An Iteratively-Designed Binary Phase Grating for Flattop Beam Generation

A binary phase grating capable of shaping an incident Gaussian beam to a flattop beam in a Fourier domain is designed iteratively. It is essential in grating design to consider the phases of diffracted waves by the grating, in addition to their amplitude uniformity and diffraction efficiency. The optimized grating phase produces the in-phase diffracted waves that interfere constructively to form a uniform amplitude and phase profile. The dependence of the shaped profile on the illuminating amplitude distribution, the grating misalignment, and the lens focusing error is investigated by computer simulation and optical experiment.     

On the effect of nonequidistance of dielectric coatings and the groove profile on the energy characteristics of holographic diffraction gratings

The diffraction efficiency and the resistance to radiation damage of gratings with a multilayer dielectric coating, which are used for compression of high-power laser pulses, are studied. The effect of smoothing of the profile of the metallized surface of the grating upon deposition of dielectric coatings on the energy characteristics of the grating at the wavelength λ=1.05 μm is analyzed. Gratings with various profiles of the metallic surface relief and with different contrast of the refractive indices of the dielectrics forming the coating are considered.     

Airy beam laser

A method to design lasers that emit an arbitrary beam profile is studied. In these lasers, output-coupling is performed by a diffraction grating that imposes a phase and amplitude distribution onto the diffracted light. A solid-state laser emitting beams with a two-dimensional Airy intensity profile is demonstrated both theoretically and experimentally. In this case, the diffraction grating adds a transverse cubic phase to the diffracted light. An Airy beam is obtained by performing optical Fourier transform of the out-coupled light. The laser beam profile and power characteristics are shown to agree with theory.     

Optimization of reflection spectra for phase-only sampled fiber Bragg gratings

In this paper, the reflection spectra of a phase-only sampled fiber Bragg grating is obtained by optimizing its phase profile. The standard simulated annealing method is improved for optimization, and superior phase profiles which contain as few segments as possible per sampling period are obtained for 8, 16 and 32 identical channels. As very well known, increased number of WDM channels results in higher grating length and refractive index modulation amplitude. It is observed that application of these phase profiles limits the increases in both of these parameters considerably.     

Lineshape and polarization mode dispersion of waves diffracted by apodized and chirped fiber Bragg gratings in reflection

The amplitude and phase of a light wave propagating in an apodized and chirped Bragg grating is given by the superposition of two orthogonal coupled wave functions that are the solution of a non-linear Riccati equation. An analytical solution, in the form of an integral transform, that predicts the amplitude, phase, and intensity profile of the light diffracted by grating, in which the local Bragg wavelength is asymmetric, and the forward and counter propagating modes are non-degenerate is presented. For even apodization and odd chirp the lineshape has an asymmetrical Gaussian form the result of mixing of the real and imaginary components of the apodized grating wave function. The effect of chirping is to shift the resonance wavelength, increase the grating bandwidth and polarization mode dispersion. The dependence of linewidth and dispersion on parameters that alter apodization and chirp after fabrication, is also discussed.     

Theory of laser-induced amplitude and phase gratings including photoselection,orientational relaxation and population kinetics

The generation of amplitude and phase gratings in an absorbing medium is discussed, including the effects of light polarization, population kinetics and orientational relaxation. A theory is given which describes light diffraction by a combination of an amplitude and a phase grating. It is shown that the coherent coupling effect in transient absorption measurements is solely due to the amplitude grating. Weak absorption and a low triplet yield favour diffraction of the probing beam by the phase grating in triple-beam experiments. Phase grating experiments can be performed with highly soluble absorber dyes, the absorption maximum of which is far away from the laser wavelength. Due to photoselection, diffraction by an amplitude grating depends on the polarization of the probing beam while phase grating diffraction is insensitive to this. Perpendicular polarization of the two exciting pulses prevents the buildup of a phase grating and results in light diffracted by the amplitude grating that is proportional to the transient dichroism signal as known from the common absorption relaxation.     

