Mathematical Approach of Array Waveguide Grating in Dense Wavelength Division Multiplexing & Demultiplexing

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1 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 Mathematial Approah of Array Waveguide Grating in Dense Wavelength Division Multiplexing & Demultiplexing Salah Elfai Elrofai Assistant Professor, Shool of Eletroni, College of Engineering, Sudan University of Siene and ehnology, Sudan. Dept. of Eletrial, College of Engineering, AL-Baha University, AL-Baha, Saudi Arabia. BSRAC:his paper improve the mathematial equations of arrayed waveguide grating AWG in Dense Wavelength Division Multiplexing and demultiplexing that used to redue an aumulated rosstal and optimize the bandwidth seond and third asade onfiguration of small AWGs. his paper onerned about the derivation of mathematial equations of the two asade AWG stages and three stages, these equations improved their mathematial orretness and they are useful designing the AWGs iruit board. EYWORDS: AWG,Dense wavelength division-multiplexing and demultiplexing, Aumulated rosstal. I. INRODUCION Several tehniques have been used to improve the use of a ommuniation hannel, time division multiplexing DM, frequeny division multiplexing FDM, and wavelength division multiplexing WDM [] and []. With FDM eah user is assigned to a ertain frequeny slot transmitting only with the orresponding arrier, sharing the bandwidth. his tehnique used in radio transmissions. he FDM ould not be used high hannel apaity due to the limitation of using frequeny multiplexing at that level to meet this tehniques, the dense wavelength division multiplexing DWDM is used. his tehnique opens up new horizons in term of transmission apaity [].he latest push and vision in networing is the idea of the all optial networ where all protools are arried transparently end to end in optial domain []. WDM and DWDM transmit more signals along the ommuniation lin with no timing or protool [].DWDM systems require lasers with exellent single-mode permane, preise spetral operation aording to IU- speifiations and low-ost fabriation tehniques.optial multiplexers and demultiplexers are essential DWDM omponents. A multiplexer devie allows more than one signal to be ombined and then transmitted over a single hannel, on the other side the optial signals are retrieved or demultiplexed to their individual signals at the reeiver [].From the standpoint of system design, integrated demultiplexers with low insertion losses are preferred. An interesting approah uses a phased array of optial waveguides that at as a grating. Suh gratings are alled arrayed waveguide gratings whih is better suited a higher number of hannels. AWG is apable of inreasing transmission apaity of single optial fiber []. he silia-based waveguides are developed AWGs use as DWDM filters. AWG onsists of one input waveguide, several output waveguides and two fousing star ouplers slab waveguides also alled free propagation region whih are onneted via an arrayed-waveguides with a onstant path length differene between them [6].he rosstal beomes the major limiting fator in the sensitivity of the array in a DWDM optial ommuniation system. Optial rosstal arises when the light inident on one hannel is oupled to another hannel usually the adjaent one by refletions or poor fiber-to-photodetetor oupling [7]. he rosstal in AWG is aused by the sidelobes and sattered light of the foused beam in the interfae between the seond slab waveguide and output waveguide [8]. he asade onnetion tehniques are used to redue the rosstal of onventional AWG filter [9]. Copyright to IJIRCCE DOI: /IJIRCCE

2 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 II. RELAED WOR [0] the author state that therosstal of nano sized AWG has been a very big hallenge in their wor, so they proposed novel asaded waveguide grating filter CWGF to derease the rosstal of AWG.he authors demonstrated a very low rosstal SiN-based interleaver with asaded AWGs, heir measured results show arosstal less than -db with good suppression to the adjaent and non-adjaent rosstal in []. Reduing total adjaent rosstal and aumulated total hannel rosstal values ranging from - to -5 db are ahieved by asading a very large hannelount arrayed waveguide grating filter of -Hz-spaed hannels. his large sale AWG is onsidered as a primary or first stage of asading, and it funtions as a demultiplexer of ten output bandpass this introdues by authors in [].Another example of asading two stages of AWGs as a solution to the problem of rosstal aumulation in large-sale AWG multiplexers and demultiplexers is that of asaded AWG module resulting in a very low baground rosstal aent rosstal,his tehnique involves optimizing the bandwidth of the bandpass stage seond stage AWG by estimating the spetral harateristis of the whole asaded AWG as a funtion of its bandwidth and its enter wavelength differene. Using a Gaussian spetral profile assumed the transmittane in linear unit []. More related wors in[ 5] in whih the authors using WDM_phasor designing 8hannel, 6hannels, and hannels with different hannels spaing whih onlude that the asade onnetion is an attrative methods improve the AWG aumulated rosstal. III. CROSSAL AND PROPOSED SOLUION A rosstal in onventional AWG has a large-sale limitation. he rosstal of the AWG based on multiplexer/demultiplexer an be lassified in two types adjaent rosstal, and aent rosstal, shown in equation. O adj N Where N is the number of hannels of AWG, adj and are the rosstal from the adjaent and aent hannels respetively. For using silia onventional AWG, the level of adjaent rosstal is about -0dB, and typially -0dB aent rosstal [5-6]. On the other hand the rosstal an be found from theratio of the transmittaneof i two optial hannels. the fiber optis systems the transmittane is the fration of light transmitted through the system [7]. adj i,,...,,... N, N N i i, i From Figure, i an onlude that the worst ase of the total rosstal is -5dB theree i eted that AWG hannels value limited to several hundred. Also the main omponent that affets the total rosstal is the aent rosstal. Copyright to IJIRCCE DOI: /IJIRCCE

