Design of antireflection gratings with approximate and rigorous methods

High-spatial-frequency gratings can be used as an alternative to thin-film antireflection coatings to reduce the reflectivity at the boundary between two different media. In the case of one-dimensional gratings, the conditions on the grating structure can be approximately determined by the effective medium theory (EMT) in combination with the thin-film theory. For two-dimensional gratings, which can be used to reduce the polarization sensitivity, a corresponding EMT does not exist. We present an estimation of the effective permittivity of two-dimensional gratings. The range of validity of the antireflection grating design by the EMT is determined by the use of rigorous electromagnetic theory. Beyond the validity of EMT, rigorous theory is used to design antireflection gratings with a maximized feature size.     

Design and fabrication of a novel reflection filter

Reflection filters are useful in optical communication, display, and other systems. A novel reflection filter is designed and fabricated. Analytical design formulas have been put forward and show good agreement with the measured maximum reflectance as well as with the bandwidth at the central wavelength. The effective admittance and distribution of the electrical field intensity are also calculated to analyze the properties of the filter. This novel filter with high peak reflectance, narrow bandwidth, and deep cutoff, is simple to design, easy to fabricate and convenient to integrate, compared with the conventional dielectric multilayer reflection filters.     

Infrared filters and coatings for the High Resolution Dynamics Limb Sounder (6-18 microm)

We describe the spectral design and manufacture of the narrow-bandpass filters and 6-18-mum broadband antireflection coatings for the 21-channel High Resolution Dynamics Limb Sounder. A method of combining the measured spectral characteristics of each filter and antireflection coating, together with the spectral response of the other optical elements in the instrument, to obtain a predicted system throughput response is presented. The design methods that are used to define the filter and coating spectral requirements, choice of filter materials, multilayer designs, and deposition techniques are discussed.     

Multiline two-dimensional guided-mode resonant filters

A novel multiline filter using a two-dimensional guided-mode resonant (GMR) filter is proposed. The filter concept utilizes the multiple planes of diffraction produced by the two-dimensional grating. Multiple resonances are obtained by matching the guided modes in the different planes of diffraction to different wavelengths. It is shown that the location and the separation between resonances can be specifically controlled by modifying the periodicity of the grating and the other physical dimensions of the structure. This is in contrast to the one-dimensional GMR filters where the location of the resonances is material dependent. Two-line reflection filter designs with spectral linewidths less than 1 nm and a controllable spectral separation of up to 23% of the short resonance wavelength are presented using rectangular-grid grating GMR structures. Three-line filters are designed in hexagonal-grid grating GMR structures with two independently controllable resonance locations.     

Metal/dielectric transmission interference filters with low reflectance. 1. Design

For many applications the high reflectance of conventional multilayer interference filters is undesirable. It is possible to design and construct interference filters in which the transmittance and reflectance are independently controlled and in which the reflectance is very low. However, to do this it is necessary to employ absorbing coating materials and, as a result, a reduction in the peak transmittance must be accepted. We describe three different methods for the design of such coatings. Examples are given of a number of bandpass filters, neutral density filters, cutoff filters, and of an xˉ(λ) tristimulus filter, all having a low reflectance. This reflectance is frequently 15 to 50 times lower than that of conventional filters.     

Multilayer waveguide-grating filters

The properties of guided-mode resonance reflection filters constructed with multiple thin-film layers are addressed. Greatly improved filter characteristics are shown to follow by the incorporation of multiple homogeneous layers with the spatially modulated layer. Calculated results for single-layer, double-layer, and triple-layer filter structures are presented. Whereas good filter characteristics are obtainable with single layers that are half-resonance-wavelength thick, there remains a residual reflection in the sidebands unless the cover and the substrate permittivities are equal. With double-layer and triple-layer designs, extensive wavelength ranges with low sideband-reflectance values are shown to be possible without requiring equal cover and substrate permittivities. The antireflection properties of the layer stack can be understood if the modulated layer is modeled as a homogeneous layer characterized by its average relative permittivity. However, as the grating-modulation index increases, this approximation deteriorates. In particular it is found that, for a given high modulation index, the double-layer antireflection thin-film approximation fails, whereas for the same modulation in a triple-layer system it holds firmly. Multilayer designs can thus have significantly large filter passbands, as they may contain heavily modulated resonant gratings without corruption of the ideal filter characteristics.     

