Diffraction properties of azimuthally symmetric gratings in a hollow circular dielectric waveguide

•Diffraction modes of HDW in some cross-section of such waveguide is considered.•Appropriate calculation method for solution of problem is proposed based on FDTD.•Different types of grating that are changed with radius increasing is homogeneous.•Inhomogeneous way is considered: periodical, Fresnel and Fibonacci grating.•The dependencies are analyzed, some resonances from the dependencies are revealed. Diffraction gratings can be used in cavities of terahertz lasers for generating wave beams with special polarization. Adequate using of such gratings needs preliminary theoretical investigation of their diffraction properties. To solve the problem a specially adopted numerical method should be used because the structures under study frequently have many elements (many periods) and well-known theoretical approaches or commercial solvers cannot cope with such task. In this paper, a Finite Difference in Time Method for Body of Revolution (BOR FDTD) is applied to the problem. Updating formulae for electromagnetic field and some calculation features of the method are presented. Different types of diffraction gratings that homogeneously and inhomogeneously change their properties with the radial coordinate are studied. Some physical peculiarities of diffraction modes of a hollow dielectric waveguide with different polarization are revealed and discussed.