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基于半导体量子阱中四波混频效应的高效光学非互易

盖云冉 郑康 丁春玲 郝向英 金锐博

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基于半导体量子阱中四波混频效应的高效光学非互易

盖云冉, 郑康, 丁春玲, 郝向英, 金锐博

Efficient optical nonreciprocity based on four-wave mixing effect in semiconductor quantum well

Ge Yun-Ran, Zheng Kang, Ding Chun-Ling, Hao Xiang-Ying, Jin Rui-Bo
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  • 基于半导体量子阱纳米结构中的四波混频效应, 提出了一种无磁光学非互易的理论方案. 利用实验可得的合适参数, 实现了具有高传输率的非互易传输和非互易相移. 此外, 将这种半导体量子阱纳米结构嵌入马赫-曾德尔干涉仪, 选择适当的参数, 可以实现隔离比为92.39 dB、插入损耗为0.25 dB的双端口光隔离器, 以及保真度为0.9993、光子存活率为0.9518、低插入损耗的四端口光环行器. 半导体介质具有更容易集成和参数可调的优势, 此方案可以为基于半导体固态介质的非互易性和非互易光子器件的实现提供理论指导.
    Optical nonreciprocity has been a popular research topic in recent years. Semiconductor quantum wells (SQWs) play a key role in many high-performance optoelectronic devices. In this paper, we propose a theoretical scheme to achieve nonmagnetic optical nonreciprocity based on the four-wave mixing effect in SQW nanostructures. Using the experimentally available parameters, the nonreciprocal behavior of the probe field in forward direction and backward direction is achieved through this SQW, where both nonreciprocal transmission and nonreciprocal phase shift have high transmission rates. Furthermore, by embedding this SQW nanostructure into a Mach-Zender interferometer, a reconfigurable nonreciprocal device based on high transmission nonreciprocal phase shift that can be used as an isolator or a circulator, is designed and analyzed. The device can be realized as a two-port optical isolator with an isolation ratio of 92.39 dB and an insertion loss of 0.25 dB, and as a four-port optical circulator with a fidelity of 0.9993, a photon survival probability of 0.9518 and a low insertion loss with suitable parameters. Semiconductor media have the advantages of easier integration and tunable parameters, and this scheme can provide theoretical guidance for implementing nonreciprocal and nonreciprocal photonic devices based on semiconductor solid-state media.
      通信作者: 郝向英, xyhao.321@163.com
    • 基金项目: 国家自然科学基金(批准号: 12074299, 11704290, 11705131)资助的课题.
      Corresponding author: Hao Xiang-Ying, xyhao.321@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12074299, 11704290, 11705131).
    [1]

    Malz D, Tóth L D, Bernier N R, Feofanov A K, Kippenberg T J, Nunnenkamp A 2018 Phys. Rev. Lett. 120 023601Google Scholar

    [2]

    Hu Y, Qi Y, You Y, Zhang S, Lin G, Li X, Gong J, Gong S, Niu Y 2021 Phys. Rev. Appl. 16 014046Google Scholar

    [3]

    Muñoz H A, Carusotto I 2022 Phys. Rev. A 106 063523Google Scholar

    [4]

    Singh N, Kärtner F X 2022 Opt. Express 30 5973Google Scholar

    [5]

    Bi L, Hu J, Jiang P, Kim D H, Dionne G F, Kimerling L C, Ross C A 2011 Nat. Photonics 5 758Google Scholar

    [6]

    Gao J, Wang X, Han F, Wan J, Gu W 2023 Micromachines-basel 14 33Google Scholar

    [7]

    Yang Z, Cheng Y, Wang N, Chen Y, Wang S 2022 Opt. Express 30 27993Google Scholar

    [8]

    Liang J, Li Y, Dai T, Zhang Y, Zhang X, Liu H, Wang P 2023 Opt. Express 31 8375Google Scholar

    [9]

    Wang X, Ptitcyn G, Asadchy V S, Díaz R A, Mirmoosa M S, Fan S, Tretyakov S A 2020 Phys. Rev. Lett. 125 266102Google Scholar