Self-imaging by a volume grating

The self-image phenomenon by a volume grating is proposed and theoretically analyzed. A theoretical model based on a path integral formulation to describe wave propagation through the grating inhomogeneous medium is applied. A modified version of the scalar diffraction theory Fresnel propagator is obtained which allows calculating the diffracted field amplitude by the grating. The proposed model is applied to amplitude and/or phase volume gratings. Remarkable features appear, in particular at the fractional Talbot distance 0.125z_T. In this case, if an in-phase real and imaginary grating modulation is considered a self-image intensity profile is observed for determined values of the absorptive and refractive parameters. On the other hand, a spatial comb intensity profile for a near half period shift between the real and imaginary grating modulations is found.     

Amplitude of the dynamic phase gratings in saturable Er-doped fibers

Dynamic population gratings recorded via local saturation of optical absorption/gain in rare-earth (Er, Yb) doped fibers demonstrate contributions of the amplitude and phase components. Quantitative comparison of the experimentally observed amplitude grating efficiency with that evaluated from spatially uniform saturation of the fiber optical absorption usually shows a significant discrepancy. The grating amplitude proves to be significantly weaker than its theoretical evaluation. The first results on quantitative comparison of the recorded phase grating amplitudes with spatially uniform photo-induced refractive index change in Er-doped fibers at three essentially different wavelengths (1485, 1526, and 1568 nm) are reported. As for the amplitude grating component, the experimentally observed phase grating amplitude is inferior to its theoretical evaluation; this discrepancy is spectrally dependent and is also significantly reduced in the short-wavelength region 1480–1490 nm on the Er³⁺ ion absorption.     

Holographic diffraction gratings with multilayer insulator coatings

Based on numerical modeling of metallized diffraction gratings with multilayer insulator coatings, the diffraction efficiency of such gratings is investigated, assuming that the initial profile of the metallized grat-ing is not reproduced in the course of sequential deposition of coating layers. From comparison of experimental and calculated data, it is concluded that the initial grating relief is subject to considerable smoothing. The new nontraditional range of the optimum values of layer thicknesses, which provides a high diffraction efficiency in the operating wavelength range of 1.06 μm, is suggested. The stability of the diffraction efficiency with respect to random errors in the thickness of insulator layers deposited is investigated numerically.     

Measurement of Sectional Profile of a Cylinder using a Sinusoidally Vibrating Light with Sinusoidal Intensity

A method for accurately measuring a sectional profile of a cylinder is proposed in which a sinusoidally vibrating sinusoidal grating is used to generate a sinusoidally vibrating sinusoidal intensity distribution. A light coming from the top point of the cylinder surface is extracted with an optical system to make an image of this point. A sectional profile of the cylinder is measured by detecting a phase of a time-varying signal contained in the image intensity at a position where the amplitude of the signal is maximum. Detection of the amplitude and the phase is carried out easily and exactly.     

用于光纤布拉格光栅法布里-珀罗腔的改进的Rouard算法

比较了光纤布拉格光栅法布里一珀罗腔的极限法、平衡法及传输矩阵法3种算法,证明了它们是一致的,指出了光纤布拉格光栅复振幅传输矩阵的相移特性对法布里一珀罗腔透射率的影响.对计算任意折射率调制的光纤布拉格光栅的Rouard算法进行了改进,在分层方法中考虑了折射率分布初始相位的影响,获得了更为准确的反射复振幅相位特性,将该结果应用于计算光纤布拉格光栅法布里一珀罗腔,得到了光纤布拉格光栅法布里一珀罗腔具有多峰结构的透射谱,并经过实验验证了该理论的正确性.     

