Non-Hilbert spaces: a way to new physics?

We give some examples of the problems where non-Hilbert spaces could be relevant.     

光栅衍射的初步分析

通过三角函数的计算,得到衍射光栅强度分布;并讨论了主极大、极小、次极大和缺级等现象。     

Muon spinning its way to new physics

The first results from the Fermilab Muon g–2 Experiment shed lights on the mystery surrounding the magnetic anomaly of the muon. This could become a window into a new era of particle physics.     

多缝衍射的计算机模拟与演示

利用一个多缝衍射模型模拟光和微观粒子的干涉衍射现象。该模型可演示光的双干涉、ｎ缝衍射及色散现象;也可演示微观粒子的单、双缝衍射,物质波的概率特性及粒子从量行为到经典行为的过渡。     

Echelle diffraction grating demultiplexers with a single diffraction passband

Planar multiplexers based on echelle gratings are very popular devices for optical communication applications. However, the available channel number is restricted by the concept of free spectral range (FSR) due to their high operating diffraction order. Now, we can break the restriction of the FSR concept, and most of wavelengths in the operating passband of echelle grating multiplexers can be used based on a variable diffraction order design. We present the design, fabrication, and characterization of the echelle grating multiplexer with a single diffraction passband based on silica platform.     

Methods to control parameters of a diffraction grating on the surface of lithium niobate electro-optical crystal

Optical transmission and directivity pattern of a tunable diffraction grating that is based on the X-cut lithium niobate electro-optical crystal are studied. It is demonstrated that the intensities in 0 and ±1 diffraction orders decrease by 40% relative to the original level when a voltage of 792 V is applied to electrodes on the crystal. Diffraction orders at angels of ±λ/(2d) and ±3λ/(2d) are demonstrated. The changes of directivity pattern are caused by scattering phase diffraction grating that emerges in the crystal in the presence of the electric field of electrodes and vanishes in the absence of voltage. A hysteresis dependence of the intensity of the zero diffraction order on the voltage is related to the formation of needle-shaped domains with a length of up to 100 μm and a width of up to 10 μm that are oriented perpendicularly to the electrodes. In the vicinity of the domains, the electric field causes rotation of the crystal indicatrix and depolarization and scattering of the transmitted radiation. Under normal conditions, the lifetime of the domains is several weeks when the voltage is switched off and the electrodes are not short-circuited.     

A novel single-order diffraction grating: Random position rectangle grating

Spectral diagnosis of radiation from laser plasma interaction and monochromation of radiation source are hot and important topics recently. Grating is one of the primary optical elements to do this job. Although easy to fabricate, traditional diffraction grating suffers from multi-order diffraction contamination. On the other hand, sinusoidal amplitude grating has the nonharmonic diffraction property, but it is too difficult to fabricate, especially for x-ray application. A novel nonharmonic diffraction grating named random position rectangle grating(RPRG) is proposed in this paper. Theoretical analysis and experiment results show that the RPRG is both higher order diffraction suppressing and not difficult to fabricate. Additionally, it is highly efficient; its first order absolute theoretical diffraction efficiency reaches 4.1%. Our result shows that RPRG is a novel tool for radiation diagnosis and monochromation.     

Infrared probing of a gaseous diffraction grating

The use of an infrared beam to optically probe an acoustic diffraction grating propagating in air is discussed. With the use of acoustic diffraction gratings for providing beam splitting action for intense infrared radiation, the need for determining the homogeneity of gaseous diffraction gratings has arisen. The study was performed at the Bragg reflection angle using a 10.6 μm wavelength CO₂ laser probe and an acoustic diffraction grating of 0.33 mm spacing.     

双光栅衍射场的干涉效应

双光栅衍射场的干涉效应既具有理论研究价值又具有很实际的应用价值.本文利用波前相因子分析法,推导出了双余弦光栅夫琅禾费衍射场的理论结果;分析了当两个光栅在横向有相对运动时,各级衍射斑光强的变化规律.通过实验观测映证了光强变化与数值计算结果是一致的.这一理论结果是双光栅衍射类实验设计的基础,而这类实验可以用于测量微小振动的振幅和频率.     

平面透射光栅的菲涅耳衍射

从标量场的菲涅耳衍射理论出发,研究了球面波入射平面透射光栅的衍射场,导出菲涅耳衍射场的复振幅分布,并得到光栅菲涅耳衍射角的计算公式．结果表明,在理想情况下菲涅耳衍射的每一级衍射波都是一个球面波;在对菲涅耳衍射角进行新的定义后,衍射角的计算仍然可以采用夫琅禾费衍射的光栅方程．     

Test of a diffraction grating neutron interferometer

A practical diffraction grating neutron interferometer has been tested and used to obtain the interference pattern for neutrons with a maximum wavelength of λ = 3.15 Å. Implementation of this principle for very low energy ultra-cold neutrons, permits a substantial expansion of the range of problems which can be solved by neutron interferometry.     

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.     

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.     

Radiation of a charge moving over the diffraction grating

The states of a charged particle with a finite free path are determined in the field of a resonant electromagnetic wave. The exact resonance conditions, the modulation and beam instability mechanisms, the charge and current densities (Ohm's law) are obtained for the collisionless beam of resonance particles. Quantum theory of radiation is developed for the resonant adiabatic interaction between a particle and a wave taking into account the interaction with a constant magnetic field induced at the grating surface by the charge and nonresonant waves. The radiation power, the spectrum, and the range of generated frequencies are determined. The results obtained can be used in the plasma and solid-state theories and in electronics.     

Tau lepton Michel parameters and new physics

A complete discussion of the constraints on the Michel parameters and the ambiguities of their interpretation is presented. Estimators of new physics, optimized for a very wide class of hypotheses and models, are proposed. Received: 4 October 2000 / Published online: 21 December 2000     

环形光栅的菲涅耳衍射

在圆孔的菲涅耳衍射的基础上 ,讨论环形光栅的菲涅耳衍射 ,并给出了计算机仿真结果     

Oscillations conditions in a gain grating in the Bragg diffraction regime

Coupled-wave analysis is applied to the determination of an oscillation threshold in thick periodic grating with gain (distributed-feedback oscillator). Pure phase (refractive index modulation), amplitude (gain modulation) and mixed-type gratings are considered. The origin of oscillation modes and their position on the diffraction efficiency contour is analyzed. The threshold conditions are determined on a basis of analytical expressions.     

Focussing properties of a holographic plane diffraction grating

A plane holographic diffraction grating is the simplest grating, yet very important component for many optical devices. Very little has been done with regards to its focusing properties and stigmatic conditions. In this paper, we discuss a holographic plane diffraction grating and show that the grating can exhibit focusing properties under some conditions. We also discuss the conditions for zero astigmatism.     

Fibonacci光栅衍射频谱的自相似结构

本文设计并制作了一种按Ｆｉｂｏｎａｃｃｉ数列规则排列的准周期衍射光栅，从理论和实验两方面计算与显示了该光栅的自相似衍射频谱，这对准晶体光学中非周期的频率分析研究有一定的理论和实用价值。