无序介质中的光波局域与随机激光辐射
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摘要
随机激光器是一种非传统的激光器，其基本特点是在具有增益的无序介质中可以形成受激辐射现象。在传统激光器中，反馈机制来源于激光腔对光波的限制作用。然而，在随机激光器中，为系统提供反馈机制的是介质无序性所造成的多重散射。由于其独特的物理机制以及广阔的应用前景，随机激光现象得到了广泛的研究。对于随机激光器的理论研究主要是基于局域化理论和激光物理理论。
在本论文中，我们利用随机激光的半经典理论对随机激光的辐射光特性进行了以下几个方面的理论研究：
(1)在随机激光半经典理论的基础上，给出了短脉冲泵浦随机激光器的物理模型。数值模拟的结果表明，此模型能够更加准确地描述短脉冲泵浦情形下的随机激光辐射特性。
(2)基于短脉冲泵浦随机激光器的物理模型，研究了泵浦光参数对辐射光特性的影响。结果显示，泵浦光脉冲的峰值强度和脉宽对辐射光的时域波形有很大的影响，而泵浦光的脉冲波形对辐射光特性影响甚微。当随机介质在高重复频率的短脉冲序列泵浦下，抽运过程具有累加效应，这就允许我们使用峰值强度很低的激光脉冲序列作为随机激光有效的泵浦源。
(3)基于短脉冲泵浦随机激光器的物理模型，研究了随机介质的样品参数对辐射光特性的影响。结果表明，随机介质的表面填充率越大，辐射光脉冲的强度越高，脉宽越窄，延迟时间也将缩短。散射颗粒的折射率对辐射光特性也有很大的影响，随着折射率的增大，介质中的光波从扩散态转变成局域态，并伴随着强烈的受激辐射过程。
(4)利用各向异性随机激光的半经典理论，讨论了各向异性单轴散射颗粒对光波的局域化现象。结果表明，单轴介质中两个主轴折射率之比具有一个特征值，当超过这个特征值之后光波可以形成局域化现象。
(5)基于各向异性随机激光的理论模型，研究了样品参数对光波局域化的影响，并给出了各种情况下的阈值曲线。结果表明，随机样品的表面填充率越大，局域化程度越高，辐射光的强度也随之增大。样品的面积越大，所能支撑的随机激光模式数量就越多，同时也会降低随机激光器的激发阈值。
(6)研究了二维随机介质中偏振模式的竞争以及阈值特性。结果表明，在两种偏振模式不共享反转粒子数的情形下，横磁模式比横电模式具有更低的激发阈值。如果两种偏振模式共享上能级的反转粒子数，则横电模式占据着主导作用，而横磁模式几乎被完全压制。
(7)利用共享反转粒子数情况下的随机激光偏振态竞争模型，讨论了样品参数对两种偏振模式的辐射特性影响。结果表明，增大样品的表面填充率并不能改变横磁模被压制的情况。但是，通过增大样品尺寸可以使横磁模的激发阈值降低，从而实现两种偏振模式的共存。
The random laser represents a non-conventional laser, whose basic property is that the lasing phenomeon can appear in random systerms with gain. In conventional laser systerms, the feedback mechanism comes from the light confinement by the cavity. While in random lasers, the multiple scattering origined from the randomness is the actual lasing feedback mechanism for such systerms. Ramdom lasing phenomeon are studied widely not only for their interesting physical properties, but also for their importance in technological applications. The theoretical investigation on the random lasers is based on the localization theory and laser physics.
In this thesis, by use of the time-dependment theory of random lasers, we study the emission properties in such systerms as follows:
(1) We present the physical model in short-pulse pumping regime based on the time-dependent theory of random lasers. Results show that this model can represent the emission properties more accurately in short-pulse regime.
(2) Based on the physical model of random laser in short-pulse pumping regime, we study the relationship between the parameters of the pumping pulse and the emission light properties. Results show that the peak intensity and width of the pumping pulse have much influence on the emission pulse in temporal regime, while the shape of the pumping pulse can hardly influence the emission light. When the random media is pumped by a pulse train with high repetition rate, the pumping process has an accumulate effect. This will allow us to use the pulse train with low peak intensity as the effective pumping source of the random laser systerms.
(3) We study how the sample parameters of the random media will influence the emission light properties by use of the physical model of random laser in short-pulse pumping regime. Results show that with the increase of the surface-filling fraction of the random media, the intensity of the emission light becomes higher, at the same time the pulse width becomes narrower and the delay time becomes shorter. The refractive index of the scatterer will also affect the emission light property. The lightwave in the random media behave the transition from diffusion to localization state with the increase the of the refractive index, accompanied by the intensive stimulate emission process.
(4) The light localization phenomenon originated from the anisotropic uniaxial scatterer is discussed based on the time-dependent theory for the anisotropic regime. There is a characteristic value for the ratio of two principal refractive indexes. The lightwave in the random media can be localized when this ratio exceed a specific value.
(5) Based on the theoretical model of the anisotropic random laser, we study the relationship between the sample parameters and the lightwave localization. The threshold curves for different conditions are presented. Results show that with the increase of the surface-filling fraction, the localization level becomes higher and the emission light will become more intensive. When the sample size is enlarged, it can support more lasing modes and the lasing threshold will be decreased simultaneously.
(6) The competition and threshold property between two polarization states in two-dimensional random medium are studied. Results show that the transverse magnetic state has a lower lasing threshold than transverse electric state when they do not share the inverted population. If these two states share the inverted population, the transverse electric state dominates the lasing process while the transverse magnetic state is strongly suppressed.
