Off-axis pivot mounting for aberration-corrected concave gratings at normal incidence

The off-axis pivot-point mounting for toroidal uniform line-space (TULS) gratings and spherical varied line-space (SVLS) is presented: One scans the spectrum by rotating the grating about the pivot point. The best choice for the location of the point is discussed: For a monochromator the location is chosen such that the grating is moved approximately along the bisector of the subtended angle; for a spectrometer, it is chosen such that the grating is moved approximately along the direction of the incident ray. Minimizing the spectral defocusing caused by the rotation of the grating determines the optimum length of the pivot arm. The pivot points for TULS and SVLS gratings are found to be located on opposite sides with respect to the normal to the grating. In a comparison of the optical performance, the spectral focusing is similar, but the spatial aberrations can be fewer for a SVLS grating.     

相位扫描法制作变栅距光栅

提出了一种制作变栅距(VLS)光栅的相位扫描方法。该方法的主要装置包括一个用于控制刻划机运动的光栅干涉仪和一个相位扫描机构。如果调整光栅干涉仪,保证接收场中只有两条干涉条纹,然后改变用于对条纹进行计数的光电传感器的位置,就可以刻划出具有变栅距的刻槽。对光电式光栅刻划机的控制系统和结构都做了详细论述。按照上述方法成功刻划出了试验性的VLS光栅,它的最小栅距增量为0.33nm,并对在制作过程中产生的误差进行了讨论。采用测量衍射角的方法进行了栅距检测试验,由变栅距光栅和等栅距光栅作出的拟合曲线表明:相位扫描方法是加工具有亚纳米栅距增量的VLS光栅的有效方法,该方法对超精密定位也具有借鉴作用。     

Coma correction and extension of the focusing geometry of a soft-x-ray monochromator

I show analytically and numerically how to use a varied line-space grating to reduce coma aberration in a soft-x-ray synchrotron radiation monochromator: a plane grating in combination with one or more spherical mirrors arranged in front of the grating and rotated around a fixed axis outside the mirror surface. It seems that the variation extent of groove spacing is too small to be manufactured; thus, a holographic grating of equivalent imaging properties is proposed. Based on the analysis of a focusing equation, I found that, if the plane grating is replaced by a spherical one, the monochromator can also be made free of defocus.     

First-generation holographic, grazing-incidence gratings for use in converging, extreme-ultraviolet light beams

We present two holographic recording solutions that produce gratings suitable for use at grazing incidence in the extreme ultraviolet. The rulings are formed when the interference pattern of two spherical wave fronts is recorded on a planar substrate. Each grating is designed to minimize or eliminate the dominant aberration terms in order to maximize the spectral and spatial resolution of the system. In the first design, the dominant astigmatism term in a power-series expansion of the light path function is eliminated; in the second design, the dominant comatic terms are minimized. Each grating is placed directly in a converging light beam at grazing incidence to provide high system efficiency in the extreme ultraviolet. The aberration control afforded by both recording solutions is excellent, providing detector-limited spatial and spectral resolution over much of the usable bandpass. Furthermore, the aberration control is maintained over a wide range of beam speeds and off-axis angles, thereby outperforming conventional varied line-space gratings for use in the extreme ultraviolet. We discuss the methodology used to develop the recording solutions, model and compare the performance of the gratings, and discuss possible space-based applications for these gratings.     

Examination of the +1, −1 Surface Plasmon Mini-gap on a Gold Grating

Abstract

An energy gap in the excitation of surface plasmons is found for light at normal incidence to a gold grating. This gap occurs at the crossing of the plus and minus first order surface plasmons. It arises directly as a consequence of distortion of the grating from sinusoidality, the first harmonic of the grating providing coupling between the plus and minus one orders. Experiments have been performed using both wavelength scans, where at a fixed angle of incidence the wavelength of excitation is varied, and angle of incidence scans, where for a fixed wavelength the angle of incidence is varied a few degrees either side of normal to the grating. By fitting the angular dependent reflectivity scans using grating modelling theory the gold grating is characterized at all wavelengths. This then allows a detailed comparison of the theoretical dispersion curve with that obtained experimentally. The agreement for both p-polarized light (for angle dependence with the plane of incidence normal to the grating grooves) and for s-polarized light (angle dependence with the plane of incidence perpendicular to the grating grooves) is excellent. An apparent momentum gap in the lower energy branch of the dispersion curve, attributed to the loss of coupling strength, is found to move to the upper branch if the grating profile is inverted.     

Fourier-synthesis custom-coherence illuminator for extreme ultraviolet microfield lithography

Scanning illumination systems provide for a powerful and flexible means for controlling illumination coherence properties. Here we present a scanning Fourier synthesis illuminator that enables microfield extreme ultraviolet lithography to be performed on an intrinsically coherent synchrotron undulator beamline. The effectiveness of the system is demonstrated through a variety of print experiments, including the use of resolution enhancing coherence functions that enable the printing of 50-nm line-space features by use of a lithographic optic with a numerical aperture of 0.1 and an operational wavelength of 13.4 nm.     

