Nonlinear continual growth model of nonuniformly scaled reliefs as applied to the rigorous analysis of the X-ray scattering intensity of multilayer mirrors and gratings

It is revealed that certain terms entering into the nonlinear continual equation describing thin-film growth enable its application to the simulation of the surfaces of multilayer mirrors and gratings with a large height and/or jumps of boundary-profile gradients. The proposed model characterizes both variations in the power spectral-density function of the surface of Al/Zr multilayer mirrors and the smoothing and shift of the boundaries of Mo/Si and Al/Zr gratings grown on Si substrates with triangular groove profiles by means of magnetron and ion-beam deposition. Rigorous calculations indicate that the intensities of diffuse X-ray scattering by Au mirrors, which have similar boundary profiles with Gaussian and exponential autocorrelation functions, differ substantially from each other. Computer simulation of the growth of Mo/Si and Al/Zr multilayer gratings is performed. On the basis of the calculated boundary profiles, the absolute diffraction efficiencies of the Mo/Si and Al/Zr gratings are found via the integral equation method in the extreme UV region. It is demonstrated that the proposed comprehensive approach to calculations of the boundary profiles and the intensities of short-wavelength scattering from multilayer mirrors and gratings makes it possible to carry out studies comparable in accuracy to measurements based on synchrotron radiation.     

SiC/W/Ir multilayer-coated grating for enhanced efficiency in 50-100 nm wavelength range in Seya-Namioka mount

A broadband [SiC/W/Ir](2) multilayer coating was deposited onto a diffraction grating to enhance the grating efficiency in the 50-100 nm wavelength range in a Seya-Namioka mount. The holographic ion-beam etched grating had a laminar profile with 1200 lines/mm. The coating was designed by using the subquarterwave multilayer theory. The measurement results show that the efficiency in the -1st diffraction order is greater than 9.3% throughout the wavelength range of 50-100 nm, which is obviously higher than that of single-layer gratings with SiC, Ir, or Au coatings.     

Optical properties of sliced multilayer gratings

Fabrication, calculation and optical properties of gratings fabricated by bevel cutting multilayer structures are discussed. Such gratings have very short period (about 100 nm) and provide high angular dispersion as compared to ruled, holographic or multilayer coated gratings without reduction of diffraction efficiency. Using graded multilayers it is possible to produce sliced multilayer gratings (SMG) with graded period (GSMG), which can focus radiation in one direction. Examples of SMG for various wavelengths in the interval 2–20 nm are considered.     

Co/C and W/Si multilayers deposited by ion-beam sputtering for the soft X-ray range

We deposited Co/C multilayer mirrors for a wavelength of 4.77 nm and W/Si multilayer mirrors for a wavelength of 1.77 nm by use of ion-beam sputtering. The small-angle diffraction spectrum was used to analyze the structure of the multilayers. With a combination of the experimental diffraction spectra and Apeles’ theory for calculation of the interfacial roughnesses of the multilayers, the interfacial roughnesses of Co/C and W/Si are 0.80 nm and 0.60 nm, respectively, which are lower than that of the substrate. The reflectivity of the Co/C multilayer is measured to be about 20% and that of the W/Si multilayer about 1% at the grazing incidence angle of about 12°. Received: 30 May 2000 / Accepted: 1 August 2000 / Published online: 11 February 2002     

Compact middle-wave infrared Fabry-Perot interferometer with double metallic subwavelength gratings

We demonstrate a compact middle-wave IR (MWIR) Fabry-Perot (FP) interferometer by replacing the traditional distributed Bragg reflectors consisting of thick multilayer films with two identical metallic subwavelength gratings. The transmission efficiency, resonance peak position, and finesse of the FP interferometer can be controlled by tuning the structural parameters. The performance of the MWIR FP interferometer is verified by experiment, which shows its potential application as, for example, narrowband MWIR filter for gas detection.     

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.     

