Optical constants of float glass, nickel, and carbon from soft-x-ray reflectivity measurements

Angular-dependent reflectivity was measured with a dynamic range of 5-6 orders of magnitude at ~20 different photon energies in the range from 40 to 800 eV with the HASYLAB reflectometer with synchrotron radiation. Several float-glass substrates and a number of sputtered Ni and C films were investigated to improve the accuracy. The optical constants were obtained from least-squares fits of theoretical reflectivity curves, taking into account the influence of film thicknesses and surface and interface roughnesses. All samples with Ni and C films were produced on float-glass substrates, with Ar as the sputter gas, in the low-pressure triode-assisted sputtering facility of the Sincrotrone Trieste.     

Improved method for determination of optical constants of organic thin films from reflection and transmission measurements

A new technique for determining the optical properties of organic thin films is presented. A detailed evaluation of the accuracy of the determined optical constants has been performed, and the best combination of measured values yielding the smallest errors in the index of refraction for realistic experimental uncertainties has been found. The proposed method utilizes the fact that optical constants are smooth continuous functions, which reduces the possibility of encountering multiple solutions. The method consists of two steps. In the first step the optical constants at all wavelengths and the film thickness are determined. In the second step the thickness and the imaginary part of the index of refraction are kept fixed while we reevaluate the real part of the index of refraction by using a different objective function with improved sensitivity to the refractive index. After verifying that the proposed method is capable of an accurate estimation of optical constants, we determine the index of refraction data of vanadyl-phthalocyanine in the visible spectral range.     

Simultaneous determination of the optical constants and thickness of very thin films by using soft-x-ray reflectance measurements

A nonlinear, least-squares curve-fitting method is described that simultaneously determines the optical constants and the thickness of a very thin (? 100-?) film from reflectance versus angle of incidence (R - θ) data measured in the soft-x-ray region. The method is applied to R - θ data obtained for very thin, sputtered films of carbon (65 ? thick) and gold (94 ? thick) at photon energies of 60-900 eV. The results show that the present method is capable of accurately determining the thickness of very thin films even for transparent materials, and that the obtained optical constants are in good agreement with values reported for films with a thickness of 1000 ?.     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Optical constants in the IR from thin film interference and reflectance: the reststrahlen region of muscovite mica

A new technique for determining the IR optical constants of materials that can be formed into thin films is presented. At a given wavelength the thickness of the film t, the index of refraction n, and the extinction coefficient k combine to produce interference effects in the film, which in turn control reflectance from the film. When reflectance is plotted vs thickness the resultant curve is a unique function of n and k. Values of n and k are determined by curve fitting. The technique is illustrated using thin films of muscovite mica, and values of n and k are reported for wave numbers from 1200 to 400 cm-1, which include the reststrahlen region of mica.     

Optical constants in the ultraviolet region of evaporated high index thin films

A suitable method to determine the optical constants of high index thin films is essential for developing high efficiency dielectric thin film devices in theuv region from 240 nm to 400 nm. A quick and accurate method is established to determine these constants. Using this method the optical losses, refractive index, absorption coefficient and extinction coefficient of ZrO₂ films prepared by the method of reactive evaporation were evaluated in theuv region.     

Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region

Efficiency measurements of a grazing-incidence diffraction grating in the off-plane mount were performed using polarized synchrotron radiation. The grating had 5000 grooves/mm, an effective blaze angle of 14 degrees, and was gold coated. The efficiencies in the two polarization orientations (TM and TE) were measured in the 1.5-5.0 nm wavelength range and were compared with the efficiencies calculated using the PCGrate-SX code. The TM and TE efficiencies differ, offering the possibility of performing unique science studies of astrophysical, solar, and laboratory sources by exploiting the polarization sensitivity of the off-plane grating.     

Direct index of refraction measurements at extreme-ultraviolet and soft-x-ray wavelengths

Coherent radiation from undulator beamlines has been used to directly measure the real and imaginary parts of the index of refraction of several materials at both extreme-ultraviolet and soft-x-ray wavelengths. Using the XOR interferometer, we measure the refractive indices of silicon and ruthenium, essential materials for extreme-ultraviolet lithography. Both materials are tested at wavelength (13.4 nm) and across silicon's L2 (99.8 eV) and L3 (99.2 eV) absorption edges. We further extend this direct phase measurement method into the soft-x-ray region, where measurements of chromium and vanadium are performed around their L3 absorption edges at 574.1 and 512.1 eV, respectively. These are the first direct measurements, to our knowledge, of the real part of the index of refraction made in the soft-x-ray region.     

Optical analysis of absorbing double layers by combined reflection and transmission ellipsometry

A method known as combined ellipsometry, which utilizes the simultaneous interpretation of the ellipsometric parameters determined for light reflected and transmitted by the air side and by the substrate side of thin films, was used to obtain an optical analysis of absorbing double layers deposited onto a non-absorbing substrate. It is shown that the use of this method enables the evaluation of all the optical parameters characterizing absorbing double layers consisting of a non- absorbing and an absorbing thin film. Combined ellipsometry can be used for analysing the double layers formed by two highly absorbing thin films in a reasonable way if this method is complemented by a precise auxiliary method, e.g. the Fizeau method. These conclusions are demonstrated by experimental results obtained for samples of the following double layers: MgF₂/Al, Al/MgF₂, TiO/Au and Au/Ni. The ellipsometric parameters were measured at a wavelength λ of 632.8 nm.     

