【作者】 杨琛；

【导师】 史保森； 周志远；

【作者基本信息】 中国科学技术大学 ， 物理学， 2022， 博士

【摘要】 光的干涉不仅是揭示光的波动性的基本物理现象,也是很多应用的基础,例如光学相干层析、傅里叶变换光谱仪、引力波测量等。在线性光学中,干涉现象是由两束或多束光的叠加产生的,但光的频率不变;而在非线性光学中,两束或多数光的叠加可以产生新的频率光,如和频或三次谐波等。最近的研究表明,将非线性效应与干涉相结合会产生新的干涉现象,并极大地丰富干涉仪的应用,例如基于参量放大的非线性干涉仪的灵敏度相对于传统线性干涉仪有较大提升、基于自发参量下转换的非线性干涉仪可以实现用可见相机做红外成像。本论文围绕二阶非线性效应与干涉的结合,系统研究了多种二阶非线性辐射光(包括倍频光、自发参量下转换的单光子和双光子)的干涉现象,揭示其中的物理机理,并深入探讨这些现象可能带来的新应用,如矢量光束的频率变换、干涉仪相位差放大、干涉仪零臂差位置的校准等。本论文的主要研究内容如下:1.基于二阶非线性的光学频率变换可用于连接两个不同工作波长的量子通信模块,即用作量子接口。例如铷原子量子存储器的一个工作波长是795 nm,光纤通信的工作波长是1550 nm,频率变换技术使得光子可在两模块之间传递,而这两个波段的和频或差频过程需要1632 nm的激光作为泵浦光。为此,本文设计并搭建外腔增强的差频装置以产生1632 nm的激光输出。在谐振腔的设计阶段,使用了分步傅里叶方法对差频中的能量转换过程和效率进行数值仿真,并依据模拟结果设计谐振腔中的光腰半径。实验中得到的最高增强因子为17.3、最高转换效率为55%、最高输出功率为300 mW,输出光的一小时功率稳定度为0.51%。该装置可作为后续量子接口实验的泵浦光源。2.矢量光束因为其超衍射聚效的特性最近受到广泛关注。通过基于二阶非线性效应的光学频率变换技术可用于扩展现有矢量光束波段,例如可通过倍频或差频产生紫外或中红外等光学器件尚不成熟的波段的矢量光束。但是通常非线性效应只响应某一特定线偏振光,因此不能对具有非均匀偏振分布的矢量光束直接进行频率变换。为解决该问题,本文提出基于Sagnac结构的偏振光干涉仪对矢量光束进行倍频的方案,并在实验上进行了原理验证,实现了 1550 nm的角向偏振和径向偏振柱矢量光束的倍频,产生了 775 nm的柱矢量光束,观察到了拓扑荷翻倍的现象。该方案可推广到利用和频与差频过程实现矢量光束的频率上转换和下转换。3.干涉条纹的变化能反映干涉仪中相位差的微小变动,因此干涉仪可用于测量能引起相位差变化的物理量。如果可以放大干涉仪的相位差,则可以提高测量的分辨率。本文提出一种基于谐波干涉的相位差放大方案,并在实验上基于偏振光的二次谐波和四次谐波干涉,实现了将迈克尔逊干涉仪中的相位差放大到2倍和4倍。基于该干涉方案,原来引起干涉曲线变化1个周期的光程差,现在可引起干涉曲线4个周期的变化,即该方案将光程差测量的分辨率提高到4倍,并且该方案可推广到使用高次谐波产生实现更高倍率的相位差放大。4.自发参量下转换可产生有频率关联特性的一对光子,在满足一定相位匹配条件时,可使得一个光子在可见波段而另一个光子在红外波段。利用这种性质,在基于自发参量下转换的非线性干涉仪中,可通过检测可见光子来测量红外波段的物理量,如红外折射率、红外光谱、红外图像等,这避免了红外探测器相对于可见探测器在噪声性能、探测效率、性价比等方面的不足。本文搭建了一个基于非简并自发参量下转换光子的迈克尔逊结构的非线性干涉仪,关联光子对的中心波长为797 nm和1540 nm。本文验证了在该干涉仪中,可只对797 nm光子的干涉条纹进行探测,实现对待测晶体在1540 nm折射率的测量,也可通过等厚干涉测量晶体两通光面间的夹角。本文还研究了该干涉仪中的等倾干涉现象,改变晶体到干涉仪之间一段公共路径的长度,可观测到不同数量的等倾干涉条纹,该现象可用于距离测量。5.等倾干涉是一种基本的干涉现象,其原理是光程差与光线的角度有关,故干涉的相长或相消取决于光线的角度,在圆对称的光学系统中等倾干涉条纹是一系列同心圆环。本文利用非简并自发参量下转换产生的关联光子对中的一个光子在迈克尔逊干涉仪中做单光子干涉,观察到了类似等倾干涉的干涉现象。其干涉原理是光的频率与光线的角度有关,故干涉的相长或相消也取决于光线的角度,其干涉条纹也是一系列同心圆环。由于频率与角度的依赖关系来自于特殊的角度频率谱,本文将这种干涉称为角度频率谱干涉。本文在理论上推导了角度频率谱干涉的解析表达式,并根据等倾干涉公式定义等效波长,定量地描述角度频率谱干涉的条纹分布,实验和理论结果相符合且都反映出这种干涉具有超短的等效波长,该特性使得角度频率谱干涉有望用于提高对干涉仪零臂差位置的校准精度。6.通常测量自发参量下转换的角度频率谱或调谐曲线常使用的方法是利用可移动的小孔在透镜的傅里叶面上扫描,并用光谱仪测量不同傅里叶模式下的光谱或中心波长,最终合成角度频率谱或调谐曲线。本文提出一种非简并自发参量下转换调谐曲线的测量方法,只需对干涉图案进行分析,而不需要使用小孔扫描。方法是在上述角度频率谱干涉的光路中插入一个光栅,可观察到彗尾状干涉条纹,彗尾状条纹有一条抛物线包络,本文推导出调谐曲线的近似表达式以及与抛物线包络的解析关系,基于此关系可以通过测量条纹的抛物线包络来推测调谐曲线。本文的创新点如下:1.提出并实验实现了基于Sagnac结构的偏振光干涉仪对矢量光束进行倍频的方案,该方案可推广到矢量光束的和频与差频,并用于扩展矢量光束的可用波段。2.提出并实验验证了基于谐波产生的非线性干涉仪进行相位差放大的方案,基于该方案有望大幅度提高干涉仪的相位分辨率。3.实验观测并理论解释了基于自发参量下转换过程产生的非独立角度频率谱光子的类等倾干涉现象,干涉条纹变化的等效超短波长性质有望用于提高对干涉仪零臂差位置的校准精度。4.实验观测并解释了角度频率谱干涉中出现的彗尾状干涉条纹,基于该现象提出通过测量条纹的抛物线包络推测自发参量下转换调谐曲线的方案,并实验验证其可行性。更多还原

【Abstract】 Optical interference is not only the basic physical phenomenon to reveal the wave nature of light,but also the basis of many applications,such as optical coherence tomography,Fourier transform spectrometer,gravitational wave detection.In linear optics,the interference phenomenon is produced by the superposition of two or more beams of light,but the frequency of light remains unchanged;while in nonlinear optics,the superposition of two or more beams can produce new frequency light,such as sum-frequency process or third-harmonic generation.Some recent researches show that the combination of nonlinear effect and interference will produce new interference phenomena and greatly enrich the application of interferometer.For example,the sensitivity of nonlinear interferometers based on parametric amplification is greatly improved compared with traditional linear interferometers,and the nonlinear interferometers based on spontaneous parametric down-conversion(SPDC)can realize infrared imaging with undetected visible photons.Focusing on the combination of second-order nonlinear effect and interference phenomenon,we systematically study a variety of interference phenomena with light from the different second-order nonlinear processes,such as second-harmonic generation(SHG)and SPDC,to reveal the physical mechanism and find the possible new applications of these phenomena,such as frequency conversion of vector beam,phase difference amplification,calibration of zero arm difference position of an interferometer,etc.The main research contents and significance are as follows:1.The frequency conversion based on the second-order nonlinear optical effect