Discrete damage traces from filamentation of Gauss-Bessel pulses

Filamentation of Bessel-Gauss pulses propagating in borosilicate glass is found to produce damage lines extending over hundreds of micrometers and consisting of discrete, equidistant damage spots. These discrete damage traces are explained by self-regeneration of Gauss-Bessel beams during propagation and are potentially applicable in laser microfabrication of transparent materials.     

Rates of convergence in the CLT for linear random fields

In this paper, we study sums of linear random fields defined on the lattice Z ² with values in a Hilbert space. The rate of convergence of distributions of such sums to the Gaussian law is discussed, and mild sufficient conditions to obtain an approximation of order n ^−p are presented. This can be considered as a complement of a recent result of [A.N. Nazarova, Logarithmic velocity of convergence in CLT for stochastic linear processes and fields in a Hilbert space, Fundam. Prikl. Mat., 8:1091–1098, 2002 (in Russian)], where the logarithmic rate of convergence was stated, and as a generalization of the result of [D. Bosq, Erratum and complements to Berry–Esseen inequality for linear processes in Hilbert spaces, Stat. Probab. Lett., 70:171–174, 2004] for linear processes.     

On the asymptotic form of convex hulls of Gaussian random fields

We consider a centered Gaussian random field X = {X _t : t ∈ T} with values in a Banach space $\mathbb{B}$ defined on a parametric set T equal to ? ^m or ? ^m . It is supposed that the distribution of X _t is independent of t. We consider the asymptotic behavior of closed convex hulls W _n = conv{X _t : t ∈ T _n}, where (T _n ) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b _n ) _n≥1 with probability 1, (in the sense of Hausdorff distance), where the limit set is the concentration ellipsoid of . The asymptotic behavior of the mathematical expectations Ef(W _n ), where f is some function, is also studied.     

On Beveridge-Nelson decomposition and limit theorems for linear random fields

We consider linear random fields and show how an analogue of the Beveridge-Nelson decomposition can be applied to prove limit theorems for sums of such fields.     

Formation of embedded patterns in glasses using femtosecond irradiation

Channel formation in glasses is demonstrated and discussed. Photosensitive glass (Foturan) was microstructured using femtosecond irradiation at 800 nm and 400 nm wavelengths, with subsequent thermal annealing, and HF etching of a lithium-silicate phase formed by exposure-annealing. It was found that there is a significant difference in the volume of lithium-silicate when the exposure was made with and without optical breakdown. Channels with a minimum cross section of approximately 10 m were achieved.In silicate glasses, the optically induced dielectric breakdown was used for the recording of channel patterns. The highest wet etching rate in a HF based solution was observed when the irradiance corresponded to the 2.5–3.0 thresholds of dielectric breakdown and the adjacent pulses were overlapping by more than 50% of the diameter of the focussed beam. Under these conditions, the formation of a void inside the glass was confirmed by optical observation of single shot damage under a microscope. The mechanism of selective wet etching in silicate glasses is discussed in terms of the stress corrosion effect, which explains crack propagation in glasses via the reaction of stretched Si–O–Si bonds at the tip of a crack with water, resulting in SiOH formation. It is shown that intra-connection of voxels was the key factor to achieve etching of high aspect ratio patterns in silica glass. PACS 42.70.Ce; 81.05.Kf; 82.50.Pt; 87.80.Mj     

Spectrally-resolved atomic-scale length variations of gold nanorods

Functionality of gold nanorod structures as ultra-sensitive optical rulers is demonstrated. Arrays of gold nanorods were fabricated by electron beam lithography and lift-off techniques with high accuracy and uniformity. Their longitudinal plasmon scattering spectra were found to exhibit extreme sensitivity to the length of the nanorods. This phenomenon enables optical detection of the nanorod length variations comparable to the thickness of a few atomic layers of gold.     

CLT for linear random fields with martingale increments

In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations were proved. In this paper, which can be regarded as a continuation of the above-mentioned paper, CLT for sums of linear random field are proved in the case where innovations form martingale differences on the plane (that can be defined in several ways). In both papers, the so-called Beveridge–Nelson decomposition is used.     

On estimation of parameters for spatial autoregressive model

In the paper asymptotic properties of the estimated coefficients of multi-indexed autoregressive model are investigated. Considering Least Squares estimates we use some kind of self-normalization and obtain limit normal law independent of unknown parameters. In the proof of this result we use recent result on the Central Limit Theorem for dependent summands.      

Spiral three-dimensional photonic crystals for telecommunications spectral range

Three-dimensional photonic crystals consisting of periodic arrays of spiral columns were fabricated in a commercially available photoresist (SU-8) by a direct laser writing technique. Tailoring the pre- and post-processing conditions for the photoresist has enabled the recording of extended, self-supporting periodic structures with sub-diffraction resolution. Pronounced photonic stop gaps were observed at wavelengths between 1.5 and 1.8 μm, close to the telecommunications region. These structures can be used as accurate and robust templates for subsequent infiltration by materials with higher refractive index. PACS 42.65.Re; 42.70.-a; 42.70.Qs