The trajectory of all nonparaxial accelerating two-dimensional (2-D) light beams known to date cannot bend higher than a semicircle. A recent paper by Alonso and Bandres suggested the use of an additional mirror to generate an accelerating beam's path that would be curved greater than a semicircle but less than an entire circle. We, for the first time, show how to generate a 2-D light field with its power flux circulating about a ring. Also, we consider accelerating nonparaxial asymmetric 2-D Bessel beams, which are obtained from a conventional 2-D Bessel beam by shifting its center to the complex plane. We show numerically that with increasing asymmetry parameter of the Bessel beam, its curved path becomes shorter, whereas the side-lobes are suppressed with respect to the central peak. Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/16/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Optical Engineering 111303-3 November 2015 • Vol. 54(11) Kotlyar, Kovalev, and Zaskanov: Light field with its power flux circulating along a ring Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/16/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Optical Engineering 111303-6 November 2015 • Vol. 54(11) Kotlyar, Kovalev, and Zaskanov: Light field with its power flux circulating along a ring Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/16/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx