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垂直腔是光子学、光电子学和腔量子电动力学的重要研究平台，是激光器、探测器、滤波器、传感器等器件的核心结构[1-6]。垂直腔由在垂直方向上的两个反射镜构成。人们曾采用金属作为反射镜构建垂直腔，但是金属存在吸收损耗，影响器件的性能[7-8]。由介质或者半导体构成的分布布拉格反射镜（Distributed Bragg reflector，DBR）损耗小，反射率高且带宽大，广泛用于构建垂直腔。为了达到99.5%的反射率，需要20~30对DBR，材料生长相对困难[9]。近年来, 人们发现一维和二维高折射率差亚波长光栅（High-index-contrast subwavelength grating，HCG）具有宽带高反射率，可以用作反射镜构建垂直腔，且材料生长相对简单[10-12]。
垂直腔的光场分布对激光器的性能、滤波器的谱宽、传感器的灵敏度等方面具有重要的影响。垂直腔的结构影响垂直腔的光场分布，从而影响基于垂直腔的器件设计、制作以及其性能。近年来, 人们围绕垂直腔的构建及其光场调控做了大量的研究，在理论基础以及器件应用等方面取得了显著进展。垂直腔结构由传统的上/下DBR垂直腔逐渐演变成一维和二维HCG基复合腔。这种垂直腔结构的演化不只是材料生长难度降低，器件结构简单和尺寸减小，同时还有垂直腔物理机理的变化和相关器件性能的提升。
文中将介绍传统上/下DBR垂直腔的色散特性，和其光场调控的方法以及它们在激光器和滤波器等领域的应用；再介绍基于一维和二维HCG基复合腔的色散特性和光场调控，和它们在新型激光器及其阵列和单片集成多波长滤波器阵列等领域的应用；最后对垂直腔及其应用进行了总结和展望。
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DBR由厚度为四分之一波长的高/低折射率材料交替生长形成，不同高/低折射率材料界面反射光之间相长干涉可以实现近100%的高反射率。DBR的反射相位随入射光的入射角度轻微变化。当垂直腔由上/下DBR构成时，它在
$ {k_\parallel } = 0 $ 附近的色散曲线可以表示为$ \omega ({k_\parallel }) \approx {\omega _0}[1 + {{k_\parallel ^2} \mathord{\left/ {\vphantom {{k_\parallel ^2} {(2{{({n_c}{\omega _0}/c)}^2})}}} \right. } {(2{{({n_c}{\omega _0}/c)}^2})}}] $ ，它近似为二次型曲线，其中$ {k_\parallel } $ 为垂直腔平面内的波矢分量，$ {n_c} $ 为垂直腔的折射率，$ {\omega _0} $ 为$ {k_\parallel } = 0 $ 时腔模的角频率，c为真空中的光速。垂直腔的色散主要由上/下DBR构成的F-P（Fabry-Pérot）腔决定，其色散曲线的曲率在$ {k_\parallel } = 0 $ 处为正，而且各向同性。上/下DBR垂直腔通常由材料外延制作，它构建完之后，人们很难调控其色散曲线。如今，上/下DBR垂直腔已广泛用于垂直腔面发射激光器和滤波器。在上/下DBR构成的垂直腔面发射激光器（vertical-cavity surface-emitting laser，VCSEL）中，模式和光场的调控直接影响其阈值电流、效率、能效、以及调制带宽等性能。如图1（a）所示，在VCSEL中，高Al组分层（如Al0.98Ga0.02As）经过高温湿法氧化形成低折射率绝缘Al2O3氧化层，从而形成氧化孔径，实现对载流子和光场的双重限制。因此，氧化孔径的引入实现了VCSEL的高效电注入，降低了VCSEL的阈值电流；同时氧化层引入的氧化区和非氧化区之间的折射率差可以实现横模控制和光场调控[13]。实验结果表明，当氧化孔径减小到约3 μm时，VCSEL可以实现基横模工作，输出圆形高斯光束，同时可以降低功耗，能效到近50 fJ/bit[14-16]。此外，氧化层位置能影响VCSEL的工作模式，剪裁VCSEL输出光束的形貌，以及调控光束的发散角[17-19]。
图 1 （a）VCSEL的激光腔中引入氧化孔径[13]；（b）VCSEL的激光腔中引入相移台面和选择性费米能级钳制界面[20]；（c）VCSEL的上DBR引入单缺陷光子晶体微结构[22-25]；（d）VCSEL的上DBR表面引入反相层[28-30]；（e）垂直腔内引入衍射光栅[35]；（f）垂直腔内引入金属层[36-38]
