Electron Probe Microanalysis of Transition Metals using L lines: The Effect of Self-absorption

Electron microprobe-based quantitative compositional measurement of first-row transition metals using their L $\alpha$ X-ray lines is hampered by, among other effects, self-absorption. This effect, which occurs when a broad X-ray line is located close to a broad absorption edge, is not accounted for by matrix corrections. To assess the error due to neglecting self-absorption, we calculate the L $\alpha$ X-ray intensity emitted from metallic Fe, Ni, Cu, and Zn targets, assuming a Lorentzian profile for the X-ray line and taking into account the energy dependence of the mass absorption coefficient near the absorption edge. We find that calculated X-ray intensities depart increasingly, for increasing electron beam energy, from those obtained assuming a narrow X-ray line and a single fixed absorption coefficient (conventional approach), with a maximum deviation of $\sim$ 15% for Ni and of $\sim$ 10% for Fe. In contrast, X-ray intensities calculated for metallic Zn and Cu do not differ significantly from those obtained using the conventional approach. The implications of these results for the analysis of transition-metal compounds by electron probe microanalysis as well as strategies to account for self-absorption effects are discussed.

Exceptional points in composite structures consisting of two dielectric diffraction gratings with Lorentzian line shape

Using scattering matrix formalism we derive analytical expressions for the eigenmodes of a composite structure consisting of two dielectric diffraction gratings with Lorentzian profile in reflection. Analyzing these expressions we prove formation of two distinct pairs of exceptional points, provide analytical approximations for their coordinates and by rigorous simulation demonstrate eigenmodes interchange as a result of encircling said exceptional points.

How Laser Physics Brought Optics to the World of Photonic Crystals

A brief review of authors’ research is presented. An emphasis is made on the photon localization in the helical structure of a chiral liquid crystal (CLC), which was first experimentally registered by the authors. An analysis of the spectral and lasing characteristics of distributed feedback (DF) lasers based on natural CLCs (type 1) and on chiral nematics (type 2) led to a conclusion that the model of photonic crystal is suitable to describe the lasing mechanism in type-2 CLC lasers, but not in type-1 ones. This conclusion is evidenced by the absence of lasing bands at the opposite edges of the selective reflection (SR) band; at the same time, the lasing line is located at its center. It is shown that if the SR band of the CLC overlaps the maximum of the laser dye fluorescence band, the lasing line coincides with the SR band center to an error of ±1 nm. If the layer thickness in the CLC lasers of both types does not exceed 50 мm, when a high-quality planar texture is retained and a low generation threshold is achieved, a significant difference between their optical characteristics takes place. Namely, the SR spectrum for a type-1 CLC laser is approximately described by a Lorentzian profile, whereas the contour of the SR spectrum for a type-2 CLC laser has a profile characteristic of the transmittance through multilayer dielectric mirrors. The origins of the differences between the optical and laser characteristics of the CLC lasers of both types have been analyzed from the viewpoint of two lasing models: DF and photonic-crystal ones.

Study of Diffraction of Surface Plasmon Polaritons at the Rectangular Edge of a Metall-Dielectric Interface in the Terahertz Region

Surface plasmon polaritons diffraction at the rectangular edge of a plane gold-dielectric interface was studied using monochromatic terahertz radiation of Novosibirsk free electron laser. Experimental results were compared with the exact solution of the two dimensional diffraction problem. For short distances from the sample edge experimental data reasonably agreed with theory. The field intensity distribution beyond the edge is not symmetrical regarding to the sample surface and extends mainly in the upper hemisphere. In the far zone the electromagnetic field forms a freely-propagating wave which has Lorentzian profile with the divergence depended on the surface impedance. The propagation length of surface plasmon polaritons along bare gold and gold covered with a submicron ZnS layers were measured and amounted to tens of millimeters

Quantifying Resolving Power in Astronomical Spectra

The spectral resolving power R = λ/δλ is a key property of any spectrograph, but its definition is vague because the ‘smallest resolvable wavelength difference’ δλ does not have a consistent definition. Often, the FWHM is used, but this is not consistent when comparing the resolution of instruments with different forms of spectral line-spread function. Here, two methods for calculating resolving power on a consistent scale are given. The first method is based on the principle that two spectral lines are just resolved when the mutual disturbance in fitting the fluxes of the lines reaches a threshold (here equal to that of sinc2 profiles at the Rayleigh criterion). The second criterion assumes that two spectrographs have equal resolving powers if the wavelength error in fitting a narrow spectral line is the same in each case (given equal signal flux and noise power). The two criteria give similar results and give rise to scaling factors that can be applied to bring resolving power calculated using the FWHM on to a consistent scale. The differences among commonly encountered line-spread functions are substantial, with a Lorentzian profile (as produced by an imaging Fabry–Perot interferometer) being a factor of two worse than the boxy profile from a projected circle (as produced by integration across the spatial dimension of a multi-mode fibre) when both have the same FWHM. The projected circle has a larger FWHM than its true resolution, so using FWHM to characterise the resolution of a spectrograph which is fed by multi-mode fibres significantly underestimates its true resolving power if it has small aberrations and a well-sampled profile.

THE ESCAPE PROBABILITIES FOR SLAB AND SPHERICAL GEOMETRIES IN PLASMA SPECTROSCOPY

In this paper, the concepts of the photon escape probability and the transmission factor are reviewed and the photon escape probabilities for infinite plane-parallel slab and spherical geometries are discussed. The photon escape probabilities using the transmission factor, for Lorentzian profile and Holtsmarkian profile, are discussed. Finally, the photon escape probabilities we calculated are compared with that calculated using before method for Lorentzian profile and Holtsmarkian profile, and some useful conclusions are drawn.

Experimental Study of Laser-Induced Brass and Copper Plasma for Spectroscopic Applications

This paper presents time-resolved and space-integrated laser-induced breakdown spectroscopic (LIBS) analysis of copper and brass plasma. It was observed that copper emission is very strong during the first hundred nanoseconds of the plasma, but then some lines (e.g., at 327.4 nm) decrease in intensity, while others (e.g., 521.8 nm) slightly increase. Zinc lines, on the other hand, did not decrease significantly in intensity even two microseconds after ablation, but they became narrower due to the decrease of the density of free electrons. Copper line intensities showed the same characteristics regardless whether the plasma was created in a metallic copper or brass sample. Assuming local thermodynamic equilibrium, plasma temperature, and electron density is obtained from Boltzmann plot and Lorentzian profile fitting, respectively. The effect of subsequent irradiation on the same spot was investigated, and the number of necessary shots for surface cleaning was determined.

Resonance Escape Factor and Abundance of Plasma Li I Resonance Lines at 671nm

To study the spectrum of lithium plasma, the resonance escape factors of three resonance absorption lines that making up the LiⅠ671nm line are discussed theoretically, for both Lorentzian profile and Voigt profile. The number density of the absorbing atoms in the ground state, the oscillator strength, and the optical depth at the line center are also discussed in the calculation. The abundance of lithium relative to hydrogen is evaluated.The results we calculated are in good agreement with the experimental results. This calculation will be significant in the research of plasma lithium plasma.