Dichroic rugate filters

We reduce the sidelobes that are present in the bandpass zones of rugate filters, using antireflection coatings to design dichroic rugate filters. Our designs are based on the formalism of equivalent systems that allow us to consider a rugate filter a simple equivalent layer with equivalent optical admittance and equivalent phase thickness functions. Rugate filters with apodization were considered.     

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.     

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.     

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.     

Band filters: two-material technology versus rugate

We demonstrate theoretically and experimentally a band filter with two reflection and broadband transmission ranges, which was obtained with standard two-material technology. The fabricated filter has transmission and reflectivity characteristics better than those achievable with rugate technology.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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。     

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.     

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.     

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.     

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.     

Coupled Tamm waves guided by an isotropic and homogeneous dielectric layer in a rugate filter

The propagation of Tamm waves (also known as Bloch surface waves) guided by a layer of homogeneous dielectric material in a rugate filter was studied theoretically. A canonical boundary-value problem was set up and a dispersion equation was obtained. The solution of the dispersion equation indicated the existence of coupled modes of Tamm waves that were absent when the homogeneous dielectric material was taken to occupy a half space. The spatial profiles of the electric and magnetic fields of Tamm waves showed that Tamm waves propagate localized to either one or both interfaces. Multiple Tamm waves may lead to multi-analyte chemical sensors and multi-channel communication.