半导体耦合微盘谐振腔的模式特征研究
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摘要
半导体微腔激光器具有小体积,低功耗,低阈值等优点,在光子集成和光电子集成等方面有广阔的应用前景。半导体微盘激光器作为最早发展起来的微腔激光器,已经被各国科学家进行了广泛的研究。最近,耦合微盘激光器也因为能通过光刻技术这个简单的制作方法来实现而引起了科学家们的广泛关注。
本论文运用二维时域有限差分方法(FDTD)并参照二维微盘的解析解,模拟和分析了半径(R)相同,折射率为n的两个微盘构成的耦合微盘随两个微盘之间的距离发生变化时的模式特征。对于同一阶回音壁模式(Whisper-Gallery Mode),当模场分布呈不同对称性时,模式波长和品质因子(Q值)随微盘间距的大小的变化出现分裂现象。结果还显示一阶回音壁模式和二阶回音壁模式在一定情况下会发生耦合,并且当耦合区大小变化时一阶模和二阶模的模式耦合特征中出现了反交叉耦合现象。
运用FDTD方法对于n=3.2,R=1μm的耦合微盘的模拟时发现,模场分布关于Y轴呈对称分布时,一阶WGM TE9,1模和二阶WGM TE6,2模的模式特征随微盘间距大小变化时,模式特征的变化存在反交叉耦合模现象。而当n=2.8时,TE9,1和TE6,2也发生耦合,且模场分布关于Y轴呈反对称分布时,模式波长出现耦合交叉现象。若改变微盘的半径,同样存在基模和高阶模的耦合现象。
一阶和二阶WGM的耦合会导致一阶WGM模式Q值的下降。因此在做器件的时应避开这些耦合模,使品质因子处于最大值,从而实现激光器的低阈值激射。
Semiconductor microcavity layers have many advantages such as ultrasmall volume and ultralow threshold. They have great potential applications in optoelectrinics integration. As one of the important types of microcavity lasers, microdisk lasers have been investigated all over the world. Recently, evanescent-coupled microdisks have attracted a great attention, because they can be fabricated easily by the lithographic technique.
Numerical simulation is the fabricate elements for the semiconductor microdisks. In this paper, The mode characteristics for twin coupled microdisks are investigated by 2-D finite-difference time-domain(FDTD) technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first and second order WGMs can have a cross point in some case.
For the two coupled microdisks with the radius R = 1μm and the refractive index n = 3.2. The anti-crossing coupling exists between the coupled WGMs TE9,1 and TE6,2 for the field pattern is symmetry to the Y axis. When change n to 2.8. The mode wavelengths of the two coupled WGMs TE9,1 and TE6,2 have a cross point in some place. When change R. The mode coupling between the first and the second WGM is existent too.
The mode coupling between the first and the second order WGMs can greatly reduce the mode Q-factor of the coupled first order WGMs. So we can avoid these phenomena when fabricate semiconductor coupled microdisks.
本论文运用二维时域有限差分方法(FDTD)并参照二维微盘的解析解,模拟和分析了半径(R)相同,折射率为n的两个微盘构成的耦合微盘随两个微盘之间的距离发生变化时的模式特征。对于同一阶回音壁模式(Whisper-Gallery Mode),当模场分布呈不同对称性时,模式波长和品质因子(Q值)随微盘间距的大小的变化出现分裂现象。结果还显示一阶回音壁模式和二阶回音壁模式在一定情况下会发生耦合,并且当耦合区大小变化时一阶模和二阶模的模式耦合特征中出现了反交叉耦合现象。
运用FDTD方法对于n=3.2,R=1μm的耦合微盘的模拟时发现,模场分布关于Y轴呈对称分布时,一阶WGM TE9,1模和二阶WGM TE6,2模的模式特征随微盘间距大小变化时,模式特征的变化存在反交叉耦合模现象。而当n=2.8时,TE9,1和TE6,2也发生耦合,且模场分布关于Y轴呈反对称分布时,模式波长出现耦合交叉现象。若改变微盘的半径,同样存在基模和高阶模的耦合现象。
一阶和二阶WGM的耦合会导致一阶WGM模式Q值的下降。因此在做器件的时应避开这些耦合模,使品质因子处于最大值,从而实现激光器的低阈值激射。
Semiconductor microcavity layers have many advantages such as ultrasmall volume and ultralow threshold. They have great potential applications in optoelectrinics integration. As one of the important types of microcavity lasers, microdisk lasers have been investigated all over the world. Recently, evanescent-coupled microdisks have attracted a great attention, because they can be fabricated easily by the lithographic technique.
Numerical simulation is the fabricate elements for the semiconductor microdisks. In this paper, The mode characteristics for twin coupled microdisks are investigated by 2-D finite-difference time-domain(FDTD) technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first and second order WGMs can have a cross point in some case.
For the two coupled microdisks with the radius R = 1μm and the refractive index n = 3.2. The anti-crossing coupling exists between the coupled WGMs TE9,1 and TE6,2 for the field pattern is symmetry to the Y axis. When change n to 2.8. The mode wavelengths of the two coupled WGMs TE9,1 and TE6,2 have a cross point in some place. When change R. The mode coupling between the first and the second WGM is existent too.
The mode coupling between the first and the second order WGMs can greatly reduce the mode Q-factor of the coupled first order WGMs. So we can avoid these phenomena when fabricate semiconductor coupled microdisks.
引文
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[2] B. Gayral et al, High-Q wet-etched GaAs microdisks containing InAs quantum boxes[J], Appl. Phys. Lett., 75, 1908(1999).
