Dispersion and Dispersion Slope Compensation of an Optical Delay Line Filter (DLF) based on Mach-Zehnder Interferometers

Transcription

1 Dispersion and Dispersion Slope Compensation of an Optial Delay Line Filter (DLF) based on Mah-Zehnder Interferometers P.Pavithra 1, K.Karthika 2 1,2 Department of Eletronis and Communiation Engineering, Kumaraguru College of Tehnology, Coimbatore, Tamil Nadu, India. Abstrat Design and analysis on 10 Gb/s single hannel transmission in standard Single Mode Fiber (SMF) for dispersion ompensation of an optial Delay Line Filter (DLF) in signal proessing appliations have been implemented and realized using Mah-Zehnder Interferometers based on integrated photonis. Two approahes viz dispersion ompensation and dispersion slope ompensation are studied. The filter along with the fiber opti link is simulated in OptiSystem tool and the link parameters suh as Eye Pattern, Maximum Q fator and Minimum BER are determined. Keywords: Dispersion, Dispersion Compensation, Dispersion Slope Compensation, Single Mode Fiber (SMF), Delay Line Filter (DLF), Coupler. Introdution Dispersion is one of the limiting effets in high-data-rate optial transmission systems due to distortion [1], [2]. Dispersion is the phenomenon in whih the phase veloity or alternatively group veloity of a wave depends on its frequeny. Dispersion indues pulse broadening and distortion of the bits, whih ultimately lead to errors. Dispersion is sometimes alled Chromati Dispersion (CD) to highlight its wavelength-dependent nature, or Group-Veloity Dispersion (GVD) to signify the role of the group veloity. The various dispersion ompensation and management tehniques ould be broadly lassified as: Delay Line Filter (DLF), Dispersion Compensation Fibers (DCF), hirped Fiber Bragg Gratings (FBG), and High-Order Mode (HOM) fiber. The filter o-effiients that generates the desired transfer funtion is obtained through delay line filter in whih the transfer funtion is fully ontrolled by their filter oeffiients [1].This ompensation method an be done by using the positive dispersive elements like Single Mode Fiber (SMF) as the transmission fibers whih is periodially balaned by DLF. Delay Line Filters an be realized as Mah Zehnder interferometers. These filters have been implemented to ompensate dispersion and dispersion slope ompensation whih are modeled using the Z-transform of the filter [2]. The Delay Line Filter (DLF) is analyzed for a single hannel system operating at a data rate of 10 Gb/s with a transmitting wavelength of 1550 nm at a power of 0dBm, over 100 km single mode fiber. The Maximum Q fator, minimum BER and Eye opening penalty of the link is ompared. In this paper, dispersion and dispersion slope ompensation methodology to overome fiber opti distortions leading to minimum BER is implemented. As the ompensation tehniques are based on the onept of optial group delay and their dispersive properties is used to determine the group delay response. Group delay per unit length is defined as, τ g L = dβ dω = 1 dβ dβ 2π dλ dk = λ2 (1) The total delay differene over a distane L is δτ = dτ g dλ δλ = L dβ (2λ 2π dλ + d2 β λ2 dλ2) δλ = dτ dω δω = d dω ( L ) δω = L ( d2 β V g dω 2) δω (2) β 2 = d2 β dω2 is alled Group Veloity Dispersion (GVD) parameter, and shows how muh a light pulse broadens as it travels along an optial fiber. The more ommon parameter is alled Dispersion, and an be defined as the delay differene per unit length per unit wavelength as follows: D = 1 L dτ g dλ = d dλ ( 1 V g ) = 2π λ 2 β 2 D has a typial unit of [ps/(nm.km)]. Dispersion Compensation Optial delay line filters onsists of MZI stages whih onsists of one delay line, one phase shifter and two ouplers with the amplitude oupling oeffiients K 1 = 1 K 1 2 and K 2 = 1 K 2 2.Transfer funtion of AMZI, H(Z) AMZI = H(Z) COUPLER1. H(Z) DELAY. H(Z) PHASE. H(Z) COUPLER2 (4) The omparison of the transfer funtion of the delay line filter and the MZI obtain the expressions Ψ 0 = ϕ S and ρ 0 = K 1 2 K 2 2 K 1 K 2 in whih ρ 0 depends on K 1 and K 2. So the dispersion an be altered by hanging the oupling oeffiient of the Asymmetri MZI. Evaluating the equation (17) for different ρ 0 shows a sawtooth like waveform with linear dispersion slope over a ertain bandwidth. The sign of the dispersion slope an be hanged by inverting ρ 0 and the dispersion funtion is point symmetri about the roots whih yields the relations, (3) 2135

