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Enhanced dye lasing emission by guided-mode resonance grating with mesoporous silica as spacing layer

Cui Tao Wang Kang-Ni Gao Kai-Ge Qian Lin-Yong

Enhanced dye lasing emission by guided-mode resonance grating with mesoporous silica as spacing layer

Cui Tao, Wang Kang-Ni, Gao Kai-Ge, Qian Lin-Yong
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  • The enhancement of lasing emission intensity of dye laser is particularly important and urgently required due to a broad range of optical and electrical applications. The guided-mode resonance (GMR) effect occurs in a periodic waveguide structure where an incident wave is coupled to a leaky waveguide mode, and yields a resonance peak. The resonance wavelength can be easily controlled by adjusting the period of the grating, thickness of the waveguide layer, and refractive index of the covering materials. By using band edge states, one may be able to excite optical resonances extended over the entire structure surface, thereby achieving field enhancement over a large area. In this study, mesoporous silica with low refractive index is introduced between the grating layer and the substrate layer of the GMR structure to significantly enhance the contact between local electric field and gain medium. For comparison, another structure using SU-8 with high refractive index as the spacing layer is also proposed. It is clearly observed that the maximum of the electric field intensity is highly localized inside the SU-8 waveguide grating layer. However, it is shifted upward to the gain medium layer in the mesoporous silica structure due to the reverse symmetry waveguide structure design. Therefore, the interaction between laser dye and electric field is increased to further enhance the lasing emission.Besides the refractive index, the waveguide layer, other structural parameters such as thickness of each layer and grating period also affect the electric field distribution in the GMR structure. Based on the finite-difference time-domain method, the structural parameters are analyzed and optimized. According to the simulation results, the structure parameters TWG = 3.5 μm, Λ = 700 nm, and $ T_{\rm TiO_2} = 20 $ nm are chosen as the guideline for designing the dye laser, which generates the resonance wavelength of 820 nm the same as the absorption wavelength of dye molecules. Additionally, the laser characteristics excited by pump light with the wavelength of 820 nm are studied. The continuous laser output is obtained. The energy threshold is about 2.5 mJ/cm2, and the linewidth is about 0.3 nm. The proposed structure can effectively regulate the surface local electric field and enhance the interaction between pump light and gain medium. It can not only be used in lasers, but also provide reference for designing other light-emitting devices.
      Corresponding author: Wang Kang-Ni, yishuihetian@126.com ; Qian Lin-Yong, leonqly@126.com
    [1]

    Sorokin P P, Lankard J R 1966 Ibn. J. Res. Dev. 10 162

    [2]

    Wang G M, Zhang Z H 2011 Laser Phys. 21 981

    [3]

    刘秋武, 王晓宾, 陈亚峰, 曹开法, 胡顺星, 黄见 2017 光学学报 37 338

    Liu Q W, Wang X B, Chen Y F, Cao K F, Hu S X, Huang J 2017 Acta Opt. Sin. 37 338

    [4]

    蔡慧敏, 张少渊, 翁达玲, 王培晶 2004 应用激光 24 418

    Cai H M, Zhang S Y, Weng D L, Wang P J 2004 Applied Laser 24 418

    [5]

    黄峰, 汪岳峰, 牛燕雄, 王金玉 2005 激光与红外 35 137

    Huang F, Wang Y F, Niu Y X, Wang J Y 2005 Lasers & Infrared 35 137

    [6]

    Magnusson R, Wang S S 1992 Appl. Phys. Lett. 61 1022

    [7]

    杨赛, 盛斌, 张大伟, 钱林勇, 陈鹏, 黄元申 2015 中国激光 42 323

    Yang S, Sheng B, Zhang D W, Qian L Y, Chen P, Huang Y S 2015 Chin. J. Las. 42 323

    [8]

    桑田, 蔡托, 刘芳, 蔡绍洪, 张大伟 2013 物理学报 62 326

    Sang T, Cai T, Liu F, Cai S H, Zhang D W 2013 Acta Phys. Sin. 62 326

    [9]

    Wawro D D, Tibuleac S, Magnusson R, Liu H 2000 Proc. SPIE 3911, Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II San Jose, CA, United States, May 3 2000 86

    [10]

