随机激光辐射特性的理论研究与数值模拟
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摘要
随机介质通常是指一种折射率在光波长尺度内随机变化的介质,光波在这样的介质中表现出许多光学特性,其中随机激光(Random Lasers)是最令人感兴趣的现象。这种随机增益介质中的受激辐射现象,不需要传统的激光腔,而是形成于光子的局域化。对这一现象的研究开辟了光波局域化和激光物理的新领域,而且可能研制出一种新型微腔激光器。本文基于激光物理、固体物理和光波局域化理论,分析了随机激光器的形成机制和光学特性。
详细介绍了有限时域差分法和传输矩阵法的理论和算法,着重讨论和分析了激励源、PML 吸收边界条件、准态模的测量技术等几个关键问题,这些因素直接影响模拟结果。根据概率论和数理统计的有关知识,我们建立了描述一维、二维ZnO 随机介质统计模型,并用传输矩阵法(TMM),有限时域差分法(FDTD)计算了介质中电场的空间分布和时间演化特性。为了描述电磁场的放大特性,我们采用了几种不同的方法将光学增益引入到模型中,这构成几种不同的模型。我们研究和对比了这几个模型的特点和应用范围。
基于光波局域化理论,详细地研究了1D 和2D 随机介质中,介电常数的空间涨落对光波空间分布和准态模频谱特性的影响。模拟结果显示,介质中散射微粒的不同分布将形成不同结构的随机介质。这些结构对光波的多重散射,将延长光波在介质中的滞留时间,其作用类似于一个谐振腔。这种类光腔结构随机地分布在介质中,其数量、位置和分布决定于散射微粒的随机结构。准态模的Q 值是和随机激光密切相关的参数。TMM 法模拟的结果显示,在1D 随机介质中准态模的Q 值依赖于随机强度的大小,在某些随机强度下准态模具有很高的Q 值。
基于激光物理的选模理论,研究了随机激光器的选模技术。几种不同的选模技术,包括局域泵浦、调整增益曲线和改变介质的边界等用于准态模的选择激发。模拟结果显示,这些方法可以有效地控制准态模的放大。
通过分析随机激光器的阈值,探讨了降低随机激光器阈值的方法和技术。模拟结果显示,局域化较强的准态模有较小的阈值,能够首先激发。双光子泵浦是一种有效
Random media usually refer to electromagnetic media with a random spatial variation of the refractive index in optical wavelength scale. Such a medium possesses much optical characteristics in which random lasing is the most interesting optical phenomenon. This kind of lasing phenomenon does not require a pre-defined physical cavity but originates from photon localization. The study on this phenomenon will open up land of photon localization and new field of laser physics, and expect to develop a kind of new-type micro-cavity laser. In this dissertation, Finite Difference Time Domain (FDTD) and Transfer Matrix Method (TMM) are developed to analyse the feedback mechanism and optical characteristic of random lasers.
Based on laser physics, solid physics and conventional theory and algorithm of the FDTD method, several models are analyzed in detail,in which their application range and features are discused and compared with each other. The theory and algorithm of TMM and FDTD method are studied in detail and implemented in a unique and efficient approach. Several essential questions including excitation sources, detection techniques and Perfectly Matched Layer (PML) boundary conditions are analyzed to obtain the accurate information from simulations. The combination of the FDTD and TMM method provides a powerful tool for simulation and analysis of random lasers with high performance.
Based on theory of photon localization, the effects of the dielectric constant fluctuation on the spatial distribution of light waves are investigated in detail in one-dimension and two-dimensional random media. Results show that the fluctuation on dielectric constant results in some special configurations forming in a random medium. Such configurations trap the lightwave and delay relaxation time of the photon in it, and play a role similar to an optical resonator, which results in lasing oscillation in a random
medium with a pump beam. Such optical resonators distribute randomly in the random medium and their amount and distributing characteristics depend on the strength of the dielectric constant fluctuation. The quality factor is vital to understand the random lasers. Resulsts obtained from TMM method in one-dimensional random media, show that the strength of randomness affects the quality factor of quasi-state modes. It is possible for high quality factor of quasi-state mode to be formed in random medium with some degree of disorder strength. Based on theory of mode selection, the selectively excitation of quasi-state modes is studied in detail. Several mode-selecting techniques,such as the local pumping, adjusting gain curve and changing the shape of the random medium, are applied to mode selcetion. The results show that above techniques affect the excitation of quasi-state modes. Finally, on the basis of analysis of lasing threshold, the low-threshold random lasers are analyzed in detail. Results show that the quasi-state modes with a stronger spatial localization have lower threshold and can be amplified preferentially. The two-photon pump is an effective method to reduce threshold while partially random media serve as another material to realize the low-threshold random laser. Results show that the threshold is closely related to the strength of randomness and the lasing threshold reachs a minimum value at some value of disorder strength.