can be used as a quantum interface that can connect two quantum communication modules with different working wavelengths.For example,the working wavelength of a rubidium atomic quantum memory is 795 nm while the working wavelength in fiber communication is 1550 nm.The frequency conversion technology enables photons to be transmitted between the two modules based on the sum-frequency generation(SFG)or difference-frequency generation(DFG)processes which require a 1632 nm laser as pump light.Therefore,a cavity that is used to enhance the DFG process is designed and built to obtain the 1632 nm laser beam.To design the cavity,the split-step Fourier method is used to simulate the energy conversion process and efficiency in the DFG process,and the optical waist radius in the cavity is designed based on the simulation results.The highest enhancement factor obtained in the experiment is 17.3,the highest net quantum conversion efficiency is 55%,the highest output power is 300 mW,and the one-hour power stability of the output light is 0.51%.The cavity-enhanced DFG device can be used as a pump light source for future quantum interface experiments.2.Vector beams have attracted much attention recently because of their unique super-diffraction limiting properties.The frequency conversion technology based on the second-order nonlinear effect can be used to expand the waveband of vector beams,for example,UV or mid-infrared where the manufacture of optical elements is not yet mature.Generally,the nonlinear effect only responds to lights with a certain linear polarization,which prevents frequency conversion of vector beams that have non-uniform polarization distribution.A scheme solving how to implement the frequency conversion of cylindrical vector beams based on a polarized Sagnac interferometer is proposed and experimentally verified.The SHG processes of the azimuthally and radially polarized vector beams with a wavelength of 1550 nm are realized,the cylindrical vector beams of 775 nm are generated,and the phenomenon of topological charge doubling is observed.This scheme can be generalized to realize the frequency up-conversion and down-conversion of vector beams based on SFG and DFG.3.The change of interference fringes can reflect the change of phase difference in an interferometer,therefore,an interferometer can be used to measure physical quantities that can cause the change of phase difference.If the phase difference of an interferometer can be amplified,the measurement resolution can be improved.In this paper,a phase difference amplification scheme based on interference of harmonic light is proposed.Experimentally,the phase difference in a Michelson interferometer is amplified by 2 times and 4 times based on the polarized interference of second-harmonic and fourth-harmonic light,respectively.As a result,an optical path difference(OPD)that causes the change of the fundamental interference curve for one cycle can now cause the change of the SH and FH interference curve for 2 and 4 cycles,therefore,the SH and FH interferometers improve the measurement resolution of the OPD by 2 and 4 times.The scheme proposed here can be generalized to the interference of higher harmonic light to realize higher phase difference amplification.4.The nondegenerate SPDC process can produce a pair of photons with frequency correlation characteristics and the two photons can be in the visible and infrared band respectively when a certain phase-matching condition is satisfied.In the nonlinear interferometer based on SPDC,the physical quantities in the infrared band,such as infrared refractive index,infrared spectrum,infrared image,etc.,can be measured by detecting visible photons,which avoids the shortcomings of infrared detector compared with the visible detector in noise performance,detection efficiency,cost performance and so on.In the present dissertation,a nonlinear Michelson interferometer based on the photons from the nondegenerate SPDC process of a PPKTP crystal is built.The center wavelengths of the associated photon pairs are 797 nm and 1540 nm.It is verified that in this interferometer,only the interference fringes formed by 797 nm photons be detected to realize the