Parametric optimization of narrow bandstop optical filters using the self-suspended subwavelength grating for TE polarization

Instead of a conventional fixed multilayer grating, a self-suspended subwavelength grating (SSG) which consists of a single grating layer and possesses tunable functions, is investigated by the rigorous coupled-wave method in detail. Through optimizing various parameters including the incident wavelength, the grating period, the grating thickness and the grating filling factor, we demonstrate that the silicon dioxide (SiO₂) SSG owns a narrow reflectance linewidth in the case of TE polarization. For the SiO₂ SSG, the reflectance peak splits into two branches when the incident light deviates from normal incidence. In addition, the reflectance property of the SiO₂ SSG with unoptimized parameters is also presented for comparison, which exhibits a much larger reflectance linewidth. It is expected that the SiO₂ SSG should be used as narrow bandstop optical filters for TE polarization in micro optics systems.     

Low sideband guided-mode resonant filter

A guided-mode resonant filter with low sideband reflections is proposed. It is shown that, for serious reduction of out-of band reflectance, the combination of waveguide-grating filter design with conventional antireflective stack design methods is not adequate. To achieve symmetrical low sideband reflectances, independent control of various layer thicknesses is necessary. At a given illumination angle with appropriate control of the waveguide thickness, a specific resonant grating filter is designed whose out-of-band reflectance on both sides of the resonant peak is well below 10(-4). Even 50 nm away from the peak, on both sides, the out-of-band reflectance remains below 10(-3). Analysis of the variation in the main manufacturing parameters indicates that such filters can be reliably produced with present-day technologies.     

Nonpolarizing guided-mode resonant grating filter for oblique incidence

A new type of guided-mode resonant grating filter is described. The filter is independent of polarization state for oblique incidence. The filter has a crossed grating structure, and the plane of incidence on the filter contains the symmetric axis of the grating structure. Theoretical considerations and numerical calculations using two-dimensional rigorous coupled-wave analysis show that a rhombic lattice structure is suitable to such filters. In this configuration an incident light wave is diffracted into the waveguide and is divided into two propagation modes whose directions are symmetric with respect to the plane of incidence. In particular, when the propagation directions of the two modes are perpendicular to each other, the fill factor of grating structure can be approximately 50%. The filter was designed for an incident angle of 45 degrees. Tolerances of setting errors and fabrication errors for this filter were estimated by numerical calculations.     

Application of microwave technology to design an optical multilayer bandpass filter

The principles of microwave bandpass filter design are applied to design optical multilayer bandpass filters. The examples include several bandpass filters for wavelength division multiplexing.     

Design of a robust thin-film interference filter for erbium-doped fiber amplifier gain equalization

Gain-flattening filters (GFFs) are key wavelength division multiplexing components in fiber-optics telecommunications. Challenging issues in the design of thin-film GFFs were recently the subject of a contest organized at the 2001 Conference on Optical Interference Coatings. The interest and main difficulty of the proposed problem was to minimize the sensitivity of a GFF to simulated fabrication errors. A high-yield solution and its design philosophy are described. The approach used to control the filter robustness is explained and illustrated by numerical results.     

Holographic interference filters for infrared communications

We demonstrate that high-quality interference filters for the wavelength range 1300-1600 nm can be holographically fabricated in DuPont HRF-800X001 photopolymer material by use of visible laser illumination. We also summarize a chain-matrix technique, which we call thin-film decomposition, that is useful for modeling multilayer films with an arbitrary index profile n(z). We use the thin-film-decomposition technique to create design curves that allow one to choose the proper exposure angle and film thickness with which to fabricate a holographic interference filter with a desired transmission efficiency and bandwidth at a particular wavelength. These curves are of general utility and are not confined to any particular holographic recording medium. Excellent agreement between theory and experiment is found.     

Efficiency and long-term stability of a multilayer-coated, ion-etched blazed holographic grating in the 125-133-Å wavelength region

The efficiency of an ion-etched blazed holographic grating was measured by the use of synchrotron radiation in the 125-133-? wavelength range and at near-normal incidence. The grating had a Mo-Si multilayer interference coating that resulted in a peak normal-incidence efficiency of 13% in the second grating order and at a wavelength of 128 ?. This is the highest efficiency obtained to date from a multilayer-coated grating in this wavelength region and at normal incidence. These measurements are compared with similar measurements performed on the same grating 4.5 years later. Over this time the peak grating efficiency decreased from 13% to 8%, and this result is attributed to the decrease in the reflectance of the multilayer coating from 55% to 42%. Oxidation and contamination of the multilayer with carbon appear to be the causes of these losses. The groove efficiency of the grating substrate in the second order is 23%.     