    Mizutani A, Kikuta H, Iwata K 2005 J. Opt. Soc. Am. A 22 355

    [11]

    李志全, 张明, 彭涛, 岳中, 顾而丹, 李文超 2016 物理学报 65 105201

    Li Z Q, Zhang M, Peng T, Yue Z, Gu E D, Li W C 2016 Acta Phys. Sin. 65 105201

    [12]

    Soria S, Thayil K N A, Badenes G, Bader M A, Selle A, Marowsky G 2005 Appl. Phys. Lett. 87 081109

    [13]

    Pokhriyal A, Lu M, Chaudhery V, Huang C S, Schulz S, Cunningham B T 2010 Opt. Express 18 24793

    [14]

    Takashi K, Yoshiaki K, Kazuhiro H 2005 Appl. Phys. Lett. 87 151106

    [15]

    Magnusson R, Ding Y, Lee K J, Shin D, Priambodo P S, Young P P, Maldonado T A 2003 Optical Science and Technology, SPIE's 48 th Annual Meeting San Diego, California, United States 2003 p20

    [16]

    江孝伟, 关宝璐 2019 光子学报 48 0114005

    Jiang X W, Guan B L 2019 Acta. Photon. Sin. 48 0114005

    [17]

    贾艳萍, 马姣, 张兰河, 董长青, 王孝强 2014 硅酸盐通报 33 3206

    Jia Y P, Ma J, Zhang L H, Dong C Q, Wang X Q 2014 B. Chin. Ceram. Soc. 33 3206

    [18]

    熊怀, 唐永兴, 胡丽丽, 沈斌, 李海元 2019 光学学报 39 0831001

    Xiong H, Tang Y X, Hu L L, Shen B, Li H Y 2019 Acta Optica Sin. 39 0831001

    [19]

    Vu D T, Chiu H W, Nababan R, Le Q M, Kuo S W, Chau L K, Ting C C, Kan H C, Hsu C C 2018 ACS Photonics 5 3263

    [20]

    Wang S S, Magnusson R, Bagby J S, Moharam M G 1990 J. Opt. Soc. Am. A 7 1470

    [21]

    Zhou W, Dridi M, Suh J Y, Kim C H, Co D T, Wasielewski M R, Schatz G C, Odom T W 2013 Nat. Nanotechnol. 8 506

  • 图 1  激光器结构示意图

    Figure 1.  Schematic of laser structure.

    图 2  (a) TE偏振下多孔二氧化硅结构的反射谱随入射角和波长的变化曲线; (b) 3.7°入射角下多孔二氧化硅结构的反射谱; (c) 3.7°入射角下多孔二氧化硅结构的820 nm共振峰; (d) 21.3°入射角下SU-8结构的820 nm共振峰

    Figure 2.  Calculated reflection in TE mode as a function of incident angle and wavelength for mesoporous silica structure; (b) calculated reflection spectrum of mesoporous silica structure at the incident angle of 3.7°; (c) resonance wavelength of 820 nm at the incident angle of 3.7° for mesoporous silica structure; (d) resonance wavelength of 820 nm at the incident angle of 21.3° for SU-8 structure.

    图 3  TE偏振入射下共振波长处的电场强度|E|2分布图: (a)多孔二氧化硅结构和(b)局部放大图; (c) SU-8结构和(d)局部放大图

    Figure 3.  Electric field intensities |E|2 for the TE-polarized light incidence at resonance wavelength: (a) mesoporous silica structure and (b) partially enlarged view; (c) SU-8 structure and (d) partially enlarged view.

    图 4  增益介质区域的局域电场均方值$ \left\langle {|E|^2} \right\rangle $)和共振角度随 (a)多孔二氧化硅层厚度, (b)光栅周期与(c)TiO2厚度的变化曲线

    Figure 4.  Calculated $ \left\langle {|E|^2} \right\rangle $ value and resonance angle versus (a) the thickness of the mesoporous silica, (b) the grating period and (c) the thickness of TiO2.

    图 5  两种结构的激光出射归一化强度谱线

    Figure 5.  Normalized emission spectra of the laser with SU-8 and mesoporous silica.

