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  1. 1. Reza Khodadadi, Mir Ali Ghasemi, Hamed Alipour Banaee / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.272-276 Adjustable Filters For Optical Communications Systems Based On One-Dimensional Photonic Crystal Structures Reza Khodadadi * , Mir Ali Ghasemi ** , Hamed Alipour Banaei *** *( Department of Electrical Engineering, Ahar Branch, Islamic Azad University, Ahar, Iran.) **( Department of Electrical Engineering, Ahar Branch, Islamic Azad University, Ahar, Iran.) ***( Electrical Department, Faculty of Engineering, Tabriz Branch, Islamic Azad University,Tabriz, Iran.) ABSTRACT IN this paper design and simulation of all optical filters [9], optical multiplexers [10] andoptical filters have been done by one-dimensional optical di-multiplexers [11].photonic crystal structures based on some Photonic crystal structures are designed inmaterials like Silicon (Si) and Germanium (Ge). one-dimensional, two-dimensional and three-By using of Transfer Matrix Method (TMM), dimensional types [12]-[14]. Parameters as layersoptical fiber with too narrow bandwidth is refractive index, distances among layers, layersgained. Also the defect effect has been studied in number and their arranging method are all effectivefrequency feature of filters and it has been on the type of structure act [5]. To analyze theseshowed that by replacing defects in suitable structures, various numerical methods like TMMplaces of designed structure, bandwidth and [15], FDTD and other methods are used. In thiscentral frequency face changes that we can paper, all optical filters design has been done byregulate their parameters according to using of natural characteristics of photonic crystalsapplication type of filters. Also by increasing the in passing or reflecting light. Therefore the base ofnumber of layers, bandwidth of filter decrease. this paper is following levels:One of the most important advantages of this At first, we discuss about the advantages ofstructure is having some passing-bands. Wave optical telecommunications systems and then designlength limits of mooted structure are about one and simulation levels of considered structure aremicrometer. explained. After that we do essential simulation for structure and design narrow band filters, finally theKeywords — transfer matrix method , photonic results of study are presented.crystal , defect , filter , Bandwidth. I - 1) Advantages Of Optical FiberI. INTRODUCTION telecommunications Systems Nowadays, modern networks of optical In brief, the advantages of opticaltelecommunications are able to transfer voice and telecommunications systems are presented ascomputer images and data with a speed that is one follows:hundred times more than telecommunications a) Having high bandwidth and transferringnetworks with copper cables [1]. The process and high volume of modulated information withalteration of optical signals into electric current is optical fiber toward radio bands .troublesome in high speeds, so if the width of optical b) Having low dimensions and thickness andpulses become less, the need to more expensive and being isolator in comparison with metalcomplicated electronic circuits will increase that is cables for sparking and immunity against co-difficult and costly. In this condition, the simpler, hearing and resulted effects of thunder .faster and more economic solution is complete c) Having too low casualties, high flexibility,transferring of optical signs from one point to cost and assurance coefficient in the actionanother point that such all optical networks can be of optical fibers toward metal cables .replaced with present optical fiber systems whichhave optoelectronic devices. Seeking photonic all So most of today`s researches in opticaloptical networks technology is necessary in this telecommunications are about the most importantsituation [2],[3]. Photonic crystals of periodic development in manufacturing optical amplifiers.Instructures are dielectric materials that optical waves this way beside power and amplifica-tion ,the(electromagnetic) can not pass them in special need to alter optical signs is removed .Becausefrequency spans, this section has been named they`re able to amplify digital data in speedsphotonic band gap (PBG) [4], [5], by photonic band of multi hundred Giga bits per second and evengap engineering as defect, we can change their band multi Tera bits per second and amplify somestructure [6],[7]. Also they have a main role in different wave length simultan- eously . So thedesigning all optical devices as optical switches [8], condition of optical multiplex and the wave width of system (WDM) let us to profit in more economic 272 | P a g e