Optimized optical design of thin-film transistor arrays for high transmittance and excellent chromaticity

Transmittance and chromaticity are essential requirements for optical performance of thin-film transistor (TFT) arrays. However, it is still a challenge to get high transmittance and excellent chromaticity at the same time. In this paper, optimized optical design by using antireflection film theory and optical phase modulation is demonstrated in low temperature poly-silicon (LTPS) TFT arrays. To realize high transmittance, the refractive index difference of adjacent films is modified by using silicon oxynitride (SiO_xN_y) with adjustable refractive index. To realize excellent chromaticity, the thicknesses of multilayer films are precisely regulated for antireflection of certain wavelength light. The results show that the transmittance and chromaticity have been improved by about 6% and 18‰, respectively, at the same time, which is a big step forward for high optical performance of TFT arrays. The device characteristics of the TFT arrays with the optimal design, such as threshold voltage and electron mobility, are comparable to those of conventional TFT arrays. The optimized optical design results in enhanced power-conversion efficiencies and perfects the multilayer film design on the basic theory, which has great practicability to be applied in TFT arrays.     

Grazing-incidence efficiencies in the 28-42-A wavelength region of replicas of the Skylab 3600-line/mm concave grating with multilayer and gold coatings

The efficiencies of replicas of the Skylab 3600-line/mm concave grating with multilayer and gold coatings were measured by using synchrotron radiation at an angle of incidence of 79 degrees and in the 28-42-A wavelength range. The blaze angle of the grating facets that faced the incident radiation was 3.1 degrees , and the average angle of the opposite facets was 6 degrees . For the gold grating, the -1 outside order had the highest efficiency of any diffracted order (excluding the zero order) over the entire wavelength range. Calculations of the grating efficiency indicated that the high efficiency in the -1 order resulted from the rather small angle (6 degrees ) of the facets opposite the incident radiation. For the multilayer grating, the efficiency in the on-blaze +2 inside order was enhanced in the 30-34-A wavelength region as a result of the high reflectance of the multilayer coating. The maximum efficiency in the +2 order occurred at the wavelength (32 A) corresponding to the peak of the reflectance of the multilayer coating on the facets facing the incident radiation. These results further demonstrate that a multilayer coating can be used to enhance the efficiency, in a selected wavelength range and in the on-blaze order, of a grating operating at a small grazing angle (11 degrees ).     

Polarization filters with an autocloned symmetric structure

The process of fabricating photonic crystals comprised of alternately stacked high- and low-index dielectric materials on periodic substrates to form zigzag films is called the autocloning technique. In this study, we have fabricated TiO2/SiO2 two-dimensional polarization filters by using electron beam gun evaporation with ion-beam-assisted deposition. The shape of the zigzag structure is preserved, and the total thickness is 8?μm. The symmetric structural design can be utilized as an antireflection coating applied to reduce ripples and achieve a 200?nm working wavelength range.     

Theoretical study of amplitude and phase filtering of guided waves

The design of integrated optics filters by use of refinement software based on the Abelès thin-film computation method and the film mode matching method is studied. The results obtained with the two computation methods are compared. Good agreement is obtained provided that the fill factor of the guided mode in the component is high and that modal losses between waveguide sections are simulated by absorption with the Abelès computation method. Integrated optics devices that manage either the amplitude of guided waves such as a dense wavelength division multiplexing narrow-bandpass filter and a gain-flattening filter or the phase of guided waves such as a broadband dispersion compensator are     

Guided-mode resonant grating filter with an antireflection structured surface

We describe a new structure of guided-mode resonant grating (GMRG) filters with low sideband reflectance. This GMRG filter consists of a high-index thin film on an antireflective structured surface called "moth-eye structure." Since the high-index film undulates along the surface structure, the film acts as a modulated optical waveguide. An incident light wave satisfying a resonant condition is reflected by the GMRG filter, and nonresonant light waves pass through the filter. This GMRG filter is valid for reducing reflection of nonresonant light waves in a wide spectral range. The resonant reflection of this new filter was investigated by numerical calculation based on an electromagnetic grating analysis. In the case of a triangular antireflective surface structure whose thickness is 2x greater than its period, the sideband reflectance for nonresonant light waves was lower than 0.5% for TM-polarized light in a wide range of wavelengths.     

Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-A wavelength region

We characterized a laminar grating with a Mo/Si multilayer coating by using synchrotron radiation and atomic force microscopy. The grating substrate had 2400 grooves/mm, 40-A groove depth, and 2080-A groove width. The microroughness of the grating substrate was 5 A rms. The multilayer coating was optimized to have peak normal-incidence reflectance at a wavelength near 150 A. For an angle of incidence of 10 degrees the peak grating efficiency was 16.3% in the +1 order and 15.0% in the -1 order. The efficiency in the zero order was lower by a factor of 40 owing to the excellent matching of the groove depth and groove width to the wavelength of the incident radiation. By dividing the grating efficiencies by the measured reflectance of the multilayer coating, we obtained inferred groove efficiencies of 34% and 32% in the +1 and -1 orders, respectively.