Measurement of nonlinear optical coefficients by the z-scan technique: Correctness of the technique and investigation of a new compound-lutetium diphthalocyanine complex

Correctness of z-scan measurements of nonlinear refractive indices for optical media is considered. It is shown that accuracy of these measurements is greatly affected by the thickness of the nonlinear medium layer (as compared with the diffraction length of the laser beam). Nonlinear refractive indices of nitrobenzene are measured at different laser pulse durations (7 ns and 350 ps); the nonlinearity mechanism is discussed. It is shown that at the pulse duration 350 ps the orientation mechanism of nonlinearity is less effective than at the pulse duration 7 ns due to its time lag. Nonlinear refractive indices are measured for the solution of a new synthesized compound-hexadecabutyl-substituted lutetium diphthalocyanine.     

克尔介质表面缺陷对高斯-谢尔模型光束的调制

利用惠更斯-菲涅耳衍射积分公式,推导了高斯-谢尔模型光束经非线性克尔介质的表面缺陷调制后的交叉谱密度公式,研究了受调制高斯-谢尔光束的光强演化特性。数值模拟表明：缺陷也可导致部分相干光束在介质后表面产生一个极强点,缺陷越大,极强点越远离介质。非线性折射率为正值或负值的介质也分别使部分相干光束发生会聚或发散现象。空间相干长度越长以及附加相移和缺陷尺寸越大,光场受调制越厉害。     

Nonlinear interaction and reflection of incoherent light beams

The interaction dynamics between two incoherent light beams in a medium with thermal nonlin-earity is studied both experimentally and theoretically. It is shown that in the mode of a nonlinear reflection the transformation of a spatial structure of a weak signal beam can be theoretically described in the framework of a spatially distributed model for a nonlinear change in the refractive index of the medium.     

克尔介质表面缺陷对高斯-谢尔模型光束的调制

利用惠更斯-菲涅耳衍射积分公式,推导了高斯-谢尔模型光束经非线性克尔介质的表面缺陷调制后的交叉谱密度公式,研究了受调制高斯-谢尔光束的光强演化特性。数值模拟表明:缺陷也可导致部分相干光束在介质后表面产生一个极强点,缺陷越大,极强点越远离介质。非线性折射率为正值或负值的介质也分别使部分相干光束发生会聚或发散现象。空间相干长度越长以及附加相移和缺陷尺寸越大,光场受调制越厉害。     

Light propagation in media with a highly nonlinear response: An analytical study

The problem of light propagation in highly nonlinear media is studied with the help of a recently introduced systematic approach to the analytical solution of equations of nonlinear optics [L.L. Tatarinova, M.E. Garcia, Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics, Phys. Rev. A 78 (2008) 021806(R)(1—4)]. Numerous particular cases of media exhibiting high-order nonlinear refractive indices are considered. We obtain analytical expressions for determining the self-focusing position and a new exact expression for calculating the filament intensity. The constructed solutions allowed us to revise a so-called self-focusing scaling law, i.e., the functional dependence of the self-focusing position on the initial light peak intensity. It was demonstrated that this dependence is governed by the form of the nonlinear refractive index and not by the laser beam shape at the boundary.     

高斯光束通过非线性介质后的远场衍射图样的研究

 利用菲涅尔－基尔霍夫衍射积分公式，对发散和会聚高斯光束通过薄非线性介质时形成的远场衍射图样进行了研究。模拟计算结果表明：当发散高斯光束通过自散焦介质或会聚高斯光束通过自聚焦介质时，远场均会出现中央较暗、向外围逐渐增强、分布尺度较大的粗衍射环；当发散高斯光束通过自聚焦介质或会聚高斯光束通过自散焦介质时，远场均会出现中心强度最大、向外围逐渐减弱、分布尺度较小的细衍射环。不同远场衍射图样归根结底是入射高斯光束因介质折射率变化造成的空间自相位调制及其波前曲率共同作用的结果。     

Near-diffraction-limited dark hollow beam generated by using a hybrid control way

We propose and demonstrate the generation of dark hollow beam with plane wavefront in the near field based on a hybrid control way by using dual phase only liquid crystal spatial light modulators (LC-SLMs). One phase only LC-SLM redistributes the intensity to the target distribution based on refractive beam shaping system and the other phase only LC-SLM adaptively compensates the wavefront of the output beam by using stochastic parallel gradient descent (SPGD) algorithm. Compared with conventional refractive beam shaping system, the hybrid control way can not only improve the far-field energy concentration of the output beam, but also can correct the phase distortion of the system. Influences of phase distortion on laser beam shaping are analyzed in detail. The theoretical and experimental results show that the near-diffraction-limited dark hollow beam can be successfully generated by using this hybrid control way. The power in the main lobe of the airy disk pattern area in the far field is 2.3 times larger than that without being adaptively compensated.     