Figure 1. (a) VCSEL with a oxide aperture[13]; (b) Introducing phase shift mesa and selective Fermi level pinning interface in the laser cavity of VCSEL[20]; (c) Upper DBR of VCSEL introduces single defect photonic crystal microstructure[22-25]; (d) An anti-phase layer is introduced on the upper DBR surface of VCSEL[28-30]; (e) Vertical cavity with a diffraction grating[35]; (f) Vertical cavity with a metal layer[36-38]
为了避免VCSEL中引入氧化层引入带来的应力、可控性、均匀性等问题，Deppe研究组在材料外延中采用光刻工艺制作相移台面，引入费米能级钳制界面，如图1（b）所示。这种结构实现了对载流子和光场的限制，出光孔径为1 μm时，单模VCSEL的输出功率达5 mW[20-21]。但是这种方案需要采用二次外延技术，制作工艺相对复杂。基于后生长的垂直腔光场调控方法更为简便，同时也能调控VCSEL的横模。如图1（c）所示，在VCSEL上DBR引入单缺陷光子晶体微结构，利用类似折射率导引的光子晶体光纤平面外能带特性选择基横模输出，同时光子晶体对上DBR折射率分布的局部微弱调制可以降低输出光束的远场发散角[22-25]。进一步地，基于相干耦合机制，在VCSEL上DBR引入多缺陷光子晶体或者环形缺陷微结构，可以提高VCSEL的输出功率和调控其远场形貌[26-27]。在VCSEL上DBR表面引入金属或者反相层，如图1（d）所示，通过对上DBR的反射相位调制也可以实现对VCSEL激光腔内光场的调控[28-30]。
除了对构成垂直腔的DBR结构进行修饰实现对垂直腔的光场和模式调控外，人们直接在垂直腔内引入光学元件，实现对共振波长、传输方向、光子有效质量的调控[31-35]。Kumari等人在垂直腔内引入衍射光栅（如图1（e）所示），可实现高效耦合和偏振选择，单侧水平波导输出功率73 μW，边模抑制比达到29 dB，可以用作平面光子集成回路光源[35]。而在引入垂直腔内金属层（如图1（f）所示），可以实现腔模和Tamm模的耦合，用于实现电注入微腔激光器和研究光与物质的相互作用[36-38]。
基于上/下DBR垂直腔的滤波器广泛用于光谱仪、传感器等领域。在垂直腔内引入亚波长光栅，如图2（a）所示，利用亚波长光栅的透射相位随结构参数变化的性质，调制垂直腔共振波长，实现单片集成多波长滤波器阵列，用于片上高精度光谱仪[39]。通过灰度曝光或者3D纳米压印技术控制腔长，实现基于上/下DBR垂直腔的单片集成多波长滤波器阵列，如图2（b）所示，可以和探测器阵列或者CCD（Charge-coupled device）集成实现微型光谱仪[40-41]。在上/下DBR构成的垂直腔两侧引入电极，通过静电吸引改变空气腔的腔长，从而实现波长调谐，用于焦平面探测器阵列[42-47]。
图 2 （a）垂直腔内引入亚波长光栅实现单片集成多波长滤波器阵列[39]；（b）采用3D纳米压印技术改变垂直腔的腔长实现单片集成多波长滤波器阵列[40]
Figure 2. (a) Vertical cavities with subwavelength gratings to realize a monolithic multi-wavelength filter array[39]; (b) Monolithic multi-wavelength filter array with different cavity lengths by 3D nano imprint technology[40]
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HCG具有宽带高反射率[10-11]，它的反射相位强烈依赖于入射光的入射角度，且依赖于HCG的结构参数[48]。当垂直腔由HCG构成时，垂直腔在
$ {k_\parallel } = 0 $ 附近的色散曲线可以表示为：$$ \begin{split} \omega = {\omega _0} + \dfrac{1}{2}\left[ \dfrac{c}{{2{n_c}( {{L_{eff,1}} + {L_{eff,2}}} )}} \left( {\dfrac{{{\partial ^2}{\varphi _1}}}{{\partial k_\parallel ^2}}} + {\dfrac{{{\partial ^2}{\varphi _2}}}{{\partial k_\parallel ^2}}} + {\dfrac{{2c{L_c}}}{{{\omega _0}{n_c}}}} \right) \right]k_{\parallel ^2} \end{split} $$ (1) 式中：
