Yousef Fazea*, Mustafa Muwafak Alobaedy and Zeyid T. Ibraheem Performance of a Direct-Detection Spot Mode Division Multiplexing in Multimode Fiber https://doi.org/10.1515/joc-2017-0135 Received August 15, 2017; accepted September 27, 2017 Abstract: Multimode fiber (MMF) regarded as an excellent choice for providing large capacity and high-speed for applications such as data centers due to its adaptability and unwavering quality. The ceaseless development and the increase of Internet users that emphasis on increasing data capacity have promoted mode division multiplexing (MDM) as a promising contender for providing further level of multiplexing freedom by propagating several and dissimilar channels in different mode stream. This paper investigates and analyzes the effects of launching MDM spot mode with various vortex order using verticalcavity surface-emitting laser array in conjunction with equalization scheme. A capacity of 40 Gbit/s transmitted over MMF long distance of 1500 m has been achieved at a wavelength of 1550.12 nm. Keywords: mode division multiplexing, spot mode, multimode fiber, equalization 1 Introduction Huge organizations are in a genuine need for supercomputing performance and productive processing execution to suit the expandingdevelopmentofInternet users and the tremendous growth of the amount of data. Thus, organizations are moving to data centers for their cloud computing infrastructure [1]. Data centers is characterized for being positioned in huge buildings for data connectivity, information availability, and disaster recovery [2], where multimode fiber (MMF) is frequently utilized in data centers for its adaptability and reliability [3]. To maintain the persistent needs of supercomputing and proficient information processing, multiplexing schemes based on code, polarization [4], wavelength [5, 6], and time [7] have been explored. Mode division multiplexing (MDM) has been postured for expanding the limit of optical fiber in in multipleinput-multiple-output (MIMO) systems. In MDM, few modes are multiplexed to propagate data in a parallel stream through a single optical fiber, then those modes are demultiplexed into their designated channels to increase the aggregated data rate [8, 9]. MDM capacity improvement can be realized using gratings [10, 11], spatial light modulators[12], digital signal processing [13–15], photonic crystal fiber, modal decomposition methods, few mode fiber (FMF) [16–18], multi-core fibers (MCF) [19, 20] or multi-ring fibers [21, 22], and modal demultiplexing methods [23]. A few dispatch modes have been deployed for MDM, for example, Hermite-Gaussianmodes[10,24],Laguerre- Gaussian (LG) modes [25, 26], doughnut modes [27–29], spot modes [30–32] and helical-phase mode [33] to improvethelimitofMMFandreducemodecoupling. In Refs [30, 31], 6-spot couplers have been considered and examined, introducing low-loss couplers with a mode subordinate loss under 1 dB which is possible for a colossal number of modes. Furthermore, electronic dispersion compensation (EDC) considered as another data transfer capacity improvement system to upset the flag at the beneficiary side of the modular multiplexing after it transmitted through the MMF scheme. This paper investigates a new launching scheme using spot modes with various vortex orders in MMF utilizing a vertical-cavity surface-emitting laser (VCSEL) array in conjunction with EDC for further enhancement of MMF. Transverse electric field which used the output spatial electric field to be matched with the input spatial electric field, in order to calculate the power coupling efficiency and determine the validity of the received signal, bit-error-rate (BER) which used to assess end-to-end performance of a system including the transmitter, receiver, and the medium in between thetwo,andthequalitativeeyediagramareusedasa measurement metrics. This paper progress as follows: the designing of MDM spot mode is shown in Section 2. Section 3 investigation the outcome and present the discussion then the conclusion and future work presented in Section 4. *Corresponding author: Yousef Fazea,InterNetWorks Research Laboratory, School of Computing, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia, E-mail: yosiffz@internetworks.my Mustafa Muwafak Alobaedy,School of Computing, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia Zeyid T. Ibraheem,Ministry of Science and Technology, Baghdad, Iraq J. Opt. Commun. 2017; aop Brought to you by | Göteborg University - University of Gothenburg Authenticated Download Date | 12/22/17 5:49 PM 2 Methodology and simulation The proposed MDM spot mode is shown in Figure 1. Optsim 5.2 [34] in conjunction with Matlab [35] has been used to mode and simulate MDM spot mode. The model may have divided into three distinct: the first part is the transmitter part, where the input incident field has been generated using a pseudo-random binary sequence (PRBS), and modulated to a non-return-to-zero (NRZ), then emits the spot mode at wavelength of 1550.12 using VCSEL array laser. The electric field of the spot mode can be expressed as [34]: ψr,φðÞ= k,0≤r≤r max 0,r>r max
