Propagation Property of a Second-order Noncanonical Optical Vortex Beam in a Strongly Focusing System

The noncanonical optical vortex is an optical vortex with a nonconstant phase gradient around its center, i.e. the phase is not a linear function of the azimuthal angle. The expression of the strongly focused field of a (conventional) second order noncanonical vortex beam has been derived analytically and the field distribution is discussed. It has been found that the intensity distribution at the focal plane can exbibit rich patterns, which is more complicated than that of the first-order. The transverse focal shift phenomenon in current case also exits and is changed with the semi-aperture angle α in a different way. It also can be seen that the intensity maxima can be one to four on the focal plane. Our research may provide a new method for controlling of the structured optical field, and will give theoretical supports for the study of higher-order noncanonical optical vortices.

On discrete weighted Hardy type inequalities and properties of weighted discrete Muckenhoupt classes

In this paper, first we prove some new refinements of discrete weighted inequalities with negative powers on finite intervals. Next, by employing these inequalities, we prove that the self-improving property (backward propagation property) of the weighted discrete Muckenhoupt classes holds. The main results give exact values of the limit exponents as well as the new constants of the new classes. As an application, we establish the self-improving property (forward propagation property) of the discrete Gehring class.

Directivity and Bandwidth Enhancement of Patch Antenna using Metamaterial

This manuscript is the outcome of detailed research. A novel metamaterial structure is proposed in this paper to improve the directivity of the antenna. In this research paper a method of implementing metamaterial over the patch is used to enhance the directivity of rectangular microstrip patch antenna. From the results proposed expectation has been achieved, it is noted that in the presence of the LHM, the antenna is more directive and has a higher gain. This proposed patch is designed at the frequency of 2.75 GHz. The proposed structure is a combination of circular rings by virtue of its backward wave propagation property and negative reflection it improve the parameters of antenna.

No light at the end of the tunnel

The tunneling model for laser-induced processes implies the replacement of the propagating field of a laser by an oscillatory electric field. The view of the electric field as the primary influence in charged particle interactions fails for laser processes where the propagation property is important. Electric fields lack several quintessential laser-field properties that become dominant at high intensities and/or low frequencies. Quantum tunneling is not a concept generally suited to laser light. Conversely, laser criteria do not apply to electric-field phenomena like Sauter–Schwinger pair production in the vacuum, contrary to a widespread assumption. Graphic abstract

An L2-approximation method for construction and smoothing estimates of Markov semigroups for interacting diffusion processes on a lattice

We develop an [Formula: see text]-approximation strategy to study Markov semigroups generated by an infinite system of elliptic diffusion processes on a lattice. The proposed dynamics incorporate nearest neighbor interactions influencing diffusivity, which has received little attention so far as a mathematical problem. We prove the existence and the smoothness of Markov semigroups by extending the well-known pointwise estimation techniques such as the finite speed of propagation property and the Lyapunov function methods.

Compact Band-Selective Power Divider Using One-Dimensional Metamaterial Structure

A band-selective power divider is demonstrated for the first time. By replacing lumped element right-handed (RH) and left-handed (LH) transmission lines (TL) in a conventional Wilkinson power divider, it is possible to achieve both power division and filtering simultaneously. By utilizing the positive phase propagation property of an RHTL, which works as a low-pass filter, and the negative phase propagation property of an LHTL, which works as a high-pass filter, the band-selective quarter-wave sections required to construct a Wilkinson power divider are implemented. The fabricated circuit shows an insertion loss in the range 1.7 dB–2.5 dB in the passband, with the circuit dimensions of merely 12 mm by 10 mm.