强散射体像面散斑对比度及超快激光脉冲的近场和远场散射的研究
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摘要
对随机表面的统计特性以及对其标定方法的研究是一个多年来倍受关注的课题，它在材料加工、工件加工和光学元件制造等许多科研技术领域有着重要的理论意义和应用价值。近场光学是研究距离介质分界面一个波长以内(即近场区域)的光学现象的新型交叉学科，随着近场光学显微镜的快速发展，对近场光学的研究也获得了相当大的进展。超快脉冲是由一系列单色光波叠加组成的持续时间非常短暂的激光脉冲。本文对粗糙随机表面光散射及像面散斑对比度、超快脉冲的近场散射以及费涅尔衍射的一些特性进行了理论上和计算模拟的研究。全文共分四章。
第一章对随机表面参量及其统计特性和标定方法、光散射的基本原理、近场光学以及超快激光脉冲的一些特性进行了综述。
第二章利用像面散斑场光波复振幅的一般形式和双重指数函数近似以及像面散斑场光波复振幅的实部和虚部的旋转变换法，得到了强散射体在4f成像系统中像面散斑对比度与随机表面统计参量以及光学成像系统参量之间相关联的直接表达式。根据这个表达式我们可以看出，在滤波孔比较小的情况下强散射体像面散斑对比度与表面均方偏差粗糙度w、横向相关长度ξ以及滤波孔径R之间都有密切的依赖关系。本章的结果与现有文献中包含随机表面相关面积或散射基元数目的隐含表达式相比具有明显的改进，而且对标定高斯相关随机表面的散斑对比度法的应用具有重要的意义。
第三章给出了关于通过一个亚波长孔径传播的超快激光脉冲的数值解方法。首先把随时间变化的超快激光脉冲看作是一系列简单的单色谐波的叠加，对于具有单一频率的谐波光场可以用电磁波格林积分方程进行求解。然后把这种数值解方法分别运用到所有频率的单色波即可就出其对应的光场，而且对所有的这些数值解作逆付里叶变换就可以将其转换为时间领域的光场。通过计算模拟求出光波通过亚波长孔径后的强度分布，计算结果可以体现出沿着介质表面传播的光场的一些特性。本文中的方法和结果对理解近场领域中倏逝波的形成和传播是非常重要的。
摘要
第四章对超快激光脉冲经随机表面在菲涅耳衍射区形成的散斑场的统计特性进
行理论和计算模拟研究，首先根据超快脉冲本身的性质以及简化随机表面光场自相关
的表达式求出散斑光场自相关函数，然后由它和光强的系综平均求出散斑场光强自相
关函数。计算模拟的结果给出散斑场的一些与单色光照明的情况不同的特性，我们发
现随着时间的推迟，散斑颗粒逐渐减小而且散斑场出现周期性振荡，并在理论上对这
些特性给出合理的解释。
Great attention has been paid to the study of the statistical properties of random surfaces, and it is of great importance in many science and technology fields such as the growth of thin films, the fine machining, the manufacture of optical devices, etc. Near-field optics is a new interdisciplinary subject which studies the optical phenomena within one wavelength, and with the rapid development of near-field optical microscopy, considerable advancement has been achieved in the studies of near-field optics. Femtosecond laser pulse is the laser pulse that consists of a coherent superposition of many frequency components. This dissertation is concentrated on theoretical and simulational studies on the contrast of image speckles and the scattering and the diffraction of femtosecond laser pulse from rough random surfaces in the near-field and the Fresnel regions. The whole dissertation is divided into four chapters.
In chapter 1, we give a summary and an overall review for the statistical properties and measurements of random surfaces, the fundamental theories of light scattering, and the properties of near-field optics and femtosecond laser pulse.
In chapter 2, using the generic expression of the complex amplitude of speckle and the approximation of the double exponential function and the rotational transformation of the real and imaginary parts of the complex amplitude of speckle, we obtain the expression for the contrast of the image speckles produced by strong scattering-objects in the 4/ optical imaging system, which is explicitly related to the statistical parameters of random surface and to the parameters of the imaging system. Based on the obtained results, we can see that the contrast of the image speckles produced by strong scattering-objects is related to roughness w, lateral correlation length , and aperture length R when R is little
enough. Our results are an obvious improvement on the literature, where the relations including such implicit quantities as the average size of the scattering grains of the random surface and the number of scattering grains are usually used. The results would be of great significance for the characterization of random surface by speckle contrast.
In chapter 3, we propose the method for the numerical calculations of the femtosecond laser pulse propagation through a subwavelength aperture. The time-dependent laser pulse is first decomposed into the superposition of series of monochromatic simple harmonic waves. For the light field of the harmonic wave with a single frequency, the numerical calculation is made on the basis of solution of the Green's integral equation set of electromagnetic waves. Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform. The light intensity distributions transmitted from the subwavelength aperture are calculated and the results show the propagation of the light field along the direction of the medium interface. The method and the results would be important in understanding the process of the construction and the propagation of the evanescent waves in the area of near-field optics.
