【作者】 蒲继雄；

【导师】 吕百达；

【作者基本信息】 四川大学 ， 光学， 2003， 博士

【摘要】 光谱分析是最重要的科学分析手段之一。在光谱分析中，经常假定光在自由空间传输中其光谱保持不变。在最近十多年，这一被认为是理所当然的假定受到了质疑。1986年，美国著名的光学专家Wolf教授证明：当光源的光谱相干度满足所谓的定标定律时，从光源发出的光在传输中才保持光谱不变。反之，从违反定标定律的光源发出的光在传输过程中，其光谱将会发生变化。这种现象称为相关诱导的光谱变化。之后，人们还发现，当满足定标定律的部分相干光被光阑衍射时，在衍射光场也会出现光谱变化。这种光谱变化有时也称为衍射诱导的光谱变化。 在一般情况下，由两个相同发光光谱的点光源发出的光在迭加区的归一化光谱与两个点光源的归一化光谱不同。在迭加区的归一化光谱被两个点光源之间的相干性调制了。当两个点光源是非相干的，迭加光场观测到的归一化光谱才等于点光源的归一化光谱。 准均匀光源是自然界和实验室常见的光源。可以得到从准均匀光源发出的光在远场的光谱与光源光谱之间的关系。结果表明，在一般情况下，在远场的归一化光谱并不等于光源的归一化光谱，而是依赖于光源的光谱相干度和观测方向。为了使准均匀光源的归一化发光光谱保持传输不变性，光源的光谱相干度必须满足如下式子： μ（r′）=h（kr′）， （1）式中，r′为光源平面两点r₁和r₂的位置矢量差，即r′=r₂-r₁。k=ω/c是波数，c为真空中的光速。 （1）式就是定标定律。应用这个定标定律，我们能判断从准均匀光源发出的光的光谱是否发生变化。庆幸的是，自然界和实验室某些常见的光源都满足定标定四少11大学博士学位论文律 高斯一谢尔模型（GSM）光束是一种特殊的部分相干光束。GSM光束的光强分布和空间相干度分布均为高斯分布的部分相干光束。我们研究了宽频带GSM光束在传输中的光谱变化。当GSM光束在自由空间中传输，其光谱在一般情况下也会发生变化。这种光谱变化依赖于GSM光源的半径w0和有效相干宽度外与频率。的依赖关系。为了使GSM光束在传输中保持光谱不变，GSM光源的有效相干宽度内（。）必须满足 W。一，^血、_甘on吸口少j二二-气二二二二二二二二二““了，，一1（2）式中，假设GSM光束的半径w0与频率无关，夕是一正常数。 根据光线传输矩阵的传输公式，我们还推导了GSM光束经过ABCD光线传输矩阵描述的光学系统的传输公式。据此，我们可以发现:GSM光束经过光学系统传输之后，其光谱也会发生变化。这种光谱变化不仅取决于GSM光束的参数，而且还取决于光学系统的光线传输矩阵元。作为一个特殊的例子，我们研究了GSM光束经过色差光学透镜的聚焦。结果发现，光学透镜适量的色差就导致了聚焦光场的光谱发生显著的变化。并且，这种光谱变化还与GSM光束的相干度有关，GSM光束的相干度愈低，色差对聚焦光场光谱的影响就愈小。 完全相干光被衍射光栅的衍射是一个熟知的光学过程。但是，当部分相干光被衍射光栅的衍射时，部分相干光的空间相干度对衍射光束的影响如何却不清楚。我们研究了GSM光束经过全息光栅的衍射。我们发现当一束GSM光束经过全息光栅衍射，在衍射光场得到了三束GSM光束，即零级GSM光束和士1级GSM光束。零级GSM光束的光谱变化与GSM光束在自由空间中传输时的光谱变化情况相同。而士1级的光谱却发生了很大的变化。这种光谱变化不仅依赖于全息光栅的频率;而且还依赖于GSM光源的半径和空间相干度。 当满足定标定律的宽频带部分相干光被光阑衍射时，在衍射光场的光谱与光阑处光的光谱不同。我们发现，在衍射光场的近场和远场的光谱均发生了变化。这种光谱变化取决于衍射光阑处部分相干光的空间相干度。在衍射光场的近场，光谱分裂成两个峰。通过测量光谱位移与:/:。的变化关系，我们发现，在一般情况下，光谱位移随着:/z0的变化而呈现缓慢的变化。但是，当:/z0等于某特殊值时，光四川大学博士学位论文谱位移从红移（或蓝移）快速地变成蓝移（或红移）。这种光谱位移的快速变化的现象就是光谱开关。 我们还研究了另一类型的部分相干光被光阑衍射时，在衍射光场的远场发生的光谱变化。理论结果表明，在远场处的光谱也发生变化，并且光谱位移随着光阑处部分相干光的空间相干度的改变而呈现缓慢的变化。但是，当光阑处的部分相干光的空间相干度等于某一特定值时，在远场也发生光谱开关。另外，在远场的轴外点也出现光谱开关。并且，在不同的衍射角v的光谱探测器（输出口）出现光谱开关所对应的空间相干度不同。据此，我们提出了lxN光谱开关。在这种光谱开关中，通过控制输入口（衍射光阑）的空间相干度，使特定衍射角的输出口发生光谱位移的快速变化（即光谱开关）。 我们所获得的光谱开关的理论结果己被印度国家物理实验室H.c.KandPal博士等人实验证实。更多还原

