台阶光栅衍射的傅里叶分析

提出了一种台阶光栅模型 ,并应用傅里叶光学方法推导出了反射式衍射光强的表达式。分析计算了衍射光强随台阶数、入射波长、衍射角和轮廓角 (闪耀角 )的变化关系。结果表明 ,台阶光栅能起到闪耀作用 ,台阶对衍射强度分布有影响 ,但不改变衍射光极大值的位置 ,随台阶数的增加 ,能量逐渐向闪耀方向集中。当台阶数等于 8时 ,其衍射效率可接近三角形闪耀光栅的衍射。台阶光栅衍射的傅里叶分析对光栅制作有一定的指导意义     

Hartmann－Shack波前传感器的Fourier光学分析

Ｈａｒｔｍａｎｎ－Ｓｈａｃｋ波前传感器是自适应光学中几种重要的波前传感器之一。本文利用Ｆｏｕｒｉｅｒ光学方法分析研究了Ｈａｒｔｍａｎｎ－Ｓｈａｃｋ波前传感器的原理，导出了辐照度分布质心与子孔径波前倾斜的解析表达式，说明了辐照度分布质心及其算法的物理意义，总结了该传感器的若干重要特点。     

Fiber Fourier optics

The Fourier transform of a coherent optical image can be evaluated physically by use of a single lens plus free-space propagation, thereby providing the basis for the field of Fourier optics. I point out that one can similarly evaluate the discrete Fourier transform of a sampled or pixelated optical array physically by passing the discrete array amplitudes through a network of single-mode fibers or optical waveguides. A passive optical network that evaluates the fast Fourier transform of a coherent array can be fabricated by use of (N/2)log(2)[N] optical 3-dB couplers plus small added phase shifts. Implementing such networks in fiber or integrated optical form could provide the basis for a possible technology of fiber Fourier optics.     

In-fiber grating sensors

The period of in-fiber grating can be changed due to the change of pressure or temperature that the in-fiber grating bears. The reflecting wavelength of in-fiber grating will shift as its period changes. This characteristic trait of in-fiber grating can render it to be used as a sensor element to detect pressure or temperature. The key issue is how to interrogate the reflecting wavelength shift accurately. The techniques of in-fiber grating sensors are reviewed with an emphasis on interrogation approaches to reflecting wavelength shift induced by measurement quantities. Some suggestions are also made in this paper.     

闪耀光栅的傅里叶分析

用傅里叶光学来解决周期性结构的衍射问题既准确方便又容易理解。从研究透射闪耀光栅的透射函数及反射闪耀光栅的反射函数出发 ,利用傅里叶光学原理 ,从理论上分析了闪耀光栅衍射图样的复振幅和光强分布与闪耀角及波长的关系 ,并利用计算机进行了模拟计算。计算的效率曲线与实际刻划的闪耀光栅效率曲线吻合的很好。     

Generalized fiber Fourier optics

A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.     

Temperature-compensating multiple fiber Bragg grating strain sensors with a metrological grating

A novel approach based on multiple fiber Bragg gratings for measuring the distributed strain, which is temperature compensated, is demonstrated. Especially, in order to increase the measurement accuracy, a metrological grating is employed to read out the output of the system. The measurement resolution of the system is less than 0.5 μ.     

A theoretical analysis of refractive-index grating waveguide structures for integrated optics

Based upon equivalent transmission line method, a perturbation analysis on the guiding properties of refractive-index gratings is presented. By numerical calculation, the leakage parameter which influences the leakage energy into the diffracted orders due to the grating scatter, is achieved as functions of the grating period, thickness of the waveguide and index modulation Δn. Our results reveal that, although the index modulation Δn is much less than that of the etched or deposited grating, refractive-index gratings can still reach a high leakage parameter because of the prominent increase of the grating height.     