    图 6  (a) 不同入射角下的激光出射谱线; (b) 3.7°共振条件时多孔二氧化硅层厚度与激光出射谱线的关系

    Figure 6.  (a) Normalized emission spectra of the laser at different incident angles; (b) normalized emission spectra of the laser at the incident angle of 3.7° vs. thickness of the mesoporous silica.

    图 7  (a) 非共振激发(θ = 3.4°)条件下的局域电场强度|E|2和(b)局部放大图; (c) 非共振激发(θ = 4.0°)条件下的局域电场强度|E|2和(d) 局部放大图

    Figure 7.  (a) Calculated TE mode |E|2 obtained with θ = 3.4° (off-resonance) and (b) partially enlarged view; (c) calculated TE mode |E|2 obtained with θ = 4.0° (off-resonance) and (d) partially enlarged view.

    图 8  (a) 激光出射谱随抽运能量的变化曲线; (b) 出射线宽和强度随抽运能量的变化曲线

    Figure 8.  (a) Laser emission spectra as a function of input pump energy; (b) linewidth and maximum emission intensity as a function of input pump intensity.

    图 9  (a) 不同入射角下多孔二氧化硅结构激光器的出射强度随抽运能量的变化曲线; (b) 出射阈值和共振角度随多孔二氧化硅折射率的变化曲线

    Figure 9.  (a) Emission intensity as a function of input pump energy for different resonance angles; (b) calculated lasing threshold and resonance angle versus the refractive index of the mesoporous silica.

  • [1]

    Sorokin P P, Lankard J R 1966 Ibn. J. Res. Dev. 10 162

    [2]

    Wang G M, Zhang Z H 2011 Laser Phys. 21 981

    [3]

    刘秋武, 王晓宾, 陈亚峰, 曹开法, 胡顺星, 黄见 2017 光学学报 37 338

    Liu Q W, Wang X B, Chen Y F, Cao K F, Hu S X, Huang J 2017 Acta Opt. Sin. 37 338

    [4]

    蔡慧敏, 张少渊, 翁达玲, 王培晶 2004 应用激光 24 418

    Cai H M, Zhang S Y, Weng D L, Wang P J 2004 Applied Laser 24 418

    [5]

    黄峰, 汪岳峰, 牛燕雄, 王金玉 2005 激光与红外 35 137

    Huang F, Wang Y F, Niu Y X, Wang J Y 2005 Lasers & Infrared 35 137

    [6]

    Magnusson R, Wang S S 1992 Appl. Phys. Lett. 61 1022

    [7]

    杨赛, 盛斌, 张大伟, 钱林勇, 陈鹏, 黄元申 2015 中国激光 42 323

    Yang S, Sheng B, Zhang D W, Qian L Y, Chen P, Huang Y S 2015 Chin. J. Las. 42 323

    [8]

    桑田, 蔡托, 刘芳, 蔡绍洪, 张大伟 2013 物理学报 62 326

    Sang T, Cai T, Liu F, Cai S H, Zhang D W 2013 Acta Phys. Sin. 62 326

    [9]

    Wawro D D, Tibuleac S, Magnusson R, Liu H 2000 Proc. SPIE 3911, Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II San Jose, CA, United States, May 3 2000 86

    [10]

    Mizutani A, Kikuta H, Iwata K 2005 J. Opt. Soc. Am. A 22 355

    [11]

    李志全, 张明, 彭涛, 岳中, 顾而丹, 李文超 2016 物理学报 65 105201

    Li Z Q, Zhang M, Peng T, Yue Z, Gu E D, Li W C 2016 Acta Phys. Sin. 65 105201

    [12]

    Soria S, Thayil K N A, Badenes G, Bader M A, Selle A, Marowsky G 2005 Appl. Phys. Lett. 87 081109

    [13]

    Pokhriyal A, Lu M, Chaudhery V, Huang C S, Schulz S, Cunningham B T 2010 Opt. Express 18 24793

    [14]

    Takashi K, Yoshiaki K, Kazuhiro H 2005 Appl. Phys. Lett. 87 151106

    [15]

    Magnusson R, Ding Y, Lee K J, Shin D, Priambodo P S, Young P P, Maldonado T A 2003 Optical Science and Technology, SPIE's 48 th Annual Meeting San Diego, California, United States 2003 p20

