Abstract. In this work we consider laser beam diffraction by narrow elongated axicon with conical angle, which is small enough for multiple internal reflection arising. Those sorts of tapers are widely used in micro and nanooptics. We have to take into account more than one internal reflection for correct description of beam propagation through the axicon. The diffraction is simulated with two approaches: pure "geometrical optics" and Helmholtz equation solving with "Finite Elements Method". Based on ray optics we derive analytic formulas for conical angles meanings, which provide maximums and minimums of intensity on optical axis. Derived numerical simulation verifies theoretically obtained results.
IntroductionAxicons [1, 2] can be used to create nondiffraction Bessel beams in classical Optics [3,4]. Metalized axicons with small cone angles are also utilised as near-field probes and tapers for sharp focusing in Nanophotonics [5,6] and especially in nearfield microscopy [7-9] and spectroscopy [10]. To determine the optimum parameters of such tapers we need to provide simulation in accordance with the assumptions of the rigorous vectorial diffraction theory [11][12][13][14].Working of metal conical structure is explained by the lightning-rod effect [15] which can be observed near dielectric structures [16]. The lightning-rod effect lies in the fact that longitudinal electric field component are enhanced near sharp structures. It can be observed, for example, in cases where radially polarized beams [17][18][19] or linearly polarized beams [20][21][22] are focused.The dielectric characteristics of axicons can be approximately estimated with ray and scalar optical theory [23,24], and then defined more accurately with more rigorous methods.