分频光栅的衍射特性及误差分析

 基于标量衍射理论推导出了分频光栅的各级衍射效率公式，分析了分频光栅的衍射特性，发现入射光波在满足相应的相位延迟条件时，能被分频光栅以最大效率衍射进３个中央级次中的某一级。分析和比较了两种制作工艺中的刻蚀深度误差、占空比误差对衍射效率的影响。在惯性约束聚变（ICF）应用中，对于同一要求的３倍频光的衍射效率范围，两种工艺的刻蚀误差容限是相同的，但是两种工艺的相同刻蚀误差却带来不同的衍射效率。在不计其它误差时，占空比误差不会对３倍频光的衍射效率产生影响，但可以对基频光和2倍频光产生相反的影响，占空比误差还可以使基频光和2倍频光的主要衍射级次的效率都降低，同时增大它们的0级衍射效率。     

T-matrix analysis of electromagnetic wave differaction from a Fourier grating

This paper is described for T-matrix analysis of the electromagnetic wave diffraction from a Fourier grating that the boundary value problem is treated by applying the extended boundary condition. The rigorous form of the expression of matrix elements is presented in the term of Bessel functions of the first kind. The error of power conservation versus the truncated number has been examined for mode number. Diffraction efficiencies versus groove depth and wavelength for a second or third harmonic wave of Fourier grating have been discussed. Numerical results are in good agreement with those obtained from other method and experimental values. Reasonable numerical results are presented for a groove depth per period of the Fourier grating less than 0.25.     

分频光栅的衍射特性及误差分析

基于标量衍射理论推导出了分频光栅的各级衍射效率公式,分析了分频光栅的衍射特性,发现入射光波在满足相应的相位延迟条件时,能被分频光栅以最大效率衍射进３个中央级次中的某一级。分析和比较了两种制作工艺中的刻蚀深度误差、占空比误差对衍射效率的影响。在惯性约束聚变（ICF）应用中,对于同一要求的３倍频光的衍射效率范围,两种工艺的刻蚀误差容限是相同的,但是两种工艺的相同刻蚀误差却带来不同的衍射效率。在不计其它误差时,占空比误差不会对３倍频光的衍射效率产生影响,但可以对基频光和2倍频光产生相反的影响,占空比误差还可以使基频光和2倍频光的主要衍射级次的效率都降低,同时增大它们的0级衍射效率。     

Double Fourier interferometry with IR single-mode fiber optics

An implementation of double Fourier interferometry with IR single-mode, all-fiber optics is described, in which the optical path difference modulations and beam combinations are performed within waveguides. A laboratory prototype is presented, and the first experimental results that prove the validity of the concept.     

Multiplexing fiber bragg grating sensors

Abstract

Bragg reflection gratings and out-coupling taps for sensors can be written holographically within the core of many commercial fibers available today. The gratings appear to be permanent and have been tested to temperatures in excess of 500°C. Quasi-distributed temperature, strain, pressure, chemical, and interferometric sensors can be made with the wavelength selective, reflection gratings, and taps. The fiber gratings, and the different types of sensors they can make, conveniently lend themselves to (wavelength-division multiplexing) WDM, (time-division multiplexing) TDM, and (frequency-division multiplexing) FDM types of multiplexing schemes. Instrumentation to detect the multiple sensors and measure their spectral shift for localized and quasi-distributed sensing is currently under development.     

Tilted fiber Bragg grating sensors

Optical fiber gratings have developed into a mature technology with a wide range of applications in various areas, including physical sensing for temperature, strain, acoustic waves and pressure. All of these applications rely on the perturbation of the period or refractive index of a grating inscribed in the fiber core as a transducing mechanism between a quantity to be measured and the optical spectral response of the fiber grating. This paper presents a relatively recent variant of the fiber grating concept, whereby a small tilt of the grating fringes causes coupling of the optical power from the core mode into a multitude of cladding modes, each with its own wavevector and mode field shape. The main consequence of doing so is that the differential response of the modes can then be used to multiply the sensing modalities available for a single fiber grating and also to increase the sensor resolution by taking advantage of the large amount of data available. In particular, the temperature cross‐sensitivity and power source fluctuation noise inherent in all fiber grating designs can be completely eliminated by referencing all the spectral measurements to the wavelength and power level of the core mode back‐reflection. The mode resonances have a quality factor of 10⁵, and they can be observed in reflection or transmission. A thorough review of experimental and theoretical results will show that tilted fiber Bragg gratings can be used for high resolution refractometry, surface plasmon resonance applications, and multiparameter physical sensing (strain, vibration, curvature, and temperature).     