3 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 Fig. otal rosstal of onventional AWG ompared with the total adjaent rosstal and total aent rosstal. Crosstal level required in large-sale AWG an be adjusted by reduing the total aent rosstal to be less than -0dB. hat means two stages the aent rosstal should be around -80dB ideal double filtration these value reasonable 000 hannels [6]. But the future there is a need of more than two stages of asaded AWG, to over the large band ranged from 00nm up to 600nm due to the ontribution of zero-water-pea fiber. he aent rosstal should be around -0dB the three stages. IV. PROPOSED AWG CASCADE CONNECION DESIGN For meeting the rosstal requirement of the large sale AWG, i propose a MU/DEMU with small AWG asade in three stages, onfigure in figure.he first stage is an AWG based on an interleaver filter. hat means its outputs are even hannels and odd ones in other words the output should be double the input spaing, these tehnique maing the input to the seond stage more relax. he seond stage omposes of two branhes asading to the first stage using PLC-PLC tehnique, the same asading done stage two to stage three. Fig. Estimated total rosstal as a funtion of its total aent rosstal. Copyright to IJIRCCE DOI: /IJIRCCE

4 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 Fig. he proposed AWG asaded onnetion he requirements designing the asaded AWG, is to minimize the iruit and optimized the bandwidth of the seond and the third AWG. V. BANDWIDH OPIMIZAION OF CASCADED AWGS For design the bandwidth of AWG of the seond stage and the third stage, i have to onsider that the bandwidth of eah stage must be wide but not too broadband; otherwise it will not redue the aent rosstal. I should onsider the differenes between the enter wavelengths of the first AWG and the AWGs of the two asaded stages, and optimize the bandwidth to absorb the enter wavelength differenes. he optimization of the bandwidth of the two asaded stages an be done by estimated of the spetral harateristis of the asaded AWG as a funtion of the bandwidth, and the enter wavelength differenes due to the following alulations. I assumed the transmittane in linear units first stage AWG, whih has a Gaussian spetral where,, and are the wavelength, the ith hannel wavelength, and the bandwidth respetively, the seond stage enter at hannel i =. the lower limit of the spetrum is, this means the first stage aent rosstal is,.i set so that the first stage AWG adjaent rosstal is adj,, in whih Where is hannel spaing. adj,,,, I assumed the transmittane and the seond, and the third stages. Where and are the bandwidths of stage number two and three of proposed design respetively and are the enter wavelength differenes from the hannel wavelength., Copyright to IJIRCCE DOI: /IJIRCCE

5 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05,,,,,, Calulated the produt of the transmittane of the two and the three AWGs to estimate the asaded transmittane C and the spetral harateristis AWG, also alulated C whih is the bandwidth of these asaded AWG as an equation 7 two stages asaded and also an equations number 8 and 9 the three AWGs asaded. t.t Ln Ln Ln NAdj, Ln NAdj, NAdj, NAdj,. NAdj, NAdj, NAdj, 7 Copyright to IJIRCCE DOI: /IJIRCCE

6 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 Copyright to IJIRCCE DOI: /IJIRCCE t t t,,,,,,,,,,,, 8 9 VI. -SAGE AWG EQUAION DERIVAION. t t t 7 But the original relationship is: t.t t = ] ][ [ 0 the following the two equations 7 and 0 will have their onents anded and manipulated in the hope that the two equations agree:now equation 0; its onent is multiplied by to yield that: t Now anding the squared braets of ] [ ] [ t xp

7 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 Copyright to IJIRCCE DOI: /IJIRCCE Rearranging ] [ ] [ t hen:.heree equation number will be: ] [ ] [ t Now is the turn equation 7 onential to be anded as: t 5 hen ompare and agreement,it ould be notied that the two equations agree diretly all terms one one exept that the disagreement is in that: - Equation has the oming term: ] [ 6 - Also equation has this term:, then tae oeffiient ones: 7 Same oeffiient obtained as in equation 5.From the relationships between hannel spaing, hannel bandwidth, and hannel adjaent rosstal xadj,. Obtain this mula: t = then Considering hannel

