一维与二维铁电体超晶格中若干倍频效应的研究
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摘要
本文以同成分钽酸锂晶体为例,研究了若干铁电晶体中的非线性光学过程。以二倍频发生为主线,阐释了近年来相关领域中的热点问题,主要包括：体块材料中非线性切伦科夫辐射,弹性散射准相位匹配锥形辐射,局域准相位匹配等效应。全文内容如下——
前言部分由第一章与第二章构成,这一部分对目前基于各类相位匹配模式下的激光倍频过程作一概览。其中第一章给出本论文总的研究背景,第二章则简介了铁电晶体钽酸锂的晶体基本线性光学属性以及与激光倍频过程相关的非线性系数张量属性,同时详述了铁电极化样品的制备流程,和准相位匹配理论基础,为后续章节作一铺垫,方便本论文自成体系。后续章节围绕其中与论文作者研究相关的三个方向给出较为细致的讨论。
第三章从简介非线性切伦科夫辐射概念及其成因入手,利用时空限域平面波模型导出了体块材料中的非线性切伦科夫辐射空间角谱分布条件,以及在基波激发的非线性极化相位纵向调制情况下的非线性切伦科夫辐射空间角谱条件；并从该模型得出了非线性切伦科夫辐射与二维非共线准相位匹配之间的关联。通过实验验证了前述的空间角谱。
第四章概述了弹性散射锥形辐射当前的研究状态,鉴于弹性散射锥形辐射与切伦科夫辐射在空间分布上有相似性,本章尝试对两者之间的异同进行了一些讨论。本章特别针对高阶弹性散射作了实验和理论探索,在现有弹性散射准相位匹配规律下,导出了弹性散射倍频锥形辐射投影曲线族的代数方程,并导出了该过程中的有效非线性系数。另外,通过实验观察了一维和二维周期结构的弹性散射准相位匹配倍频高阶效应,尤其是在二维铁电体超晶格中发现了高阶弹性散射下准相位匹配锥形辐射的包络效应——即在高阶情形,弹性散射准相位匹配往往不能输出空间上可观测的单个或分立的多个锥形辐射,而是给出由各高阶倒格矢参与下的准相位匹配锥形辐射的空间包络,这一现象在各类铁电体超晶格实验现象中比低阶弹性散射更具普遍性。由于高阶效应同时可匹配的模式较多,文中发明了矢量球壳法统一对一维与二维铁电体超晶格中的弹性散射准相位匹配从整体上进行了较为细致的分析预测。利用此方法,我提出了“一切共线入射于非线性超晶格中的基波实现的共线准相位匹配或非共线准相位匹配过程都是弹性散射准相位匹配过程的特例”的这一论断,并通过实验确证；同时基于此方法,我设计了高阶弹性散射的旋转动力学实验,该旋转方式可以为铁电畴结构探测提供更多的倒格矢分量,给出了利用激光倍频方式精确解析厘米级尺度铁电体超晶格微观畴结构的新思路。本章还讨论并验证了旋转过程中的锥形光束存在的简并现象。
第五章重点描述了局域准相位匹配理论,并通过对局域准相位匹配理论生成的毫米及尺度的畴结构进行快速傅里叶变换获得其倒空间结构,从而对局域准相位匹配理论进行了二次发现,指出局域准相位匹配理论中的倍频单点聚焦是由于样品结构倒空间中对应传统准相位匹配的倒格矢存在连续横向展宽造成的,且这些展宽倒格矢都处于非线性Ewald球上。在总结该方向工作的基础上,提出了将散点局域准相位匹配推广至准连续形式的线或面的局域准相位匹配,并提出一个简单的倍频缩束的设想。本章最后总结了目前局域准相位匹配理论可能存在的不足和一些可行的改进方向。
第六章总结本论文工作,并指出了目前与本论文相关的铁电体超晶格中可能开展的和正在进行的非线性频率转换效应方面的一些工作。
This thesis focuses on the nonlinear phenomena occuring during the interaction between near infrared laser fundamental waves and ferroelectric materials. It keeps second harmonic (SH) generation as its thread, and set congruent LiTaO3(CLT) crystal samples as the main subject under examination. Throughout the thesis, several hot topics of the field in recent years are discussed, which include-nonlinear Cherenkov radiation (NCR) in bulk materials, elastic scattering quasi-phase matching (ESQPM) conical radiation, and local quasi-phase matching (LQPM) process, et al. The contents of the whole thesis are as the following:
The first chapter is set as a background report of the thesis, making an outline to the latest research works in the fields which closely related to this thesis, and of my interest, of course, with personal bias. Its next chapters are designed to fixate on the details of three individual topics mentioned herein separately.
