Properties of spectral covariance for linear processes with infinite variance

We consider a measure of dependence for symmetric α-stable random vectors, which was introduced by the second author in 1976. We demonstrate that this measure of dependence, which we suggest to call the spectral covariance, can be extended to random vectors in the domain of normal attraction of general stable vectors. We investigate the asymptotic of the spectral covariance function for linear stable (Ornstein–Uhlenbeck, log-fractional, linear-fractional) processes with infinite variance and show that, in comparison with the results on the properties of codifference of these processes, obtained two decades ago, the results for the spectral variance are obtained under more general conditions and calculations are simpler.     

On-chip fraction collection for multiple selected ssDNA fragments using isolated extraction channels

High efficiency and high-purity fraction collection is highly sought in analysis of fragments-of-interest from selective polymerase chain reaction (PCR) products generated by High Coverage Gene Expression Profiling (HiCEP) methods. Here we demonstrate a new electrophoretic chip device enabling automatic high-efficient fractionation of multiple ssDNA target fragments during a run of separation. We used thoroughly isolated extraction channels for each selected target to reduce the risk of cross-contamination between targets due to cross-talk of extraction channels. Fragments of 35, 108 and 138 b, were successfully isolated, then the recovery was PCR-amplified and assessed by capillary electrophoresis (CE) analysis. Total impurity level of the targets due to unwanted fragments of 0.7%, 2% and 6% respectively, was estimated. Difficulties in collecting multiple target factions are due to band diffusion and DNA adsorption to the walls for the fragments in the separation channel, which is generated by transferring the DNA target fraction from the extraction section to the target reservoir. Therefore, we have carefully measured band broadening and analyzed its influence on the separation resolution due to the delay.     

Computation of <Emphasis Type="BoldItalic">p</Emphasis>-variation

A code for computing the p-variation of a piecewise monotone function is introduced. The code is publicly available in the R environment package under the name pvar. The algorithm is based on some properties of the p-variation of a piecewise monotone function proved in this paper. The mathematical results may have their own interest.     

Nanoparticle plasmon-assisted two-photon polymerization induced by incoherent excitation source

We demonstrate the possibility to achieve optical triggering of photochemical reactions via two-photon absorption using incoherent light sources. This is accomplished by the use of arrays of gold nanoparticles, specially tailored with high precision to obtain high near-field intensity enhancement.     

Formation of amorphous sapphire by a femtosecond laser pulse induced micro-explosion

We report on structural characterization of void-structures created by a micro-explosion at the locus of a tightly focused femtosecond laser pulse inside the crystalline phase of Al₂O₃ (R3c space group). The transmission electron microscopy (TEM), micro-X-ray diffraction (XRD) analysis, and Raman scattering revealed a presence of strongly structurally modified amorphous regions around the void-structures. We discuss issues of achieving the required resolution for structural characterization and assignment of newly formed phases of nano-crystallites by TEM, XRD, and Raman scattering from micro-volumes of modified materials enclosed inside the bulk of the host phase.     

Three-dimensional woodpile photonic crystal templates for the infrared spectral range

High-quality templates of three-dimensional woodpile photonic crystals are fabricated in photoresist SU-8 by use of femtosecond laser lithography. The samples have smooth surfaces, are mechanically stable, and are resistant to degradation under environmental and chemical influences. Fundamental and higher-order photonic stopgaps are identified in the wavelength range 2.0-8.0 microm. These templates can be used for subsequent infiltration by optically active or high-refractive-index materials.     

Ultrabright femtosecond source of biphotons based on a spatial mode inverter

A method of enhancing the efficiency of entangled biphoton sources based on a type II femtosecond spontaneous parametric downconversion (SPDC) process is proposed and implemented experimentally. Enhancement is obtained by mode inversion of one of the SPDC output beams, which allows the beams to overlap completely, thus maximizing the number of SPDC photon pairs with optimum spatiotemporal overlap. By use of this method, biphoton count rates as high as 16 kHz from a single 0.5-mm-long beta-barium borate crystal pumped by second-harmonic radiation from a Ti:sapphire laser were obtained.     

Optical properties of nanoengineered gold blocks

We report on control over the extinction spectrum of tetragonal gold nanoblocks by changing their lateral aspect ratio. Nanoblocks were patterned on a glass substrate by electron-beam lithography and were 40-400 nm in lateral dimensions and spanned from 1 to 9 in aspect ratio. This allowed us to tune the localized surface plasmon bands from 700 nm to 1.5 microm (longitudinal mode) and from 700 to 550 nm (transverse mode). Unprecedented polarization selectivity of the transverse and longitudinal plasmon bands was achieved via alignment and 3D control of the dimensions of the nanoblocks.     

Three-dimensional high-aspect-ratio recording in resist

We demonstrate a method of capillary force reduction during wet processing of three-dimensional structures photo-polymerized in resist by femtosecond pulses. A rinse in water was added as the final step of wet processing for recovery of free-standing photo-polymerized structures with feature sizes of ～100 nm. The hydrophobicity of resist was utilized for reduction of the capillary drainage force. We show a possibility of holographical recording of a three-dimensional woodpile structure, which has a good permeability and can be fabricated by the proposed modified wet processing.