Calculation of the frequency response in step-index plastic optical fibers using the time-dependent power flow equation Branko Drljac ˇa a , Svetislav Savovic ´ a,n , Alexandar Djordjevich b a Faculty of Science, R. Domanovic ´a 12, 34000 Kragujevac, Serbia b City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China article info Article history: Received 25 October 2010 Received in revised form 17 January 2011 Accepted 18 January 2011 Available online 5 February 2011 Keywords: Plastic optical fiber Frequency response Bandwidth abstract The time-dependent power flow equation, which is reduced to its time-independent counterpart is employed to calculate frequency response and bandwidth in addition to mode coupling and mode- dependent attenuation in a step-index plastic optical fiber. The frequency response is specified as a function of distance from the input fiber end. This is compared to reported measurements. Mode- dependent attenuation and mode dispersion and coupling are known to be strong in plastic optical fibers, leading to major implications for their frequency response in data transmission systems. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Plastic optical fibers (POFs) are often considered for high- performance short-distance data transmission systems including high-bandwidth local-area networks and multi-node bus net- works [1–4]. In addition to being a more affordable, flexible and rugged alternative to glass fibers, POFs are also easier to handle. Their large-core diameter (0.5–1 mm or larger) allows pairing with LED sources using low-precision plastic components. This results in inexpensive but robust systems that are easy to interconnect. Variety of POF applications have been commercialized ranging from simple light-transmission guides in displays and power delivery systems to sensors and short-haul communication links [4]. Installations within buildings or vehicles, where sharp corners and branches are many or the network is repeatedly reconfigured, represent a domain with growth potential for POF applications. Transmission properties of step-index (SI) multimode optical fibers, such as frequency response and bandwidth, depend strongly upon mode-dependent attenuation, modal dispersion and the rate of mode coupling (power transfer from lower to higher order modes) caused by intrinsic perturbation effects (primarily due to microscopic bends, irregularity of the core- cladding boundary and refractive index distribution fluctuations). Different models have been used to simulate these three impor- tant effects for SI optical fibers. The ray tracing model can determine the output angular power distribution while account- ing for the mode-dependent attenuation. The time delay between individual rays can also be calculated in presence of modal dispersion. This model is computationally intensive because large number of ray-trajectories must be simulated. In contrast, the time-independent power flow equation [5] is effective in model- ing mode-dependent attenuation, mode coupling, and how these influence the output angular power distribution with fiber length for different launch conditions. However, the frequency response and bandwidth are not calculated. We have overcome this limitation using the time-dependent power flow equation and have determined the POF frequency response and bandwidth in addition to mode coupling and mode- dependent attenuation. Verified against measurements by Mateo et al. [6], we showed how the resulting change in bandwidth with fiber length is strongly affected by mode coupling typical of POFs. 2. Time-dependent power flow equation We use Gloge’s time-dependent power flow equation to describe the evolution of the modal power distribution along the axis of the SI POF (as the z-coordinate). Individual modes are characterized by their inner propagation angle y measured with respect to fiber axis. Gloge’s time-dependent power flow equation can be written as [7]: @Pðy, z, tÞ @z þ @t @z @Pðy, z, tÞ @t ¼aðyÞPðy, z, tÞþ 1 y  @ @y yDðyÞ @Pðy, z, tÞ @y   ð1Þ where t is the time, Pðy, z, tÞ is the power distribution over angle, space and time, respectively, aðyÞ is the mode-dependent attenuation, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlaseng Optics and Lasers in Engineering 0143-8166/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2011.01.016 n Corresponding author. Fax: + 381 34 335040. E-mail address: savovic@kg.ac.rs (S. Savovic ´). Optics and Lasers in Engineering 49 (2011) 618–622