Bend-insensitive long-period fiber grating sensors

A novel bend-insensitive long-period fiber grating (LPFG) sensor written using focused CO₂ laser pulses is demonstrated, for the first time, to our knowledge. It is found that the central wavelength shift of such a LPFG is only −0.018 nm even for a curvature of 1.1 m⁻¹ at the most bend-insensitive position of the LPFG. Experimental results show that the bend sensitivity of the central wavelength of the LPFG has a periodic distribution along its circular directions. Such a bend-insensitive sensor could be used to solve the problem of cross-sensitivity between bend and other measurands, such as temperature, strain or refractive index, which is an unsolved problem for LPFG sensors in practice. In addition, the bend sensitivity of the LPFG can be adjusted by selecting its circular positions.     

Multiplexing fiber bragg grating sensors

Bragg reflection gratings and out-coupling taps for sensors can be written holographically within the core of many commercial fibers available today. The gratings appear to be permanent and have been tested to temperatures in excess of 500°C. Quasi-distributed temperature, strain, pressure, chemical, and interferometric sensors can be made with the wavelength selective, reflection gratings, and taps. The fiber gratings, and the different types of sensors they can make, conveniently lend themselves to (wavelength-division multiplexing) WDM, (time-division multiplexing) TDM, and (frequency-division multiplexing) FDM types of multiplexing schemes. Instrumentation to detect the multiple sensors and measure their spectral shift for localized and quasi-distributed sensing is currently under development.     

Fiber grating sensors for high-temperature measurement

Two fiber grating sensors for high-temperature measurements are proposed and experimentally demonstrated. The interrogation technologies of the sensor systems are all simple, low cost but effective. In the first sensor system, the sensor head is comprised of one fiber Bragg grating (FBG) and two metal rods. The lengths of the rods are different from each other. The coefficients of thermal expansion of the rods are also different from each other. The FBG will be strained by the sensor head when the temperature to be measured changes. The temperature is measured based on the wavelength-shifts of the FBG induced by the strain. In the second sensor system, a long-period fiber grating (LPG) is used as the high-temperature sensor head. The LPG is very-high-temperature stable CO₂-laser-induced grating and has a linear function of wavelength–temperature in the range of 0–800 °C. A dynamic range of 0–800 °C and a resolution of 1 °C have been obtained by either the first or the second sensor system. The experimental results agree with theoretical analyses.     

Dispersion properties of silicon nanophotonic waveguides investigated with Fourier optics

We experimentally investigate the dispersion relation of silicon-on-insulator waveguides in the 1.5 microm wavelength range by using a technique based on far-field Fourier-space imaging. The phase information of the propagating modes is transferred into the far field either by linear probe gratings positioned 1 microm away from the waveguide core or by residual gratings located on the sidewalls of the waveguide. As a result, the dispersion curve of rectangular and slot waveguides as well as the group index dispersion are accurately determined.     

Temperature-compensated dual-polarization fiber grating laser sensors

We report on temperature compensation for beat-frequency-encoded dual-polarization fiber laser sensors based on a cleave-rotate-splice method. By cleaving the laser cavity into two segments with comparable lengths,aligning them with a rotated angle of 90°,and then fusion splicing the two halves,the temperature sensitivity in terms of beat-frequency variation can be greatly reduced from-1.99 to-0.30 MHz∕°C(or by 84.9%).In contrast,the sensitivity to point loaded mass hardly changes. We also find that the beat-frequency fluctuation decreases from 30 to 25 kHz as a result of the temperature compensation.