正方形光学微腔模式的FDTD计算
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摘要
随着信息技术的不断发展,半导体激光器的应用越来越广。而半导体激光器结构中的重要一部为光学谐振腔。光学微腔以其独特的性质——形状直接影响和决定着光场分布,受到人们的越来越多的关注。它在光学滤波器、光波分复用器、光开关、光调制及非线性频率转换器等得到了广泛的运用。
本文主要研究及仿真了正方形光学微腔的模式特性。通过时域有限差分方法讨论、分析及导出了光学微腔的模式公式:将麦克斯韦微分方程离散化,场空间沿着三个轴向分成多个网格空间,得到有限差分形式的场方程。其中网格剖分是FDTD方法的关键问题。然而任何腔体的边界都不是完美的,引入的完全吸收边界条件正好弥补了此缺点。时域有限差分方法得到的信号是时域的,而谐振腔的重要参数一般是在频域里计算,则引用了中间桥梁-傅立叶变换把时域信号转变成频域信号的集合。为了获得数值结果的准确性,得到理论支持,用马卡梯里近似解法讨论了二维正方形微腔模式的解析解,获得了腔体的光场分布,并加以讨论得出计算模式的本征方程及与传播常数之间应满足的关系式。运用全波仿真软件的时域有限差分法模拟出了正方形光学微腔的横模图及纵模图,从而分析了正方形光学微腔的模式特性,得到了较高的品质因子。然而,想要得到光滑而分辨率高的频谱图,需注意FDTD输出选项的FFT最大幂指数及FFT最小幂指数选项,须为2的指数倍才可出现我们所需的光滑频谱图。红绿斑点回音壁模式的交替出现并随阶数的增高逐渐模糊的情况来看,正方形光学微腔在低阶模的应用较好,随阶数的增高其性能会减退。比较了数值模拟与解析结果,发现结果及其相近,也与已有文献上的结果相吻合。从而说明时域有限差分方法的全波仿真软件是很实用的一部软件,对光学腔体及光波导之类的器件,应用是非常有前景的。然而任何腔体都不是完美的,最后总结了正方形光学微腔的展望和存在的问题。
With development of the information technology, semiconductor laser has applied widely. A section of laser structure is optical-resonator. Unique feature of a resonator is widely attended to optical field distribution that a shape effected and decided. it is used to optical-filter、switcher、optical-modulation and non-linear frequency transformation.
This paper have mainly studied and simulated the mode feature of a square resonator. The mode formula of a square resonator is calculated and analyzed by finite-difference time-domain. Maxwell's equation is discrete via central differences in time and space, then numerically solving these equations. Grid analysis of finite-difference time-domain numerical calculation method is a critical core question. But any boundary of a resonator is imperfect, PML boundary condition is introduced for the destination. Acquired information by FDTD is in a time field, but significant factor of a resonator is in a frequency field, so to have introduced intermediate bridge - Fourier transform. Theory analysis is introduced about two dimension Square resonator by Marcatili's approximation method and have obtained field distribution and mode equation. FDTD simulation of Square resonator is studied. Transverse mode figures and vertical mode spectrum of a square resonator is simulated by FullWAVE and have analyzed the mode feature of the resonator. But you'd like to acquired high resolution spectrum, it is important to note the FFTMaxPow2 and FFTMixPow2 used is most efficient when the number of data points is a power of 2. By existing of red green resonant mode and number addition, application of square optical resonator is preferably in the lower mode, performance is slipping by mode heightening. Having obtained numerical result is accurate, and are compared with the FDTD results and shown to be in good agreement. The result is equal the having record. So it is shows that the utility of FullWAVE is very practical, the software is to foreground to appliance of the resonator and waveguide and so on. But any resonator is not perfect, at the end of the paper, prospect and questions about a square is discussed.
本文主要研究及仿真了正方形光学微腔的模式特性。通过时域有限差分方法讨论、分析及导出了光学微腔的模式公式:将麦克斯韦微分方程离散化,场空间沿着三个轴向分成多个网格空间,得到有限差分形式的场方程。其中网格剖分是FDTD方法的关键问题。然而任何腔体的边界都不是完美的,引入的完全吸收边界条件正好弥补了此缺点。时域有限差分方法得到的信号是时域的,而谐振腔的重要参数一般是在频域里计算,则引用了中间桥梁-傅立叶变换把时域信号转变成频域信号的集合。为了获得数值结果的准确性,得到理论支持,用马卡梯里近似解法讨论了二维正方形微腔模式的解析解,获得了腔体的光场分布,并加以讨论得出计算模式的本征方程及与传播常数之间应满足的关系式。运用全波仿真软件的时域有限差分法模拟出了正方形光学微腔的横模图及纵模图,从而分析了正方形光学微腔的模式特性,得到了较高的品质因子。然而,想要得到光滑而分辨率高的频谱图,需注意FDTD输出选项的FFT最大幂指数及FFT最小幂指数选项,须为2的指数倍才可出现我们所需的光滑频谱图。红绿斑点回音壁模式的交替出现并随阶数的增高逐渐模糊的情况来看,正方形光学微腔在低阶模的应用较好,随阶数的增高其性能会减退。比较了数值模拟与解析结果,发现结果及其相近,也与已有文献上的结果相吻合。从而说明时域有限差分方法的全波仿真软件是很实用的一部软件,对光学腔体及光波导之类的器件,应用是非常有前景的。然而任何腔体都不是完美的,最后总结了正方形光学微腔的展望和存在的问题。
With development of the information technology, semiconductor laser has applied widely. A section of laser structure is optical-resonator. Unique feature of a resonator is widely attended to optical field distribution that a shape effected and decided. it is used to optical-filter、switcher、optical-modulation and non-linear frequency transformation.
This paper have mainly studied and simulated the mode feature of a square resonator. The mode formula of a square resonator is calculated and analyzed by finite-difference time-domain. Maxwell's equation is discrete via central differences in time and space, then numerically solving these equations. Grid analysis of finite-difference time-domain numerical calculation method is a critical core question. But any boundary of a resonator is imperfect, PML boundary condition is introduced for the destination. Acquired information by FDTD is in a time field, but significant factor of a resonator is in a frequency field, so to have introduced intermediate bridge - Fourier transform. Theory analysis is introduced about two dimension Square resonator by Marcatili's approximation method and have obtained field distribution and mode equation. FDTD simulation of Square resonator is studied. Transverse mode figures and vertical mode spectrum of a square resonator is simulated by FullWAVE and have analyzed the mode feature of the resonator. But you'd like to acquired high resolution spectrum, it is important to note the FFTMaxPow2 and FFTMixPow2 used is most efficient when the number of data points is a power of 2. By existing of red green resonant mode and number addition, application of square optical resonator is preferably in the lower mode, performance is slipping by mode heightening. Having obtained numerical result is accurate, and are compared with the FDTD results and shown to be in good agreement. The result is equal the having record. So it is shows that the utility of FullWAVE is very practical, the software is to foreground to appliance of the resonator and waveguide and so on. But any resonator is not perfect, at the end of the paper, prospect and questions about a square is discussed.
引文
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