Effect of Laser Fluence on the Structural and Optical Properties of Tantalum Oxide Films Ablated by Pulsed Laser

The influence of laser fluence on the properties of thin films of tantalum oxide is studied in this paper, varying the laser fluence from 5.7 to 8.3 J/cm². Thin films of tantalum oxide were deposited on glass substrates using pulsed-laser ablation technique. X-ray diffraction studies confirm the amorphous/nanocrystalline nature of all the films irrespective of the laser fluence. The Tauc plot analysis suggests that tantalum oxide is an indirect band gap material, whose band gap decreases with increase in laser fluence. The refractive index of the films is found to decrease with increase in laser fluence but the extinction coefficient of the films increases with increase in laser fluence. Fourier transform infrared studies suggest the use of tantalum oxide thin films as oxygen sensors. Micro-Raman analysis reveals the sensitiveness of Ta-O-Ta and Ta-O vibration modes to laser fluence. Among all the films, the film deposited at a laser fluence of 7 J/cm² is found to be superior in quality.     

Unidirectionally Emitting Quantum Cascade Microcavity Lasers with Patterned Contacts

We investigate unidirectionally emitting quantum cascade microcavity lasers with semicircle-patterned top contacts. We employ novel patterned top contacts while fabricating notched ellipse-shaped cavity lasers. We study experimentally the microcavity-structure-based quantum cascade (QC) laser material with a long infrared wavelength of ~10 μm. Then we characterize microcavity lasers with patterned contacts and compare them with nonpatterned ones and observe a lower operating injection threshold current as a consequence of this relatively straightforward technique, with the unidirectional emission feature being kept. We obtain a maximum light output peak power of 16 mW with unidirectional emission at a far-field divergence angle of ~7° at a full width of half maximum, while the patterned device shows low threshold even in the microcavity laser with a size of 150 μm. Furthermore, we also carry out a reliability test of the QC microcavity lasers with semicircle-patterned top contacts, and the testing results show no sudden failure or severe light-output-power drop during an operating time of thousand hours.     

Using Laser Measuring and SFM Algorithm for Fast 3D Reconstruction of Objects

Effective measurement of the reflective or transparent surface of an object has always been a disadvantage in laser scanning modeling. We propose a fast and complete three-dimensional (3D) reconstruction method for small static objects using laser scanning and the structure from motion (SFM) algorithm. Meanwhile, a complete reconstruction workflow is designed and a multi-angle 3d reconstruction system is set up. To generate the complete point cloud model of the object, the SFM algorithm is used to reconstruct the surface part of the object, the data for which cannot be obtained by the laser measuring instrument. The experimental results show that this method not only improves the speed, accuracy, integrity, and visual effect of 3D reconstruction of small objects, but also extends the scope of 3D reconstruction of laser measurement.     

Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.     

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski’s Coagulation Equation with Inverse Power Law Kernels

Uniqueness of mass-conserving self-similar solutions to Smoluchowski’s coagulation equation is shown when the coagulation kernel K is given by \(K(x,x_*)=2(x x_*)^{-\alpha }\), \((x,x_*)\in (0,\infty )^2\), for some \(\alpha >0\).     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

Conformal Galilei algebras,symmetric polynomials and singular vectors

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras \({\mathfrak {cga}}_\ell (d,\mathbb {C})\) with \(d=1\) for any integer value \(\ell \in {\mathbb {N}}\). The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.     

Modularity of logarithmic parafermion vertex algebras

The parafermionic cosets \(\mathsf {C}_{k} = {\text {Com}} ( \mathsf {H} , \mathsf {L}_{k}(\mathfrak {sl}_{2}) )\) are studied for negative admissible levels k, as are certain infinite-order simple current extensions \(\mathsf {B}_{k}\) of \(\mathsf {C}_{k}\). Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to \(\mathsf {C}_{k}\), irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-modules are obtained from those of \(\mathsf {L}_{k}(\mathfrak {sl}_{2})\). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible \(\mathsf {B}_{k}\)-modules. The irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the \(\mathsf {B}_{k}\) are \(C_2\)-cofinite vertex operator algebras.     

Synthesis of some new triamide derivatives via Ugi five-component reaction in aqueous solution

Triamide derivatives have been synthesized in good yields in a novel, one-pot, five-component, and efficient process by the reaction of Z-oxazolone, water, primary amines, aldehydes, isocyanides, in the presence of catalytic amount of KAl(SO₄)₂·12H₂O (alum) as a non-toxic, reusable, inexpensive, and easily available reagent via Ugi reaction in aqueous solution.     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.