Surface profiling using fringe projection technique based on Lau effect

In this paper, the surface profile of objects is determined by using a grating projection system. The method is based on the concept of self-imaging, namely, the Lau effect. Periodic fringe patterns are generated from the projection of a grating illuminated by multiple mutually incoherent quasi-plane wavefront. The fringe patterns are then projected on to the object surface and the deformed grating image is captured by a CCD camera for subsequent analysis. Phase shifting techniques have been employed to determine the phase value. With suitable calibration of the system and the phase value obtained, the surface profile of the objects can be determined. The phase variation is achieved by using a linear translation stage incorporated to the grating. In this study, two specimens are tested to demonstrate the validity of the method. One is a spherical cap with a height of 4 mm, and the other is a coin. The experimental results are compared with results obtained by mechanical stylus method. In the case of the spherical cap the results are also compared with fringe projection method based on Talbot effect.     

π相移光纤光栅对超声波致非均匀应变场的传感特性

π相移光纤光栅用于水中超声传感时,超声波沿光纤轴向入射和垂直光纤入射时的传感波形及幅度显著不同。针对这一现象,本文建立了基于光学传递矩阵的光纤光栅声传感理论模型,计算了超声波分别沿轴向和沿垂直方向入射时π相移光纤光栅中的非均匀应变场分布,进而分析了光谱偏移,揭示了两种入射角度下π相移光纤光栅的传感特性与声传播导致的应变场分布相关,并通过实验进行了验证。结果表明,两种入射角度产生的不同的非均匀应变场分布对π相移光纤光栅的传感特性影响明显。超声波垂直入射时的传感波形和幅度均优于轴向入射,且π相移处对传感有显著作用。当入射位置远离π相移处时,垂直入射的响应也明显降低。本研究可为π相移光纤光栅超声传感的机理分析提供参考。     

Diffraction Properties of Field Adjustable Polymer Network Stabilized Liquid Crystal Grating

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Simultaneous diffraction of two finite waves at non-uniform dynamic volume reflection gratings

Based on the two-dimensional coupled-wave theory, the simultaneous diffraction of two finite waves with non-constant amplitude distribution at a finite non-uniform dynamic volume reflection grating is described. A coupled differential equation is derived and solved numerically with the aid of a two-dimensional Runge-Kutta method. The results for the chosen example of a planar volume reflection grating both for pure phase and absorption gratings show the dependence of the fidelity and diffraction efficiency on the normalized parameter grating strength, on the phase shift with respect to the interference pattern of the read-out waves and on the absorption modulation. In contrast to the transmission grating, a high fidelity of the enhanced beam can be achieved for reflection gratings. The numerical results are compared with the solution of the one-dimensional theory.     

A modified phase diversity diffraction wavefront sensor with a grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.     

A modified phase diversity wavefront sensor with a diffraction grating

Phase diversity wavefront sensor is one of the useful tools to estimate the wavefront aberration, and it is often used as a wavefront sensor in adaptive optics system. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.     

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating

Dual phase grating x-ray interferometry is compatible with common imaging detectors,and abandons the use of an absorption analyzer grating to reduce the radiation dose.When using x-ray tubes,an absorbing source grating must be introduced into the dual phase grating interferometer.In order to attain a high fringe visibility,in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility.Theoretical analysis shows that with the generalized Lau condition satisfied,the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar.And the influence of the source grating profile on the fringe visibility is independent of the phase grating type.Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar.Under a given transmission,one can always find an optimal duty cycle to maximize the fringe visibility.These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.     

基于莫尔拓扑与图像处理的三维形貌术

本文叙述了一种新型三维物体表面测量方法,该方法利用单光栅投射待测物体表面而获取变形光栅像,然后应用图像处理方法,通过微机计算出物体表面各点高度。该方法测试精度高,速度快。文中对其原理进行了详细的叙述。并讨论了该法的测量范围、灵敏度。     

Transfer characteristics of rectangular phase gratings in interference microscopy

In this Letter, the transfer characteristics of rectangular periodic phase objects are studied. It turns out that there are significant differences compared to amplitude objects. The imaging of an amplitude object can be understood as a linear process, whereas phase objects behave nonlinearly. It is shown that under certain conditions the correct shape of a rectangular phase grating can be obtained by an interference microscope as long as the first order diffraction component passes the optical imaging system. This result is in a good agreement with experimental observations and computer simulation results.