The second chapter takes a brief tour of the material properties of the ferroelectric crystal CLT, including its nonlinear optical tensor properties. The rest of this chapter was put to illustrate the procedure of the room temperature poling technique of the CLT, as to complete this thesis as a self-contained source. Within this chapter, in the hope of making this thesis a self-contained source, I also make a brief introduction to the theory of quasi-phase matching.
The third chapter gently leads the way through the Cherenkov radiation, a classical electromagnetic shocking wave to its counterpart in the nonlinear optical regime. It explains the formation of NCR and its mutation, radiation of the similar root, yet with a longitudinal phase tuning. With a space-time confined plane wave model, it succeeds in formulating the output angle spectrum of NCR, and finds out the relationship of NCR and the conventional two-dimensional quasi-phase matching. Careful experiments verified the validity of these output conditions.
The fourth chapter deals with what are elastic scattering SHG conical beams and their present researching status. Considering its resemblance with NCR in its spatial distribution profile, I tried to argue the differences between these two effects. Most of the efforts were dedicated to high-order performance of elastic scattering conical beams, both in theory and in experiments. Based on the known output angle formula, I presented the algebric equaton of the SH projection curve set. And in keeping with the popular idea of harmonics intensities being related to the effective nonlinear coefficiencts, I deduced the effective nonlinear coefficiencts in this case. Experiments showed that phase-matched conical radiation with high-orders reciprocal vectors present a collective phenomenon other than low-orders, usually, only their spatial envelopes show up due to overlapping effect. I invented a vector shell method to decide the possible quasi-phase matching proccess in the experiment. And based on this method, I concluded and then verified it with experiments that "All quasi-phase matching processes with collinear incident fundamental waves are elastic scattering quasi-phase matching processes." I also proposed a rotational dynamic experiment of the high-order ESQPM, which could reveal more Fourier coefficients of the superlattice structure, and a degeneration phenomenon of the conical beams during the dynamic process was discussed.
The fifth chapter describes the local quasi-phase matching theory. By paraphrasing the whole theory and observing the theory-determined domain structures with discrete Fourier transformation, a second discovery of the theory was achieved. In the reciprocal space of the local quasi-phase matching structure, the conventional phase matching reciprocal lattice vector has a transverse expansion, and the expansion is locating on the nonlinear Ewald sphere, which leads to the focusing effect of the LQPM.Then I proposed to extend this theory to manipulate wave front and a simple example was provided with both ferroelectric structure and numeric results of the outputs. At the end of this chapter, I discussed the potential weakness and possible improvements of the theory.
The sixth chapter summarizes the thesis, and points out some potential research directions in the near future and my on-going research works.
前言部分由第一章与第二章构成,这一部分对目前基于各类相位匹配模式下的激光倍频过程作一概览。其中第一章给出本论文总的研究背景,第二章则简介了铁电晶体钽酸锂的晶体基本线性光学属性以及与激光倍频过程相关的非线性系数张量属性,同时详述了铁电极化样品的制备流程,和准相位匹配理论基础,为后续章节作一铺垫,方便本论文自成体系。后续章节围绕其中与论文作者研究相关的三个方向给出较为细致的讨论。
第三章从简介非线性切伦科夫辐射概念及其成因入手,利用时空限域平面波模型导出了体块材料中的非线性切伦科夫辐射空间角谱分布条件,以及在基波激发的非线性极化相位纵向调制情况下的非线性切伦科夫辐射空间角谱条件；并从该模型得出了非线性切伦科夫辐射与二维非共线准相位匹配之间的关联。通过实验验证了前述的空间角谱。
第四章概述了弹性散射锥形辐射当前的研究状态,鉴于弹性散射锥形辐射与切伦科夫辐射在空间分布上有相似性,本章尝试对两者之间的异同进行了一些讨论。本章特别针对高阶弹性散射作了实验和理论探索,在现有弹性散射准相位匹配规律下,导出了弹性散射倍频锥形辐射投影曲线族的代数方程,并导出了该过程中的有效非线性系数。另外,通过实验观察了一维和二维周期结构的弹性散射准相位匹配倍频高阶效应,尤其是在二维铁电体超晶格中发现了高阶弹性散射下准相位匹配锥形辐射的包络效应——即在高阶情形,弹性散射准相位匹配往往不能输出空间上可观测的单个或分立的多个锥形辐射,而是给出由各高阶倒格矢参与下的准相位匹配锥形辐射的空间包络,这一现象在各类铁电体超晶格实验现象中比低阶弹性散射更具普遍性。由于高阶效应同时可匹配的模式较多,文中发明了矢量球壳法统一对一维与二维铁电体超晶格中的弹性散射准相位匹配从整体上进行了较为细致的分析预测。利用此方法,我提出了“一切共线入射于非线性超晶格中的基波实现的共线准相位匹配或非共线准相位匹配过程都是弹性散射准相位匹配过程的特例”的这一论断,并通过实验确证；同时基于此方法,我设计了高阶弹性散射的旋转动力学实验,该旋转方式可以为铁电畴结构探测提供更多的倒格矢分量,给出了利用激光倍频方式精确解析厘米级尺度铁电体超晶格微观畴结构的新思路。本章还讨论并验证了旋转过程中的锥形光束存在的简并现象。
第五章重点描述了局域准相位匹配理论,并通过对局域准相位匹配理论生成的毫米及尺度的畴结构进行快速傅里叶变换获得其倒空间结构,从而对局域准相位匹配理论进行了二次发现,指出局域准相位匹配理论中的倍频单点聚焦是由于样品结构倒空间中对应传统准相位匹配的倒格矢存在连续横向展宽造成的,且这些展宽倒格矢都处于非线性Ewald球上。在总结该方向工作的基础上,提出了将散点局域准相位匹配推广至准连续形式的线或面的局域准相位匹配,并提出一个简单的倍频缩束的设想。本章最后总结了目前局域准相位匹配理论可能存在的不足和一些可行的改进方向。
