# Overcoming Challenges in Large-Core SI-POF-Based System-Level Modeling and Simulation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{TM}and ModeSYS

^{TM}.

## 1. Introduction

## 2. POF Modeling Challenges

## 3. Component Modeling

#### 3.1. SI-POF Modeling

_{g}(θ) is an angle-dependent group velocity accounting for modal dispersion, α(θ) is an angle-dependent power attenuation accounting for differential mode attenuation (DMA), and D(θ) is the diffusion function that accounts for power coupling during propagation. We define the angle-dependent group velocity as [29]:

_{core}is the core index. For D(θ), we use a sigmoid function [23]:

_{0}, D

_{1}, D

_{2}, and σ

_{d}are fitting parameters of our experimental data for a specific fiber type. Optionally, we may set D(θ) = D

_{0}[23], thereby neglecting any angular dependence. For α(θ), the angular dependence can be modeled quadratically using [20]:

_{2}is a fitting parameter. Alternatively, following the treatment in [23], we may define α(θ) using:

_{1}, σ

_{2}, θ

_{1}, and θ

_{2}are fitting parameters.

_{max}(which may be larger than the maximum as determined by the fiber’s NA [23,29]) and then, as described in [29], we discretize the θ dimension by sampling over the interval [0, θ

_{max}] at N points, each of which corresponds to a discrete internal angle θ whose intensity in the fiber is described by p(θ, z, t). We then numerically solve the resulting equations to determine the output intensity p(θ, z = L, t), where L is the fiber length. An iterative time domain split-step procedure can be applied [53,54], wherein the algorithm alternates between propagation over a distance ∆z, and coupling/attenuation calculated via numerical integration [55].

_{1}, the intensity at a longer length z

_{2}can be calculated with the following matrix equation:

**P**(z,ω) are vectors, whose components are the intensity values for each discretized angle and are different at each z and for each frequency ω. Although it is usually called a propagation matrix,

**M**(ω) is, in fact, not only one matrix but a set of tri-diagonal matrices that are calculated from the angular diffusion and attenuation functions as defined in Equations (3) and (5). To fully characterize the fiber, we need the complete set of matrices

**M**(ω), one for each frequency, which have complex values except for

**M**(0). For the typical case where z

_{1}is at the input source,

**P**(ω) =

_{in}**P**(0,ω) and the output is at the end of a fiber segment of length L,

**P**(ω) =

_{out}**P**(L,ω), Equation (11) describes how the output intensity at the end of that fiber segment can be obtained from the input intensity:

**M**(ω) are obtained as powers of the basic tri-diagonal matrices,

_{L}**M**(ω)

^{L/}

^{∆z}, and account for the effect of the fiber on the input optical intensity. Therefore, to obtain the intensity after propagation through a given length L, it is necessary to calculate the matrix product in Equation (11) for each frequency. The resulting output intensity

**P**(ω) contains the information required to obtain all the important spatial and temporal parameters related to fiber transmission. Figure 1a illustrates the operation described in Equation (11) with a set of vectors at the input (right) and another at the output (left), which is obtained by performing the corresponding matrix product of the former with the set of matrices. The absolute values of matrices

_{out}**M**(ω

_{L}_{i}) are shown in Figure 1b as an example for the case of a commercial SI-POF of 25 m and three different values of frequency.

#### 3.2. Transmitter Modeling

_{ext}, i.e., the angle outside the fiber, related to the internal or propagation angle θ by θ

_{ext}= asin(n

_{core}sin(θ)):

_{ext}is the full-width at half maximum, specified in degrees. Similar expressions can also be used as a function of internal angle. This way, different means of describing the launch intensity can be used to satisfy the needs of most system designers: either launch intensity as a function of external or internal angle: p(θ

_{ext}, z = 0) and p(θ, z = 0), respectively, or encircled angular flux: EAF(θ

_{ext}) or EAF(θ).

_{ext}) is related similarly to p(θ

_{ext}).

#### 3.3. SI-POF Injection

**M**, in which the output intensity at some angle θ

_{inj}_{i}is a weighted linear summation of the input powers at all input angles [29]. Using our discretized angles approach, the output intensity as a function of the input intensities can be represented as:

_{inj}(θ

_{i}, θ

_{j}) is a coupling coefficient between the input at θ

_{j}and the output at θ

_{i}and t indicates that the signals are in the time domain. If we represent the intensities as vectors

**P**(t) = [p

_{out}_{out}(θ

_{i},t)]

^{T}and

**P**(t) = [p

_{in}_{in}(θ

_{j},t)]

^{T}, we can also represent this relationship as

**M**is the injection matrix with elements m

_{inj}_{inj}(θ

_{i}, θ

_{j}).