Simple measuring technique for the diffraction efficiency of slanted volume gratings at various wavelengths

To measure diffraction efficiencies of gratings as a function of wavelength, it is necessary to have quasi-monochromatic light sources of various wavelengths. We propose a method to measure the wavelength dependence of the grating diffraction efficiency by using a quasi-monochromatic light source. This method of estimating the real diffraction characteristics of the gratings for various wavelengths is very useful and simple. First the diffraction efficiency of the grating as a function of various incident-beam angles of monochromatic light is measured, then, using these data, we can obtain the diffraction efficiencies for various wavelengths of the same incident angle of light by virtue of a mathematical-conversion method. The mathematical-conversion results for two laminated differently slanted angle gratings of the same volume grating period are in good agreement with the experimental ones.     

Phase-based Bragg intragrating distributed strain sensor

A strain-distribution sensing technique based on the measurement of the phase spectrum of the reflected light from a fiber-optic Bragg grating is described. When a grating is subject to a strain gradient, the grating will experience a chirp and therefore the resonant wavelength will vary along the grating, causing wavelength-dependent penetration depth. Because the group delay for each wavelength component is related to its penetration depth and the resonant wavelength is determined by strain, a measured phase spectrum can then indicate the local strain as a function of location within the grating. This phase-based Bragg grating sensing technique offers a powerful new means for studying some important effects over a few millimeters or centimeters in smart structures.     

Unified design of sinusoidal-groove fused-silica grating

A general design rule of deep-etched subwavelength sinusoidal-groove fused-silica grating as a highly efficient polarization-independent or polarization-selective device is studied based on the simplified modal method, which shows that the device structure depends little on the incident wavelength, but mainly on the ratio of groove depth to incident wavelength and the ratio of wavelength to grating period. These two ratios could be used as the design guidelines for wavelength-independent structure from deep ultraviolet to far infrared. The optimized grating profile with a different function as a polarizing beam splitter, a polarization-independent two-port beam splitter, or a polarization-independent grating with high efficiency of -1st order is obtained at a wavelength of 1064 nm, and verified by using the rigorous coupled-wave analysis. The performance of the sinusoidal grating is better than a conventional rectangular one, which could be useful for practical applications.     

Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry

Sinusoidal structured illumination is used widely in three-dimensional (3-D) sensing and machine vision. Phase algorithms, for example, in phase-measuring profilometry, are inherently free of errors only with perfect sinusoidal fringe projection. But it is difficult to produce a perfect sinusoidal grating. We propose a new concept, area modulation, to improve the sinusoidality of structured illumination. A binary-coded picture is made up of many micrometer units. An aperture is open in every micrometer unit, and its area is determined by the value of the sinusoidal function. When such a grating is projected onto an object surface, the image of the grating becomes sinusoidal because of the convolution function of an optical system. We have designed and manufactured an area modulation grating for sinusoidal structure illumination using a large-scale integration technique. The area modulation grating has been used in the high-precision phase-measuring profilometry system, and the phase errors caused by the area modulation grating are reduced to 0.1%. The grating guaranteed the entire measuring accuracy to a 1% equivalent wavelength. The experimental results proved that area modulation grating would be of significant help in improving the phase-measurement accuracy of the 3-D sensing system.     

Achromatic quarter-wave plates using the dispersion of form birefringence

We propose achromatic quarter-wave plates of a subwavelength grating structure. When the period of the grating structure is smaller than the wavelengths of the incident light, the structure is considered to be an optically anisotropic medium. The effective refractive indices strongly depend on the wavelengths, especially when the period is close to the wavelength. Using this feature, we can design a grating quarter-wave plate whose phase retardation is maintained at pi/2 for a wide wavelength range. A design method using the effective medium theory is described, and the wave plates designed were evaluated by numerical calculation with a rigorous electromagnetic grating theory. The calculation results led to the possibility of an achromatic quarter-wave plate whose retardation errors are smaller than 3 degrees for a +/-10% change in wavelength.     

光纤光栅半导体激光器激射波长与Bragg波长的偏离

利用包含光纤布拉格光栅(FBG)反射率分布的光纤光栅外腔半导体激光器(FGSL)的理 论模型,对FGSL 的激射波长进行了研究。结果表明激射波长并不一定在FBG布拉格反射波长处;布拉格反射波长相对于激射波长的偏移量与FBG的反射率分布、半导体增益介质的增益谱分布及增益峰值波长有关;激射波长可大于或小于布拉格反射波长。     

Analytical determination of reflection-peak wavelengths of chirped sampled fiber Bragg gratings

An analytical expression for calculating the position of the reflection-peak wavelength of a chirped sampled fiber Bragg grating (C-SFBG) is obtained for what is believed to be the first time. Using Fourier theory, the chirped sampling function of the C-SFBG is expanded, and an equivalent local Bragg period is then obtained to derive the expression of the peak wavelength. The calculated results based on the expression are in excellent agreement with the numerical reflection spectra obtained by the conventional transfer-matrix method.     