2 D N (ρ 0 ) = D N ( 1 ρ 0 ) (5) D N (Ω on + Ω) = D N (Ω on Ω) where n=1,2 (6) Figure 3: Four port Coupler shemati showing a Asymmetri Mah-Zehnder interferometers Relating the transfer funtion to an optial delay line filter as shown in Fig. 3 results in the struture of Asymmetri Mah- Zehnder Interferometer (AMZI) whih onsists of two ouplers with the oupling oeffiients of K 1 and K 2 as 0.5, delay = 100 ps and ϕ S = 90 0 and Fig. 4 shows the optial transmission system onsisting of a transmitter, fiber transmission hannel, tunable Dispersion Compensator (Asymmetri MZI) and a reeiver implemented in OptiSystem. Figure 4: Four port Coupler layout showing Delay Line Filter struture of a tunable asymmetri Mah-Zehnder interferometer Dispersion Slope Compensation Dispersion slope ompensator or delay line filter onsists of both asymmetri MZI and symmetri MZI. Dispersion slope is defined as the variation of dispersion with respet to wavelength. Dispersion and dispersion slope depend on ρ 0. Figure 5: Blok diagram of a delay line filter onsists of tunable symmetri and asymmetri Mah-Zehnder interferometers using four port Coupler Figure 6: Layout of a Casaded filter struture for dispersion slope ompensation implemented using optisystem Optial Delay Line Filter Design and Priniples Digital filters suh as Infinite-Impulse Response (IIR) and Finite-Impulse Response filters (FIR) are well known from digital signal proessing theory. There are some approahes to ompensate dispersion is the use of either reursive DLFs (omparable to digital IIR filters) or non-reursive DLFs (omparable to digital FIR filters). The optial delay lines an be implemented using fiber segments of ontrolled fiber lengths [3], [4]. In optial FIR filters, the transmission harateristis is expressed by polynomials where as in optial IIR filters, they are expressed by rational funtions. Optial delay line filter have several onfigurations i.e., transversal form and lattie form based on its appliation [4]. In order to realize the inverse hannel harateristi, the filter oeffiients is to be determined to minimize the bit error rate and to inrease the bit rate distane produt. The main objetive is to implement delay line filter and subsequently to inrease bit rate distane produt (i.e., Bit rate times the possible transmission distane L), using 2x2 oupler. Fiber apaity is speified in terms of the bit rate-distane produt BL whih is given by, BL < n 2C n 2 1 where n 1 is refrative index of the ore, n 2 is refrative index of the ladding, is refrative index differene and is the veloity of light in vauum, B is the bit rate and L is the repeater spaing. Opti ouplers either split optial signals into multiple paths or ombine multiple signals on one path. The number of input (N)/ output (M) ports, (i.e., N x M size) haraterizes a oupler. Coupling the fiber to soures and detetors reates losses due to dispersion, espeially when it involves mismathes in numerial aperture or in the size of optial fibers. By introduing a DLF, the average dispersion is lose to zero [5]. Mathematial Model The Z-transform funtion of a first order system is determined by, H(Z) = b 0 + b 1 Z 1 (7) whih is expressed in zero Z 0 = ρ 0 e j Ψ 0 by its phase (Ψ 0 ) and radius (ρ 0 ) as we know that Z = e jω. H F (Z) = b 0 (1 ρ 0 e j(ω Ψ 0 ) ) (8) Using the normalized frequeny, Ω = [0,2π] (i.e., normalized to the Free Spetral Range (FSR)) makes it possible to design filters without regarding frequeny range leading to the normalized group delay τ N (Ω) and the normalized dispersion 2136

3 D N (Ω). The phase response of the transfer funtion is, ρ 0 sin(ω Ψ 0 ) ϕ(ω) = arg(b 0 ) + artan [ 1 ρ 0 os(ω Ψ 0 ) ] ± π (9) Normalized group delay τ N (Ω) is written as, τ N (Ω) = dϕ(ω) (10) τ N (Ω) = ρ 0(ρ 0 os(ω Ψ 0 )) 1 2ρ 0 os(ω Ψ 0 ) 2 + ρ 0 (11) whih results in normalized dispersion given by Ω ꞌ = Ω Ψ 0, D N (Ω) = dτ(ω) (12) 2πρ 0 (1 ρ 2 0 )sin(ω ꞌ ) D N (Ω) = 1 4ρ 0 os(ω ꞌ ) + 4ρ ρ 2 0 os(2(ω ꞌ )) 4ρ 3 0 os(ω ꞌ ) 4 + 4ρ 0 (13) Normalized frequeny is given as, Ω=2π 1 (f C ) + 1 FSR FSR 2 (14) Dispersion value is alulated by using the formula, D = FSR 2 λ2 D N (Ω) (15) where λ is the enter wavelength and is the veloity of light. Dispersion slope of H(z) is, S N (Ω) = 2π dd N (Ω) (16) And dispersion slope is alulated by using, 2 S = FSR 3 λ3 S N (Ω) (17) Results and Disussions The data rate of 10 Gb/s single hannel transmission in standard Single Mode Fiber (SMF) for dispersion ompensation of an optial transmission system onsists of transmitter, fiber transmission hannel, dispersion ompensator (DLF) and a reeiver. A single span of Continuous Wave (CW) Laser soure operating at a frequeny of 193.1THz ( 1.55µm) is taken into analysis. A Non- Return-to-Zero waveform is generated by a pseudorandom binary sequene length of 128, is provided to the Mah Zehnder modulator. An optial fiber transmission hannel omprising of 100 km of SMF and loss is overome by an amplifier with a Gain of 20dB and 12.8 db is onsidered. The reeiver onsists of a PIN photodiode and a low pass bessel filter with a ut-off frequeny of 75% of the data rate. BER Analyzer is used to analyze the performane measure of the link in terms of Q fator, BER and an Eye-Opening Penalty (EOP). In this analysis, the DLF is implemented as a transfer funtion in OptiSystem tool. From Fig. 8, shows the performane omparison among Maximum Q fator, minimum BER and BER pattern of AZMI. Results of dispersion and dispersion slope ompensation Without Filter Dispersion Compensation Maximum Q=3.87 Maximum Q=5.19 Casaded two-stage parallel serial Filter Struture Considering the 4x4 oupler as shown in the Fig. 7 Minimum BER=5.35e-05 Minimum BER=1.03e-07 Figure 7: Blok diagram of a two-stage parallel serial filter using 4x4 Coupler A two stage parallel-serial filter is omposed of three symmetri 4 4 ouplers whih are onneted by two sets of delay lines [2]. In eah set the delay lines have a time differene of τ = 100 ps. The filter has a total maximum delay of 600 ps. One of the four input and output ports of the ouplers an be used for oupling input and output signals respetively. Figure 8: Comparison on Maximum Q fator, minimum BER and BER pattern of Dispersion Compensation From Fig. 9, shows the performane omparison among Maximum Q fator, minimum BER and BER pattern of MZI. 2137

