Vector Bessel-like beams with quadrature phases of electric and magnetic fields

The peculiarities of propagation of vector Bessel – Gaussian (BG) beams, the distinguishing feature of which is the quadrature of phases of electric and magnetic fields, are considered. The expression for vector BG beams is obtained on the basis of common approach in a form of linear superposition of known accurate solutions of the Maxwell equations. By selection of weight function of superposition there are found the equations for all components of electric and magnetic field of the BG beam, and also expressions for square field functions, such as linear density of energy, pulse and pulse moments along the direction of beam propagation. The particular case is considered when weight functions of the superposition do not depend on azimuthal mode index m of the vortex beam. For this case the expression is found for the ratio of linear density of the pulse moment to linear density of BG beam energy with a quadrature of electric and magnetic fields. From the equation obtained it follows that linear density of the pulse moment per one photon for non-paraxial beams essentially differs from the value ћ ( m + 1) for large cone angles (of about several tens of degrees). Particularly, this result is important for the correct estimation of angular momentum of the field on the basis of measurement by the photoreceivers with direct detection of azimuthal index m , which are being developed in the recent time. It is also shown that when increasing the cone angle of BG beam its polarization differs from angular one, and the longitudinal component increases. Here the functional dependence of transverse and longitudinal components on radial coordinate is different. The obtained results are important when developing compact elements for the optical communication systems, microscopy, laser tweezers and others.