    [16]

    江孝伟, 关宝璐 2019 光子学报 48 0114005

    Jiang X W, Guan B L 2019 Acta. Photon. Sin. 48 0114005

    [17]

    贾艳萍, 马姣, 张兰河, 董长青, 王孝强 2014 硅酸盐通报 33 3206

    Jia Y P, Ma J, Zhang L H, Dong C Q, Wang X Q 2014 B. Chin. Ceram. Soc. 33 3206

    [18]

    熊怀, 唐永兴, 胡丽丽, 沈斌, 李海元 2019 光学学报 39 0831001

    Xiong H, Tang Y X, Hu L L, Shen B, Li H Y 2019 Acta Optica Sin. 39 0831001

    [19]

    Vu D T, Chiu H W, Nababan R, Le Q M, Kuo S W, Chau L K, Ting C C, Kan H C, Hsu C C 2018 ACS Photonics 5 3263

    [20]

    Wang S S, Magnusson R, Bagby J S, Moharam M G 1990 J. Opt. Soc. Am. A 7 1470

    [21]

    Zhou W, Dridi M, Suh J Y, Kim C H, Co D T, Wasielewski M R, Schatz G C, Odom T W 2013 Nat. Nanotechnol. 8 506

  • Citation:
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  • Abstract views:  589
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Publishing process
  • Received Date:  29 June 2020
  • Accepted Date:  23 August 2020
  • Available Online:  14 December 2020
  • Published Online:  05 January 2021

Enhanced dye lasing emission by guided-mode resonance grating with mesoporous silica as spacing layer

    Corresponding author: Wang Kang-Ni, yishuihetian@126.com
    Corresponding author: Qian Lin-Yong, leonqly@126.com
  • 1. School of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
  • 2. School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China

Abstract: The enhancement of lasing emission intensity of dye laser is particularly important and urgently required due to a broad range of optical and electrical applications. The guided-mode resonance (GMR) effect occurs in a periodic waveguide structure where an incident wave is coupled to a leaky waveguide mode, and yields a resonance peak. The resonance wavelength can be easily controlled by adjusting the period of the grating, thickness of the waveguide layer, and refractive index of the covering materials. By using band edge states, one may be able to excite optical resonances extended over the entire structure surface, thereby achieving field enhancement over a large area. In this study, mesoporous silica with low refractive index is introduced between the grating layer and the substrate layer of the GMR structure to significantly enhance the contact between local electric field and gain medium. For comparison, another structure using SU-8 with high refractive index as the spacing layer is also proposed. It is clearly observed that the maximum of the electric field intensity is highly localized inside the SU-8 waveguide grating layer. However, it is shifted upward to the gain medium layer in the mesoporous silica structure due to the reverse symmetry waveguide structure design. Therefore, the interaction between laser dye and electric field is increased to further enhance the lasing emission.Besides the refractive index, the waveguide layer, other structural parameters such as thickness of each layer and grating period also affect the electric field distribution in the GMR structure. Based on the finite-difference time-domain method, the structural parameters are analyzed and optimized. According to the simulation results, the structure parameters TWG = 3.5 μm, Λ = 700 nm, and $ T_{\rm TiO_2} = 20 $ nm are chosen as the guideline for designing the dye laser, which generates the resonance wavelength of 820 nm the same as the absorption wavelength of dye molecules. Additionally, the laser characteristics excited by pump light with the wavelength of 820 nm are studied. The continuous laser output is obtained. The energy threshold is about 2.5 mJ/cm2, and the linewidth is about 0.3 nm. The proposed structure can effectively regulate the surface local electric field and enhance the interaction between pump light and gain medium. It can not only be used in lasers, but also provide reference for designing other light-emitting devices.

