appl. Phys. Lett. 93 113110Google Scholar

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出版历程
  • 收稿日期:  2019-06-22
  • 修回日期:  2019-07-29
  • 上网日期:  2019-11-01
  • 刊出日期:  2019-11-20

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