Single-material inhomogeneous optical filters based on microstructural gradients in plasma-deposited silicon nitride

Transparent hydrogenated amorphous silicon nitride (SiNx:H) coatings were prepared by dual-mode microwave-radio-frequency plasma-enhanced chemical vapor deposition. By controlling the effects of plasma density and ion energy on the film growth, it was possible to modify the microstructure of the coatings and hence the refractive index n. Using this method, we were able to vary n from 1.6 to 2.0, at 550 nm, by adjusting the power levels of the radio-frequency and microwave components while keeping the gas composition (SiH4, N2) and pressure constant. An inhomogeneous bandpass filter with a controlled refractive-index depth profile was fabricated, and its optical performance was compared with that of its multilayer counterpart. Besides the attractive optical features of such single-material rugate filters, we found that the mechanical resistance of inhomogeneous films is superior to that of multilayer systems.     

Rugate filters fabricated by a radio frequency magnetron sputtering system by use of an optical in situ monitoring technique

We propose, for the first time to our knowledge, a new feedback fabrication technique for rugate filters with sinusoidal refractive index distribution. The technique uses an in situ optical monitoring system, in contrast to conventional techniques for rugate filters that are based on time control, which is generally unsuitable for accurate fabrication of a continuous index distribution. We employed a-SiOx:H thin film as the material for the rugate filters because its refractive index can be successively controlled. Using the proposed technique and material, we fabricated near-infrared rugate minus filters having multiple and continuous refractive index distributions. The experimental and calculated spectra were well correlated as a result of applying the proposed feedback fabrication technique.     

Narrow line-width filters based on rugate structure and antireflection coating

Filters that have high transmittance over the passband region of the reflectance spectrum are designed by combining rugate structures and antireflection (AR) coatings. It is found that, under certain conditions, the refractive index of the substrate could be “converted” to the air-side refractive index of the graded-refractive-index coating. A method for the fabrication of graded-index coatings by rapidly alternating deposition of low (SiO₂) and high (Nb₂O₅) refractive index materials is introduced, and this technology was used to fabricate a rugate structure. An AR coating with a refractive index of 1.23 was grown onto the rugate structure by glancing angle deposition technology. Optical measurements of the combined structure show excellent transmittances over the wavelength regions around the reflection band and high reflectances in the stopband.     

Application of constrained optimization to the design of quasi-rugate optical coatings

The constrained optimization approach is applied to the design of quasi-rugate optical coatings. These coatings are defined as multilayers with no thin layers where refractive index profiles resemble rugate-type refractive index profiles and where spectral properties are typical for rugate filters. It is shown that all design problems that are usually solved using rugate filters can be solved successfully in the frame of quasi-rugate optical coatings. Comparison between quasi-rugate and two-component multilayer designs is provided.     

Sequences of exact analytical solutions for plane waves in graded media

We present a new method for building sequences of solvable profiles of the electromagnetic (EM) admittance in lossless isotropic materials with 1D graded permittivity and permeability (in particular profiles of the optical refractive index). These solvable profiles lead to analytical closed-form expressions of the EM fields, for both TE and TM modes. The Property-and-Field Darboux Transformations method, initially developed for heat diffusion modelling, is here transposed to the Maxwell equations in the optical-depth space. Several examples are provided, all stemming from a constant seed potential, which makes them based on elementary functions only. Solvable profiles of increasingly complex shape can be obtained by iterating the process or by assembling highly flexible canonical profiles. Their implementation for modelling optical devices like matching layers, rugate filters, Bragg gratings, chirped mirrors or 1D photonic crystals, offers an exact and cost-effective alternative to the classical approaches.     

Double slit interferometry to measure the EUV refractive indices of solids using high harmonics

Accurate values of the extreme ultraviolet (EUV) optical properties of materials are required to make EUV optics such as filters and multilayer mirrors. The optical properties of aluminum studied in this report are required, in particular, as aluminum is used as an EUV filter material. The complex refractive index of solid aluminum and the imaginary part of the refractive index of solid iron between 17 eV and 39 eV have been measured using EUV harmonics produced from an 800 nm laser focused to 10(14) Wcm(2) in an argon gas jet impinging on a double slit interferometer.     

Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity

We show numerically that the reflectivity of multilayer extreme-UV (EUV) mirrors tuned for the 11-14-nm spectral region, for which the two-component, Mo/Be and Mo/Si multilayer systems with constant layer thickness are commonly used, can be enhanced significantly when we incorporate additional materials within the stack. The reflectivity performance of the quarter-wavelength multilayers can be enhanced further by global optimization procedures with which the layer thicknesses are varied for optimum performance. By incorporating additional materials of differing complex refractive indices-e.g., Rh, Ru, Sr, Pd, and RbCl-in various regions of the stack, we observed peak reflectivity enhancements of as much as ~5% for a single reflector compared with standard unoptimized stacks. We show that, in an EUV optical system with nine near-normal-incidence mirror surfaces, the optical throughput may be increased by a factor as great as 2. We also show that protective capping layers, in addition to protecting the mirrors from environmental attack, may serve to improve the reflectivity characteristics.     

Admittance of rugate filters derived from a 2 × 2 inhomogeneous matrix

Admittance diagrams are used to analyze qualitatively and quantitatively the behavior of inhomogeneous thin films with an arbitrary refractive-index function. From this study it follows that one can treat the behavior of rugate filters by using the concept of effective refractive indices, which are associated with the phase integral in a simple way. These results are applied to the study of periodic systems, and, as expected, one can consider high and low effective refractive indices to determine the important parameters of these stop bands. With these ideas it is possible that one can deal with rugate filters more closely as homogeneous periodic systems by taking advantage of the existing theory.     

Multilayer reflectors with absent higher-order reflectance bands

Explicit equations are presented for the refractive indices of all-dielectric multilayers that reflect at a longer wavelength and transmit over a broad range of shorter wavelengths. Equations are given for the refractive indices of the layers of a simulated rugate reflector.     

基于Rugate理论的负滤光片设计研究

研究基于Rugate理论设计负滤光片。分析了折射率剖面函数各参数对光谱性能影响,提出了基于Rugate理论负滤光片设计方法,并给出了两组基于Rugate负滤光片设计的实例。研究表明,折射率峰-峰幅值、光学厚度、中心波长分别决定负滤光片反射带宽度、截止深度和位置。     

Extended-bandwidth reflector designs by using wavelets

Optical interference coatings have been designed by using combinations of wavelets (fully apodized sine-wave refractive index groups). Like a single-line rugate filter, a single wavelet produces a stop band without harmonics and, in addition, has no sidelobes. The rules for combining wavelet refractive index structures have been derived for extended-bandwidth reflectors.     

Multi-encoded rugate porous silicon as nerve agents sensors

The nanostructured rugate porous silicons (PSi) containing multiple photonic band gaps have been generated by an electrochemical etching through applying a composite waveform summed three computer-generated pseudo-sinusoidal current waveforms. They exhibit three sharp photonic band gaps in the optical reflectivity spectrum, corresponding to the each of the sine components varied from 0.42, 0.36, and 0.30 Hz, with a spacing of 0.06 Hz between each sine component. The sensing experiments using multi-encoded rugate PSi for the detection of nerve agents such as triethyl phosphate (TEP), diethyl chlorophosphate (DCP), dimethyl methylphosphonate (DMMP), and diethyl ethylphosphonate (DEEP) have been achieved. Capillary condensation in the pores causes the reflectivity of rugate PSi to shift to longer wavelengths due to an increase in refractive indices of the porous medium.     

Sol–gel derived photonic bandgap coatings for solar control

Sol–gel derived photonic bandgap films have been investigated as possible multilayer coatings for solar control glass applications. Multilayer Bragg mirrors, in particular, have been modelled by the Transfer Matrix method, designed to have either near-UV or near-IR reflectivity, but visible transparency, based on alternating aluminosilicate glass/titania quarter-wave stacks. Such composite multilayer structures have been deposited by sol–gel processing on selected glasses and other types of substrates and their optical characteristics have been measured by optical absorption and reflection spectroscopies, as well as spectroscopic ellipsometry to determine the single layer refractive index and thickness. The UV–visible-IR absorption and reflection characteristics of these multilayer coatings revealed solar control properties, due to the presence of peaks near ∼350–400 nm and ∼900–1000 nm, with reflectivities of the order of 70%, which appear promising for solar control application.     

