Multilayer Optics Research Articles

The Language of Einstein Spoken by Optical Instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.

Optical characterization of a dual-frequency hybrid aligned nematic liquid crystal cell

The dielectric anisotropy of a highly dispersive dual-frequency nematic liquid crystal (MDA-00-3969 (Merck KGa)) has been determined using the optical fully-leaky guided-mode technique. A 4Vrms sinusoidal voltage was applied across a 5microm hybrid aligned nematic (HAN) cell at various frequencies in both the positive and negative dielectric anisotropy regime. Optical data was collected at each frequency enabling the director profile in each case to be determined using a multi-layer optics model in combination with a liquid crystal free-energy minimization routine. The thresholdless response of the HAN cell combined with the extreme sensitivity of the optical characterization technique has allowed subtle changes in dielectric permittivity with frequency to be observed. The resulting measured dispersion shows excellent agreement with a single Debye-type relaxation model.

405 窓ガラス用太陽エネルギー制御多層膜の最適設計 : 複数の入射角に対する多層膜構造に関する検討(太陽熱利用,環境保全型エネルギー技術)

Optical multilayer coatings are able to control the solar energy by means of the multiple interference of light. In this paper, the optimum structure of the multilayer coatings is designed to achieve the target spectrum characteristic for using window pane both as summer season and winter season. Three cases of the structure of the window pane with a certain number of thin film layers - in case of the films are coated on the front side, the both sides or the back side are examined. The plural incident angles of sunlight is considered. The results of optimum design results and comparing the three cases in some patterns are shown.

Focus on Laboratory Equipment

Focus on Laboratory Equipment

Interference effects in Pancharatnam wave plates

The effects of multiple-beam interference within a series of wave plates whose principal axes are rotated with respect to each other are explored. This is done by expanding the formulation of the matrix algebra which was originally developed for multilayer thin-film optics. As an important example, the new method has been applied to a Pancharatnam configuration for achromatic and superachromatic half-wave plates. It is demonstrated that spectral fringes occur in all of the descriptive polarimetric parameters of these devices, i.e., the transmittance, polarizance, phase delay and effective principal axis. Depending on the wavelength resolution and accuracy of any subsequent measurements, any of these spectral fringes may be deleterious to the intended application of such compound wave plates. Removing the effects of the fringes in data reductions requires extreme care in establishing appropriate calibration experiments.

Porous silicon optical devices for sensing applications

Porous silicon (PS) has a great potential in a wide range of fields due to its tuneable effective refractive index, which can be tailored through the precise control of the formation parameters. In particular, high/low porosity layer stacks result in optical multilayer interference filters, such as Bragg reflectors and optical microcavities. In addition, due to its large internal surface, the optical properties of porous silicon are highly sensitive to the environmental conditions. Hence, a change in these conditions results in a shift of the optical spectrum of the PS multilayer structures. In the present work, the optical behavior of PS mirrors is studied, revealing good performance in the visible wavelength range, and showing a great sensitivity to different liquids infiltrated into the porous structure. Furthermore, optical microcavities are also demonstrated to filter the photoluminescence emission of porous silicon, narrowing its spectral width and resulting in highly chromatical light emitting devices. These devices, along with the immobilization of biomolecules on the PS surface, will allow the development of low cost, high sensitivity optical biosensors.

D-17 Recent Developments of Multilayer Optics for X-ray Diffractometry

D-17 Recent Developments of Multilayer Optics for X-ray Diffractometry

D-112 Quantitative Evaluation of Graded Parabolic Multilayer Optics—Invited

D-112 Quantitative Evaluation of Graded Parabolic Multilayer Optics—<i>Invited</i>

Lorentz group in classical ray optics

It has been almost 100 years since Einstein formulated his special theory of relativity in 1905. He showed that the basic space–time symmetry is dictated by the Lorentz group. It is shown that this group of Lorentz transformations is not only applicable to special relativity, but also constitutes the scientific language for optical sciences. It is noted that coherent and squeezed states of light are representations of the Lorentz group. The Lorentz group is also the basic underlying language for classical ray optics, including polarization optics, interferometers, the Poincar´ es phere, one-lens optics, multi-lens optics, laser cavities, as well multilayer optics.

Fast and accurate boundary variation method for multilayered diffraction optics.

A boundary variation method for the forward modeling of multilayered diffraction optics is presented. The approach permits fast and high-order accurate modeling of periodic transmission optics consisting of an arbitrary number of materials and interfaces of general shape subject to plane-wave illumination or, by solving a sequence of problems, illumination by beams. The key elements of the algorithm are discussed, as are details of an efficient implementation. Numerous comparisons with exact solutions and highly accurate direct solutions confirm the accuracy, the versatility, and the efficiency of the proposed method.

Small Angle X-Ray Scattering with Cobalt Radiation for Nanostructure Characterization of Fe-Based Specimen

A laboratory system (NanoSTAR) based on a combination of specially designed X-ray multilayer optics (Göbel Mirrors) with optical bench, pinhole collimators, sample changer and primary beam stop as well as a two dimensional multiwire detector (HI-STAR) was equipped with a sealed cobalt X-ray tube. This solution was chosen because the CoKα has a wavelength close to that of copper but allows to overcome the problem of excessive fluorescence in Fe-samples. Various measurements were performed using this configuration of the NanoSTAR to demonstrate the performance of SAXS using cobalt radiation. A comparison is given to the primary beam intensity of the NanoSTAR with Co radiation with respect to the Cu radiation. Examples for the use of the Co radiation are given by investigating the coarsening behavior of precipitates in several Fe-based alloys. The change in size and shape of these precipitates under different heat treatment conditions are characterized.

