Simulating the diffraction pattern in the focal plane of a lens-axicon system

Laser beam concentration into a narrow ring with a lens and axicon is considered, as there are applications in working surfaces, cutting wafers and slices, and in welding or soldering tubes to heat-exchanger plates. A model is constructed and a working formula is derived for the diffraction pattern in the focal plane of such a system when the axicon is illuminated by a plane wave. For large h/, where h is axicon height and is wavelength, a formula is obtained that passes asymptotically into the approximate Belanger and Rioux ones.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 36–41, December, 1987.     

Electron emission from Al,Pt, Ag,and Au surfaces under the action of resonant photons with λ=2537 and 1850 Å

An original variant of an electronic device is described, which can be used for gamma-process selection under ionized gas conditions. The device is based on a Hanley and Schaffernicht electron gun. Selection of photons and metastable atoms is performed by a quartz tube located in axial symmetry with the primary electron gun. The desired signal is measured from the flow of secondary electrons emitted from Al, Pt, Ag, and Au surfaces under the action of resonant photons radiated from the levels Hg(6³P₁) and Hg(6¹P₁). For =2537 Å the following values were obtained for _ph 9.1, 3.8, 1.1, 0.25. Analogous values of _ph for =1850 Å were equal to 45.5, 10.8, 6.5, 3.2. The _ph values are in units of 10^–4.Translated from Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 68–74, December, 1987.     

Self-activated luminescence of zinc sulfide

The nature of the luminescence of zinc sulfide in the spectral range (360), 380–420 nm (SAL) at 80K is analyzed. It is shown that the appearance of SAL radiation is accompanied by additional absorption in the region (350) 365–370 nm at 80K. The low-temperature spectra of sphalerite, exposed to different radiation and subjected to different treatment, are studied. The multiband luminescence of the isoelectronic sulfur impurity in ZnO deposits in the region 383–640 nm is discussed. It is concluded that SAL luminescence is attributable to the localization of excitons in ZnS on clusters, whose formation precedes the precipitation of the ZnO·S phase. The formation of oxygen clusters and deposits on dislocations in ZnS is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 60–66, February, 1987.     

Algebraic structure of the amplitude of elastic scattering by a two-dimensional crystal

The coherent scattering of spin-S particles by a monatomic crystal film is considered, with rescattering taken into account. A relation between the amplitudes q_j of different diffraction orders and the dielectric tensor () of the two-dimensional crystal is found. The relation can be used to obtain () for an arbitrary frequency (including resonant frequencies) in terms of elastic scattering data. The possibility of bound states of the particles in the monatomic film is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April, 1987.The author thanks V. L. Vinetskii for interest in the work and for useful discussions.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

Two-photon absorption and energy band structure of orthorhombic Hg2Cl2 crystals

Dependence of two-photon absorption (TPA) rate on the state of polarization of a laser beam is investigated in the low-temperature orthorhombic modification of Hg₂Cl₂ crystals. Theoretical calculations of the dependence of TPA rate on the direction of polarization vector of the beam are performed for centrosymmetric points, Y, Z, T, R andS of the Brillouin zone. The domain structure of real crystals is taken into consideration and it is shown that periodicity of the polarization dependence may indicate whether TPA is due to transitions either at, Y, Z, T orR, S points. The polarization dependence of TPA cannot, however, distinguish between points inside these two groups. Comparison of theory with a low-temperature (T 8·5 K) experimental curve of polarization dependence is discussed. It is shown that the experiment can be explained in main features by a model of noninteracting oriented linear dipoles. Further, on the basis of TPA measurements, a simple energy band structure of Hg₂Cl₂ is proposed regarding Hg₂Cl₂ crystal as a linear chain of molecules.The authors express thanks to Dr. . Barta for supplying the Hg₂Cl₂ crystals, Dr. Z. Bryknar for critical comments and Dr. B. Velický for stimulating discussion. We thank also Dr. V. Kohlová for assistance during measurement.     

An Euler-Maclaurin Transformation of a Slowly Convergent Series with an Application to Fourier Coefficient Evaluation

A standard procedure in numerical treatment of a slowly convergentseries is to transform it into a new series, convergent or asymptotic,so that far fewer terms of the new series are required to obtainthe desired accuracy. Particularly, when the general term ofthe original series depends on a small-valued parameter , oneis tempted to consider an expansion in powers of , which istantamount to interchanging the order of summation. We considerseries where, as a result of this interchange, almost all theseries formally corresponding to the coefficients of ascendingpowers of diverge. Invoking the Euler-Maclaurin summation formula,it is shown that under certain simple conditions, these divergentseries can be replaced by values obtained from the analyticcontinuation of a Dirichlet series at decreasing values of itsargument. Several examples are discussed, including an applicationto Fourier coefficient evaluation of certain periodic analyticfunctions.     

Vibrational modes and infrared absorption of interstitial oxygen in silicon

A quasi-linear Si₂O molecule model (QLMM) is suggested from an analysis of the configuration and the interactions of an isolated oxygen atom with its neighbor silicon atoms. The vibrational modes are assigned and the infrared absorption spectra are calculated in detail with the model. The theoretical results are in reasonably good agreement with reported experimental values. This agreement shows that for the analysis of the vibrational modes of the interstitial oxygen atom in silicon crystals it is not necessary to consider the coupling of the molecule with the rest of the lattice. The interaction of the oxygen atom with its six second-nearest silicon atoms only causes the level separation of the ₂ mode and the formation of the fine structure.     

Analysis of the 3-dimensional electron distribution in silicon using directional Compton profile measurements

A method of reconstructing the electron momentum density (p), and its Fourier transform,B(t), from a series of directional Compton profiles is described. It is based on a double Fourier inversion technique and an expansion in lattice harmonic functions. The effect of random errors has been analysed, and the implications for the data collection discussed. We have used the reconstruction technique to obtain (p) andB(t) for silicon from six directional Compton profiles measured with 412 KeV gamma-radiation. The experimental result is in good agreement with earlier measurements and with available solid state theories. A recent Wannier function calculation for silicon using orthogonalised bond orbitals provides a useful tool for identifying the physical origins of the observed anisotropies. A comparison between the information presented in position and momentum space shows that the ease of interpretation depends upon the degree to which the various interactions give rise to localised features in each representation.