光纤布拉格传感器兰姆波检测的反射谱分析

传统的兰姆波多采用压电陶瓷换能器激发和接收。建立了新的超声兰姆波无损检测系统,其基本思想是采用布拉格光纤传感器作为兰姆波的接收器。光纤光栅传感的基本原理是通过检测光栅反射的中心波长移动实现对外界参量如超声的测量。超声作用下光纤光栅的反射谱发生变化,对超声作用下光纤光栅的反射谱变化进行了数值分析,结果表明,超声对光栅反射谱的影响与超声波长与光栅长度的比值是高度相关的。只有当这个比值相当大时,反射谱的形状才不会变化而中心波长发生偏移,此时光纤传感器可用来探测兰姆波。这个结论为利用新的兰姆波无损检测系统在布拉格光栅长度的设计和兰姆波波长的选择方面提供了有用的工具。     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Temperature dependence properties of holographic gratings in phenanthrenquinone doped poly(methyl methacrylate) photopolymers

We examine the temperature dependence of edge-illuminated holographic filters formed in phenanthrenquinone doped poly(methyl methacrylate) (PQ/PMMA) operating at 1550 nm. It was found that the thermally induced change to the refractive index and volume can be used to select the wavelength filtered by the grating. The temperature can be varied over a range of 15 degrees C without introducing noticeable hysteresis effects. The wavelength can be tuned at a rate of 0.03 nm/degrees C over this temperature range. A model for the temperature tuning effect is presented and compared to experimental results.     

Effect of light source spectral modulation on wavelength interrogation in fiber Bragg grating sensors and its reduction

In the fiber Bragg grating sensing using a superluminescent diode as the light source and an arrayed waveguide grating as the wavelength interrogator, the wavelength measurement error due to the spectral modulation of the superluminescent diode is theoretically formulated and quantitatively analyzed by computer simulation. It is shown that the wavelength measurement errors produced with the use of real superluminescent diodes are in very good agreement with the theoretical results. In order to reduce the wavelength measurement error due to the spectral modulation of superluminescent diode, two different types of remedies are proposed that utilize the temperature switching of superluminescent diode and that adjust the bandwidths of fiber Bragg grating and arrayed waveguide grating, and their efficacies are experimentally demonstrated together with good quantitative agreement with the theoretical calculation.     

Aberrations and convergence characteristics of a concentric-circular focusing grating coupler: analysis

The convergence characteristics of the previously proposed concentric-circular focusing grating coupler (CFGC) are analyzed, and aberration functions for such typical errors as wavelength errors, effective index errors, grating pattern distortion, and CFGC eccentricity are derived for evaluation of their allowances. The analyzed results prove that the Strehl intensity deterioration caused by a wavelength error and an effective index offset can be minimized by optimization of the annular aperture of the CFGC. In the case of Marechal's criterion, a wavelength error of ±8.6% at the annular aperture of NA = 0.440-0.607 and an effective index error of ±20.4% at NA = 0.500-0.652 are permissible, and these values are ～100 times greater than those that are seen in a conventional focusing grating coupler that has a rotationally asymmetrical structure with respect to its optical axis.     

Quadratic behavior of fiber Bragg grating temperature coefficients

We describe the characterization of the temperature and strain responses of fiber Bragg grating sensors by use of an interferometric interrogation technique to provide an absolute measurement of the grating wavelength. The fiber Bragg grating temperature response was found to be nonlinear over the temperature range -70 degrees C to 80 degrees C. The nonlinearity was observed to be a quadratic function of temperature, arising from the linear dependence on temperature of the thermo-optic coefficient of silica glass over this range, and is in good agreement with a theoretical model.     

Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry

A spatiotemporal phase-unwrapping method is presented that combines the dynamic fringe-projection method and the phase-shifting technique and extends the phase-unwrapping method, which measures two phase maps at different sensitivities. The most important feature of the method is that it makes possible the automatic three-dimensional shape measurement of discontinuous objects with large dynamic range limits and high precision because the effective wavelength of the fringe-projection profilometry can be continuously varied over several orders of magnitude by rotation of the projection grating in its own plane. Only one grating and several steps of rotating the grating are required; therefore the method is inherently simple, fast, and robust. In the experiment, choosing the rotation angle was crucial for optimizing the measurement speed and the measurement accuracy. A criterion is presented for the choice of the minimum number of rotational steps for a given accuracy. The experimental results demonstrate the validity of the proposed method.