$ {L_{eff,i}} $ （$ = - \dfrac{c}{{2{n_c}}}\dfrac{{\partial {\varphi _i}}}{{\partial \omega }}, \; i = 1,2 $ ）为上/下反射镜的相位趋肤深度[49-50]，$ {\varphi _i}\;(i = 1,2) $ 为反射相位，$ {L_c} $ 为腔长；方括号项代表HCG基垂直腔在$ {k_\parallel } = 0 $ 附近的色散曲线的曲率，主要由腔长和反射镜的反射相位角度响应决定，其中与腔长的相关项为正，而与反射镜的反射相位角度响应的相关项可以为负，也可以为0或者正。因此，HCG基垂直腔的色散曲率可以为负、0或者正，而且各向异性，和偏振相关[48, 51]。通过比较HCG基垂直腔和上/下DBR垂直腔在
$ {k_\parallel } = 0 $ 附近的色散曲线，可以发现HCG基垂直腔在$ {k_\parallel } = 0 $ 附近的色散由两部分组成：垂直方向的F-P腔色散（类似上/下DBR垂直腔的色散）和HCG反射相位$ {\varphi _i} $ 对入射角度的响应，其中HCG反射相位$ {\varphi _i} $ 对入射角度的响应和HCG中的模式共振密切相关。因此和上/下DBR垂直腔不同，HCG基垂直腔为复合腔。通过对HCG结构参数的调控，可以实现HCG基复合腔在$ {k_\parallel } = 0 $ 附近色散曲线的剪裁，从而控制HCG基复合腔的共振波长和场分布以及远场。HCG基复合腔也已广泛应用面发射激光器和滤波器等领域。为了制作由上/下DBR构成的垂直腔，人们需要精确控制上百层材料的组分和厚度，且DBR的总厚度达到数微米，材料外延难度极大。传统垂直腔中的DBR被百纳米厚度的HCG取代，构建HCG-DBR或者HCG-HCG复合腔，可以降低材料外延难度。同时基于HCG的独特性能，可以实现特殊功能的器件。
采用HCG替代上/下DBR垂直腔中的一个DBR，利用HCG的宽带高反射率、以及偏振选择和反射性能依赖入射角度的特性，构建如图3（a）所示的HCG-VCSEL，实现了近红外波段单模、单偏振VCSEL和可调谐VCSEL[52-56]。同时，利用HCG的反射性能随入射角度和结构参数的依赖特性实现了集成光束整形功能的HCG-VCSEL阵列，如图3（b）所示，可以在一个HCG-VCSEL阵列中输出单瓣、双瓣等多种远场光斑[57]。HCG结构参数的优化可以对HCG基复合腔的色散曲线剪裁，调控有限尺寸HCG的横向光场泄漏，同时调控输出光束的远场[58-59]。在HCG-VCSEL中，Chung等人提出将HCG既作为反射镜又作为耦合器，通过HCG基复合腔的色散调控实现将HCG-VCSEL垂直振荡的激光高效定向耦合至水平方向，用于光子集成芯片的光源[60]。Park等人采用SOI （Si-on-insulator）基HCG构建1 550 nm HCG-VCSEL，如图3（c）所示，实现了水平波导输出，光泵浦下的-3 dB带宽达到27 GHz[61-62]。相比DBR，HCG能降低光场的趋肤深度，从而提高HCG-DBR复合腔的场强和品质因子，有利于HCG-DBR复合腔中激子和光子的强耦合，从而实现极化激元激光器激射[6, 63-64]，图3（d）为极化激元激光器结构示意图和极化态的实空间谱分辨图。
图 3 （a）HCG-VCSEL结构示意图[53]；（b）集成光束整形功能的HCG-VCSEL结构示意图和远场图[57]；（c）Si基HCG-VCSEL结构示意图(SOI基HCG作为反射镜和耦合器)[60]；（d）极化激元激光器结构示意图[64]
Figure 3. (a) Schematic of HCG-VCSEL[53]; (b) Schematic of HCG-VCSEL with beam shaping and far field profiles[57]; (c) Schematic of Si-based HCG-VCSEL (SOI-based HCG for reflector and coupler)[60]; (d) Schematic of polariton laser[64]
采用上/下HCG构建垂直腔，可以进一步降低材料外延难度，易拓展VCSEL的工作波长范围。Viktorovitch研究组和Zhou研究组采用一维和二维硅基HCG构建垂直腔，实现了1.55 μm硅基面发射激光器，并通过色散调控和引入异质结构减小光场的横向泄漏[65-68]。由于HCG的反射相位依赖于其结构参数，通过改变HCG的占空比或者周期，调谐HCG的反射相位，可以实现单片集成多波长VCSEL阵列，用于波分复用[69-71]。