8 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November 05 be then at:+ with = + - = hannel spaing, then: t = adj, =, heree ln adj, = ln adj,, = and so: ln adj, = /. VII. HREE SAGEBANDWIDHDERIVAION 8 his relation the band width of -stage AWG asaded:where main AWG, and bandpass AWG.aing this relationship 8 as it is, then with the main AWG and first bandpass AWG together as the new main AWG and with being the bandwidth of the seond bandpass AWG with d being the bandwidth of the three AWGs in asade d Substituting from 8 then: d 9 Whih agree with equation 9. VIII. CONCLUSION summary i have investigated the asading onnetion AWGs. I found that asaded onnetion redues the rosstal, and optimizes the bandwidth WB also i design three stages of AWG asaded aording to the mathematial equations, enhane the rosstal by ontrolling its aent rosstal. REFERENCES. HDB, M., Design Handboo Fiber opti ommuniation systems, 5A7 Otober 99.. rauss, O., DWDM and optial Networs, 00 by publisommuniations ageny.. Elmirghani, J. M.H., All-optial wavelength onversion: ehnologies and appliations in DWDM Networs, IEEE ommuniation, Magazine marh EFO Eletro-optial.., Quebe. Canada, nd edition. 5. Oamoto..H.Y. Oazai.Y.Ohmori. ato.., Fabriation of large saleintegrated-opti NxN star ouplers, IEEE photonis eh. Lett.:0-05,99 Hibino, Y., Reent Advane in high-density and large-sale AWG Multi/Demultiplexers with higher dex-contrast Silia-based PLCs IEEE Journal of seleted opis in Quantum Eletronis vol. 8, No. 6November/ Deember Chin,. S., Yang,., Zhang,., Hung Lu, L., atehi, L. P. B., and Bhattaharya,P. vestigation of Adjaent Channel Crosstal inmultihannel Monolithially tegrated 550nm Photoreeiver Arrays, Journal of Lightwave ehnology, VOL.. 5, No. 0, Otober 997. Copyright to IJIRCCE DOI: /IJIRCCE

9 ISSNOnline: ISSN Print: ternational Journal of novative Researh in Computer and Communiation Engineering An ISO 97: 007 Certified Organization Vol., Issue, November aneo, A., Reent Progress on Arrayed-Waveguide Grating WDM Appliations, N Photonis Laporatories, /99/$ IEEE. 8. awia,., and Obara, H., Crosstal redution in NxN WDM Multu/Demultiplexers by asading small Array Waveguide Gratings, G s, Journal of lightwave ehnology, Vol 5, No. 0, Otober WDM_Phasar, Phased Array WDM Devie Design Software, Optiwave Corporation, 6 Conourse Gate, Suite 00 Nepean, Ontario E 7S8, Yang, D. Yuan, L.Dingshan, G. Low rosstal array waveguide grating filter, rd international photoni & optoeletronis meeting POEM 00.. Lianxi, J. Qing, F. Junfeng, S. Mingbin, Y. and Guoqiang, L. Ultra-Low Crosstal Optial ter Leaver Filter Based on Sin Platm with Casaded AWGs, ternational Journal of mation and eletronis Engineering, Vol., No.6 November 0.. amei, S., aneo,a.,ishii, M.,Shibata,., oue, Y., and Hibino, Y., Crosstal redution in arrayed-waveguide grating multiplexer/demultiplexer using asade onnetion, Journal of lightwave tehnology, VOL.., No. 5,May amei, M. Ishii, M., itagawa,., Itoh, M., and Hibino,Y., 6-hannel ultra-low rosstal arrayed-waveguide grating multi/demultiplexer module using asade onnetion tehnique, Eletronis letters 9th January 00VOL. 9 NO... SALAH, E., andabdeen, A., Crosstal Redution using Casade Connetions of Multiplexer/Demultiplexer with different Channels 8&6 Spaing Based Array Waveguide Grating in Dense Wavelength Division Multiplexing,IJISE - ternational Journal of novative Siene, Engineering & ehnology, Vol. Issue 0, Deember SALAH, E., andabdeen., Aumulated Crosstal Enhanement of Array waveguide Grating With different Channels Spaing,IJIRCCE- ternational Journal of novative Researh in Computer and Communiation Engineering, Vol., Issue,Febrory 05. BIOGRAPHY Salah Elfai Elrofai, Ph.D., Sudan University of Siene and ehnology, College of Engineering, Shool of Eletronis.Eastern Diems, hartoum, Sudan, P.O. Box 7. Ph.D. in eletroni Engineering, Communiation, SUS and Malaysia UM 007. M.S. in Computer Engineering & Networing 00, Gezira University. BS. Honors, at Sudan University of Siene and ehnology in Eletronis Engineering 997. Area of Speialization: Communiation Engineering optial Communiation Systems & devies. Assistant Professor Department of eletroni Engineering Sudan University of siene and tehnology SUS. Chair of Eletroni Department sine May 009 up to 0 volved in evaluation team selfevaluation of undergraduate. Head of Sheduling and Exams Eletroni Department. Evaluate and translate omputer Engineering Program and eleommuniation program Aademy of Engineering Siene, AES. Assistant Professor Department of Eletrial Engineering at AL-Baha University sine 0. Copyright to IJIRCCE DOI: /IJIRCCE