【Abstract】 The spectral analysis of radiation is one of most important analytic methods in science. Implicit in its use is the assumption that the spectrum of light does not change as the radiation propagates in free space. This assumption has been called into question for past ten years. In 1986, Professor Wolf, a famous optics researcher of America, showed that only when the spectral degree of coherence of a source satisfies the so-called scaling law, does the spectrum of the radiation from the source keep the spectral invariance during its propagation. Conversely, when the source does not satisfy the scaling law, the spectrum of the radiation from the source will experience spectral change. This kind of phenomenon is termed correlation-induced spectral changes. Later it is also found that when partially coherent light whose spectral degree of coherence satisfies the scaling law is diffracted by an aperture, the spectrum of the light in the diffracted field will be changed as well. This kind of spectral changes sometimes is called the diffraction-induced spectral changes.Generally the normalized spectrum of the radiation generated by two point sources, with the same normalized spectrum, is different from the normalized spectrum of each source. The normalized spectrum of the light at the superposition of region is modulated by the correlation of the two sources. Only when the two sources are completely uncorrelated, is the normalized spectrum of the light of the superposition region equal to the normalized spectrum of each source.Quasi-homogenous sources are frequently encountered in nature and laboratory. The relation between the spectrum of the light in the far zone radiated from the source and the spectrum of the source has been derived. It is shown that the normalized spectrum of the light in the far zone is not equal to the normalized spectrum of the source, but is dependent on the spectral degree of coherence of the source and the observed direction. To ensure the normalized spectrum of the light radiated from the quasi-homogenous source be the same throughout the far zone, the spectral degree of coherence of the source should satisfy following equation:here, r’ denotes the vector difference between the two points r, and r2 , i.e., r’= r2 -r1. k = ω/ c is the wave-number associated with the frequency ω . c is the light speed in vacuum.Formula (1) is just the scaling law. Based on formula (1), we can judge that the spectrum of radiation from a source changes or not. Fortunately some of most commonly occurring sources found in the nature and in laboratory satisfy formula (1).A Gaussian Schell-model (GSM) beam is one special kind of partially coherent beam. Both the intensity distribution and the coherence distribution of the GSM beam are Gaussian distribution. We have studied the spectral changes of a GSM beam during its propagation. It is shown that even when a GSM beam propagates in free space, its normalized spectrum will change. The spectral changes are dependent on the frequency dependence of the GSM source radius w0 and of the effective coherencewidth σ0 (ω) . To keep the spectral invariance of the GSM beam propagating in the free space, the effective coherence width σ0 (ω) should behere w0 is assumed to be independent of frequency ω , and y is a positive constant.Based on the ray matrix method, the generalized formulas for describing the propagation of a GSM beam through an optical system of ABCD ray matrix are derived. It is shown that in general the spectral changes also take place as the beam propagates through the optical system, and the spectral changes are not only dependent on the parameters of the GSM beam, but also on the elements of the ray matrix of the optical system. As a special example, the focusing of a GSM beam by a lens with chromatic aberration is presented. We show that suitable chromatic aberration of the lens will lead to remarkable spectral changes of the light near the focus. The spectral changes also depend on the coherence, the lower coherence of th更多还原