Application of multilayer structures at millimeter wavelengths

The paper presents results of theoretical analyses and experimental investigations of the optical characteristics of devices based on multilayer dielectric structures and intended for the millimeter wave band. As is shown, multilayer dielectric structures can prove useful in devices with variable optical characteristics representing coupling elements for quasioptical open resonators, adjustable reflection coefficient mirrors in narrow-band interference Fabry-Perot filters or adjustable multilayer polarizers.     

多层膜闪耀光栅衍射的运动学研究

用 X射线运动学理论对软 X射线多层膜闪耀光栅的衍射特性进行了详细的研究 ,得到了衍射规律的一般表达式 ,讨论了产生衍射极大值的条件、光谱特性 ,不同于光栅和多层膜的色散特性。以及用作软 X射线单色器的一般性问题。发现只要选择合适的光栅参数 ,便可以将衍射光的大部分能量集中到某一个非零衍射级上。     

高衍射效率亚波长结构Dammann光栅的设计

传统的Dammann光栅是基于标量衍射理论设计的二值相位等光强分束器件，其衍射效率的典型值为80%左右.基于严格耦合波分析理论和遗传算法，提出了一种设计亚波长结构Dammann光栅的新方法，且该新型二值相位光栅具有较高的衍射效率.同时利用自编的仿真程序包设计了多个光栅，并分析了制作误差对其衍射效率和光强均匀性的影响.仿真结果表明，用该方法所设计的Dammann光栅的衍射效率超过92%.     

基于多层膜技术的硬X射线Laue透镜衍射效率的理论研究

采用耦合波理论分析了X射线在多层膜Laue透镜中的传播,选择Cu的Kα线作X射线光源,计算了多层膜Laue透镜的衍射效率.材料为WSi2/Si,最外层宽度为10 nm,深度为8 500 nm的多层膜Laue透镜,倾斜情况下外层区域局部光栅的衍射效率可达59%,理论上证明了多层膜Laue透镜是实现X射线聚焦的有效手段.     

Intracavity gain gratings

Intracavity gain gratings are theoretically demonstrated to exhibit diffraction efficiencies that are 100 times larger than unity at pump powers substantially below the lasing threshold. Experiments performed using a Nd:YVO4 microlaser pumped below threshold by two interfering Ti:sapphire laser beams are described. Huge enhancement of the diffraction efficiency (5000X) and a large increase of the angular selectivity (10X) are demonstrated despite the angular reduction of the Fabry-Perot cavity finesse. Much better results are expected using gain gratings with larger areas or thinner cavities such as vertical cavity surface-emitting lasers. Such large fan-out values could be very interesting for applications to optical signal processing.     

Theory of the Fabry-Perot interferometer with nonparallel reflectors

Taking into account the wave structure of the light beam, determined by diffraction theory, we consider the harmful effect of the inclination of the mirrors of a Fabry-Perot interferometer when fringes of equal inclination are being observed. It is found that the contrast and resolution of the fringes of equal inclination are reduced as the angle of the wedge so formed is increased, and the interferometer (resonator) completely loses its high-resolution capability (Q-factor) when the mirrors deviate from parallelism by an angle equal to half the diffraction angle at its aperture. The advantages of stopping down both the incoming and outgoing beams in improving the contrast and increasing the resolution of the fringes of equal inclination are pointed out.The author thanks Professor F. A. Korolev for his interest.     

软X射线多层膜光栅的衍射特性

用X射线运动学理论对软X射线多层膜光栅的衍射特性进行了研究。发现其衍射规律与多层膜的布拉格衍射和普通光栅衍射有本质的区别,可将衍射能量集中于某一衍射级上,同时它又保持了多层膜的高反射率和光栅的高分辨本领等优良特性。     

Two-Frequency Brillouin Fiber Laser Based on Bragg Grating Fabry-Perot Cavity

A novel and simple two-frequency Brillouin fiber laser is presented. It is based on a fiber Fabry-Perot cavity with fiber Bragg gratings as reflectors. The model of stimulated Brillouin scattering in fiber grating-based Fabry-Perot resonator is investigated. The laser allows conversion efficiency of close to 100% and suppresses the higher-order Stokes waves. The theoretical prediction is presented and the experimental demonstration is realized.     

