Attenuation and modal dispersion models for spatially multiplexed co-propagating helical optical channels in step index fibers Syed H. Murshid n , Abhijit Chakravarty, Raka Biswas Optronics Laboratory, Department of Electrical and Computer Engineering, Florida Institute of Technology, 150 W University Boulevard, Melbourne, FL 32901, USA article info Article history: Received 19 March 2010 Received in revised form 15 June 2010 Accepted 17 June 2010 Available online 6 August 2010 Keywords: Optical fiber communication Optical multiplexing Skew rays abstract Spatial reuse of optical frequencies has been shown to be possible through a novel spatial domain multiplexing (SDM) technique that uses spatial multiplexer at the input end to launch multiple channels of the same wavelength inside a single strand of carrier fiber and then employs spatial filtering methods to de-multiplex the different optical channels at the output end. The individual SDM channels are confined to dedicated spatial locations inside the fiber while traversing through it owing to helical propagation of light. This presents attenuation and dispersion models of such a system. Experimentally obtained beam profile and resultant crosstalk of two such spatially multiplexed co-propagating SDM channels of the same wavelength over standard step index multimode optical fibers are also presented. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction Fiber optic data transfer facilities have gradually become an integral part of the infrastructure at data centers worldwide. Current infrastructure used at most data centers is generally a decade old and requires up-gradation as legacy multimode fibers are typically used for low bandwidth applications and these fibers can only support limited distances at data rates exceeding 1 Gb/s. However optical fibers employed in building back bones are generally limited to 100–300 m in length and they are seldom replaced as new fibers are usually added to the same conduit as the old fibers. As a result many investigative endeavors have been undertaken on various methods for extending the distance of multimode fibers at higher data rates such as bandwidth enhancement in multimode fiber, electronic dispersion compen- sation, and wavelength tuning control loops [1]. Most of these techniques are incremental in nature and the goal of increasing total capacity in optical communications and networking requires new concepts for basic transmission media. SDM is a novel multiplexing technique that employs helical propagation of light and can significantly enhance the data rates by allowing co-propagating channels of the same wavelength inside step index optical fibers. Spatial reuse of optical frequencies has been a cherished goal in optical fiber communications for a long time; however it proved elusive for all practical purposes until SDM was reported as it was almost impossible to rule out interference owing to the small dimensions of core region of the fibers. Many different techniques such as mode group diversity [2,3] and modal multiplexing [4] using slightly off-axis meridional rays have been mentioned in the literature but these are mostly limited to graded index fibers and proved to be useful only for short distances as predicted by Gloge’s power flow equation [5]. Gambling et al. [6] showed that the steady state solution to Gloge’s power flow equation does support donut shaped output rings but these rings collapse to a Gaussian beam profile after propagating short distances. Multiple papers [7,8] have presented solutions to Gloge’s power flow equation using experimental, numerical and analytical techniques, ever since it was first published in 1971. All these endeavors unanimously attest to the fact that modal multiplexing is not feasible for any reasonable distances as the length of the fiber greatly affects the output pattern, and a sufficiently long fiber produces a circular Gaussian profile. After a fiber length of 100–200 m donut shaped beam collapses into a disk type circular output. As a result such modal multiplexing techniques could not be used for any reasonable distances and its application was limited to short distances and they often require complex signal processing algorithms such as zero forcing algorithm [2], which renders them to be very expensive for most applications. On the contrary the SDM has already been successfully tested for distances exceeding a kilometer where multiple fiber patches, on different spools, were integrated together using mechanical and fusion splices. This approach offers a practical solution for increasing the bandwidth distance product of most legacy multimode fibers as it supports both step index and graded index fibers where helically propagating channels are launched using selective input angles at the input end and simple spatial filtering techniques are used to descramble the channels at the output end. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlastec Optics & Laser Technology 0030-3992/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2010.06.004 n Corresponding author. E-mail address: murshid@ee.fit.edu (S.H. Murshid). Optics & Laser Technology 43 (2011) 430–436