高功率激光装置中局部波前畸变的非线性传输

 根据高功率激光装置中强激光束传输的特点,建立了描述光束通过光学元件时引入的局部波前畸变模型,并利用纹波传输的线性化处理方法,研究了带有局部波前畸变的高强度光束的传输规律。以一个连续的非增益激光介质为例,用该模型进行数值模拟,给出了不同空间尺度的局部波前畸变的频谱分布、不同空间频率的纹波引起的振幅非线性增长曲线、不同B积分的非线性增益随光束传输距离的变化曲线,光束振幅非线性增益达到最大时光束的传输距离和标准传输距离不同时由局部波前畸变引入的振幅分布。研究表明为了防止光学元件损坏,应避免光学元件表面出现半径为0.5~2.0 mm的局部瑕疵。     

电磁感应透明介质中的弱光空间暗孤子环

利用多重尺度方法,解析地研究了Λ型三能级冷原子气及一束较强耦合光组成的电磁感应透明介质体系中的非线性动力学性质.结果表明：一束较弱的探测光能在电磁感应透明介质中形成弱光空间暗孤子,当弱光空间暗孤子沿轴向传播时,它会逐渐演化成一个稳定的弱光空间暗孤子环,这是衍射效应和自散焦效应相互平衡的结果. 关键词： 电磁感应透明 弱光空间暗孤子环 多重尺度方法     

Fresnel phase retrieval method using an annular lens array on an SLM

Wavefront aberrations play a major role when focusing an ultrashort laser pulse to a high-quality focal spot. Here, we report a novel method to measure and correct wavefront aberrations of a 30-fs pulsed laser beam. The method only requires a programmable liquid-crystal spatial light modulator and a camera. Wavefront retrieval is based on pupil segmentation with an annular lens array, which allows us to determine the local phase that minimizes focusing errors due to wavefront aberrations. Our method provides accurate results even when implemented with low dynamic range cameras and polychromatic beams. Finally, the retrieved phase is added to a diffractive lens codified onto the spatial light modulator to experimentally demonstrate near-diffraction-limited femtosecond beam focusing without refractive components.     

高功率超高斯光束传输的非线性补偿研究

 分析了高功率超高斯光束在非线性介质中传播的基本理论，用分步傅里叶变换方法计算了10阶超高斯光束在非线性介质内的传输过程，最后采用具有负折射率系数的非线性介质作为补偿材料，对不同的补偿方式进行了对比分析。研究表明，四种补偿方式均可以大大减小光束的B积分，有效防止超高斯光束边缘的非线性增长，降低光束的小尺度自聚焦，同时选用后补偿作为最佳补偿方式。     

非线性介质中强光对弱光聚焦的控制研究

从理论和实验上分析了强光控制弱光脉冲聚焦的方法, 该方法可以灵活地控制弱光的聚焦过程和特性. 通过研究两光束共同传输, 利用强抽运光在相互作用时为弱探测光提供诱导非线性效应, 从而使弱探测光发生聚焦. 得到了在抽运光保持不变情况下探测光的解析解, 并在实验上得到验证. 进一步研究了强抽运光对弱探测光焦点位置的影响. 结果显示: 通过改变抽运光功率、束宽能够有效地控制弱探测光的聚焦过程和焦点位置. 关键词： 诱导聚焦 自聚焦 非线性折射率     

Wavefront sensing with random amplitude mask and phase retrieval

A light beam with an ideal wavefront that is transmitted or reflected from an object is modified by different characteristics of the object such as shape, refractive index, density, or temperature. Wavefront sensing therefore yields valuable information about the system or the changes happening to the system. A new method for wavefront sensing using a random amplitude mask and a phase retrieval method based on the Rayleigh-Sommerfeld wave propagation equation is described. The proposed method has many potential applications ranging from phase contrast imaging and measurement of lens aberration to shape measurement of three-dimensional objects.     

高功率超高斯光束传输的非线性补偿研究

分析了高功率超高斯光束在非线性介质中传播的基本理论,用分步傅里叶变换方法计算了10阶超高斯光束在非线性介质内的传输过程,最后采用具有负折射率系数的非线性介质作为补偿材料,对不同的补偿方式进行了对比分析。研究表明,四种补偿方式均可以大大减小光束的B积分,有效防止超高斯光束边缘的非线性增长,降低光束的小尺度自聚焦,同时选用后补偿作为最佳补偿方式。     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

Nonlinear computer-generated holograms

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.     

High precision refractometry based on Fresnel diffraction from phase plates

When a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic parallel beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The visibility of the diffraction fringes varies periodically with changes in incident angle. The visibility period depends on the plate thickness and the refractive indices of the plate and the surrounding medium. Plotting the phase change versus incident angle or counting the visibility repetition in an incident-angle interval provides, for a given plate thickness, the refractive index of the plate very accurately. It is shown here that the refractive index of a plate can be determined without knowing the plate thickness. Therefore, the technique can be utilized for measuring plate thickness with high precision. In addition, by installing a plate with known refractive index in a rectangular cell filled with a liquid and following the described procedures, the refractive index of the liquid is obtained. The technique is applied to measure the refractive indices of a glass slide, distilled water, and ethanol. The potential and merits of the technique are also discussed.     

Ability and Limitation of Effective Medium Theory for Subwavelength Gratings

In the recent researches of subwavelength relief gratings, the effective refractive indices are used for calculating the coefficients of reflection and transmission of light waves. The effective refractive indices are given by the effective medium theory for light waves propagating in a bulky stratified medium. This paper describes the ability and limitation of the theory applied to estimate the performance of such subwavelength gratings. The limitation is revealed by numerical calculations using a rigorous electromagnetic grating theory and the effective medium theory. As a result, an understanding of the wave behavior in the subwavelength grating has been acquired, which explains the limitation of the effective medium theory.     

Controlling the diffused nonlinear light generated in random materials

We describe a method for shaping the wavefront of the second-harmonic light generated in nonlinear materials with a disordered structure using a spatial light modulator on the fundamental beam. We show that, for the case of a transparent strontium-barium niobate crystal with a random distribution of antiparallel domains, the speckle generation can be concentrated into a single spot.     

由菲涅尔反射测量平行平面介质的折射率

一激光束投射在一平行平面介质的表面上，在此表面有一反射光束和从介质内折射出来的另一光束，只要测出这两光束的Ｐ光和Ｓ光的强度，就可计算该介质的折射率。本文介绍测量原理及方法。