Ultra-high efficiency multilayer blazed gratings through deposition kinetic control

Diffraction efficiency of multilayer-coated blazed gratings (MBG) strongly depends on the perfection of the sawtooth-shaped layers in the overall composite structure. Growth of multilayers on sawtooth substrates should be carefully optimized to reduce groove profile distortion and, at the same time, to avoid significant roughening of multilayer interfaces. In this work, we report on a way to optimize growth of sputter-deposited Mo/Si multilayers on sawtooth substrates through variation of the sputtering gas pressure. We believe a new record for diffraction efficiency of 44% was achieved for an optimized MBG with groove density of 5250 lines/mm at the wavelength of 13.1 nm.     

软X射线双频光栅剪切干涉法研究

本文中设计了一种利用软X射线双频光栅作为剪切干涉元件的剪切系统, 使剪切干涉法在软X射线波段得到了应用. 介绍了软X射线双频光栅的结构及衍射特性, 在同步辐射光束线对双频光栅的效率分布进行了测试实验, 两个剪切级次的效率比值高于75%, 干扰级次效率低于5%. 利用软X射线双频光栅为剪切干涉光学元件, 对待测靶进行了静态检测, 得到了对比度高, 稳定的干涉条纹, 验证了该方法在软X射线等离子体密度诊断中的可行性. 关键词： 双频光栅 剪切干涉仪 软X射线 等离子体诊断     

High-dispersive mirror for pulse stretcher in femtosecond fiber laser amplification system

We present a high-dispersive multilayer mirror for pulse stretching in a femtosecond fiber laser amplification system. The designed mirror contains 54 layers with a total physical thickness of 7.3 μm, which can provide a positive group delay dispersion (GDD) of 600 fs² and a high reflectance over 99.9% from 1010 to 1070 nm. The samples were prepared by dual ion beam sputtering. The measured transmittance matches well with the theoretical result. The GDD characteristics of samples were tested by home-made white light interferometer. The measured GDD is higher than the design results, an average GDD of +722 fs² from 1010 nm to 1070 nm. The mirrors were employed in a Yb-doped large-mode-area photonic crystal fiber amplification system. An input pulse compressed by the gratings with autocorrelation function of 83 fs is obtained with a stretched FWHM of 1.29 ps after 28 bounces between the dispersive mirrors. The results show that the multilayer dispersive mirror could be an effective and promising technique for pulse stretching in femtosecond amplification systems.     

Characteristics of light emission from surface plasmons based on rectangular silver gratings

We investigated the characteristics of transmitted light from propagating surface plasmons based on rectangular silver gratings. The results calculated by rigorous coupled-wave analysis presented that silver diffraction gratings can produce significant transmittance and conversion efficiency, comparable to the case of dielectric gratings. Especially, silver gratings optimized at a wide range of grating thickness and period may lead to an improved diffraction efficiency larger than 64%. Moreover, the effect of silver oxide layer on the transmittance was examined and a bimetallic structure with a thin gold coating was introduced to prevent an oxidation of silver substrates. As a practical sensor application, silver grating-based surface plasmon resonance (SPR) configuration showed an enhanced sensitivity associated with an increase of surface reaction area and strong excitations of local plasmon fields, outperforming a conventional thin-film-based SPR structure.     

Interference filters for the millimeter and submillimeter spectral region

The properties of a Fabry-Perot interferometer (FPI) with mirrors in the form of metal gratings are discussed. For obtaining filters for the submillimeter and millimeter spectral region we suggest the use of an interferometer with crossed gratings, each grating being enclosed between dielectric plates. Our studies have shown that the half-width of the transmission band of such a filter amounts to 0.6 mm at =8.4 mm, the transmissivity being 77%.In conclusion, the authors wish to express their gratitude to M. A. Leontovich for valuable discussions and to V. D. Rusanov and V. M. Plekhov for their collaboration in the work.