  2. 2. Reza Khodadadi, Mir Ali Ghasemi, Hamed Alipour Banaee / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.272-276form. For example, we can equip each radio has been studied in TE mode, mathematicaltransmitter to a changeable frequency laser and equations are as follows:without image concision operation transmit a  M 11 M 12  1  N 1  M    D0  Dl Pl Dl  DS (1)television program that have high clear imageswith band width of one Giga bit per second [16].  M 21 M 22   i 1 II. OPTICAL DETECTORS 1 1  Dl    nl cos l  (2) In optical telecommunications systems,  nl cos l optical detectors sector has special importance andsensitivity. So in optical telecommunications e il 0 systems, narrow band filters are designed by Dense Pl   il  (3)Wavelength Division Multiplexing method 0 e (DWDM). Therefore we used defect technique for l  k lx d (4)periodic networks to study the results of appliedfilter. So by using of transfer matrix method (TMM), frequency response of considered filter should be k lx  nl cos l , l  0,1,2,...,N , S l (5) canalyzed in wave length of 1.1 m to 1.6 m . d l  xl  xl 1 , l  0,1,2,3,..., N (6)Indeed it is structure study of filters which are theforth generation of telecommunications fibers in  A0   AS  optical communications systems classification (see    M  (7)Table 1). For more accurate study, simulated waves  B0   BS   shapes and calculation conditions have beenanalyzed in 1.198 m to 1.2 m . In above equations, D is Dynamic matrix Table 1. Range Communication Band and P, propagation matrix. Also  l the angle of O E S C LBand incident wave, d l , the distance between two Ban Ban Ban Ban Banname d d d d d consecutive layers, A0 , B0 , AS , BS coefficientsWavelength and values of electric field matrix on first and last 1260 1360 1460 1530 1565 layer. After calculating dynamic matrix, dynamiclimit to to to to to inverse matrix and propagation matrix, the amountbased on 1360 1460 1530 1565 1625 of conducting band width is studied in boundary andNanometer TE mode conditions. Then if we assume that the angle of incident is zero and the distance between In Fig. 1 as we see, 500 layers in two consecutive layers is identical, we can observesymmetrical form, from left to right have been and conclude conduct signals (transmission). 2considered with one pair of crystal Silicon and n cos s 1Germanium with refractive indexes of nGe  4 T s (8) n0 cos 0 m11and nSi  3.45 .In the next level, the middle ofstructure from air distance with refractive index of In above equation, n 0 is refractive index of nair  1 has been used for enforcing defect ( in this  0 , the first layer, n S , refractive index of last layer,condition, because of symmetry, the number oflayers is 501) , gradually the number of defect pairs angle of incident wave in first layer and  S , theis increased and finally the effect of graded index angle of incident wave in last layer.on the act of optical filter is studied. III. SIMULATION In this section, we analyze the results of performed simulations and study filter act in three following levels. In simulations the distance between two consecutive layers has been considered equal to 0.5m(d l  0.5m) .Fig. 1. Periodic structure of 500 layers withoutdefect a) In a condition that there is no defect inII- 1 ) Mathematical Equations And Analysis considered structure.Method b) In a condition that defects are enforced to We use transfer matrix method for considered structure.numerical modeling of structure. Since the condition c) In a condition that graded index method has been used for considered structure. 273 | P a g e
  3. 3. Reza Khodadadi, Mir Ali Ghasemi, Hamed Alipour Banaee / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.272-276Explanation: In each above levels, the effect of put in 251th layer (as mentioned, discussingdistance increase between two consecutive layers is structure is a periodic structure with 500 layers thatstudied. are in symmetrical form, from left to right, with one pair of crystal Silicon and Germanium. We use aFirst level: In a periodic structure of 500 layers pair of air distance (defect) instead of a pair ofcreated by Silicon and Germanium, the characteristic crystal Si and Ge in 251th layer, the layers after 252,of filter is observed without any defect as Fig. 2 . in inverse are from Si and Ge crystals pairs orderly.According to above conditions, we duplicate the Layers number in this condition is 501). Then wedistance between two consecutive layers and observe use five pairs of air layers to analyze the effect of airthe effect of it on output in Fig. 3 . By comparing distance increase. Filter characteristic will be as 5two images, we can realize that layers width and 6 Figs.increase, decrease the amount of filter band widthnoticeably. Fig. 4. Periodic structure of 501 layers with defectFig. 2. Filter Characteristic without defect (airdistance) Fig. 5. Filter characteristic with a pair of air distance layerFig. 3. Filter characteristic without defect (airdistance) by duplicating layers width Second level: Now we study the structureof designed filter band by having defect (airdistance). In order to enforce defect in 500 layers Fig. 6. Filter characteristic with five pairs of airstructure, according to Fig. 4, a pair of air distance is distance layer 274 | P a g e