    • 染料激光器是以某种有机染料溶解于一定溶剂中作为增益介质, 采用脉冲或连续光源作为抽运源的一类激光器. 1966年, Sorokin和Lankard[1]利用花菁类染料作为增益介质, 在红宝石激光器抽运下首次获得激光辐射, 自此染料激光器开始迅速发展. 由于输出波长具有调谐范围广、输出功率高、尺寸小可用于集成化等优点, 染料激光器被广泛应用于光谱检测、大气光学、医疗和军事等领域[2-5]. 光学谐振腔是激光器的另外一个重要组成部分, 染料激光器多采用周期性的一维或二维衍射谐振腔, 以达到出射波长的连续可调谐. 基于导模共振效应的亚波长光栅是一种新型的衍射光学元件, 具有衍射效率高、共振波长和带宽可调谐以及在宽光谱范围内具有极高反射率等特性[6], 广泛应用于滤波片[7,8]、传感器[9]、光开关[10]等光学元件. 导模共振效应发生时, 结构内部产生局域场增强现象, 因此可用于增强光与物质的相互作用, 如石墨烯表面激发的高局域性表面等离子体激元[11]、荧光染料和量子点发光[12,13]、染料激光器[14]和垂直面发射激光器[15,16]等. 导模共振结构的基底层常采用二氧化硅或聚合物材料, 其折射率一般为1.5左右, 大于光栅层上表面覆盖的激光染料折射率, 因此表面局域电场集中于波导层并向基底层渗透一定深度, 不利于光场与发光物质的相互作用.

      本文在导模共振染料激光器的光栅层和基底层之间引入低折射的多孔二氧化硅, 能有效调控表面局域电场, 并增强了局域电场与增益介质的相互作用. 由于多孔二氧化硅折射率小于常用基底层材料, 使电场向染料层反向渗透, 增加了与增益介质的接触区域, 最终实现了激光出射增强. 文中以电场强度为衡量指标, 分析并优化了激光器的结构参数对电场的影响, 包括膜层厚度、光栅周期和入射角度等, 并在最优结构参数的基础上, 分析了激光器的出光特性.

    2.   结构设计与原理
    • 本文所设计的激光器结构如图1所示, 从上往下依次为激光染料层、导模共振光栅层、多孔二氧化硅层和基底层, 其中激光染料层选择IR-140并溶解于聚氨基甲酸酯溶剂(polyurethane)中, 导模共振光栅层为TiO2, 基底层为石英玻璃. 多孔二氧化硅材料具有孔隙率高、表面张力低、粘温系数小、耐高温和低温以及耐氧化稳定性等特点, 合成方法主要采用溶胶-凝胶法, 利用液体化学试剂或者溶胶为原料, 反应物均匀分散于液相中, 生成物形成稳定的溶胶体系, 一定时间静置转变为含有大量液相的湿凝胶, 通过特定条件去除液体介质后获得成品[17]. 该材料除了能满足结构对折射率的要求以外, 还具备良好的耐环境稳定性, 尤其是耐高温辐射特性, 因此在功率较高的激光装置中常采用具有高损伤阈值的多孔二氧化硅作为减反膜, 在高通量激光辐照后仍能表现出稳定的透过率, 不影响激光器整体性能, 并能提高元件使用寿命[18]. 各层折射率分别为: np = 1.3, nh = 2, nl = 1.22[19], ns = 1.51. 此外, 典型的导模共振光栅结构常在SU-8光刻胶光栅或石英光栅上直接镀高折射率介质薄膜形成, 因此本文在图1的基础上, 以SU-8光刻胶代替多孔二氧化硅作为对比结构进行研究, 其折射率为n'l = 1.55. 导模共振效应发生时需满足[20]

      Figure 1.  Schematic of laser structure.

      其中, nhnc分别表示光栅层的高、低折射率材料, nwns为波导层和基底层折射率, θ为光入射到结构最上方一层介质的角度, i为衍射级次, Λ是光栅周期, neff是光栅层的等效折射率. 由公式(1)可获得导模共振发生的波长区域, 而在结构参数确定以后, 共振波长λθ变化而变化.

