Tight focusing properties of azimuthally polarized Lorentz Gaussian vortex beam through a dielectric interface are numerically studied by vector diffraction theory. The focusing properties, such as spot size, depth of focus, and maximum intensity position, are numerically calculated by properly manipulating the Lorentz parameter with/without annular obstruction values. Thus, using annular obstruction, one can generate a highly confined focal spot of long focal depth when using an azimuthally polarized Lorentz Gaussian vortex beam. Full Text: PDF References A. Ashkin et al., "Observation of a single-beam gradient force optical trap for dielectric particles", Opt. Lett. 11, 288 (1986). CrossRef A. Ambardekar, Y.Q. Li, "Optical levitation and manipulation of stuck particles with pulsed optical tweezers", Opt. Lett. 30, 1797 (2005). CrossRef P. Zemánek, C.J. Foot, "Atomic dipole trap formed by blue detuned strong Gaussian standing wave", Opt. Commun. 146, 119(1998). CrossRef S.M. Block et al., "Bead movement by single kinesin molecules studied with optical tweezers", Nature 348, 348 (1990). CrossRef D.E. Smithet al., "The bacteriophage φ29 portal motor can package DNA against a large internal force", Nature 413, 748 (2001). CrossRef L. Oroszi et al., "Direct Measurement of Torque in an Optical Trap and Its Application to Double-Strand DNA", Phys. Rev. Lett. 97, 058301 (2006). CrossRef D.P. Biss, T.G. Brown, "Cylindrical vector beam focusing through a dielectric interface", Opt. Express 9, 490 (2001). CrossRef P. Török et al., "Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I", J. Opt. Soc. Am. A 12, 2136 (1995). CrossRef S.H. Wiersma et al., "Comparison of different theories for focusing through a plane interface", J. Opt. Soc. Am. A 14, 1482 (1997). CrossRef L.E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems", Opt. Commun. 191, 161 (2001). CrossRef P. Zhou et al., "Propagation properties of a Lorentz beam array", Appl. Opt. 49, 2497 (2010). CrossRef O.E. Gawhary, S. Severini, "Lorentz beams and symmetry properties in paraxial optics", J. Opt. A: Pure Appl Opt 8, 409 (2006). CrossRef J. Yang et al., "Focusing of diode laser beams: a partially coherent Lorentz model", Proc. SPIE 6824, 68240 A (2007). CrossRef O.E. Gawhary, S. Severini, "Lorentz beams as a basis for a new class of rectangularly symmetric optical fields", Opt. Commun. 269, 274 (2007). CrossRef H. Yu, L. Xiong, B. Lü, "Nonparaxial Lorentz and Lorentz–Gauss beams", Optik 121,1455(2010). CrossRef Z. Zhang, J. Pu, X. Wang, "Tight Focusing of Radially and Azimuthally Polarized Vortex Beams through a Dielectric Interface", Chin. Phys. Lett. 25, 1664 (2008). CrossRef