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[5] J. Vuckovic, O. Painter and Y. Xu, A. Yariv, Finite-Difference Time-Domain Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities[J], IEEE J. Quantum Electron., 35, 1168-1175(1999).
[6] E. Yablonovitch, Inhavited spontaneous emission in solid-state physics and electronics[J], Phys. Rev. Lett., 58, 2059-2062(1987)
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[9] C. J. Hood et al, The Atom-Cavity Microscope: Single Atoms Bound in Orbit by Single Photons[J], Science, 287, 1447(2000).
[10] E. M. Purcell, Spontaneous emission probabilities at radio frequencies[J], Phys. Rev. Lett., 69, 681-681(1946).
[11] B. Gayral et al, Time-resolved probing of the Purcell effect for InAs quantum boxes in GaAs microdisks[J], Appl. Phys. Lett.,78, 2828(2001).
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[15] S. Ando et al, Triangular-Facet Laser with Optical Waveguides Grown by Selective Area Metalorganic Chemical Vapor Deposition[J], Japn. J. Appl. Phys., 35, L411(1996).
[16] H. C. Chang et al, Lasing modes in equilateral-triangular laser cavities[J], Phys. Rev. A, 62, 013816(2000).
[17] Q. Y. Lu et al, Mode Characteristics of Semiconductor Equilateral Triangle Microcavities With Side Length of 5–20um[J], IEEE Photon. Technol., Lett. 16, 359(2004).
[18] Y. Z. Huang, Y. H. Hu, Q. Chen, et al,Room-temperature continuous-wave electrically injected InP-GaInAsP equilateral-triangle-resonator lasers[j], IEEE Photon. Technol. Lett., 19, 963(2007).
[19] A. W. Poon et al, Multimode resonances in square-shaped optical microcavities[J], Opt. Lett., 26, 632(2001).
[20] H. J. Moon et al, Single spatial mode selection in a layered square microcavity laser[J], Appl. Phys. Lett., 82, 2963(2003).
[21] H. J. Moon et al, Guided mode lasing in a double-layered square microcavity[J], Appl. Phys. Lett., 83, 2521(2003).
[22] W. H. Guo et al, Modes in square resonators, IEEE J. Quantum Electron., 39, 1563(2003).
[23] L. Rayleigh, The problem of the Whispering Gallery[D], Scientific Papers (Cambridge University, Cambridge, England) 5, 617(1912).
[24] S. L. McCall et al, Whispering-gallery mode microdisk lasers[J], Appl. Phys. Lett., 60, 289(1992).
[25] A. F. J. Levi et al, Room temperature operation of microdisc lasers with submilliamp threshold current[J], Electron. Lett., 28, 1010(1992).
[26] A. F. J. Levi, Room temperature operation of submicrometre radius disk laser[J], Electron. Lett., 29, 1666(1993).
[27] M. Fujita, K. Inoshita and T. Baba, Room temperature continuous wave lasing characteristics of GaInAsP/InP microdisk injection laser[J], Electron. Lett., 34, 278-279(1998).
[28] S. M. K. Thiyagarajan, A. F. J. Levi and C. K. Lin, Continuous room-temperature operation of optically pumped InGaAs/InGaAsP microdisk lasers[J], Electron. Lett., 34, 2333-2334(1998).
[29] S. M. K. Thiyagarajan, D. A. Cohen and A. F. J. Levi, Continuous room-temperature operation of microdisk laser diodes[J], Electron. Lett., 35, 1252-1254(1999).
[30] M. Fujita, R. Ushigome and T. Baba, Continuous wave lasing in GaInAsP microdisk injection laser with threshold current of 40μA[J], Electron. Lett., 36, 790-791(2000).
[31] M. Fujita, R. Ushigome, and T. Baba, Large Spontaneous Emission Factor of 0.1 in a Microdisk Injection Laser[J], IEEE Photon. Technol. Lett., 13, 403-405(2001).
[32] X. Liu, W. Fang and Y. Huang, Chang, Optically pumped ultraviolet microdisk laser on a silicon substrate[J], Appl. Phys. Lett., 84, 2488(2004)
[33] E. D. Haberer, R. Sharma and C. Meier, Free-standing, optically pumped, GaN/InGaN microdisk lasers fabricated by photoelectrochemical etching[J], Appl. Phys. Lett., 85, 5179-5181(2004).
[34] A. F. J. Levi et al, Directional light coupling from microdisk laser[J], Appl. Phys. Lett., 62, 561(1993).
[35] D. Y. Chu et al, Double-disk structure for output coupling in microdisk lasers[J], Appl. Phys. Lett., 65, 3167(1994).
[36] S. C. Hagness et al, FDTD microcavity simulations design and experimental realization of waveguide coupled single mode ring and whispering gallery mode disk resonators[J], J. Lightwave Technol., 15, 2154(1997).
[37] Y. Baryshnikov et al, Whispering gallery modes inside asymmetric resonant cavities[J], Phys. Rev. Lett., 93, 133902(2004).
[38] S. K. Kim et al, Highly directional emission from few-micron-size elliptical microdisks[J], Appl. Phys. Lett., 84, 861(2004).
[39] M. Bayer, T. Gutbrod andJ. P. Reithmaier, Optical Modes in Photonic Molecules[J], Phy. Rev. Lett., 81, 2582-2585(1998).
[40] A. Nakagawa, S. Ishii, and T. Baba, Photonic molecule laser composed of GaInAsP microdisks[J], Appl. Phys. Lett., 86, 041112(2005).
[41] S. Ishii, A. Nakagawa, and T. Baba, Modal Characteristics and Bistability in Twin Microdisk Photonic Molecule Lasers[J], IEEE J. Sel. Topics Quantum Electron., 12, 71-77 (2006).
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