详细介绍了有限时域差分法和传输矩阵法的理论和算法,着重讨论和分析了激励源、PML 吸收边界条件、准态模的测量技术等几个关键问题,这些因素直接影响模拟结果。根据概率论和数理统计的有关知识,我们建立了描述一维、二维ZnO 随机介质统计模型,并用传输矩阵法(TMM),有限时域差分法(FDTD)计算了介质中电场的空间分布和时间演化特性。为了描述电磁场的放大特性,我们采用了几种不同的方法将光学增益引入到模型中,这构成几种不同的模型。我们研究和对比了这几个模型的特点和应用范围。
基于光波局域化理论,详细地研究了1D 和2D 随机介质中,介电常数的空间涨落对光波空间分布和准态模频谱特性的影响。模拟结果显示,介质中散射微粒的不同分布将形成不同结构的随机介质。这些结构对光波的多重散射,将延长光波在介质中的滞留时间,其作用类似于一个谐振腔。这种类光腔结构随机地分布在介质中,其数量、位置和分布决定于散射微粒的随机结构。准态模的Q 值是和随机激光密切相关的参数。TMM 法模拟的结果显示,在1D 随机介质中准态模的Q 值依赖于随机强度的大小,在某些随机强度下准态模具有很高的Q 值。
基于激光物理的选模理论,研究了随机激光器的选模技术。几种不同的选模技术,包括局域泵浦、调整增益曲线和改变介质的边界等用于准态模的选择激发。模拟结果显示,这些方法可以有效地控制准态模的放大。
通过分析随机激光器的阈值,探讨了降低随机激光器阈值的方法和技术。模拟结果显示,局域化较强的准态模有较小的阈值,能够首先激发。双光子泵浦是一种有效
Random media usually refer to electromagnetic media with a random spatial variation of the refractive index in optical wavelength scale. Such a medium possesses much optical characteristics in which random lasing is the most interesting optical phenomenon. This kind of lasing phenomenon does not require a pre-defined physical cavity but originates from photon localization. The study on this phenomenon will open up land of photon localization and new field of laser physics, and expect to develop a kind of new-type micro-cavity laser. In this dissertation, Finite Difference Time Domain (FDTD) and Transfer Matrix Method (TMM) are developed to analyse the feedback mechanism and optical characteristic of random lasers.
Based on laser physics, solid physics and conventional theory and algorithm of the FDTD method, several models are analyzed in detail,in which their application range and features are discused and compared with each other. The theory and algorithm of TMM and FDTD method are studied in detail and implemented in a unique and efficient approach. Several essential questions including excitation sources, detection techniques and Perfectly Matched Layer (PML) boundary conditions are analyzed to obtain the accurate information from simulations. The combination of the FDTD and TMM method provides a powerful tool for simulation and analysis of random lasers with high performance.
Based on theory of photon localization, the effects of the dielectric constant fluctuation on the spatial distribution of light waves are investigated in detail in one-dimension and two-dimensional random media. Results show that the fluctuation on dielectric constant results in some special configurations forming in a random medium. Such configurations trap the lightwave and delay relaxation time of the photon in it, and play a role similar to an optical resonator, which results in lasing oscillation in a random
medium with a pump beam. Such optical resonators distribute randomly in the random medium and their amount and distributing characteristics depend on the strength of the dielectric constant fluctuation. The quality factor is vital to understand the random lasers. Resulsts obtained from TMM method in one-dimensional random media, show that the strength of randomness affects the quality factor of quasi-state modes. It is possible for high quality factor of quasi-state mode to be formed in random medium with some degree of disorder strength. Based on theory of mode selection, the selectively excitation of quasi-state modes is studied in detail. Several mode-selecting techniques,such as the local pumping, adjusting gain curve and changing the shape of the random medium, are applied to mode selcetion. The results show that above techniques affect the excitation of quasi-state modes. Finally, on the basis of analysis of lasing threshold, the low-threshold random lasers are analyzed in detail. Results show that the quasi-state modes with a stronger spatial localization have lower threshold and can be amplified preferentially. The two-photon pump is an effective method to reduce threshold while partially random media serve as another material to realize the low-threshold random laser. Results show that the threshold is closely related to the strength of randomness and the lasing threshold reachs a minimum value at some value of disorder strength.
引文
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