Helical-core fiber analog of a quarter-wave plate for orbital angular momentum C. N. Alexeyev, B. P. Lapin, A. V. Volyar, and M. A. Yavorsky* Taurida National V.I. Vernadsky University, Vernadsky Prospekt, 4, Simferopol, Crimea 95007, Ukraine *Corresponding author: maxyavorsky@yahoo.com Received May 8, 2013; accepted May 21, 2013; posted May 29, 2013 (Doc. ID 190299); published June 25, 2013 We have studied the effect of a twist defect on the conversion of the fundamental mode (FM) into an optical vortex (OV) in a helical-core fiber (HCF). We have shown that if such a twist defect is situated in the middle of the HCF, which converts the FM into an OV, such a fiber system can continuously change the orbital angular momentum (OAM) of the output field from 0 to 1 (in a.u.). This control of the OAM is achieved by variation of the twist angle. In this action upon the OAM, this system has analogy with the quarter-wave plate, which is able to change the spin angular momentum. We also introduced the generalized Stokes parameters (SPs) and Poincaré sphere to visualize evolution of the superposition of states with zero and nonzero OAM. Connection of SPs with geometric character- istics of the location of singularity is made. © 2013 Optical Society of America OCIS codes: (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.1155) All-optical networks; (260.6042) Singular optics. http://dx.doi.org/10.1364/OL.38.002277 Since early studies on twisted fibers, it has been estab- lished that twisting fiber leads to the reduction of polari- zation mode dispersion for pitch values of tens of centimeters [ 1]. In this application, the goal of making fiber act upon light of different polarizations in a similar manner has been achieved. Such fibers were also found to maintain circularly polarized light and in this way resemble the hi–bi monomode fibers, which maintain lin- early polarized light [ 2]. Recently, the focus of research has somewhat shifted to quite an opposite feature of twisted fibers—their ability to affect light depending on its type of circular polarization. Extensive research carried out by Chiral Photonics, Inc. [ 3] revealed that chi- ral fibers (CFs) with pitch values H of less than 100 μm exhibit selectivity with respect to the sign of circular polarization [ 4]. For long-period CFs (H ∝ 100 μm), this selectivity is caused by the resonant coupling of core modes to copropagating cladding modes [ 5]. In inter- mediate-period CFs with lesser values of H, such selec- tivity is ensured by coupling to other transverse modes [ 4]. In addition, Bragg CFs feature polarization sensitivity in the stop-band area [ 3, 6]. Such unique properties of CFs open great vistas for their application as fiber sensors [ 7]. The above-mentioned research has mostly been con- cerned with monomode fibers. Meanwhile, since the pioneering work by Poole et al., it has been established that helical fiber gratings can transform the fundamental mode (FM) into the higher-order l  1 mode, l  0; 1; 2… being the orbital number of the mode [ 8]. The same prop- erty has also been established for helical fiber gratings [ 9]. Recently, this question has been revisited in connec- tion with the propagation and generation of optical vor- tices (OVs) in helical-core fibers (HCFs). The ability of Bragg HCFs in the linear operating regime to maintain the propagation of a single OV in the stop-band region has been demonstrated [ 10]. Such fibers were shown to be able to change the topological charge (TC) of the in- coming field by a unity, thus operating as mode convert- ers [ 11, 12]. In general, twisted fibers with an l-fold symmetry of the transverse cross section can change the TC by l units [ 13]. Such systems with embedded chirality enable transitions between the fiber modes with different orbital numbers, which is important for various applica- tions [ 14, 15]. Those papers, however, report only possible discrete operations with orbital angular momentum (OAM) of the incoming field. At the same time, it is desirable to have devices enabling continuous operation with the OAM of the transmitted field. In this connection, in this Letter we propose a scheme that makes possible in the linear operating regime an all-fiber continuous control of the OAM of the optical field transmitted through the sys- tem of long-period HCFs. In the proposed scheme the section of the HCF, which while taken separately can generate an OV of TC 1 from the input FM, is cut into two equal pieces that can be twisted around their mutual axis with respect to each other. We show that such a fiber system can continuously change the OAM of the field from 0 to 1 (in a.u.) upon variation of the twist angle provided the input field is the FM. In general, such a sys- tem is able at a certain wavelength to change the OAM from l to l  1 provided the input field has a well-defined OAM of l units. As is known, if the lattice vector q  2π∕H of the HCF satisfies the resonance condition q ≈ q 0 ≡ ~ β 0 − ~ β 1 , where ~ β 0 and ~ β 1 are the scalar propagation constants of the HE 11 and LP 11 modes, intensive hybridization of these modes takes place. The structure of coupled modes near resonance is jΨ 1 icos χ j1; 0ie iqz  sin χ j1; 1ie iβ  z ; jΨ 2 i− sin χ j1; 0ie iqz  cos χ j1; 1ie iβ − z ; (1) where ε  q − q 0 , β   0.5 ~ β 0  ~ β 1 − q   ϵ 2  Q 2 p , tan χ  Q∕  ϵ 2  Q 2 p − ϵ, and Q is the corresponding coupling integral [ 11]. Here in the basis of linear polar- izations, jσ;li ≡  1 iσ  e ilφ F l r , where F l r  is the radial function of the mode and cylindrical-polar coordinates r; φ;z are implied. In the following we will restrict our July 1, 2013 / Vol. 38, No. 13 / OPTICS LETTERS 2277 0146-9592/13/132277-03$15.00/0 © 2013 Optical Society of America