    [10]

    Shah M, Briggs I, Chen P K, Hou S, Fan L 2023 Opt. Lett. 48 1978Google Scholar

    [11]

    张利巍, 李贤丽, 杨柳 2019 物理学报 68 170701Google Scholar

    Zhang L W, Li X L, Yang L 2019 Acta Phys. Sin. 68 170701Google Scholar

    [12]

    Tang J S, Nie W, Tang L, Chen M, Su X, Lu Y, Nori F, Xia K 2022 Phys. Rev. Lett. 128 203602Google Scholar

    [13]

    Lan Y T, Su W J, Wu H, Li Y, Zheng S B 2022 Opt. Lett. 47 1182Google Scholar

    [14]

    刘妮, 马硕, 梁九卿 2023 物理学报 72 060702Google Scholar

    Liu N, Ma S, Liang J Q 2023 Acta Phys. Sin. 72 060702Google Scholar

    [15]

    Xia K, Nori F, Xiao M 2018 Phys. Rev. Lett. 121 203602Google Scholar

    [16]

    You Y, Hu Y, Lin G, Qi Y, Niu Y, Gong S 2021 Phys. Rev. A 103 063706Google Scholar

    [17]

    Liang C, Liu B, Xu A N, Wen X, Lu C, Xia K, Tey M K, Liu Y C, You L 2021 Phys. Rev. Lett. 125 123901Google Scholar

    [18]

    Hu X X, Wang Z B, Zhang P, Chen G J, Zhang Y L, Li G, Zou X B, Zhang T, Tang H X, Dong C H 2021 Nat. Commun. 12 2389Google Scholar

    [19]

    李鑫, 解舒云, 李林帆, 周海涛, 王丹, 杨保东 2022 物理学报 71 184202Google Scholar

    Li X, Xie S Y, Li L F, Zhou H T, Wang D, Yang B D 2022 Acta Phys. Sin. 71 184202Google Scholar

    [20]

    Zheng Y, Yang J, Shen Z, Cao J, Chen X, Liang X, Wan W 2015 Light-Sci. Appl. 5 e16072Google Scholar

    [21]

    Shui T, Yang W X, Cheng M T, Lee R K 2022 Opt. Express 30 6284Google Scholar

    [22]

    Rashidi S, Entezar S R, Rashidi A 2021 Appl. Opt. 60 8651Google Scholar

    [23]

    Mai J, Cheah K W 2022 Opt. Express 30 46357Google Scholar

    [24]

    Al M M, Xiang Q, Miura Y, Belmoubarik M, Masuda K, Kasai S, Sukegawa H, Mitani S 2021 Phys. Rev. B 103 L180408Google Scholar

    [25]

    Bouscher S, Panna D, Balasubramanian K, Cohen S, Ritter D, Hayat A 2022 Phys. Rev. Lett. 128 127701Google Scholar

    [26]

    Kinoshita K, Moriya R, Okazaki S, Zhang Y, Masubuchi S, Watanabe K, Taniguchi T, Sasagawa T, Machida T 2022 Nano Lett. 22 4640Google Scholar

    [27]

    Liu S, Yang W X, Chuang Y L, Chen A X, Liu A, Huang Y, Lee R K 2014 Opt. Express 22 29179Google Scholar

    [28]

    Hao X, Li J, Liu J, Song P, Yang X 2008 Phys. Lett. A 372 2509Google Scholar

    [29]

    Zhang Y, Wang Z, Qiu J, Hong Y, Yu B 2019 Appl. Phys. Lett. 115 171905Google Scholar

    [30]

    Qiu J, Wang Z, Ding D, Li W, Yu B 2020 Opt. Express 28 2975Google Scholar

    [31]

    Zhang S, Lin G, Hu Y, Qi Y, Gong S 2020 Phys. Rev. Appl. 14 024032Google Scholar

    [32]

    Faist J, Sirtori C, Capasso F, Pfeiffer L, West K W 1994 Appl. Phys. Lett. 64 872Google Scholar