      基于导模共振效应的染料激光器在设计时, 通常使激光染料的吸收峰与共振波长相匹配, 目的是利用共振频率产生的局域电场来增加抽运光与染料的相互作用. 导模共振结构中伴随着光子态密度的改变, 在共振波长处, 即禁带中, 态密度完全被抑制, 而在带边的群速度接近于零, 态密度显著提高, 使电场与增益物质相互作用被放大. 本文采用的染料IR-140的吸收峰位于820 nm[21], 因此需设计与之匹配的共振波长. 图2(a)是利用时域有限差分法(finite-difference time-domain, FDTD)模拟的多孔二氧化硅作为间隔层的共振波长与入射角度的关系曲线, 结构参数满足: d1 = 200 nm, d2 = 20 nm, d3 = 50 nm, d4 = 3.5 μm, Λ = 700 nm, 占空比f = 0.5. 如图2(a)所示, 当θ = 0°, 共振波长为860 nm单峰, 倾斜入射时, ± 1级衍射引起的共振峰使单峰变成双峰. 随着角度增加, 其中一个向短波长移动, 另一个向长波长移动; 当入射角θ = 3.7°时, 如图2(a)中虚线所示, 其中一个共振波长为820 nm, 另一个为908 nm, 此时反射谱如图2(b)所示. 图2(c)图2(b)反射谱中820 nm共振峰的放大图, 由于对比结构中SU-8材料折射率不同, 因此在保证相同的结构参数下, 改变入射角度可使对比结构中也出现820 nm的共振波长, 如图2(d)所示, 因此820 nm共振波长即可用于两种结构中增益介质的共振激发.

      Figure 2.  Calculated reflection in TE mode as a function of incident angle and wavelength for mesoporous silica structure; (b) calculated reflection spectrum of mesoporous silica structure at the incident angle of 3.7°; (c) resonance wavelength of 820 nm at the incident angle of 3.7° for mesoporous silica structure; (d) resonance wavelength of 820 nm at the incident angle of 21.3° for SU-8 structure.

      两种结构在820 nm处的电场分布如图3(a)(c)所示, 图3(b)(d)分别为局部区域放大图. 图3(a)(b)为多孔二氧化硅作为间隔层的激光器结构, 由于其折射率小于染料层折射率, 所以最强电场上移至光栅层和染料层, 并渗透进染料层一定深度; 图3(c)(d)为SU-8作为间隔层的激光器结构, 电场强度多集中于高折射率材料SU-8层, 而IR-140染料区域的电场很小. 在共振波长处, 慢光子效应将使光传输的群速度大大降低, 光和增益物质相互作用时间延长, 使染料对抽运光的吸收得到增强, 进一步提高了受激辐射. 因此, 相比于SU-8材料, 以低折射率材料多孔二氧化硅作为间隔层的激光器, 其染料与电场的接触面积更大, 电场强度也更强, 将更加有利于染料对抽运光的吸收.

      Figure 3.  Electric field intensities |E|2 for the TE-polarized light incidence at resonance wavelength: (a) mesoporous silica structure and (b) partially enlarged view; (c) SU-8 structure and (d) partially enlarged view.

      此外, 共振波长处的局域电场强度还受光栅周期和各层厚度等参数的影响. 因此, 为了得到共振波长为820 nm处的最强局域场分布, 对激光器的结构参数进行了分析和优化, 目的是使染料层的电场强度均方值$\left\langle {|E|^2} \right\rangle$最大. 首先, 分析多孔二氧化硅层厚度TWG对电场的影响. 图4(a)为结构参数满足TiO2层厚度$ T_{\rm TiO_2} $ = 20 nm, 光栅周期Λ = 700 nm时, 将TWG从0.5 μm逐渐增加到6 μm时增益介质区域内激发场强的均方值. 曲线表明: 当TWG小于3 μm时, 随着厚度的增加, 局域电场逐渐增加; 而当厚度大于3 μm时, 场强逐渐达到饱和状态, 厚度对激发场不再产生明显影响; 当TWG = 3.5 μm时, 局域场强达到最大, 共振角度始终保持在3.7°. 随后固定TWG = 3.5 μm, $ T_{\rm TiO_2} $= 20 nm, 分析光栅周期与共振激发场之间的关系(图4(b)). 随着光栅周期的增加, 局域场强先增加后减小, 当周期为650—700 nm, 共振角度约为3°时, 会激发最强局域场. 最后固定TWG = 3.5 μm, 光栅周期为700 nm, 探究TiO2光栅层厚度与局域电场之间的关系(图4(c)). 结果表明, 光栅层最佳厚度为20 nm, 其共振角度为3.7°. 因此, 根据上述结果可得, 激光器的最优结构参数为: TWG = 3.5 μm, Λ = 700 nm, $ T_{\rm TiO_2} $= 20 nm.

