invited article division and multiplication of the state order for data carrying orbital angular momentum beams

Invited Article: Division and multiplication of the state order for data-carrying orbital angular momentum beams Zhe Zhao, Yongxiong Ren, Guodong Xie, Long Li, Yan Yan, Nisar Ahmed, Zhe Wang, Cong Liu, Asher J Willner, Solyman Ashrafi, and Alan E Willner Citation: APL Photonics 1, 090802 (2016); doi: 10.1063/1.4968838 View online: http://dx.doi.org/10.1063/1.4968838 View Table of Contents: http://aip.scitation.org/toc/app/1/9 Published by the American Institute of Physics Articles you may be interested in Switchable polarization rotation of visible light using a plasmonic metasurface APL Photonics 2, 016103 (2016); 10.1063/1.4968840 Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal APL Photonics 2, 016102 (2016); 10.1063/1.4968043 High-speed switching of biphoton delays through electro-optic pump frequency modulation APL Photonics 2, 011301 (2016); 10.1063/1.4971313 All-optical multichannel logic based on coherent perfect absorption in a plasmonic metamaterial APL Photonics 1, 090801 (2016); 10.1063/1.4966269 APL PHOTONICS 1, 090802 (2016) Invited Article: Division and multiplication of the state order for data-carrying orbital angular momentum beams Zhe Zhao,1,a Yongxiong Ren,1 Guodong Xie,1 Long Li,1 Yan Yan,1 Nisar Ahmed,1 Zhe Wang,1 Cong Liu,1 Asher J Willner,1 Solyman Ashrafi,2 and Alan E Willner1,a Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA NxGen Partners, Dallas, Texas 75219, USA (Received 27 August 2016; accepted 25 October 2016; published online December 2016) We demonstrate all-optical division and multiplication of the state order for datacarrying orbital angular momentum (OAM) beams We use linear optical transformations between log-polar and Cartesian coordinates to: (i) divide the OAM state order to convert the OAM order from to ( = ☞5, ☞4, , +4, +5), and (ii) multiply the OAM state order from to We analyze the OAM mode purity and the bit-error-rate performance of a classical two-mode OAM multiplexed link for the case of division and multiplication of the OAM state order The experimental mode purity for halving and doubling OAM state order can reach around 87% and 40%, respectively We further study the dependence of the OAM mode purity on the displacement of SLMs in simulation The obtained results show that the transformation for doubling the OAM state order is more sensitive to the increase of the displacement than that for halving the OAM state order The link bit error rates are below the forward error correction threshold of 3.8 ì 10 for both channels â 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4968838] Orbital angular momentum (OAM) has recently gained attention in communication systems in which multiple independent OAM beams are spatially multiplexed to increase system capacity.1,2 In 1992, an electromagnetic wave with a helical wavefront exp(i θ), where is the OAM state order, θ the azimuthal angle, and the reduced Plank constant, was found to carry an OAM of per photon.3–5 The beam’s wavefront twists along the propagation axis, producing a central intensity null (i.e., phase singularity) and an annular ring shape OAM beams with different state orders are orthogonal to each other, which enables efficient OAM-based mode-division multiplexing in the optical1,2,6,7 and radio8–10 domains We note that OAM-based quantum information processing11–14 has also been used to increase the usable alphabet for quantum systems.15 For certain applications, it might be valuable to manipulate the OAM states of light, namely, translating one OAM state to another state This function could be used for reconfigurable systems, such as switching and routing applications.16 Moreover, modifying the channel spacing for OAM systems could potentially reduce OAM channel crosstalk 17 (by increasing the state spacing) or enhance mode and system efficiency (by reducing the state spacing) Several elements have been proposed to add or subtract (i.e., shift) a fixed-order number onto the OAM states of light, including spiral phase plates,18,19 spatial light modulator (SLM),20 integrated microring resonators,21 metametrials,22,23 and metasurfaces.24,25 In addition to shifting the OAM state order , it might be valuable to perform the division and multiplication of the OAM state order; note that frequency dividers26 and multipliers27,28 are fairly useful for signal processing systems in which the frequency domain is being manipulated Note: Contributed paper, published as part of the European Conference on Optical Communications (ECOC), Valencia, Spain, September 2015 aAuthors to whom correspondence should be addressed Electronic addresses: zhezhao@usc.edu and willner@usc.edu 2378-0967/2016/1(9)/090802/8 1, 090802-1 © Author(s) 2016 090802-2 Zhao et al APL Photonics 1, 090802 (2016) Previously, OAM state multiplication combined with frequency multiplication has been achieved using nonlinear harmonic generation.29,30 Another demonstration of OAM state multiplication was achieved using linear optical coordinate transformations.17 However, there have been few reports of OAM state division, nor has there been data transmission on these beams that are undergoing either division or multiplication In this paper, we demonstrate all-optical division and multiplication for data-carrying OAM beams, based on two-step linear optical coordinate transformations.31 We experimentally realize the bidirectional transformation between states | and |2 with varying from ☞5 to +5 The experimental mode purity for halving and doubling the OAM state order can reach around 87% and 40%, respectively We analyze the dependence of the OAM mode purity on the displacement of SLMs in simulation When the displacement increases from µm to 40 µm, the mode purity of OAM +4 decreases from 89% to 81% for halving OAM +8 and from 98% to 18% for doubling OAM +2 It shows the transformation for doubling the OAM state order is more sensitive to the increase of the displacement than that for halving the OAM state order We also measure the bit-error-rate (BER) performance of a classical 100-Gbit/s two-mode OAM multiplexed link after division and multiplication of the OAM state order and achieve BERs