We report on efficient nonlinear generation of ultrafast, higher order "perfect" vortices at the green wavelength. Based on Fourier transformation of the higher order Bessel-Gauss (BG) beam generated through the combination of the spiral phase plate and axicon, we have transformed the Gaussian beam of the ultrafast Yb-fiber laser at 1060 nm into perfect vortices of power 4.4 W and order up to 6...

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well a construction groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence the ultrafilter lemma is that group bi-orderable if and only it locally bi-orderable. show there exists model ZF in which free (ergo bi-orderable) not bi-orderable, can be giv...

We proposed a mechanism to generate giant anisotropic second harmonic nonlinear response via double resonance effect, achieved through band nesting electronic band-structure engineering. The ideal setup would be triplet of nested bands separated by the fundamental energy $\ensuremath{\hbar}\ensuremath{\omega}$. demonstrate theoretically that phenomenon can realized in bilayer SnS tuning with pe...