宽带高反射率HCG体积小、质量轻，是构建F-P腔滤波器的理想光学单元[72-73]。Wang等人在HCG-DBR复合腔中引入有源层，实现了共振增强型探测器，通过静电效应调谐波长，在1 550 nm波段实现了1 A/W的响应度，波长调谐范围达33.5 nm，谱宽1.2 nm[74]。Faraone研究组为了避免Ge/ZnS基DBR应力以及良率等问题，采用二维Ge基HCG构建HCG-DBR复合腔实现了长波红外可调谐滤波器，透射率超过85%，谱宽为500 nm，用于多光谱成像[75]。双HCG构建的滤波器（如图4（a）所示）可以实现单片集成多波长阵列，和探测器阵列集成实现片上微型光谱仪[76]。通常一维HCG及其滤波器具有偏振选择性，采用两个一维HCG相互正交放置（如图4（b）所示）或者两个二维HCG构建滤波器，可以实现偏振不敏感滤波器，用于传感和多光谱成像等领域[77-78]。
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垂直腔是激光器、滤波器、传感器等器件的核心结构。传统上/下DBR垂直腔在
$ {k_\parallel } = 0 $ 附近的色散曲线近似为二次型曲线，已广泛用于垂直腔面发射激光器和滤波器等领域。上/下DBR垂直腔构建完（通常通过材料外延制作）之后，很难调控其色散曲线。通过在上/下DBR垂直腔引入氧化孔径、光栅和金属等结构，以及采用后生长方法调控垂直腔的光场和模式，提高了垂直腔面发射激光器的单模、效率、功耗、能效等性能，并拓展了上/下DBR垂直腔的应用范围。采用HCG替代传统DBR构建HCG基复合腔，它在
$ {k_\parallel } = 0 $ 附近的色散曲线可以通过后生长的办法调控，为HCG基复合腔的光场调控提供了新途径，可以实现具有独特性能的器件。同时基于HCG垂直腔的器件材料生长相对容易，有益于器件工作波长的拓展。目前基于HCG的垂直腔面发射激光器已经实现了单模、单偏振和波长调谐工作，而且可以实现多样化的远场形貌和定向耦合输出。基于HCG的滤波器及其阵列具有体积小、质量轻、快速波长调谐等特点，可以用于片上光谱仪和多光谱成像等领域。近年来，新材料和拓扑光子学等兴起[79-80]，它们与垂直腔结合，有望实现高性能新型发光器件，观察到光与物质相互作用的新奇现象，拓展人们的认知。
Optical manipulation of vertical cavity and its applications (Invited)
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摘要: 垂直腔是激光器、探测器、滤波器、传感器等器件的核心结构，垂直腔的光场分布对激光器、滤波器、传感器等的性能具有重要的影响。垂直腔的结构影响垂直腔的光场分布，从而影响基于垂直腔的器件设计、制作以及其性能。近年来，人们围绕垂直腔的构建及其光场调控做了大量的研究，在理论基础以及器件应用等方面取得了显著进展。首先，介绍了传统上/下分布布拉格反射镜垂直腔的色散特性，和其光场调控的方法以及它们在激光器和滤波器等领域的应用；其次，介绍了基于一维和二维高折射率差亚波长光栅基复合腔的色散特性，和它们在新型激光器和单片集成多波长滤波器阵列等领域的应用；最后，对文章进行总结并展望了垂直腔的新应用。Abstract: The vertical cavity is the core structure of lasers, detectors, filters, sensors and so on. The optical field distribution of the vertical cavity has an important impact on the performance of these devices. The structure of the vertical cavity affects the optical field in the vertical cavity, thus affecting the design, fabrication, and performance of devices based on the vertical cavity. In recent years, many studies have been done on the construction and optical manipulation of vertical cavity, and remarkable progresses have been achieved in fundamental theory and device applications. Firstly, the dispersion characteristics