    [33]

    Wang Z, Zhang Y, Paspalakis E, Yu B 2020 Phys. Rev. A 102 063509Google Scholar

    [34]

    Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135Google Scholar

    [35]

    Li E Z, Ding D S, Yu Y C, Dong M X, Zeng L, Zhang W H, Ye Y H, Wu H Z, Zhu Z H, Gao W, Guo G C, Shi B S 2020 Phys. Rev. Res. 2 033517Google Scholar

    [36]

    Hsiao Y F, Chen H S, Tsai P J, Chen Y C 2014 Phys. Rev. A 90 055401Google Scholar

    [37]

    Cong G W, Akimoto R, Akita K, Hasama T, Ishikawa H 2007 Appl. Phys. Lett. 90 181919Google Scholar

    [38]

    Zhang C, Yang W, Song X, Xu Z 2009 J. Phys. B: At. Mol. Opt. Phys. 42 125604Google Scholar

    [39]

    武香莲, 赵珂, 贾海洪, 王富青 2015 物理学报 64 233301Google Scholar

    Wu X L, Zhao K, Jia H H, Wang F Q 2015 Acta Phys. Sin. 64 233301Google Scholar

  • 图 1  本文考虑的理论模型 (a)被$ {\mathrm{Al}}_{0.33}{\mathrm{Ga}} _{0.67}{\mathrm{As}} $势垒隔开的GaAs调制掺杂量子阱结构的单周期能带示意图, 图中还显示了电子能级的位置及相应的波函数. (b)能级排列示意图. 前向传输时光场$ \varOmega_{{\mathrm{p}}}^{{\mathrm{f}}} $(红色), $ \varOmega_{{\mathrm{c}}} $(深蓝色), $ \varOmega_{{\mathrm{d}}} $(浅蓝色)与相应能级跃迁相互作用, 产生混频场$ \varOmega_{{\mathrm{m}}}^{{\mathrm{f}}} $(绿色); 后向传输时, 三个光场$ \varOmega_{{\mathrm{p}}}^{{\mathrm{b}}} $(玫红色), $ \varOmega_{{\mathrm{c}}} $, $ \varOmega_{{\mathrm{d}}} $耦合相应的能级跃迁. (c) SDQW样品与光场相互作用示意图

    Fig. 1.  Theoretical model considered in this paper: (a) Schematic band diagram of a single period of the GaAs modulation-doped quantum wells structure separated by a $ {\mathrm{Al}}_{0.33}{\mathrm{Ga}} _{0.67}{\mathrm{As}} $ barrier. The positions of the calculated energy subbands and the corresponding modulus squared of the electronic wave functions are also displayed. (b) Schematic of the energy level arrangement. During forward transmission, the light fields $ \varOmega_{{\mathrm{p}}}^{{\mathrm{f}}} $ (red), $ \varOmega_{{\mathrm{c}}} $ (dark blue), $ \varOmega_{{\mathrm{d}}} $ (light blue) interact with the corresponding energy level transitions to generate a mixing field $ \varOmega_{{\mathrm{m}}}^{{\mathrm{f}}} $ (green); during backward transmission, the three light fields $ \varOmega_{{\mathrm{p}}}^{{\mathrm{b}}} $ (rose red), $ \varOmega_{{\mathrm{c}}} $, $ \varOmega_{{\mathrm{d}}} $ are coupled with corresponding energy level transitions. (c) Schematic diagram of the SDQW sample interacting with all optical fields.