第六章总结本论文工作,并指出了目前与本论文相关的铁电体超晶格中可能开展的和正在进行的非线性频率转换效应方面的一些工作。
This thesis focuses on the nonlinear phenomena occuring during the interaction between near infrared laser fundamental waves and ferroelectric materials. It keeps second harmonic (SH) generation as its thread, and set congruent LiTaO3(CLT) crystal samples as the main subject under examination. Throughout the thesis, several hot topics of the field in recent years are discussed, which include-nonlinear Cherenkov radiation (NCR) in bulk materials, elastic scattering quasi-phase matching (ESQPM) conical radiation, and local quasi-phase matching (LQPM) process, et al. The contents of the whole thesis are as the following:
The first chapter is set as a background report of the thesis, making an outline to the latest research works in the fields which closely related to this thesis, and of my interest, of course, with personal bias. Its next chapters are designed to fixate on the details of three individual topics mentioned herein separately.
The second chapter takes a brief tour of the material properties of the ferroelectric crystal CLT, including its nonlinear optical tensor properties. The rest of this chapter was put to illustrate the procedure of the room temperature poling technique of the CLT, as to complete this thesis as a self-contained source. Within this chapter, in the hope of making this thesis a self-contained source, I also make a brief introduction to the theory of quasi-phase matching.
The third chapter gently leads the way through the Cherenkov radiation, a classical electromagnetic shocking wave to its counterpart in the nonlinear optical regime. It explains the formation of NCR and its mutation, radiation of the similar root, yet with a longitudinal phase tuning. With a space-time confined plane wave model, it succeeds in formulating the output angle spectrum of NCR, and finds out the relationship of NCR and the conventional two-dimensional quasi-phase matching. Careful experiments verified the validity of these output conditions.
The fourth chapter deals with what are elastic scattering SHG conical beams and their present researching status. Considering its resemblance with NCR in its spatial distribution profile, I tried to argue the differences between these two effects. Most of the efforts were dedicated to high-order performance of elastic scattering conical beams, both in theory and in experiments. Based on the known output angle formula, I presented the algebric equaton of the SH projection curve set. And in keeping with the popular idea of harmonics intensities being related to the effective nonlinear coefficiencts, I deduced the effective nonlinear coefficiencts in this case. Experiments showed that phase-matched conical radiation with high-orders reciprocal vectors present a collective phenomenon other than low-orders, usually, only their spatial envelopes show up due to overlapping effect. I invented a vector shell method to decide the possible quasi-phase matching proccess in the experiment. And based on this method, I concluded and then verified it with experiments that "All quasi-phase matching processes with collinear incident fundamental waves are elastic scattering quasi-phase matching processes." I also proposed a rotational dynamic experiment of the high-order ESQPM, which could reveal more Fourier coefficients of the superlattice structure, and a degeneration phenomenon of the conical beams during the dynamic process was discussed.
The fifth chapter describes the local quasi-phase matching theory. By paraphrasing the whole theory and observing the theory-determined domain structures with discrete Fourier transformation, a second discovery of the theory was achieved. In the reciprocal space of the local quasi-phase matching structure, the conventional phase matching reciprocal lattice vector has a transverse expansion, and the expansion is locating on the nonlinear Ewald sphere, which leads to the focusing effect of the LQPM.Then I proposed to extend this theory to manipulate wave front and a simple example was provided with both ferroelectric structure and numeric results of the outputs. At the end of this chapter, I discussed the potential weakness and possible improvements of the theory.
The sixth chapter summarizes the thesis, and points out some potential research directions in the near future and my on-going research works.
引文
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