(7) By use of the competition model of two polarization states which share the inverted population, we discuss the sample structure dependence of the lasing properties in this two-dimensional medium. Numerical results show that by increasing the surface-filling fraction of the sample, one can hardly change the situation that the transverse magnetic state was suppressed. However, we can decrease the lasing threshold of the transverse magnetic state by enlarging the sample size, which will achieve the coexist of the two polarization states.
在本论文中，我们利用随机激光的半经典理论对随机激光的辐射光特性进行了以下几个方面的理论研究：
(1)在随机激光半经典理论的基础上，给出了短脉冲泵浦随机激光器的物理模型。数值模拟的结果表明，此模型能够更加准确地描述短脉冲泵浦情形下的随机激光辐射特性。
(2)基于短脉冲泵浦随机激光器的物理模型，研究了泵浦光参数对辐射光特性的影响。结果显示，泵浦光脉冲的峰值强度和脉宽对辐射光的时域波形有很大的影响，而泵浦光的脉冲波形对辐射光特性影响甚微。当随机介质在高重复频率的短脉冲序列泵浦下，抽运过程具有累加效应，这就允许我们使用峰值强度很低的激光脉冲序列作为随机激光有效的泵浦源。
(3)基于短脉冲泵浦随机激光器的物理模型，研究了随机介质的样品参数对辐射光特性的影响。结果表明，随机介质的表面填充率越大，辐射光脉冲的强度越高，脉宽越窄，延迟时间也将缩短。散射颗粒的折射率对辐射光特性也有很大的影响，随着折射率的增大，介质中的光波从扩散态转变成局域态，并伴随着强烈的受激辐射过程。
(4)利用各向异性随机激光的半经典理论，讨论了各向异性单轴散射颗粒对光波的局域化现象。结果表明，单轴介质中两个主轴折射率之比具有一个特征值，当超过这个特征值之后光波可以形成局域化现象。
(5)基于各向异性随机激光的理论模型，研究了样品参数对光波局域化的影响，并给出了各种情况下的阈值曲线。结果表明，随机样品的表面填充率越大，局域化程度越高，辐射光的强度也随之增大。样品的面积越大，所能支撑的随机激光模式数量就越多，同时也会降低随机激光器的激发阈值。
(6)研究了二维随机介质中偏振模式的竞争以及阈值特性。结果表明，在两种偏振模式不共享反转粒子数的情形下，横磁模式比横电模式具有更低的激发阈值。如果两种偏振模式共享上能级的反转粒子数，则横电模式占据着主导作用，而横磁模式几乎被完全压制。
(7)利用共享反转粒子数情况下的随机激光偏振态竞争模型，讨论了样品参数对两种偏振模式的辐射特性影响。结果表明，增大样品的表面填充率并不能改变横磁模被压制的情况。但是，通过增大样品尺寸可以使横磁模的激发阈值降低，从而实现两种偏振模式的共存。
The random laser represents a non-conventional laser, whose basic property is that the lasing phenomeon can appear in random systerms with gain. In conventional laser systerms, the feedback mechanism comes from the light confinement by the cavity. While in random lasers, the multiple scattering origined from the randomness is the actual lasing feedback mechanism for such systerms. Ramdom lasing phenomeon are studied widely not only for their interesting physical properties, but also for their importance in technological applications. The theoretical investigation on the random lasers is based on the localization theory and laser physics.
In this thesis, by use of the time-dependment theory of random lasers, we study the emission properties in such systerms as follows:
(1) We present the physical model in short-pulse pumping regime based on the time-dependent theory of random lasers. Results show that this model can represent the emission properties more accurately in short-pulse regime.
(2) Based on the physical model of random laser in short-pulse pumping regime, we study the relationship between the parameters of the pumping pulse and the emission light properties. Results show that the peak intensity and width of the pumping pulse have much influence on the emission pulse in temporal regime, while the shape of the pumping pulse can hardly influence the emission light. When the random media is pumped by a pulse train with high repetition rate, the pumping process has an accumulate effect. This will allow us to use the pulse train with low peak intensity as the effective pumping source of the random laser systerms.
(3) We study how the sample parameters of the random media will influence the emission light properties by use of the physical model of random laser in short-pulse pumping regime. Results show that with the increase of the surface-filling fraction of the random media, the intensity of the emission light becomes higher, at the same time the pulse width becomes narrower and the delay time becomes shorter. The refractive index of the scatterer will also affect the emission light property. The lightwave in the random media behave the transition from diffusion to localization state with the increase the of the refractive index, accompanied by the intensive stimulate emission process.
(4) The light localization phenomenon originated from the anisotropic uniaxial scatterer is discussed based on the time-dependent theory for the anisotropic regime. There is a characteristic value for the ratio of two principal refractive indexes. The lightwave in the random media can be localized when this ratio exceed a specific value.
(5) Based on the theoretical model of the anisotropic random laser, we study the relationship between the sample parameters and the lightwave localization. The threshold curves for different conditions are presented. Results show that with the increase of the surface-filling fraction, the localization level becomes higher and the emission light will become more intensive. When the sample size is enlarged, it can support more lasing modes and the lasing threshold will be decreased simultaneously.
(6) The competition and threshold property between two polarization states in two-dimensional random medium are studied. Results show that the transverse magnetic state has a lower lasing threshold than transverse electric state when they do not share the inverted population. If these two states share the inverted population, the transverse electric state dominates the lasing process while the transverse magnetic state is strongly suppressed.
(7) By use of the competition model of two polarization states which share the inverted population, we discuss the sample structure dependence of the lasing properties in this two-dimensional medium. Numerical results show that by increasing the surface-filling fraction of the sample, one can hardly change the situation that the transverse magnetic state was suppressed. However, we can decrease the lasing threshold of the transverse magnetic state by enlarging the sample size, which will achieve the coexist of the two polarization states.
引文
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