Rapidly convergent series for high-accuracy calculation of the Voigt function

A rapidly convergent series, based on Fourier expansion of the exponential multiplier, is presented for highly accurate approximation of the Voigt function (VF). The corresponding algorithm enables the rapid calculation, required for its implementation as a subprogram in an interpolation approach. The numerical analysis of this VF approximation suggests that it may be more accurate than 10⁻⁹ in the Humlí?ek regions 3 and 4.     

A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function

A simple interpolating algorithm for rapid calculation of the Voigt function with high accuracy is presented. It can utilize any existing rapid algorithm as a subprogram for the pre-computation of the selected points. Such approach is particularly efficient for massive input arrays and, compared to the Wells algorithm, accelerates the computation, improves the accuracy, and increases the input vector size by factors greater than 35, 7, and 10, respectively. The calculated results were compared with exponential and arctangent expansion approximations of the Voigt function. It is found that the relative error in the Wells algorithm slightly exceeds the supposed accuracy of 10^?5.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Deep level emission of ZnO nanoparticles deposited inside UV opal

The temperature-dependent photoluminescence spectra of zinc oxide (ZnO) nanocrystals deposited inside the ultraviolet (UV) opal were studied. ZnO was grown in the voids between FCC packed SiO₂ spheres using spray pyrolysis under ultrasonic vibration in the solution containing a zinc nitrate precursor. The ZnO nanoparticles inside opal matrix with UV photonic band-gap exhibit suppression of the excitonic emission and enhancement of the deep level emission. Suppression of the excitonic lines is due to the inhibition of spontaneous emission, while enhancement and broadening of the DL emission in the green spectral region is due to Purcell effect. The infiltration of ZnO nanoparticles inside the photonic crystal may be a useful technique to increase its emission efficiency in the selected spectral region.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

Efficient intensity modulation due to surface acoustic waves on windows of the AlGaN/InGaN multiple quantum well laser

An alternative method for modulation of light generated by AlGaN/InGaN multiple quantum well laser with quartz antireflective (AR) coatings covering the resonator windows was modelled and studied theoretically. Disturbance of the piezoelectric coatings caused by surface acoustic waves (SAW) results in efficient intensity modulation of the laser beam. The model for the laser diode operating at DC demonstrates that the modulation factor can exceed 0.2 in sub-nanometer SAW displacement. For quarter-wave AR films, the carrier frequency of modulated beam has twice the frequency of SAW.     

Dominant ultraviolet-blue photoluminescence of ZnO embedded into synthetic opal

The temperature-dependent photoluminescence (PL) characteristics of zinc oxide (ZnO) embedded into the voids of synthetic opal were studied. ZnO was infiltrated into opal from aqueous solution with zinc nitrate precursor followed by thermal annealing. The PL spectra of the ZnO powder exhibit very high and broad emission peaks in the green region due to crystal defects, such as oxygen vacancies and zinc ion interstitials. In contrast to the PL spectra of ZnO powder, nanocrystals of ZnO embedded into the voids of FCC packed opal matrix exhibit dominant ultraviolet (UV)-blue and rapidly decreasing green PL emissions with decreasing temperature. The temperature-dependent PL characteristics show that the green band suppression in the ZnO nanocrystals is due to the influence of photonic crystal. The infiltration of nanoparticles into synthetic opal may be used for the fabrication of polycrystalline ZnO with dominant UV-blue PL. These results indicate that the luminescent materials embedded into photonic crystal may be promising for the fabrication of the RGB pixels in full-color displays.