of the conventional top/bottom distributed Bragg reflector vertical cavity, the optical manipulation methods and their applications in lasers and filters were introduced; Then, the dispersion characteristics of one- and two-dimensional high-index-contrast subwavelength grating (HCG) based vertical cavities were presented, and the optical manipulation of HCG-based vertical cavities in novel lasers and monolithic multi-wavelength filter arrays were reviewed; Finally, the article was summarized and the new applications of vertical cavity were prospected.
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Key words:
- vertical cavity /
- optical manipulation /
- dispersion /
- laser /
- filter
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图 1 （a）VCSEL的激光腔中引入氧化孔径[13]；（b）VCSEL的激光腔中引入相移台面和选择性费米能级钳制界面[20]；（c）VCSEL的上DBR引入单缺陷光子晶体微结构[22-25]；（d）VCSEL的上DBR表面引入反相层[28-30]；（e）垂直腔内引入衍射光栅[35]；（f）垂直腔内引入金属层[36-38]
Figure 1. (a) VCSEL with a oxide aperture[13]; (b) Introducing phase shift mesa and selective Fermi level pinning interface in the laser cavity of VCSEL[20]; (c) Upper DBR of VCSEL introduces single defect photonic crystal microstructure[22-25]; (d) An anti-phase layer is introduced on the upper DBR surface of VCSEL[28-30]; (e) Vertical cavity with a diffraction grating[35]; (f) Vertical cavity with a metal layer[36-38]
图 2 （a）垂直腔内引入亚波长光栅实现单片集成多波长滤波器阵列[39]；（b）采用3D纳米压印技术改变垂直腔的腔长实现单片集成多波长滤波器阵列[40]
Figure 2. (a) Vertical cavities with subwavelength gratings to realize a monolithic multi-wavelength filter array[39]; (b) Monolithic multi-wavelength filter array with different cavity lengths by 3D nano imprint technology[40]
图 3 （a）HCG-VCSEL结构示意图[53]；（b）集成光束整形功能的HCG-VCSEL结构示意图和远场图[57]；（c）Si基HCG-VCSEL结构示意图(SOI基HCG作为反射镜和耦合器)[60]；（d）极化激元激光器结构示意图[64]
Figure 3. (a) Schematic of HCG-VCSEL[53]; (b) Schematic of HCG-VCSEL with beam shaping and far field profiles[57]; (c) Schematic of Si-based HCG-VCSEL (SOI-based HCG for reflector and coupler)[60]; (d) Schematic of polariton laser[64]
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