Chapter 4 is concentrated on theoretical and simulational studies on the statistical properties of the speckle field in the Fresnel diffraction region produced by the scattering of femtosecond laser pulse from random surfaces. At first, we obtain the auto-correlation function of speckles by using the property of femtosecond laser pulse and the ^-correlation model of the light filed of the random surfaces, and then we obtain the auto-correlation function of light intensities. The simulational results give some statistical properties of the speckle fields, which are different from those with monochromatic light illuminations. We find that the speckle granules become smaller and speckle fields become spatially periodically oscillated with the time past. Reasonable theoretical explanation for these properties are given.
第一章对随机表面参量及其统计特性和标定方法、光散射的基本原理、近场光学以及超快激光脉冲的一些特性进行了综述。
第二章利用像面散斑场光波复振幅的一般形式和双重指数函数近似以及像面散斑场光波复振幅的实部和虚部的旋转变换法，得到了强散射体在4f成像系统中像面散斑对比度与随机表面统计参量以及光学成像系统参量之间相关联的直接表达式。根据这个表达式我们可以看出，在滤波孔比较小的情况下强散射体像面散斑对比度与表面均方偏差粗糙度w、横向相关长度ξ以及滤波孔径R之间都有密切的依赖关系。本章的结果与现有文献中包含随机表面相关面积或散射基元数目的隐含表达式相比具有明显的改进，而且对标定高斯相关随机表面的散斑对比度法的应用具有重要的意义。
第三章给出了关于通过一个亚波长孔径传播的超快激光脉冲的数值解方法。首先把随时间变化的超快激光脉冲看作是一系列简单的单色谐波的叠加，对于具有单一频率的谐波光场可以用电磁波格林积分方程进行求解。然后把这种数值解方法分别运用到所有频率的单色波即可就出其对应的光场，而且对所有的这些数值解作逆付里叶变换就可以将其转换为时间领域的光场。通过计算模拟求出光波通过亚波长孔径后的强度分布，计算结果可以体现出沿着介质表面传播的光场的一些特性。本文中的方法和结果对理解近场领域中倏逝波的形成和传播是非常重要的。
摘要
第四章对超快激光脉冲经随机表面在菲涅耳衍射区形成的散斑场的统计特性进
行理论和计算模拟研究，首先根据超快脉冲本身的性质以及简化随机表面光场自相关
的表达式求出散斑光场自相关函数，然后由它和光强的系综平均求出散斑场光强自相
关函数。计算模拟的结果给出散斑场的一些与单色光照明的情况不同的特性，我们发
现随着时间的推迟，散斑颗粒逐渐减小而且散斑场出现周期性振荡，并在理论上对这
些特性给出合理的解释。
Great attention has been paid to the study of the statistical properties of random surfaces, and it is of great importance in many science and technology fields such as the growth of thin films, the fine machining, the manufacture of optical devices, etc. Near-field optics is a new interdisciplinary subject which studies the optical phenomena within one wavelength, and with the rapid development of near-field optical microscopy, considerable advancement has been achieved in the studies of near-field optics. Femtosecond laser pulse is the laser pulse that consists of a coherent superposition of many frequency components. This dissertation is concentrated on theoretical and simulational studies on the contrast of image speckles and the scattering and the diffraction of femtosecond laser pulse from rough random surfaces in the near-field and the Fresnel regions. The whole dissertation is divided into four chapters.
In chapter 1, we give a summary and an overall review for the statistical properties and measurements of random surfaces, the fundamental theories of light scattering, and the properties of near-field optics and femtosecond laser pulse.
In chapter 2, using the generic expression of the complex amplitude of speckle and the approximation of the double exponential function and the rotational transformation of the real and imaginary parts of the complex amplitude of speckle, we obtain the expression for the contrast of the image speckles produced by strong scattering-objects in the 4/ optical imaging system, which is explicitly related to the statistical parameters of random surface and to the parameters of the imaging system. Based on the obtained results, we can see that the contrast of the image speckles produced by strong scattering-objects is related to roughness w, lateral correlation length , and aperture length R when R is little
enough. Our results are an obvious improvement on the literature, where the relations including such implicit quantities as the average size of the scattering grains of the random surface and the number of scattering grains are usually used. The results would be of great significance for the characterization of random surface by speckle contrast.
In chapter 3, we propose the method for the numerical calculations of the femtosecond laser pulse propagation through a subwavelength aperture. The time-dependent laser pulse is first decomposed into the superposition of series of monochromatic simple harmonic waves. For the light field of the harmonic wave with a single frequency, the numerical calculation is made on the basis of solution of the Green's integral equation set of electromagnetic waves. Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform. The light intensity distributions transmitted from the subwavelength aperture are calculated and the results show the propagation of the light field along the direction of the medium interface. The method and the results would be important in understanding the process of the construction and the propagation of the evanescent waves in the area of near-field optics.
Chapter 4 is concentrated on theoretical and simulational studies on the statistical properties of the speckle field in the Fresnel diffraction region produced by the scattering of femtosecond laser pulse from random surfaces. At first, we obtain the auto-correlation function of speckles by using the property of femtosecond laser pulse and the ^-correlation model of the light filed of the random surfaces, and then we obtain the auto-correlation function of light intensities. The simulational results give some statistical properties of the speckle fields, which are different from those with monochromatic light illuminations. We find that the speckle granules become smaller and speckle fields become spatially periodically oscillated with the time past. Reasonable theoretical explanation for these properties are given.
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