**M**can be derived from measurements, as described in detail in [30,32,49]. An equation equivalent to Equation (15) can be written with the intensity vectors as functions of frequency instead of time:

_{inj}_{z}of width Δz to take along the z direction. The choice of Δz is arbitrary and, therefore, it suffices to specify the fiber injection loss factor as a function of angle, the coupling terms D

_{0}and D

_{1}of Equation (3) in units of radians

^{2}(rather than radians

^{2}/m), and the number of steps N

_{z}. The parameters D

_{2}and σ

_{d}are also specified.

#### 3.4. Connector Modeling

_{i}is a weighted linear summation of the input powers at all input angles. Similar to Equation (10), the output intensity as a function of the input intensities can be represented as:

_{conn}(θ

_{i}, θ

_{j}) is a coupling coefficient between the input at θ

_{j}and the output at θ

_{i}. Likewise, if we represent the intensities as vectors

**P**and

_{out}**P**, which can be functions of either time or frequency, we can also represent this relationship as the matrix product:

_{in}**M**is a matrix with elements m

_{conn}_{conn}(θ

_{i}, θ

_{j}).

_{0}.

^{−1}is the inverse zero-order Hankel transform, J

_{1}(2π a ρ)/ρ is the Airy pattern that is the transform of the circular aperture with radius $a$ used to model the fiber surface, and G(ρ) is the transform of g(r), which is the projection of the radiation pattern. As the radiated intensity has circular symmetry, the explicit dependency on φ has been omitted.

_{p}(r

_{0}, z

_{0}) for a given pair of misalignments [51]. A more flexible approach is to calculate the proportion of light that on exiting the radiating fiber at a given angle of interest in free-space (thus, an external angle) θ

_{i,ext}, is able to reach the receiving fiber. This is equivalent to assuming that each point of the fiber radiates light in a very narrow angular range centered at that angle. Then, instead of a circular pattern, its projection onto a perpendicular plane will be a very narrow ring. The equations to calculate this angular loss function are:

**M**is a diagonal matrix whose diagonal elements are calculated from Equation (20b) after conversion from external to internal angles:

_{misalign}**M**is the product of the misalignment matrix

_{CC}**M**and the basic connector matrix

_{misalign}**M**, and is the same for the temporal and frequency approaches. Figure 5 shows the connector matrices for several misalignment pairs. The images show how the connector introduces not only attenuation but also diffusion. Misalignments do not introduce further diffusion but can considerably increase attenuation.

_{conn}#### 3.5. Fiber Bends

**M**, or via an equivalent fit of the Gloge power-flow equation [32]. The matrix will depend on the bend radius and also on the bend angle (e.g., a complete turn of 360°, will be different from a right-angle turn of 90°). Once again, the key assumption is that the output intensity at some angle θ

_{bend}_{i}is a weighted linear summation of the input powers at all input angles. In other words

_{bend}(θ

_{i}, θ

_{j}) is a coupling coefficient between the input at θ

_{j}and the output at θ

_{i}. Representing the intensities as vectors

**P**and

_{out}**P**, that can be functions of time or frequency, we can also express this relationship as:

_{in}**M**is a matrix with elements m

_{bend}_{bend}(θ

_{i}, θ

_{j}). Furthermore, similar to the Injection and Connector models, and as described in [32], it is possible to fit this matrix to the Gloge power-flow equation [20,23,29,30]. Similarly, the interpretation of the Gloge power-flow equation is the same as that of the Injection and Connector models above. The fiber bend matrix

**M**can be derived from measurements, as described in detail in [32].

_{bend}#### 3.6. Detector Coupling

_{0}is the lateral shift between the fiber axis and the detector center and z

_{0}is the longitudinal distance of the fiber end to the active area of the photodetector. Accounting for the detector possibly having a radius b that is different from the fiber core radius a, implies replacing a with b in Equation (20b). Thus, we can calculate the power-loss factor as a function of the propagation angle and the two shifts: l

_{p}(θ

_{i}, r

_{0}, z

_{0}). [50,51]. The complete model can be represented as:

**P**is the vector of output intensities,

_{out}**P**is the vector of input intensities that can be functions of time or frequency, and

_{in}**M**is a diagonal matrix with diagonal elements m

_{det}_{det}(θ

_{i}) calculated as:

## 4. System Level Modeling: Two-Step and One-Step Approaches

**P**(ω). The frequency dependence in this vector is flat, as the temporal characteristics of the transmitter are introduced in the second step. As for the fiber segments, they can be modeled with the corresponding propagation matrices

_{s}**M**(ω), i = 1, ..., 4, while ST connectors can be modeled by characteristic matrices

_{Li}**M**. Finally, matrix

_{ST}**M**is the diagonal matrix to account for angles that are not captured in the detector area, as discussed above. As in the case of the transmitter, the frequency response of the receiver and amplifier electronics is introduced in the second step. The optical intensity at the output of the whole POF layout,

_{det}**P**(ω), can then be calculated as the product of the matrices of every component of the POF link:

_{out}**F**(ω) is a single matrix that models the fiber link without the active components and all the individual matrices for each component can be derived as described in the previous sections. Additionally, connector misalignment, fiber bend and injection aspects can be easily accommodated by inserting their corresponding matrices at the appropriate points in Equation (27). Thus, for a given source with a particular spatial distribution, the frequency response of the POF layout can be derived as [29]:

_{out}(θ,ω) is the output intensity vector in the frequency domain, whose discretized version is

**P**(ω) from Equation (27), that is shown here as a function of the propagation angle, as well as of the frequency. Therefore, the spatial aspects of the system can be modeled as an equivalent linear system whose frequency response is H(ω).

_{out}^{TM}[57] and the second used the commercial simulation package OptSim

^{TM}, utilizing its MATLAB co-simulation capability to combine both steps into a single simulation event [58].

**P**(ω) at the output of the system components are represented in 2-D according to their dimensions: frequency ω and propagation angle θ.

_{out,sig}(θ,ω), that has been introduced, accounts for the output intensity containing both the spatial characteristics of the output signal and its frequency characteristics. This intensity can be calculated taking into account Equations (27) and (29):

**P**(ω) the frequency information of the transmitted data signal has been merged with the spatial information of the optical source and can be propagated in a block-by-block basis to perform system-level simulation of the POF link.

_{s,sig}## 5. Commercial Software

#### 5.1. MATLAB/Simulink

^{TM}environment [61]. The POF model formulated in the frequency domain in matrix form can be efficiently implemented in MATLAB, using Simulink as the software user interface and integration engine to build the POF simulation framework. Simulink offers two main simulation modes, denominated sample mode and frame mode, which specify how the schematic building blocks interact and process the signal that propagates throughout the model as the simulation progresses. In sample-based processing, blocks process signals one sample at a time and then propagate the processed sample to the next block. The frame mode accumulates a large number of signal samples constituting a frame. This frame is subsequently processed as a single unit by the model blocks. In our case, the frame-mode has been chosen for introducing the POF models. This simulation mode speeds up simulations significantly. Moreover, since the matrix models are in the frequency domain, working with frames is the natural way to split up the input data signal so that it can undergo a Fourier-transform.

**P**(ω), that has been defined in the description of the one-step simulation methodology.

_{s,sig}#### 5.2. ModeSYS

^{TM}is a simulation tool that is developed and marketed by Synopsys, Inc. [33]. Over the years, it has been used to model and simulate communication systems based on multimode glass optical fibers, with a primary focus on data communication applications. Unlike SI-POF, these fibers are usually of the graded-index variety made with core diameters of 50 or 62.5 microns, much less than that of SI-POF, which can be as large as 1 mm. Also, the sources are usually in the 850 or 1300 nm wavelength window. This means that, at most, only hundreds of propagating modes are supported by these fibers. Hence, ModeSYS takes the reasonable approach of simulating both the temporal waveform and spatial mode profiles of multimode glass optical fiber systems, thus combining system-level efficiency with device-level representation accuracy. It provides the user with an extensive set of measurement and analysis tools such as the basic signal representation in the time and frequency domains, but also representation of transverse mode profiles, radial power distributions, effective modal bandwidth, differential mode delay, encircled flux, eye diagram and BER.