      Figure 4.  Calculated $ \left\langle {|E|^2} \right\rangle $ value and resonance angle versus (a) the thickness of the mesoporous silica, (b) the grating period and (c) the thickness of TiO2.

    3.   激光出射特性分析
    • 将各结构参数设置为上述最优值, 利用FDTD算法对激光器出射激光的特性进行模拟仿真和分析. 采用四能级二电子系统对增益介质IR-140进行描述, 不同能级的分子密度随时间的速率方程可表示为[21]

      其中, N0, N1, N2N3分别表示四个能级的粒子数密度; τxy表示粒子在xy能级之间的跃迁寿命; ωaωb分别表示增益介质的发射频率和吸收频率; $\bar E$是总电场; ${\bar p_{\rm{a}}}$${\bar p_{\rm{b}}}$表示从能级2跃迁到能级1和从能级0跃迁到能级3的宏观极化强度. 在模拟中, 参数设置如下: ωa = 2.165 × 1015 Hz, ωb = 2.282 × 1015 Hz, τ21 = τ30 = 1 ns, τ32 = τ10 = 10 fs, N = 2.0 × 1024 m–3[21].

      首先, 分别以多孔二氧化硅和SU-8作为间隔层, 其它结构参数保持一致, 模拟两种导模共振结构激光器, 对出射激光强度进行比较, 所得的归一化强度曲线如图5所示. 由于采用同一种增益介质, 两种结构的激光出射峰均位于870 nm, 而采用多孔二氧化硅这种低折射率材料作为间隔层的结构出射激光更强, 约为SU-8间隔层对应结构的13倍, 其结果与图3一致, 由此可证明局域电场分布对激光出射强度影响很大, 本文提出的结构在共振波长下能产生更强的有效局域场.

      Figure 5.  Normalized emission spectra of the laser with SU-8 and mesoporous silica.

      在特定入射角下, 导模共振峰与增益介质的激发峰重合, 可称为共振角, 而不满足共振峰与激发峰重合的入射角称为非共振角. 对于同一种导模共振结构, 激发光以共振角与非共振角入射, 其发射光强度的对比可进一步揭示导模共振结构激光器的特性. 对于多孔二氧化硅作为间隔层的激光器结构, 其共振角θ = 3.7°, 此时导模共振波长和激发波长都为820 nm. 图6(a)给出了抽运光以共振角3.7°, 以及非共振角3.4°和4°入射到结构上时, 出射激光强度的归一化数据. 结果表明, 在共振角激发条件下的出射激光最强, 而在θ = 3.4°时出射强度为0.31, θ = 4°时出射强度为0.36, 提高了约2.7—3.2倍. 当设置入射角θ = 3.7°时, 改变多孔二氧化硅层厚度, 导模共振波长为820 nm不变, 计算得到的出射激光强度随膜层厚度的变化如图6(b)所示. 激光强度随着多孔二氧化硅层厚度的增加而增加, 当厚度超过3 μm以后激光强度的波动变化较小, 其结论与图4(a)保持一致, 证明了局域电场强度对出射激光的正面影响.

      Figure 6.  (a) Normalized emission spectra of the laser at different incident angles; (b) normalized emission spectra of the laser at the incident angle of 3.7° vs. thickness of the mesoporous silica.

      共振角激发下有最强的激光输出, 可以通过局域场强来进一步解释(图7所示. 图7(a)是激发光以非共振角θ = 3.4°入射下的局域电场分布, 此时结构的共振波长分别为823和904 nm, 图7(b)是局部放大图, 染料层电场强度最大值为30左右, 仅为共振激发条件的10%. 图7(c)是非共振角θ = 4.0°时激发的局域电场分布, 图7(d)是局部放大图, 此时结构的共振波长分别为817和912 nm, 染料层电场强度最大值为24左右, 仅为共振激发条件的8%. 因此, 在满足共振波长与染料吸收峰相匹配时, 局域场增强效果显著, 更加有利于出射激光增强. 此外, 导模共振光栅的周期性结构可有效减小平面光波导对光的损失, 能显著提高光的提取.