    图 2  前向探测场和后向探测场不同光学深度时的仿真图 (a)前向探测场$ \varOmega_{{\mathrm{p}}}^{{\mathrm{f}}} $和后向探测场$ \varOmega_{{\mathrm{p}}}^{{\mathrm{b}}} $在光学深度范围0—800内变化的相位图; (b)前向探测场和后向探测场的振幅随$ \alpha $的变化; (c)前向探测场和后向探测场的相移随$ \alpha $的变化. 其他参数取值为$ \gamma_{21}=0.2\; {\mathrm{meV }}$, $ \gamma_{31}=\gamma_{41}=2\; {\mathrm{meV }} $, $ \varOmega_{{\mathrm{c}}}=\varOmega_{{\mathrm{d}}}=24.5\varGamma $, $ \delta_{{\mathrm{p}}}=\delta_{{\mathrm{c}}}=0 $, $ \delta_{{\mathrm{d}}}=100.25\varGamma $, $ \varGamma=4\; {\mathrm{meV }} $

    Fig. 2.  Simulation diagrams of the forward probe field and the backward probe field at different optical depths: (a) Phase diagram of the forward probe field $ \varOmega_{{\mathrm{p}}}^{{\mathrm{f}}} $ and the backward probe field $ \varOmega_{{\mathrm{p}}}^{{\mathrm{b}}} $ in the optical depth range 0 to 800; (b) diagram of the amplitude of the forward probe field and the backward probe field changing with $ \alpha $; (c) diagram of the phase shift of the forward probe field and the backward probe field changing with $ \alpha $. Other parameters are $ \gamma_{21}=0.2\; {\mathrm{meV }} $, $ \gamma_{31}=\gamma_{41}=2\; {\mathrm{meV }} $, $ \varOmega_{{\mathrm{c}}}=\varOmega_{{\mathrm{d}}}=24.5\varGamma $, $ \delta_{{\mathrm{p}}}=\delta_{{\mathrm{c}}}=0 $, $ \delta_{{\mathrm{d}}}=100.25\varGamma $, and $ \varGamma=4 \; {\mathrm{meV }}$.

    图 3  不同探测场的振幅和相移在不同驱动失谐$ \delta_{{\mathrm{d}}} $时的仿真结果 (a)前向探测场和后向探测场的振幅随$ \delta_{{\mathrm{d}}} $的变化; (b)前向探测场和后向探测场的相移随$ \delta_{{\mathrm{d}}} $的变化. 其他参数取值与图2 相同, 除了$ \alpha $ = 630

    Fig. 3.  Simulation results of the amplitude and phase shift of different probe fields under different detuning of driving fields $ \delta_{{\mathrm{d}}} $: (a) Change graph of the amplitude of the forward probe field and the backward probe field with $ \delta_{{\mathrm{d}}} $; (b) change graph of the phase shift of the forward probe field and the backward probe field with $ \delta_{{\mathrm{d}}} $. Other parameters are the same as in Fig. 2, except for $ \alpha $ = 630.

    图 4  光隔离器和环行器装置的简单示意图. 对于光隔离器, 只考虑嵌入SDQW纳米结构的上分支. 为了实现光环行器, 下分支与上分支使用分束器BS 1和BS 2组成MZI

    Fig. 4.  A simple schematic of the optical isolator and circulator devices. For the optical isolator, we consider only the upper branch embedded in the SDQW nanostructure. To implement the optical circulator, the lower branch and the upper branch use beam splitters BS 1 and BS 2 to form the MZI.

    图 5  用作光隔离器时的仿真结果 (a)传输系数$ T_{12} $和$ T_{21} $随探测失谐$ \delta_{{\mathrm{p}}} $的变化图; (b)隔离比IR和插入损耗IL随探测失谐$ \delta_{{\mathrm{p}}} $的变化图. 除了$ \alpha=630 $, 其他参数取值与图2 相同

    Fig. 5.  Simulation results when used as an optical isolator: (a) Graph of transmission coefficients $ T_{12} $ and $ T_{21} $ with probe detuning $ \delta_{{\mathrm{p}}} $; (b) graph of isolation ratio IR and insertion loss IL with probe detuning $ \delta_{{\mathrm{p}}} $. Parameters are the same as in Fig. 2, except that $ \alpha=630 $.