(1) where normalization powerkis set to 1.5 × 10 −8 and maximum radiusr max of the first spot mode is set to 8 μm, whereasr max is second spot mode maximum radius which set to 12 μm. The incident filed phase and the amplitude of the spot mode that emits from the VCSEL is shown in Figure 2. The incident field then transformed into sky ray of the MMF. The applied phase that transform by the vortex lens in each run which can be expressed as in [34]: tðx,yÞ= exp−j nπr 2 2λf +mθ  (2) r=x 2 +y 2 (3) θ= tan −1 y=xðÞ(4) wherex, yis the incident coordinate,fis the lens focal length,λis wavelength,nis material index, andmis vortex order (m= 1,3,3,4). The incident field after the vortex lens is shown in Figure 3, where the phase transformation is changing at different vortex order. The incident field of the spot mode is measured before it propagates through the MMF and after. The power coupling coefficient of the desired mode at the input can be expressed as: C lmin = ÐÐ A core E in ðx, yÞ.e lm *ðx,yÞdx dy           2 ÐÐ A core E in ðx,yÞ jj 2 dxdy ÐÐ A core e lm ðx,yÞ jj 2 dx dy (5) where E in generated transverse electric file ande lm is the polarized transverse electric field of spot mode. In the Figure 1:Schematic diagram of MDM model of spot mode. Figure 2:Amplitude and phase of the incident field of spot mode. 2Y. Fazea et al.: Performance of a Direct-Detection Spot MDM Brought to you by | Göteborg University - University of Gothenburg Authenticated Download Date | 12/22/17 5:49 PM medium part, the excited modes then coupled into 1500 m MMF length with assumed core size of 25 μm. The refractiveindexoftheMMFisshowninFigure4.Inthe receiver part, two spatial receivers are used to retrieve the transverse spatial field after it propagated through the MMF. Decision feedback equalizer (DFE) is used to correct the distorted signal. The main purpose of DFE is to cancel intersymbol interference. 3 Results and discussion There are two approaches to analyze the results that obtained, subjective approach and quantifiable approach. Figure 5 introduces the spot transverse electric field after modes travel through the MMF for various vortex arrange such asm=1,m=2,m=3,m=4 and m= 5. Recognizable incident field has been obtained once (a)m=1, and (b)m= 2 contrasting with various vortex arrange, whereby in the case of (c)m=3 the spatial electric field displaysa powerless lights intensity followed by case (d)m=4. Figure 6 shows the eye Figure 3:Amplitude and phase of the incident field of spot mode (a)m=1, (b)m=2, (c)m=3, and (d)m=4. Figure 4:Measured dip refractive index profile of manufactured MMF in MDM model. Figure 5:Magnitude and phase distributions of the obtained spatial after MMF, (a)m=1, (b)m=2, (c)m=3, and (d)m=4. Y. Fazea et al.: Performance of a Direct-Detection Spot MDM3 Brought to you by | Göteborg University - University of Gothenburg Authenticated Download Date | 12/22/17 5:49 PM diagram of every vortex number in two separate positions, before and after the integration of the equalization scheme. Eye diagram metrics is observed to be distorted and narrowed before the equalization however, after the equalizer clean and widely open eyes can be observed. The significant eye in terms of widely eye opening and less noise was obtained oncem= 1 as in Figure 6 (a) and m= 2 as in Figure 6 (b). The signal is quite recovered, yet signal worsen for the casesm= 3 andm=4asinFigure6 (f) and (h). The outcome was additionally affirmed quantitatively using BER analyzer to give an exact reading as shown in Table 1, whereby the table presents the impacts of various vortex arrange on the modal multiplexing scheme. Figure 6:Power coupling coefficients versus modal delay for MDM spot mode after propagating through the MMF whereby the focal length, f=8 mm and vortex order,mis varied each run to (a)m=1, (b)m=2, (c)m=3, and (d)m=4. 4Y. Fazea et al.: Performance of a Direct-Detection Spot MDM Brought to you by | Göteborg University - University of Gothenburg Authenticated Download Date | 12/22/17 5:49 PM 4 Conclusion A spot mode was specifically launched in a MMF utilizing a VCSEL array for different vortex orders. Decent outcomes were acquired for spot size of vortex request oncem= 2 and slightly oncem= 1. A capacity of 40 Gbit/s has been achieved over a MMF length of 1500 m. The work empowers productive coupling into particular spot modes and makes ready for MDM in an integrated optics for optical interconnects. References 1. Barroso LA, Clidaras J, Hölzle U. The datacenter as a computer: an introduction to the design of warehouse-scale machines. 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