      Figure 7.  (a) Calculated TE mode |E|2 obtained with θ = 3.4° (off-resonance) and (b) partially enlarged view; (c) calculated TE mode |E|2 obtained with θ = 4.0° (off-resonance) and (d) partially enlarged view.

      最后, 为了考查出射激光的连续性和阈值特性, 改变抽运光的强度, 分析了激光强度变化趋势. 图8(a)所示为多孔二氧化硅结构的出射谱随抽运能量的变化曲线, 激光出射波长为870 nm, 强度起初很弱, 在达到阈值后迅速增加. 提取图8(a)中各谱线的出射强度和线宽值, 并绘制二者随抽运能量的变化曲线, 如图8(b)所示, 黑色“十字”标识为线宽变化曲线, 红色“十字”标识为出射强度变化曲线. 结果表明, 线宽在抽运能量大于2 mJ/cm2时急剧窄化至1 nm以下, 并逐渐减小至0.3 nm; 出射强度在抽运能量大于2.5 mJ/cm2时迅速增加, 输出斜率也大大增加, 并且该能量阈值与线宽阈值大致相等, 符合激光的判断条件, 从而也证明了激光出射的可行性和连续性. 此外, 为了对比两种结构的出射线宽和能量阈值特性, 图8(b)中两条“圆孔”标识曲线分别给出了SU-8结构的出射强度和线宽变化曲线. 由图8(b)中曲线可知, 虽然SU-8结构的线宽随着抽运能量的增加最终可以达到0.3 nm左右, 但其归一化出射能量不到多孔二氧化硅结构的10%, 线宽阈值和能量阈值也相对较高, 约为2.3和3 mJ/cm2.

      Figure 8.  (a) Laser emission spectra as a function of input pump energy; (b) linewidth and maximum emission intensity as a function of input pump intensity.

      图6(a)图7可知, 当以非共振角照射激光器时, 染料区域的电场强度和出射激光强度均大幅度下降, 因此考虑不同入射角对激光出射阈值的影响, 如图9(a)所示, 在以共振角度3.7°入射时的激光归一化强度远大于以非共振角度入射时的, 并且能量阈值相对较小. 但是, 入射角度对出光特性的影响不如更换间隔层材料对出光特性的影响大. 此外, 多孔二氧化硅材料通常由硅醇盐作为原料通过溶胶-凝胶方法制备, 所使用的材料配比不同气孔率也不同, 进而导致其有效折射率可在一定范围内变化, 通常为1.1—1.38, 本文前部分的设计中参数取值为1.22[19], 是常用的折射率数值. 但考虑到其有效折射率的变化范围, 本文讨论了多孔二氧化硅折射率从1.1到1.3的激光能量阈值变化趋势, 如图9(b)中黑色曲线所示, 模拟时为了满足820 nm的共振波长, 入射角度也随之改变(图9中红色曲线). 当折射率逐渐增大时, 共振角度逐渐增大, 激光阈值在折射率为1.2时取得最小值, 并呈现上升趋势, 但在所给出的折射率变化范围内阈值总体变化不大, 约为0.2 mJ/cm2, 因此若设计此类带有低折射率多孔二氧化硅间隔层的激光器时, 可尝试使用较低折射率取值的材料, 达到提高激光器出射性能的目的.

      Figure 9.  (a) Emission intensity as a function of input pump energy for different resonance angles; (b) calculated lasing threshold and resonance angle versus the refractive index of the mesoporous silica.

    4.   结 论
    • 本文将多孔二氧化硅这种低折射率材料作为间隔层, 构建了基于导模共振光栅结构的染料激光器. 理论计算表明, 共振时的电场强度集中于增益材料区域, 有效增加了光与物质的相互作用, 达到了增强激光出射的目的. 在共振激发条件下, 通过控制光栅周期、波导层及间隔层厚度等参数使共振波长与染料吸收峰匹配时, 出射能量达到最大, 出射线宽约为0.3 nm, 能量阈值约为2.5 mJ/cm2. 本文涉及的方法有望应用于其它光致发光材料, 如量子点、上转换发光粒子或闪烁体等材料的发光增强. 此外, 导模共振效应具有角度相关性, 还可调控激发光或发射光的方向, 为此类结构的实际应用提供了良好的基础.

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