Optical reflection from a semiinfinite nonlinear crystal

Multistability of the reflection coefficient as a function of incident amplitude is theoretically demonstrated to be possible for a semiinfinite optically homogeneous medium with the Kerr nonlinearity. The multistability arises at certain relations between the system parameters. The treatment is essentially free from the assumption that field envelopes vary slowly in space. Underlying physical processes are described.     

Optical design of a spectrometer-monochromator for the extreme-ultraviolet and soft-x-ray emission of high-order harmonics

A grazing-incidence spectrometer-monochromator for diagnostics and application of the extreme-ultraviolet (EUV) and soft-x-ray high-order harmonics generated by the interaction between a few-optical-cycle laser pulse and a gas jet has been fabricated. We address the necessity of high-resolution spectral and spatial analyses of the high-order harmonics as well as their use as short EUV backlighters in pump-probe experiments. The spectrometer that we present uses a variable-line-spaced flat grating illuminated in the converging light coming from a toroidal mirror. The spectrum is stigmatic, and the focal surface is almost flat in a wide spectral region. The detector is a microchannel plate intensifier with a phosphor screen optically coupled to a CCD camera; it can be moved by means of a linear drive to acquire different portions of the spectrum in the 5-75-nm region. The resolution is almost limited by the pixel size of the detector. We apply the same optical scheme to achieve a constant-deviation-angle monochromator by substituting an exit slit for the detector block: The rotation of the grating gives the spectral scanning. A monochromator for the 5-50 nm spectral region is achieved.     

Mo/Si multilayer-coated ruled blazed gratings for the soft-x-ray region

Two Mo/Si multilayer-coated blazed gratings have been fabricated for operation at soft-x-ray wavelengths above the Si L edge, λ ≥ 12.4 nm, at (near) normal incidence. The sawtooth profile of the grating structure was mechanically ruled into a 200-nm Au film that was deposited onto a plane glass substrate. To smooth the rough Au surface and to prevent interdiffusion of the Au film with the upper Mo/Si multilayer, a carbon film was evaporated onto the Au grating surface of one of the gratings before the deposition of the multilayer coating. We matched the multilayer grating, working on blaze in the third diffraction order, in which an absolute diffraction efficiency of 3.4% at a wavelength of 14 nm was measured, whereas only 1.1% was achieved for a similar grating (without a carbon interlayer). These efficiencies are higher than those obtained for other ruled blazed gratings reported in the literature. As a result of the multilayer and grating periodicity, the wavelength of diffraction can be tuned bya rotation of the grating, which is important for application in a soft-x-ray monochromator.     

Characterization of sputtered nickel/carbon multilayers with soft-x-ray reflectivity measurements

Several sputtered Ni/C multilayer mirrors with periods between 3.8 and 6.0 nm were investigated with the HASYLAB reflectometer to determine the peak reflectivity and the internal structure of the multilayers. The enhanced reflectivity in the Bragg maximum, especially below 284 eV (carbon K edge), is interesting for practical applications. For both materials (Ni and C), the optical constants were previously obtained from angular-dependent reflectivity measurements. The layer thicknesses, interface roughnesses, and mean thickness errors of multilayer mirrors are obtained from least-squares fits of theoretical reflectivity curves. A model is presented to describe the influence of interface roughness on other parameters obtained from the analysis. All Ni/C multilayers, with Ar as the sputter gas, were produced in the low-pressure triode-assisted sputtering facility of Sincrotrone Trieste.     

Optical design in beam steering environments with emphasis on laser transmission measurements

Optical sensors applied to practical devices often encounter beam steering: the wander and/or diffusion of laser light. Here we provide a framework for minimizing the sensitivity of transmission-based sensors to beam steering without quantitative prediction of the severity of the beam-steering field. Typical goals are increased transmission and/or minimized fluctuations in transmission; such features can improve optical sensor performance (e.g., improved signal-to-noise ratio, response time, or spectral resolution). In our framework, we introduce a parameter for characterizing beam-steering severity. We then compare two approaches for absorption spectroscopy and show that the preferred approach depends on the total spectral range monitored, the spectral resolution desired, and the severity of the beam steering.     

Identifying heat- and mass-transfer constants from measurements under transient conditions

Explicit formulas are derived for determining heat- and mass-transfer constants from measurements of transient temperatures (concentrations) in processes which can be described by a general linear parabolic equation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 2, pp. 225–230, August, 1981.     

Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet-soft-x-ray region

The refractive index n = 1 - delta + ibeta of Si in the energy range 50-180 eV is investigated with angle-dependent reflectance measurements. The optical constants delta and beta are both determined by fitting to the Fresnel equations. The results of this method are compared with the values in the atomic tables derived from experimental data for beta and implementation of the Kramers-Kronig relations for delta. The samples were prepared by UV irradiation and HF:ethanol dipping to H passivate the surface. It is found that the values of delta in the atomic tables are 8-15% too high in the region 50-90 eV. This is attributed to missing oscillator strength in the tabulated absorption coefficient for Si. The measured values of beta for crystalline Si exhibit structure below the L (2,3) edge (99.8 eV), as was previously observed in transmission measurements of Si(111). It is also found that the method of least-squares fitting reflectance data to obtain optical constants is most effective for energies well below the edge, where delta > beta, while for a range of energies around and above the edge, where delta < beta, the optical constants are determined with large uncertainties. This behavior is not unique to the Si L(2,3) edge.