Performance Stability of Microfocusing Source and Multilayer Optics Based X-Ray Diffraction System

X-ray diffraction systems based on a microfocusing X-ray source and multilayer side-by-side optics are suitable for X-ray diffraction studies in a variety of fields, such as protein crystallography, due to their compactness and low cost in maintenance. However, new problems can occur, such as intensity instability induced by source position drifting. Various investigations for the reasons and the consequences of the instability are presented in this paper. Feasible solutions and suggestions are given to obtain more stable system performance.

Applicability of a cut-off reflector for grazing incidence X-ray fluorescence analysis

The applicability of a cut-off reflector, instead of the commonly used multilayer reflector, for grazing incidence X-ray fluorescence (GI-XRF) analysis is demonstrated. Owing to the precise angular adjustment possible in the total reflection X-ray fluorescence (TXRF) spectrometer developed in house, it is possible to adjust the cut-off reflector so as to pass all X-ray energies up to Cu-K α, eliminating Cu-K β and higher X-ray energies emitted from a Cu target X-ray generator. The advantage of this technique is that one gets a higher flux of Cu-K α radiation (>98%) compared to 80–90% from a good quality multilayer optics. Moreover, the same cut-off reflector, used at different grazing angles, serves the purpose for different primary beam energies. The suitability of such an arrangement for GI-XRF analysis for surface characterization has been demonstrated by analyzing a 50 ng aqueous residue of Fe on top of a float glass substrate. The GI-XRF results thus obtained are compared with those obtained using a multilayer monochromator in the primary beam as well as with theoretical calculations.

Hyperbolic reflections as fundamental building blocks for multilayer optics.

We re-elaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to separate multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.

Slide-rule-like property of Wigner's little groups and cyclic S matrices for multilayer optics.

It is noted that 2x2 "S" matrices in multilayer optics can be represented by the Sp(2) group whose algebraic property is the same as the group of Lorentz transformations applicable to two spacelike and one timelike dimensions. It is also noted that Wigner's little groups have a slide-rule-like property that allows us to perform multiplications by additions. It is shown that these two mathematical properties lead to a cyclic representation of the S matrix for multilayer optics, as in the case of ABCD matrices for laser cavities. It is therefore possible to write the N-layer S matrix as a multiplication of the N single-layer S matrices resulting in the same mathematical expression with one of the parameters multiplied by N. In addition, it is noted, as in the case of lens optics, that multilayer optics can serve as an analog computer for the contraction of Wigner's little groups for internal space-time symmetries of relativistic particles.

Ion-beam etching for the precise manufacture of optical coatings.

We propose using ion-beam etching as an additional tool for the accurate control of the thickness of thin films during the manufacture of sensitive optical multilayer coatings. We use a dual ion-beam sputtering system in the deposition and etch modes. In the deposition mode both the assist and sputtering ion beams are used to produce dense films at deposition rates in the range of 0.1-0.3 nm/s. In the etch mode, only the assist ion beam is used to remove material at a rate of less than 0.1 nm/s. A very high precision in the layer thicknesses can be obtained by alternating between deposition and etch modes. We observed that etching did not significantly affect the surface quality and the uniformity of the coatings. We introduced etching into our current manufacturing process and demonstrated its potential for the fabrication of several optical multilayer systems with performances that are very sensitive to the thickness of their layers.

D052 Evaluation of XRPD Data from Reflection and Transmission Geometry Instruments with Multilayer and Crystal Optics Employing Point and Position-Sensitive Detectors

D052 Evaluation of XRPD Data from Reflection and Transmission Geometry Instruments with Multilayer and Crystal Optics Employing Point and Position-Sensitive Detectors

D032 Microfocusing Source and Multilayer Optics Based SAXS Camera

D032 Microfocusing Source and Multilayer Optics Based SAXS Camera

Effect of substrate roughness on Mo/Si multilayer optics for EUVL produced by UHV-e-beam evaporation and ion polishing

Our current status of Mo/Si multilayer extreme ultraviolet coatings fabricated by UHV e-beam evaporation and ion polishing is presented. Standard Mo/Si multilayer coating deposited onto 4 inch Si-wafer substrates showing peak reflectivities of 67.4% with a lateral homogeneity in coating reflectance of approximately 0.3% and a variation in peak wavelength of approximately 0.05 nm over the full aperture have been achieved. At.-wavelength reflectivities achieved for comparable multilayer coatings deposited onto Zerodur substrates with an enhanced microroughness (σ=0.55 nm) is shown to drop severely by almost 10%. A partial smoothing could be achieved by applying thin a-C buffer layers to these substrates, which in turn enhance the at-wavelength reflectivity of the Mo/Si multilayer by 0.7%.

Table-top X-ray microscopy : Sources, optics and applications

We have developed the first operative compact sub-visible-resolution x-ray microscope for the water-window region (λ = 2.3 - 4A nm). The microscope is based on a 100 Hz liquid-jet-target laser-plasma x-ray source, normal-incidence multilayer condenser optics, diffractive zone plate optics and CCD detection. In the present article we emphasize the system's aspects and summarize the recent progress on the components, all aiming at the reduction of the exposure time of a few seconds, i.e., similar to bending-magnet based microscopes. This primarily includes improved laser-plasma source, improved condenser optics using Cr/Sc multilayers, and improved image handling capability using wavelet algorithms. Such compact short-exposure time microscopes would significantly increase the applicability of the technology.