Analysis of period and visibility of dual phase grating interferometer

Dual phase grating interferometer may simultaneously achieve large field of view and high X-ray dose efficiency. In this paper, we developed a simple theoretical method to better understand the imaging process of the dual phase grating interferometer. The derivation process of fringe period and the optimal visibility conditions of the dual phase grating interferometer were shown in detail. Then, we theoretically proved that the fringe period and optimal visibility conditions of the dual phase grating interferometer included that of the Talbot interferometer. By comparing our experimental results with those of other researchers, we found that when the positions of phase gratings were far away from the positions where the fringe visibility was optimal, the fringe period of the dual π-phase grating interferometer was twice longer than the theoretical results under the illumination of polychromatic X-ray. And this conclusion may explain the contradictory research results of dual phase grating interferometer among different researchers.

Analytic Design of Segmented Phase Grating for Optical Sensing in High-Precision Alignment System

Ultra-precision measurement systems are important for semiconductor manufacturing processes. In a phase grating sensing alignment (PGA) system, the measurement accuracy largely depends on the intensity of the diffraction signal and its signal-to-noise ratio (SNR), both of which are associated with the grating structure. Although an equally segmented grating structure could increase the signal of a high odd order, it could also strengthen the signals at the zeroth and even orders which are the main contributors of stray light. This paper focuses on the practical problem of differently responding diffraction orders but in one grating structure. An analytical relationship has been established between the diffraction efficiency and the segment structure of phase grating. According to this analytic model, we then propose a design method to increase the diffraction signal at high odd orders and, meanwhile, to decrease it at the zeroth and even orders. The proposed method provides a fast and effective way to obtain the globally optimal grating structure in the valid scope. Furthermore, the design examples are also verified by means of numerical simulation tool–rigorous coupled-wave analysis (RCWA) software. As a result, the proposed method gives insight into the diffraction theory of segmented grating and the practical value to greatly improve the design efficiency.

Diffraction of a Gaussian Beam with Limited cross Section by a Volume Phase Grating under Waveguide Mode Resonance

In this work, the diffraction of a Gaussian beam on a volume phase grating was researched theoretically and numerically. The proposed method is based on rigorous coupled-wave analysis (RCWA) and Fourier transform. The Gaussian beam is decomposed into plane waves using the Fourier transform. The number of plane waves is determined using the sampling theorem. The complex reflected and transmitted amplitudes are calculated for each RCWA plane wave. The distribution of the fields along the grating for the reflected and transmitted waves is determined using inverse Fourier transform. The powers of the reflected and transmitted waves are determined based on these distributions. Our method shows that the energy conservation law is satisfied for the phase grating. That is, the power of the incident Gaussian beam is equal to the sum of the powers of the reflected and transmitted beams. It is demonstration of our approach correctness. The numerous studies have shown that the spatial shapes of the reflected and transmitted beams differ from the Gaussian beam under resonance. In additional, the waveguide mode appears also in the grating. The spatial forms of the reflected and transmitted beams are Gaussian in the absence of resonance. It was found that the width of the resonance curves is wider for the Gaussian beam than for the plane wave. However, the spectral and angular sensitivities are the same as for the plane wave. The resonant wavelengths are slightly different for the plane wave and the Gaussian beam. Numerical calculations for four refractive index modulation coefficients of the grating medium were carried out by the proposed method. The widths of the resonance curves decrease with the increasing in the refractive index modulation. Moreover, the reflection coefficient also increases.

Light diffraction from a phase grating at oblique incidence in the intermediate diffraction regime

We experimentally characterize the positions of the diffraction maxima of a phase grating on a screen, for laser light at oblique incidence (so-called off-plane diffraction or conical diffraction). We discuss the general case of off-plane diffraction geometries and derive basic equations for the positions of the diffraction maxima, in particular for their angular dependence. In contrast to previously reported work (Jetty et al. in Am J Phys 80:972, 2012), our reasoning is solely based on energy- and momentum conservation. We find good agreement of our theoretical prediction with the experiment. A detailed discussion of the diffraction maxima positions, the number of diffraction orders, and the diffraction efficiencies is provided. We assess the feasibility of an experimental test of the phenomenon for neutron matter waves.

A Switchable Cholesteric Phase Grating with a Low Operating Voltage

We demonstrate a simple fabrication method of a uniform-lying-helix (ULH) cholesteric liquid crystal (ChLC) cell for phase grating device applications. To utilize a stable ULH state, we set the pitches of ChLCs as half of the cell gap to obtain the fingerprint texture with homeotropic anchoring. With the given grating period, the diffraction efficiency of the ULH cell can be maximized by optimizing the cell gap. We found that the fabricated grating device can provide a large diffraction angle of 10° and a low operating voltage of 3 V with a diffraction efficiency of 30%. We expect potential applications of the device for diffraction optics, optical interconnects, and beam steering devices.