Theoretical and experimental studies of broadband phase-controlled attosecond mirrors

We present procedures to develop and characterise chirped multilayer mirrors for attosecond pulses. The design procedure involves a simulated annealing optimisation algorithm to obtain a multilayer structure with the desired performances. The characterisation step requires the use of well-calibrated attosecond and synchrotron beam lines, allowing one to measure the amplitude and phase response of the mirror. We illustrate these approaches with a set of mirrors designed to have zero or negative dispersion. The remarkable agreement between theoretical and experimental performances validates this overall process, and demonstrates the capability of such mirrors to control the temporal profile of attosecond pulses. These tools and techniques for developing attosecond chirped mirrors will facilitate the generalisation of such components on attosecond experiments.     

Measurements of the refractive index of yttrium in the 50-1300-eV energy region

The first experimental results to our knowledge on the refractive index n = 1 - delta + ibeta of yttrium in the extreme-ultraviolet and soft x-ray energy ranges are discussed. To determine the absorptive part beta, transmittance measurements were performed on pure yttrium films in the 50-1300-eV energy region at beamline 6.3.2 of the Advanced Light Source. The dispersive part delta was then calculated from the absorption results by means of the Kramers-Kronig transformation. Compared with prior tabulated values, the new wet of data for the refractive index of yttrium is in better agreement with the sum rules and contains previously unresolved fine structure information in the regions of the M2,3 and M4,5 absorption edges, where yttrium-based multilayer mirrors operate.     

Optical devices from porous silicon having continuously varying refractive index

We shall discuss two types of optical devices made using porous silicon, in which the refractive index distribution is continuous. In the rugate filter, the refractive index profiles is sinusoidal along the growth axis, while in the graded refractive index lenses that we fabricated from PSi, the refractive index is quadratic in the plane of the porous layer. We shall talk about the design and fabrication methods used to manufacture both of these device types, and show examples for each.     

Chromium-scandium multilayer mirrors for the nitrogen K(alpha) line in the water window region

Chromium-scandium (Cr-Sc) is a promising material combination for multilayer mirrors in the water window region. A possible x-ray source for laboratory use in this wavelength range is the nitrogen K(alpha) line at 3.16 nm. High reflectivities at this wavelength can be achieved with Cr-Sc multilayer mirrors if the interfaces between adjacent layers are smooth. The growth parameters of the magnetron sputtering process for these materials have been optimized. It is shown that the reflectivity of such mirrors can be considerably improved by the application of a proper bias voltage during film growth. The high quality of the multilayer films is demonstrated with copper K(alpha) x-ray reflection and transmission electron microscopy. The reflective properties of the multilayers close to the nitrogen K(alpha) line were measured with synchrotron radiation for different angles of incidence. Reflectivities between R = 5.9% for near-normal incidence (theta = 1.5 degrees) and R = 29.6% for theta = 59.9 degrees were measured.     

Rugate filter made with composite thin films by ion-beam sputtering

Composite films of Ta-Si oxide with refractive indices that varied from 1.48 to 2.15 were realized by using rf ion-beam sputtering. All the composite films were amorphous and had a surface roughness of less than 0.3 nm. The inhomogeneity of the composite was discussed, and a rugate filter was designed and fabricated by automatic computer control.     

Wolter type I x-ray focusing mirror using multilayer coatings

A multilayer coating is a useful addition to a mirror in the x-ray region and has been applied to normal incidence mirrors used with soft x rays. When a multilayer coating is used on grazing incidence optics, higher performance can be achieved than without it. Cr/Sc multilayers coated on a Wolter type I mirror substrate for a soft x-ray microscope are considered. The reflectivity and effective solid angle are calculated for Wolter type I mirrors with uniform and laterally graded multilayer coatings. The laterally graded multilayer mirror showed superior x-ray performance, and the multilayer tolerances were relaxed. This multilayer mirror could be especially useful in the soft x-ray microscope intended for biological applications.     

PECVD方法用于梯度薄膜材料的研究

本文研究了ＰＥＣＶＤ方法制备Ｓｉ－Ｏ－Ｍ系梯度薄膜材料，并运用计算机控制技术成功地制备了涂层折射率随膜深成正弦波形式连续变化的Ｒｕｇａｔｅ单通带滤波器样品。结果表明，采用ＰＥＣＶＤ方法可以制备性能上乘、结构复杂的梯度薄膜材料，ＰＥＣＶＤ方法在研究、开发高级光学涂层领域有着宽广的应用前景。