Intermediate regime of light diffraction by surface ultrasonic waves in planar gyrotropic optical waveguides

The intermediate regime of optoacoustic interaction, similar to the Bragg one, with Rayleigh surface ultrasonic waves in gyrotropic planar waveguides is studied. A system of equations of bound waves is presented that describes planar optoacoustic interaction in the intermediate, Raman-Natoh, and Bragg regimes of light diffraction by surface ultrasonic waves. It is shown that the optical activity of a wavequide film favors the incident light energy pumping to diffracted light for a TE-polarization wave and decelerates this process for an incident TM-polarization wave. Mozyr' State Pedagogical Institute, 28, Studencheskaya St., Mozyr', 247760, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 3, pp. 412–416, May–June, 1997.     

Sukzessive Minima mit und ohne Nebenbedingungen

Given semi-normsf andg on ⁿ and a real number >0. Then the successive minima off under the constraintg are defined by _j : = inf {: there existj linear independent vectors inZ ⁿ withf andg}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ⁿ (without constraints) coincide with the _j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.     

Chalcedony (a crystalline variety of silica): biogenic origin in electric organs from living Psammobatis extenta (family Rajidae)

The electric organs of electric fish have been used extensively for the study of peripheral cholinergic synapses. Aluminum and silicon have been observed in the electrocytes of Psammobatis extenta, a fish belonging to the family Rajidae, using a combination of scanning electron microscopy and X-ray spectrometry. Based on this evidence, the presence of silica minerals has been documented by means of mineralogical techniques. Electric organ cryostat sections and subcellular fractions were observed using a Leica DMLP mineralogical microscope. The shape, size and color, among other properties, were analyzed in plane-polarized light, while birefringence and the extinction angle, which allow for mineral identification, were observed through crossed-polarized illumination. The distribution of chalcedony, an oxide silicon mineral, in the sections and all the fractions of the electric organ was recorded. X-ray diffraction analysis of the electric organ segments showed a similar result, with a low-quartz variety. Chalcedony precipitation occurred at a specific pH (7-8) and oxidation potential (Eh; 0.0 to -0.2). This observation supports the important role played by pH and Eh conditions in silica precipitation in electrocytes, as has been reported in geological environments. It is possible that silica formation and silica degradation in electric organs are also related to the enzymes, silicatein and silicase, that direct the polymerization and depolymerization of amorphous silica in sponges. Carbonic anhydrases (silicase) are involved in physiological pH regulation. Crystallization of chalcedony via spiral growth from a partially polymerized fluid is consistent with processes known to occur in organic systems. This is the first time that a biogenically produced crystalline mineral phase (i.e., chalcedony) has been observed in the electrocytes and cholinergic nerves from living electric fish.     

Polarization-independent modulation of light in gyrotropic cubic crystals

Polarization-independent modulation of light in gyrotropic cubic crystals is investigated in the Bragg and intermediate diffraction regimes. It is found that, for crystals with considerable specific rotation, the photoelastic anisotropy is suppressed by the circular anisotropy and the observed diffraction efficiency depends weakly on the polarization azimuth of the incident light. Good agreement is obtained between modulation parameters calculated theoretically on the basis of the coupled wave theory and experimental results for a bismuth silicate crystal in the intermediate diffraction regime.