measurement of the refractive index at 1540 nm of a BBO crystal,and the included angle between the two surfaces of the BBO crystal can be measured by equal-thickness interference.Besides,the equal-inclination interference in the interferometer is also studied.By changing the length of a common path between the PPKTP crystal and the Michelson interferometer,different numbers of equal-inclination interference fringes can be observed.This phenomenon can be used for distance measurement.5.The equal-inclination interference is a basic interference phenomenon where the OPD is dependent on the incident angle of light and therefore the constructive or destructive interference depends on the incident angle.In a circular symmetric optical system,the equal-inclination interference fringes are a series of concentric rings.In this dissertation,one photon in the correlated photon pair generated by a nondegenerate SPDC process is used for single-photon interference in a Michelson interferometer and the interference fringes that are similar to the equal-inclination interference fringes are observed.The interference principle is as follows.In the nondegenerate SPDC process,the frequency of light depends on the incident angle of light,therefore,the constructive or destructive interference depends on the incident angle as well,and the interference fringes are also a series of concentric rings.In this dissertation,this kind of interference is called angular-frequency spectrum(AFS)interference because the dependence of frequency on angle comes from the special AFS.The analytical expression of angular frequency spectrum interference is deduced theoretically,and the equivalent wavelength is defined based on the formula of equal-inclination interference to quantitatively describe the fringe distribution of AFS interference.The experimental and theoretical results are consistent,and both reflect that the AFS interference has an ultra-short equivalent wavelength,based on which the AFS interference is expected to be used to improve the calibration accuracy of the equal arm position of the interferometer.6.The commonly used method to measure the AFS or tuning curve of an SPDC process is measuring the spectrums or center wavelengths corresponding to different spatial Fourier modes with a spectrometer,where the spatial Fourier modes are filtered by a movable pinhole.In this dissertation,a measurement method of the tuning curve in a nondegenerate SPDC process is proposed,which only needs to analyze the interference pattern without scanning using a pinhole.The method is to insert a grating before the detector in the setup of the above AFS interference,and the comet-tail-like interference fringes can be observed.The comet-tail-like fringes have a parabolic envelope.In this dissertation,the approximate expression of the tuning curve and its relationship with the parabolic envelope are both derived.Based on this relationship,the tuning curve can be deduced by measuring the parabola envelope of the fringe.The innovations of this dissertation are as follows:1.The scheme to realize the SHG process of vector beams based on a polarized Sagnac interferometer is proposed and experimentally verified.This scheme can be generalized to the SFG and DFG processes of vector beams and can be used to expand the waveband of vector beams.2.The scheme of phase difference amplification of nonlinear interferometer based on harmonic generation is proposed and experimentally verified.Based on this scheme,the phase resolution of interferometers is expected to greatly improve.3.The quasi-isoclinic interference phenomenon of special angular-frequency spectrum photons generated by the SPDC process is observed and explained theoretically.The property of ultrashort equivalent wavelength of the interference fringes is expected to be used to improve the calibration accuracy of the zero arm difference position of interferometers.4.We experimentally observed and explained the comet-tail-like interference fringes in angular frequency spectrum interference.Based on these fringes,a scheme to estimate the tuning curves of SPDC by measuring the parabolic envelope of fringes is proposed,which is verified experimentally.更多还原