## 6. System Level Simulation Example: PAM-4 Transmission over Large-Core Plastic Optical Fiber

^{−4}is below an FEC threshold of 3.7 × 10

^{−3}[66,67]. As described in [63], the supported bit rate for this typical system can be much higher than the 1 Gb/s used in this example. Close to the absolute bandwidth limit, we can also employ a detector coupler to eliminate the higher angle modes at the receiver, thus increasing the bandwidth; however, the resulting power loss in combination with the receiver sensitivity may force other system adjustments to meet the BER specifications.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Losada, M.A.; Mateo, J. Short Range (in-building) Systems and Networks: A Chance for Plastic Optical Fibers. In WDM Systems and Networks. Modeling, Simulation, Design and Engineering; Antoniades, N., Ellinas, G., Roudas, I., Eds.; Springer: New York, NY, USA, 2012; pp. 301–323. [Google Scholar]
- Nespola, A.; Abrate, S.; Gaudino, R.; Zerna, C.; Offenbeck, B.; Weber, N. High-Speed Communications Over Polymer Optical Fibers for In-Building Cabling and Home Networking. IEEE Photonics J.
**2010**, 2, 347–358. [Google Scholar] [CrossRef] - Grzemba, A. MOST: The Automotive Multimedia Network; Franzis Verlag: Munich, Germany, 2011; ISBN 9783645650618. [Google Scholar]
- Truong, T.K. Commercial airplane fibre optics: Needs, opportunities, challenges. In Proceedings of the 19th International Conference on Plastic Optic Fibres and Application, Tokyo, Japan, 19–21 October 2010; p. DN2-1–M. [Google Scholar]
- Lee, S.C.J.; Breyer, F.; Randel, S.; van den Boom, H.P.A.; Koonen, A.M.J. High-speed transmission over multimode fiber using discrete multitone modulation. J. Opt. Netw.
**2008**, 7, 183–196. [Google Scholar] - Breyer, F.; Lee, S.C.J.; Randel, S.; Hanik, N. Comparison of OOK- and PAM-4 Modulation for 10 Gbit/s Transmission over up to 300 m Polymer Optical Fiber. In Proceedings of the OFC/NFOEC 2008—2008 Conference on Optical Fiber Communication/National Fiber Optic Engineers Conference, San Diego, CA, USA, 24–28 February 2008; IEEE: Piscataway, NJ, USA, 2008; p. OWB5. [Google Scholar]
- Zeolla, D.; Nespola, A.; Gaudino, R. Comparison of different modulation formats for 1-Gb/s SI-POF transmission systems. IEEE Photonics Technol. Lett.
**2011**, 23, 950–952. [Google Scholar] [CrossRef] - Loquai, S.; Kruglov, R.; Ziemann, O.; Vinogradov, J.; Bunge, C.-A. 10 Gbit/s over 25 m Plastic Optical Fiber as a Way for Extremely Low-Cost Optical Interconnection. In Proceedings of the Optical Fiber Communication Conference, San Diego, CA, USA, 21–25 March 2010; OSA: Washington, DC, USA, 2010; p. OWA6. [Google Scholar]
- Loquai, S.; Kruglov, R.; Schmauss, B.; Bunge, C.-A.; Winkler, F.; Ziemann, O.; Hartl, E.; Kupfer, T. Comparison of Modulation Schemes for 10.7 Gb/s Transmission Over Large-Core 1 mm PMMA Polymer Optical Fiber. J. Light. Technol.
**2013**, 31, 2170–2176. [Google Scholar] [CrossRef] - Ziemann, O.; Krauser, J.; Zamzowr, P.E.; Daum, W. Application of Polymer Optical and Glass Fibers. In POF Handbook: Optical Short Range Transmission Systems, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 2008. [Google Scholar]
- Koike, K.; Koike, Y. Design of Low-Loss Graded-Index Plastic Optical Fiber Based on Partially Fluorinated Methacrylate Polymer. J. Light. Technol.
**2009**, 27, 41–46. [Google Scholar] [CrossRef] - Polley, A.; Kim, J.H.; Decker, P.J.; Ralph, S.E. Statistical Study of Graded-Index Perfluorinated Plastic Optical Fiber. J. Light. Technol.
**2011**, 29, 305–315. [Google Scholar] - Technologies | Perfluorinated GI-POF. Available online: https://chromisfiber.com/technology/why-perfluorinated-gi-pof/ (accessed on 16 June 2019).
- Aldabaldetreku, G.; Zubia, J.; Durana, G.; Arrue, J. Numerical Implementation of the Ray-Tracing Method in the Propagation of Light Through Multimode Optical Fiber. In POF Modelling: Theory, Measurements and Application; Bunge, C.A., Poisel, H., Eds.; Verlag Books on Demand GmbH: Norderstedt, Germany, 2007. [Google Scholar]
- Berganza, A.; Aldabaldetreku, G.; Zubia, J.; Durana, G.; Arrue, J. Misalignment Losses in Step-Index Multicore Plastic Optical Fibers. J. Light. Technol.