4 Without Filter Dispersion Slope Compensation Maximum Q=3.87 Maximum Q=6.17 Figure 10(a): Maximum Q =7.92 Minimum BER=5.35e-05 Minimum BER=3.38e-10 Figure 10(b): Minimum BER = 1.099e-15 Figure 9: Comparison on Maximum Q fator, minimum BER and BER pattern of Dispersion Slope Compensation From the above omparison, it is analyzed that Maximum Q fator, Minimum BER and Eye pattern of dispersion slope ompensation gives better performane than dispersion ompensation and the same is interpreted in the following Table I. Table I: Comparison results of dispersion ompensation and dispersion slope ompensation. Parameters Without Filter Dispersion ompensation Dispersion slope ompensation MaximQ Fator Minimum 5.35e e e-10 BER Eye Height Results of Casaded two-stage parallel serial Filter Struture Figure 10(): Figure 10(a), Figure 10(b) and Figure 10() - shows Maximum Q, Minimum BER and of a Casaded two-stage parallel serial filter with redued omplexity. Conlusion A single hannel with 100 km Single Mode Fiber ompensated by DLF at a data rate of 10 Gb/s is investigated. Delay Line Filter (DLF) design provides a better Q value of DLF implemented as asaded two-stage parallel serial filter whih is both dispersion and dispersion slope ompensated using 4x4 oupler, shows a redued omplexity in pratial implementation. 2138

5 Referenes [1] A. Rahim, Finite Impulse Response Filter Using 4- Port MMI Couplers for Residual Dispersion Compensation, IEEE Journal of Lightwave Tehnology, vol. 30, no. 7, pp , April, [2] Sebastian Gade et al., Casaded Fiber Opti Delay Line Filter for Adaptive Dispersion Slope Compensation, International Students and Young Sientists Workshop, Photonis and Mirosystems, [3] N. Neumann et al., General Design Rules for the Synthesis of Dispersion and Dispersion Slope Compensation FIR and IIR Filters With Redued Complexity, IEEE Journal of lightwave tehnology, vol. 25, no. 11, November, [4] T. Duthel et al., Quasi-analyti synthesis of non reursive optial delay line filters for reliable ompensation of dispersion effets, IEEE Journal of Lightwave Tehnology, vol. 24, no. 11, pp , November, [5] Gred Keiser, Fiber Opti Communiation, 4 th Edition, Tata MGraw Hill, Authors P. Pavithra was born in Tamilnadu, India, on June, She reeived the M.E degree in Communiation and Network Engineering from Anna University, Madras Institute of Tehnology Campus, India in She reeived her B.E degree in Eletronis and Communiation Engineering from Mepo Shlenk Engineering College, India in She is urrently an Assistant Professor from Kumaraguru College of Tehnology, India. Her researh interests inlude signal proessing and dispersion ompensation in fiber opti ommuniation. Ms. P. Pavithra is a member of Universal Assoiation of Computer and Eletronis Engineers, Siene and Engineering Institute and International Assoiation of Engineers. She reeived Young Investigator Award from Intersiene Researh Network, India in 2013 for her ontribution towards dispersion ompensation using delay line filter in fiber opti ommuniation. K. Karthika was born in Tamilnadu, India, on July, She reeived the M.E degree in Communiation Systems from Mepo Shlenk Engineering College, India in She reeived her B.E degree in Eletronis and Communiation Engineering from Maharaja Engineering College, India in She is urrently an Assistant Professor from Kumaraguru College of Tehnology, India. Her researh interests inlude antenna design and optial ommuniation.` 2139