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.     

Residual stress in Ta2O5-SiO2 composite thin-film rugate filters prepared by radio frequency ion-beam sputtering

Ta-Si oxide composite thin-film rugate filters were prepared by radio frequency ion-beam sputtering and their residual stress and substrate deflections were measured. The residual stress and substrate deflection of these composite film rugate filters were less than that of notch filters made from a series of discrete quarter-wave layers with alternate high and low indices because of the smooth modulation of composition and no interface structure of the rugate filter.     

Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering

Methods for the manufacture of rugate filters by the ion-beam-sputtering process are presented. The first approach gives an example of a digitized version of a continuous-layer notch filter. This method allows the comparison of the basic theory of interference coatings containing thin layers with practical results. For the other methods, a movable zone target is employed to fabricate graded and gradual rugate filters. The examples demonstrate the potential of broadband optical monitoring in conjunction with the ion-beam-sputtering process. First-characterization results indicate that these types of filter may exhibit higher laser-induced damage-threshold values than those of classical filters.     

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.     

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.     

Reflection from a semi-infinite rugate filter

A theoretical approach was applied to compute the reflectance spectrums of semi-infinite rugate filters with a sinusoidal refractive-index profile. Regardless of the linear polarization state of the incident plane wave, the reflectance spectrum of a sufficiently thick rugate filter contains a top-hat feature – indicative of the Bragg regime – with ripples on both flanks. The corresponding reflectance spectrum of a semi-infinite rugate filter also contains the top-hat feature, but is devoid of ripples.     

Flat-topped broadband rugate filters

A method of creating rugate interference filters that have flat-topped reflectance across an extended spectral region is presented. The method applies known relations from the classical coupled wave theory to develop a set of equations that gives the spatial frequency distribution of rugate cycles to achieve constant reflectance across a given spectral region. Two examples of the application of this method are discussed: a highly reflective coating for eye protection against harmful laser radiation incident from normal to 45 degrees , and a spectral beam splitter for efficient solar power conversion.     

Porous silicon-based rugate filters

We report an experimental study of porous silicon-based rugate filters. We performed filter apodization, following a half-apodization approach, which successfully attenuated the sidelobes at both sides of the photonic stop band. We achieved successful reduction of interference ripples through the insertion of index-matching layers on the first and last interfaces. An apodized dielectric mirror and a rugate filter are compared: Appreciable differences in the harmonic presence and stop-band performance were observed and are commented on. Bandwidth control when index contrast is modified is also demonstrated. Finally, the possibility of combining different rugate filter designs to attain more complex responses is demonstrated by the achievement of a multi-stop-band filter. Numerical calculations for design optimization and comparison with experimental data are reported too.     

Design and plasma deposition of dispersion-corrected multiband rugate filters

Inverse Fourier transform method has been commonly used for designing complex inhomogeneous optical coatings. Since it assumes dispersion-free optical constants, introducing real optical materials induces shifts in the position of reflectance bands in multiband inhomogeneous minus (rugate) filters. We propose a simple method for considering optical dispersion in the synthesis of multiband rugate filter designs. Model filters designed with this method were fabricated on glass and polycarbonate substrates by plasma-enhanced chemical vapor deposition of silicon oxynitrides and SiO2/TiO2 mixtures with precisely controlled composition gradients.     

Correlation of sidelobe suppression between rugate filters and multilayer mirrors

We present the study of the correlation between refractive index profiles and the optical response of rugate filters and multilayer mirrors. The conventionally used method in multilayer mirrors for ripple suppression in the passband will be compared with a similar simple method to remove the rugate filter sidelobes without apodization. The resulting layers are compared in performance with a typical quintic matching layer. An example based on silicon oxynitride alloys with refractive indices ranging between 1.47 and 1.83 was designed and deposited.     

Hybrid approach for rugate filter design

Fourier techniques and direct optimization are applied to the synthesis of complex rugate filters. A hybrid approach is presented. The design strategies are illustrated numerically for different spectral shapes.     

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。     

Admittance diagrams of accidental and premeditated optical inhomogeneities in coatings

Intuitive interpretation of the effect of inhomogeneous layers in optical coatings is often difficult. I use admittance diagrams to interpret some properties of accidental and premeditated optical inhomogeneities. The effect of accidental homogeneous and inhomogeneous transition layers on the spectral properties of a single film is presented. I show that such layers affect the envelope of the reflectance spectra of thick films, effects that are extended to the shorter wavelength range. Using the same approach, I evaluate the properties and limitations of quintic antireflection coatings and show that the suppression of harmonics in rugate filters is due to an absentee-layer phenomenon and not solely to an antireflection effect as is often suggested.     

New optimization algorithm for the synthesis of rugate optical coatings

A model of a rugate coating that takes into account production potentialities of the Leybold Syrus Pro 1100 deposition system is presented. An efficient algorithm for the synthesis of rugate coatings is proposed. Numerical results are also presented.     

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.     

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.     

Sputter deposition of silicon oxynitride gradient and multilayer coatings

The optical properties of silicon oxynitride films deposited by reactive dc magnetron sputtered films have been investigated. In particular the absorption characteristics of silicon nitride thin films in the visible spectrum and their optical bandgap were analyzed with regard to their composition and deposition properties. It can be shown that there is a significant difference between the absorption in the visible spectrum and the optical bandgap for these layers. The influence of unipolar and bipolar pulse modes on the optical layer properties is presented. The extinction coefficient for silicon nitride single layers could be reduced to a value of 2 x 10(-4) at 500 nm without external heating. There is also the dependence of the absorption of silicon oxynitride layers on the discharge voltage. We present the resulting spectra of rugate and edge filters that consist of these layers and offer lower absorption than single layers.     

Optimum phase for rugate filter synthesis by Fourier transforms

An optimum phase is developed for the synthesis of rugate reflectors by a simple Fourier transform. This phase belongs to a complex function of the desired spectral characteristics and is usually a free parameter. In general, it receives much less attention than the function magnitude, which is not known exactly. The current work shows that phase shaping alone produces surprisingly good results and has other advantages in rugate filter synthesis. In addition, the operating mode of this design procedure is quite unusual and interesting in itself.     

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.     

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.