**2013**, 31, 2177–2183. [Google Scholar] [CrossRef] - Berganza, A.; Aldabaldetreku, G.; Zubia, J.; Durana, G. Ray-tracing analysis of crosstalk in multi-core polymer optical fibers. Opt. Express
**2010**, 18, 22446–22461. [Google Scholar] [CrossRef] - Arrue, J.; Aldabaldetreku, G.; Durana, G.; Zubia, J.; Garces, I.; Jimenez, F. Design of mode scramblers for step-index and graded-index plastic optical fibers. J. Light. Technol.
**2005**, 23, 1253–1260. [Google Scholar] [CrossRef] - Arrue, J.; Kalymnios, D.; Zubia, J.; Fuster, G. Light power behaviour when bending plastic optical fibres. IEE Proc. Optoelectron.
**1998**, 145, 313–318. [Google Scholar] [CrossRef] - Appelt, V.; Bunge, C.; Kruglov, R.; Surkova, G.; Poisel, H.; Zadorin, A. Determination of Mode Coupling Matrix Used by Split-Step Algorithm. In POF Modelling: Theory, Measurements and Application; Bunge, C.A., Poisel, H., Eds.; Verlag Books on Demand GmbH: Norderstedt, Germany, 2007. [Google Scholar]
- Gloge, D. Optical Power Flow in Multimode Fibers. Bell Syst. Tech. J.
**1972**, 51, 1767–1783. [Google Scholar] [CrossRef] - Breyer, F.; Hanik, N.; Lee, S.; Randel, S. Getting the Impulse Respose of SI-POF by solving the Time-Dependent Power-Flow Equation Using the Crank-Nicholson Scheme. In POF Modelling: Theory, Measurements and Application; Bunge, C.A., Poisel, H., Eds.; Verlag Books on Demand GmbH: Norderstedt, Germany, 2007. [Google Scholar]
- Djordjevich, A.; Savovic, S. Investigation of mode coupling in step index plastic optical fibers using the power flow equation. IEEE Photonics Technol. Lett.
**2000**, 12, 1489–1491. [Google Scholar] [CrossRef] - Mateo, J.; Losada, M.A.; Garcés, I.; Zubia, J. Global characterization of optical power propagation in step-index plastic optical fibers. Opt. Express
**2006**, 14, 9028–9035. [Google Scholar] [CrossRef] - Stepniak, G.; Siuzdak, J. Modeling of transmission characteristics in step-index polymer optical fiber using the matrix exponential method. Appl. Opt.
**2018**, 57, 9203–9207. [Google Scholar] [CrossRef] - Jiang, G.; Shi, R.F.; Garito, A.F. Mode coupling and equilibrium mode distribution conditions in plastic optical fibers. IEEE Photonics Technol. Lett.
**1997**, 9, 1128–1130. [Google Scholar] [CrossRef] - Zubia, J.; Durana, G.; Aldabaldetreku, G.; Arrue, J.; Losada, M.A.; Lopez-Higuera, M. New method to calculate mode conversion coefficients in si multimode optical fibers. J. Light. Technol.
**2003**, 21, 776–781. [Google Scholar] [CrossRef] - Rousseau, M.; Jeunhomme, L. Numerical Solution of the Coupled-Power Equation in Step-Index Optical Fibers. IEEE Trans. Microw. Theory Tech.
**1977**, 25, 577–585. [Google Scholar] [CrossRef] - Djordjevich, A.; Savović, S. Numerical solution of the power flow equation in step-index plastic optical fibers. J. Opt. Soc. Am. B
**2004**, 21, 1437–1438. [Google Scholar] [CrossRef] - Mateo, J.; Losada, M.A.; Zubia, J. Frequency response in step index plastic optical fibers obtained from the generalized power flow equation. Opt. Express
**2009**, 17, 2850–2860. [Google Scholar] [CrossRef] - Esteban, A.; Losada, M.A.; Mateo, J.; Antoniades, N.; López, A.; Zubia, J. Effects of connectors in si-pofs transmission properties studied in a matrix propagation framework. In Proceedings of the 20th International Conference on Plastic Optical Fibres and Applications, Bilbao, Spain, 14–16 September 2011; pp. 341–346. [Google Scholar]
- Losada, M.A.; Mateo, J.; Martínez-Muro, J.J. Assessment of the impact of localized disturbances on SI-POF transmission using a matrix propagation model. J. Opt.
**2011**, 13, 055406. [Google Scholar] [CrossRef] - Losada, M.A.; López, A.; Mateo, J. Attenuation and diffusion produced by small-radius curvatures in POFs. Opt. Express
**2016**, 24, 15710. [Google Scholar] [CrossRef] - ModeSYS
^{TM}–Multimode Optical Communication Systems. Available online: https://www.synopsys.com/optical-solutions/rsoft/system-network-modesys.html (accessed on 15 June 2019). - Richards, D.H.; Losada, M.A.; Antoniades, N.; Lopez, A.; Mateo, J.; Jiang, X.; Madamopoulos, N. Modeling Methodology for Engineering SI-POF and Connectors in an Avionics System. J. Light. Technol.
**2013**, 31, 468–475. [Google Scholar] [CrossRef] - Lopez, A.; Jiang, X.; Losada, M.A.; Mateo, J.; Richards, D.; Madamopoulos, N.; Antoniades, N. Temperature sensitivity of POF links for avionics applications. In Proceedings of the 2017 19th International Conference on Transparent Optical Networks (ICTON), Girona, Spain, 2–6 July 2017; IEEE: Piscataway, NJ, USA, 2017. [Google Scholar]
- Pujols, N.; Losada, M.Á.; Mateo, J.; López, A.; Richards, D. A POF Model for Short Fiber Segments in Avionics Applications. In Proceedings of the 2016 18th International Conference on Transparent Optical Networks (ICTON), Trento, Italy, 10–14 July 2016; IEEE: Piscataway, NJ, USA, 2016. [Google Scholar]
- Raptis, N.; Grivas, E.; Pikasis, E.; Syvridis, D. Space-time block code based MIMO encoding for large core step index plastic optical fiber transmission systems. Opt. Express
**2011**, 19, 10336–10350. [Google Scholar] [CrossRef] - Lopez, A.; Losada, A.; Mateo, J.; Zubia, J. On the Variability of Launching and Detection in POF Transmission Systems. In Proceedings of the 2018 20th International Conference on Transparent Optical Networks (ICTON), Bucharest, Romania, 1–5 July 2018; IEEE: Piscataway, NJ, USA, 2018. [Google Scholar]
- Werzinger, S.; Bunge, C.A.; Loquai, S.; Ziemann, O. An Analytic Connector Loss Model for Step-Index Polymer Optical Fiber Links. J. Light. Technol.
**2013**, 31, 2769–2776. [Google Scholar] [CrossRef] - Werzinger, S.; Bunge, C.A. Statistical analysis of intrinsic and extrinsic coupling losses for step-index polymer optical fibers. Opt. Express
**2015**, 23, 22318–22329. [Google Scholar] [CrossRef] - IEEE 802.3bv-2017—IEEE Standard for Ethernet Amendment 9: Physical Layer Specifications and Management Parameters for 1000 Mb/s Operation Over Plastic Optical Fiber. Available online: https://standards.ieee.org/standard/802_3bv-2017.html (accessed on 13 June 2019).
- Mena, P.V.; Ghillino, E.; Richards, D.; Hyuga, S.; Nakai, M.; Kagami, M.; Scarmozzino, R. Using system simulation to evaluate design choices for automotive ethernet over plastic optical fiber. In Proceedings of the SPIE 10560, Metro and Data Center Optical Networks and Short-Reach Links, San Francisco, CA, USA, 30–31 January 2018; Glick, M., Srivastava, A.K., Akasaka, Y., Eds.; SPIE: Bellingham, WA, USA, 2018; Volume 10560, p. 17. [Google Scholar]
- Lopez, A.; Losada, A.; Richards, D.; Mateo, J.; Jiang, X.; Antoniades, N. Statistical Approach for Modeling Connectors in SI-POF Avionics Systems. In Proceedings of the 2019 International Conference of Transparent Optical Networks (ICTON), Angers, France, 9–13 July 2019. [Google Scholar]
- Cherian, S.; Spangenberg, H.; Caspary, R. Investigation on Harsh Environmental Effects on polymer Fiber Optic link for Aircraft Systems; Kazemi, A.A., Kress, B.C., Mendoza, E.A., Eds.; International Society for Optics and Photonics: Bellingham, WA, USA, 2014; Volume 9202, p. 92020I. [Google Scholar]
- Poisel, H. Optical fibers for adverse environments. In Proceedings of the 12th International. Conference on Plastic Optical. Fibers, Seattle, WA, USA, 14–17 September 2003; pp. 10–15. [Google Scholar]
- Chen, L.W.; Lu, W.H.; Chen, Y.C. An investigation into power attenuations in deformed polymer optical fibers under high temperature conditions. Opt. Commun.
**2009**, 282, 1135–1140. [Google Scholar] [CrossRef] - Savovic, S.; Djordjevich, A. Mode Coupling in Plastic-Clad Silica Fibers and Organic Glass-Clad PMMA Fibers. J. Light. Technol.
**2014**, 32, 1290–1294. [Google Scholar] [CrossRef] - Tao, R.; Hayashi, T.; Kagami, M.; Kobayashi, S.; Yasukawa, M.; Yang, H.; Robinson, D.; Baghsiahi, H.; Fernández, F.A.; Selviah, D.R. Equilibrium modal power distribution measurement of step-index hard plastic cladding and graded-index silica multimode fibers. In Proceedings of the SPIE 9368, Optical Interconnects XV, San Francisco, CA, USA, 9–11 February 2015; Schröder, H., Chen, R.T., Eds.; SPIE: Bellingham, WA, USA, 2015; p. 93680N. [Google Scholar]
- Losada, M.A.; Mateo, J.; Serena, L. Analysis of Propagation Properties of Step Index Plastic Optical Fibers At Non-Stationary Conditions. In Proceedings of the 16th International Conference on Plastic Optical Fibres and Applications, Turin, Italy, 10–12 September 2007; pp. 299–302. [Google Scholar]
- Mateo, J.; Losada, M.A.; Antoniades, N.; Richards, D.; Lopez, A.; Zubia, J. Connector misalignment matrix model. In Proceedings of the 21st International Conference on Plastic Optical Fibres and Applications, Atlanta GA, USA, 10–12 September 2012; pp. 90–95. [Google Scholar]
- Mateo, J.; Losada, M.A.; López, A. POF misalignment model based on the calculation of the radiation pattern using the Hankel transform. Opt. Express
**2015**, 23, 8061–8072. [Google Scholar] [CrossRef][Green Version] - Gloge, D. Impulse Response of Clad Optical Multimode Fibers. Bell Syst. Tech. J.
**1973**, 52, 801–816. [Google Scholar] [CrossRef] - Yevick, D.; Stoltz, B. Effect of mode coupling on the total pulse response of perturbed optical fibers. Appl. Opt.
**1983**, 22, 1010–1015. [Google Scholar] [CrossRef] - Stoltz, B.; Yevick, D. Influence of mode coupling on differential mode delay. Appl. Opt.
**1983**, 22, 2349–2355. [Google Scholar] [CrossRef] - Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. Numerical Recipes in C: The Art of Scientific Computing; Cambridge University Press: Cambridge, UK, 1992; ISBN 9780521431088. [Google Scholar]
- Antoniades, N.; Losada, M.A.; Mateo, J.; Richards, D.; Truong, T.K.; Jiang, X.; Madamopoulos, N. Modeling and characterization of si-pof and connectors for use in an avionics system. In Proceedings of the 20th International Conference on Plastic Optical Fibres and Applications, Bilboa, Spain, 14–16 September 2011; pp. 105–110. [Google Scholar]
- MATLAB—MathWorks—MATLAB & Simulink. Available online: https://www.mathworks.com/products/matlab.html (accessed on 14 June 2019).
- OptSim—OptSim Product Overview | RSoft Products. Available online: https://www.synopsys.com/optical-solutions/rsoft/system-network-optsim.html (accessed on 14 June 2019).
- Lopez, A.; Losada, M.A.; Mateo, J.J. Simulation framework for POF-based communication systems. In Proceedings of the 2015 17th International Conference on Transparent Optical Networks (ICTON), Budapest, Hungary, 5–9 July 2015; IEEE: Piscataway, NJ, USA, 2015; Volume 2015, p. Mo.D5.4. [Google Scholar]
- Alcoceba, A.; Lopez, A.; Losada, M.A.A.; Mateo, J.; Vazquez, C.; López, A.; Losada, M.A.A.; Mateo, J.; Vázquez, C. Building a Simulation Framework for POF Data Links. In Proceedings of the 24th International Conference on Plastic Optical Fibers, Nuremberg, Germany, 22–24 September 2015. [Google Scholar]
- Simulink—Simulation and Model-Based Design—MATLAB & Simulink. Available online: https://www.mathworks.com/products/simulink.html (accessed on 15 June 2019).
- Bosco, G.; Curri, V.; Carena, A.; Poggiolini, P.; Forghieri, F. On the Performance of Nyquist-WDM Terabit Superchannels Based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM Subcarriers. J. Light. Technol.
**2011**, 29, 53–61. [Google Scholar] [CrossRef] - Kruglov, R.; Loquai, S.; Bunge, C.-A.; Schueppert, M.; Vinogradov, J.; Ziemann, O. Comparison of PAM and CAP Modulation Schemes for Data Transmission Over SI-POF. IEEE Photonics Technol. Lett.
**2013**, 25, 2293–2296. [Google Scholar] [CrossRef] - Kruglov, R.; Vinogradov, J.; Loquai, S.; Ziemann, O.; Bunge, C.-A.; Hager, T.; Strauss, U. 21.4 Gb/s Discrete Multitone Transmission over 50-m SI-POF employing 6-channel WDM. In Proceedings of the Optical Fiber Communication Conference, San Francisco, CA, USA, 9–13 March 2014; OSA: Washington, DC, USA, 2014; p. Th2A.2. [Google Scholar]
- Erkilinc, M.S.; Thakur, M.P.; Pachnicke, S.; Griesser, H.; Mitchell, J.; Thomsen, B.C.; Bayvel, P.; Killey, R.I. Spectrally Efficient WDM Nyquist Pulse-Shaped Subcarrier Modulation Using a Dual-Drive Mach–Zehnder Modulator and Direct Detection. J. Light. Technol.
**2016**, 34, 1158–1165. [Google Scholar] [CrossRef] - Karinou, F.; Prodaniuc, C.; Stojanovic, N.; Ortsiefer, M.; Daly, A.; Hohenleitner, R.; Kogel, B.; Neumeyr, C. Directly PAM-4 Modulated 1530-nm VCSEL Enabling 56 Gb/s/λ Data-Center Interconnects. IEEE Photonics Technol. Lett.
**2015**, 27, 1872–1875. [Google Scholar] [CrossRef] - Yekani, A.; Chagnon, M.; Park, C.S.; Poulin, M.; Plant, D.V.; Rusch, L.A. Experimental comparison of PAM vs. DMT using an O-band silicon photonic modulator at different propagation distances. In Proceedings of the 2015 European Conference on Optical Communication (ECOC), Valencia, Spain, 27 September–1 October 2015. [Google Scholar]

**Figure 1.**(

**a**) Graphical representation of the calculation of the optical intensity at the output of the fiber as a function of the input intensity; (

**b**) absolute values of the fiber matrices for a 25 m step-index plastic optical fiber (SI-POF) at different values of ω that correspond to frequencies of 0, 0.5 and 1 GHz.

**Figure 2.**Normalized intensities (

**a**) and encircled angular flux (EAFs) (

**b**) as a function of the width of the Gaussian intensity profile as emitted by the source (L = 0 m) and at the output of a 150 m SI-POF.

**Figure 3.**(

**a**) Point A in the fiber end surface has a radiation pattern given by g(θ) and (

**b**) each point in the fiber end surface (A, B, C, D, etc.) acts as an independent uncorrelated source.

**Figure 4.**The radiated pattern R(r

_{0}, z

_{0}) is integrated over the receiving fiber end surface to obtain misalignment loss.

**Figure 5.**Basic connector matrix with no lateral or longitudinal misalignment (center up) and examples of connector matrices with various combined misalignments. Values of the misalignment are given in mm.

**Figure 9.**Injection model intensity profile at input and output: not normalized (

**a**) and normalized (

**b**), showing the strong initial power diffusion from lower to higher angles.

**Figure 10.**Simulated POF input (

**a**) and output (

**b**) eyes, showing the effects of intermodal dispersion and mode coupling.

**Figure 11.**(

**a**) Equalized eye at the receiver demonstrating compensation of eye closure. (

**b**) Analytical BER estimate in comparison to an ideal reference curve.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Richards, D.; Lopez, A.; Losada, M.A.; Mena, P.V.; Ghillino, E.; Mateo, J.; Antoniades, N.; Jiang, X.
Overcoming Challenges in Large-Core SI-POF-Based System-Level Modeling and Simulation. *Photonics* **2019**, *6*, 88.
https://doi.org/10.3390/photonics6030088

**AMA Style**

Richards D, Lopez A, Losada MA, Mena PV, Ghillino E, Mateo J, Antoniades N, Jiang X.
Overcoming Challenges in Large-Core SI-POF-Based System-Level Modeling and Simulation. *Photonics*. 2019; 6(3):88.
https://doi.org/10.3390/photonics6030088

**Chicago/Turabian Style**

Richards, Dwight, Alicia Lopez, M. Angeles Losada, Pablo V. Mena, Enrico Ghillino, Javier Mateo, N. Antoniades, and Xin Jiang.
2019. "Overcoming Challenges in Large-Core SI-POF-Based System-Level Modeling and Simulation" *Photonics* 6, no. 3: 88.
https://doi.org/10.3390/photonics6030088