Propagation of Bessel Gaussian beam through slabs of right-handed materials and left-handed materials

By using of ABCD matrix method and Collins diffraction theory, the analytical expression of the complex amplitude of the Bessel Gaussian beam propagating through slabs of right-handed materials and left-handed materials is deduced. The Bessel Gaussian beam can be regarded as the modulated Bessel beam that the Bessel beam multiplies the Gaussian factor as a function of the beam waist radius. Effects of the half-cone angle and the beam waist radius on propagation properties of the Bessel Gaussian beam through slabs of right-handed materials and left-handed materials are discussed. The results show that the propagation trajectories and the lobes of the Bessel Gaussian beam can be controlled by the half-cone angle and the beam waist radius.