title: Curved optical tubes in a 4Pi focusing system.
abstract: We demonstrate the possibility of creating curved optical tubes in a 4Pi focusing system. The focal fields of such optical tubes have interesting properties: the energy is concentered in the neighborhood of a prescribed three-dimensional (3D) curve while the cross section is of hollow shape. The creation of these optical tubes is based on the annular focal spot of a vortex beam, which is employed as a building block. An optical tube is thus obtained by covering the central-axis curve of the tube by various such building blocks. Each building block has a certain orientation and position, realized by a rotation plus a certain translation. The spatial spectrum (the input field as well) of the optical tube is obtained by linearly superposing the spectrum of each transformed building block. The curve is rather arbitrary. Three examples of optical tubes: a torus, a solenoid and a trefoil knot are given, showing a good agreement with the expected results.
authors.forename: Shaohui
authors.initials: S
authors.lastname: Yan
authors.forename: Xianghua
authors.initials: X
authors.lastname: Yu
authors.forename: Manman
authors.initials: M
authors.lastname: Li
authors.forename: Baoli
authors.initials: B
authors.lastname: Yao