    图 6  用作光环行器时的仿真结果 (a), (b)前向循环和后向循环传输系数与探测失谐$ \delta_{{\mathrm{p}}} $的关系; (c)光环行器的保真度F和平均光子存活率η与探测失谐$ \delta_{{\mathrm{p}}} $的关系. 除了$ \alpha=630 $, 其他参数取值与图2 相同

    Fig. 6.  Simulation results when used as an optical circulator: (a), (b) Relationship between the transmission coefficients of the forward cycle and the backward cycle and the probe detuning $ \delta_{{\mathrm{p}}} $; (c) fidelity F and average survival probability η of the optical circulator versus probe detuning $ \delta_{{\mathrm{p}}} $. Parameters are the same as in Fig. 2 except for $ \alpha=630 $.

    表 1  4个光隔离器性能指标的比较

    Table 1.  Comparing of the performance metrics for four optical isolators

    光隔离器 IR/dB IL/dB
    文献[35] 20
    文献[15] ~40 < 1
    文献[21] 79.70 0.35
    本文方案 92.39 0.25
    下载: 导出CSV

    表 2  4个光环行器性能指标的比较

    Table 2.  Comparing of the performance metrics for four optical circulators

    光环行器 F η IL/dB
    文献[15] 0.94 0.72 1.42
    文献[31] 0.98 0.85 0.7
    文献[21] 0.9985 0.9278 0.33
    本文方案 0.9993 0.9518 0.22
    下载: 导出CSV
  • [1]

    Malz D, Tóth L D, Bernier N R, Feofanov A K, Kippenberg T J, Nunnenkamp A 2018 Phys. Rev. Lett. 120 023601Google Scholar

    [2]

    Hu Y, Qi Y, You Y, Zhang S, Lin G, Li X, Gong J, Gong S, Niu Y 2021 Phys. Rev. Appl. 16 014046Google Scholar

    [3]

    Muñoz H A, Carusotto I 2022 Phys. Rev. A 106 063523Google Scholar

    [4]

    Singh N, Kärtner F X 2022 Opt. Express 30 5973Google Scholar

    [5]

    Bi L, Hu J, Jiang P, Kim D H, Dionne G F, Kimerling L C, Ross C A 2011 Nat. Photonics 5 758Google Scholar

    [6]

    Gao J, Wang X, Han F, Wan J, Gu W 2023 Micromachines-basel 14 33Google Scholar

    [7]

    Yang Z, Cheng Y, Wang N, Chen Y, Wang S 2022 Opt. Express 30 27993Google Scholar

    [8]

    Liang J, Li Y, Dai T, Zhang Y, Zhang X, Liu H, Wang P 2023 Opt. Express 31 8375Google Scholar

    [9]

    Wang X, Ptitcyn G, Asadchy V S, Díaz R A, Mirmoosa M S, Fan S, Tretyakov S A 2020 Phys. Rev. Lett. 125 266102Google Scholar

    [10]

    Shah M, Briggs I, Chen P K, Hou S, Fan L 2023 Opt. Lett. 48 1978Google Scholar

    [11]

    张利巍, 李贤丽, 杨柳 2019 物理学报 68 170701Google Scholar

    Zhang L W, Li X L, Yang L 2019 Acta Phys. Sin. 68 170701Google Scholar

    [12]

    Tang J S, Nie W, Tang L, Chen M, Su X, Lu Y, Nori F, Xia K 2022 Phys. Rev. Lett. 128 203602Google Scholar

    [13]

    Lan Y T, Su W J, Wu H, Li Y, Zheng S B 2022 Opt. Lett. 47 1182Google Scholar

    [14]

    刘妮, 马硕, 梁九卿 2023 物理学报 72 060702Google Scholar

    Liu N, Ma S, Liang J Q 2023 Acta Phys. Sin. 72 060702Google Scholar

    [15]

    Xia K, Nori F, Xiao M 2018 Phys. Rev. Lett. 121 203602Google Scholar

    [16]

    You Y, Hu Y, Lin G, Qi Y, Niu Y, Gong S 2021 Phys. Rev. A 103 063706Google Scholar

    [17]

    Liang C, Liu B, Xu A N, Wen X, Lu C, Xia K, Tey M K, Liu Y C, You L 2021 Phys. Rev. Lett. 125 123901Google Scholar

    [18]

    Hu X X, Wang Z B, Zhang P, Chen G J, Zhang Y L, Li G, Zou X B, Zhang T, Tang H X, Dong C H 2021 Nat. Commun. 12 2389Google Scholar

    [19]

    李鑫, 解舒云, 李林帆, 周海涛, 王丹, 杨保东 2022 物理学报 71 184202Google Scholar

    Li X, Xie S Y, Li L F, Zhou H T, Wang D, Yang B D 2022 Acta Phys. Sin. 71 184202Google Scholar

    [20]

    Zheng Y, Yang J, Shen Z, Cao J, Chen X, Liang X, Wan W 2015 Light-Sci. Appl. 5 e16072Google Scholar

    [21]

    Shui T, Yang W X, Cheng M T, Lee R K 2022 Opt. Express 30 6284Google Scholar

    [22]

    Rashidi S, Entezar S R, Rashidi A 2021 Appl. Opt. 60 8651Google Scholar

    [23]

    Mai J, Cheah K W 2022 Opt. Express 30 46357Google Scholar

    [24]

    Al M M, Xiang Q, Miura Y, Belmoubarik M, Masuda K, Kasai S, Sukegawa H, Mitani S 2021 Phys. Rev. B 103 L180408Google Scholar

    [25]

    Bouscher S, Panna D, Balasubramanian K, Cohen S, Ritter D, Hayat A 2022 Phys. Rev. Lett. 128 127701Google Scholar

    [26]

    Kinoshita K, Moriya R, Okazaki S, Zhang Y, Masubuchi S, Watanabe K, Taniguchi T, Sasagawa T, Machida T 2022 Nano Lett. 22 4640Google Scholar

    [27]

    Liu S, Yang W X, Chuang Y L, Chen A X, Liu A, Huang Y, Lee R K 2014 Opt. Express 22 29179Google Scholar

    [28]

    Hao X, Li J, Liu J, Song P, Yang X 2008 Phys. Lett. A 372 2509Google Scholar

    [29]

    Zhang Y, Wang Z, Qiu J, Hong Y, Yu B 2019 Appl. Phys. Lett. 115 171905Google Scholar

    [30]

    Qiu J, Wang Z, Ding D, Li W, Yu B 2020 Opt. Express 28 2975Google Scholar

    [31]

    Zhang S, Lin G, Hu Y, Qi Y, Gong S 2020 Phys. Rev. Appl. 14 024032Google Scholar

    [32]

    Faist J, Sirtori C, Capasso F, Pfeiffer L, West K W 1994 Appl. Phys. Lett. 64 872Google Scholar

    [33]

    Wang Z, Zhang Y, Paspalakis E, Yu B 2020 Phys. Rev. A 102 063509Google Scholar

    [34]

    Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135Google Scholar

    [35]

    Li E Z, Ding D S, Yu Y C, Dong M X, Zeng L, Zhang W H, Ye Y H, Wu H Z, Zhu Z H, Gao W, Guo G C, Shi B S 2020 Phys. Rev. Res. 2 033517Google Scholar

    [36]

    Hsiao Y F, Chen H S, Tsai P J, Chen Y C 2014 Phys. Rev. A 90 055401Google Scholar

    [37]

    Cong G W, Akimoto R, Akita K, Hasama T, Ishikawa H 2007 Appl. Phys. Lett. 90 181919Google Scholar

    [38]

    Zhang C, Yang W, Song X, Xu Z 2009 J. Phys. B: At. Mol. Opt. Phys. 42 125604Google Scholar

    [39]

    武香莲, 赵珂, 贾海洪, 王富青 2015 物理学报 64 233301Google Scholar

    Wu X L, Zhao K, Jia H H, Wang F Q 2015 Acta Phys. Sin. 64 233301Google Scholar

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出版历程
  • 收稿日期:  2023-07-26
  • 修回日期:  2023-09-09
  • 上网日期:  2023-10-09
  • 刊出日期:  2024-01-05

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