  4. 4. Reza Khodadadi, Mir Ali Ghasemi, Hamed Alipour Banaee / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.272-276 In this situation, by comparing 5 and 6images, we can realize that by increasing the numberof air distances, frequency shift (wave lengthtransmission on horizontal axis) is made in filteroutput. According to above act, if we duplicate thedistance between two consecutive layers with defect,filter characteristic will change as Fig. 7. Fig. 9. Filter characteristic in graded index method by duplicating layers width Gained results of simulations and above curves are observed in Table 2 . By analyzing the results of table, we can realize that the best band width for considered optical filter is when layers width is duplicated and the amount of it is aboutFig. 7. Filter characteristic with a pair of air distance duplicating layers width TABLE 2.Wavelength difference between boxing By comparing Fig. 5 and Fig. 7, we can structurerecognize that in the presence of defect by increasingthe layers width, the amount of filter band width Wavelength transmission (um) Smooth refractive index profiledecrease noticeably. Also the study of above Imagesshow enforcing defect and increasing layers width,improve filter characteristic noticeably and decrease Parameterthe width of passing band. s Layers width (um) Third level: Now we use graded index Frequencymethod. As you see in Fig. 8, the amount of band (graded index)width is decreased and it`s put in a acceptable span Airfor conducting signal. In this conditions we canchoose passing band. Duplicating the distancebetween consecutive layers, leads to this output Fig. Structure shift Gap9, also we can observe that the width of consideredoptical filter band has been decreased acceptably. 0.001 No No 0.5 No 500 layers 0.0001 No No 1 No 500 layers One 0.001 Yes No 0.5 501 layers pair Five 0.001 Yes No 0.5 501 layers pairs One 0.0001 Yes No 1 501 layers pair One 0.0001 Yes Yes 0.5 501 layers pair 0.0001 One Yes Yes 1 501 layers < pairFig. 8. Filter characteristic by graded index method 275 | P a g e
  5. 5. Reza Khodadadi, Mir Ali Ghasemi, Hamed Alipour Banaee / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 6, November- December 2012, pp.272-276By studying the following table and above curves, [5] J.D. Joannopoulos, R.D. Meade, J.N. Winn,we can conclude that increase in layers width leads Photonic Crystals: Molding the Flow ofto decrease in filter band width. This process is Light, Princeton Univ. Press, 2008observable by curve analysis of Fig. 10. [6] A. Martinez, F. Cuesta, J. Marti, “Ultrashort 2D photonic crystal directional coupler”, IEEE Photon. Technol. Lett, 2003, Vol 15 (5), pp. 694–696. [7] Kuang, W., Kim, W. J., Mock, A. & O’Brien, J. D, “Propagation loss of line- defect photonic crystal slab waveguides”, IEEE Journal of Selected Topics in Quantum Electronics, 2006, Vol 12(6), pp. 1183–1195. [8] T. Tanabe, M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, Fast on-chip all optical switches and memories using silicon photonic crystal with extremely low operating energy, in: Quantum Electronics and Laser Science Conference (QELS’05), QPDA5, Baltimore, May 22–27, 2005. [9] S.S. Oh, C.S. Kee, J.-E. Kim, H.Y. Park, T.I. Kim, I. Park, H. Lim, Duplexer usingFig. 10: Decrease of filter band width at layers microwave photonic band gap structure,distance increase ratio Appl. Phys. Lett. 76 (2000) 2301–2303. [10] C.M. Soukoulis (Ed.), Photonic Band GapIV. CONCLUSION Materials, Kluwer Academic Publisher, In this paper, an adjustable filter has been 1996.designed for optical telecommunications systems by [11] A. D’Orazio, M. De Sario, V. Petruzzelli,one-dimensional photonic structures. Simulation F. Prudenzano, Photonic band gap filter forresults by TMM method show filtering action limits wavelength division multiplexer, Opt.are about 1 micrometer and passing bands of filter Express 11 (3) (2003) 230–239.are controlled by defect. Also changing the distance [12] J.C. Chen, H.A. Haus, S. Fan, P.R.between two consecutive layers, regulates the width Villeneuve, J.D. Joannopoulos, Opticalof passing band in filter. Results show access to filters from photonic band gap air bridges,optional wave lengths in passing band of filter is J. Lightwave Technol. 14 (1996) 2019–easy and the best passing band width is gained with 2575.graded index method. [13] M. Bayindir, E. Ozbay, Dropping of electromagnetic waves through localizedREFERENCES modes in three-dimensional photonic band [1] S. McNab, N. Moll, Y. Vlasov, Ulrta-low gap structures, Appl. Phys. Lett. 81 (2002) loss photonic integrated circuit with 4514–4516. membrance-type photonic crystal [14] S. Guo, S. Albin, Numerical techniques for waveguides, Opt. Express 11 (2003) 2927– excitation and analysis of defect modes in 2939. photonic crystals, Opt. Express 11 (2003) [2] A. Rosenberg, GaN-based photonic crystals 1080–1089. and integrated optics, in: Conference on [15] Pochi Yeh, Optical Waves in Layered Lasers and Electro-Optics/Quantum Media, Wiley-Interscience, 1988 Achyut K. Electronics and Laser Science Conference Dutta, Niloy K. Dutta, Masahiko Fujiwara, and Photonic Applications Systems WDM Technologies:Active Optical Technologies, Technical Digest (CD) Components, Academi Press, 2002 (Optical Society of America, 2006), paper CTuAA6, 2006. [3] L. Thylen, M. Qiu, S. Anand, Photonic crystals – a step towards integrated circuits for photonics, J. ChemPhysChem 5 (9) (2004) 1268–1283. [4] Kazuaki Sakoda , 2005 , “Optical Properties of Photonic Crystals”, 2nd ed., Springer-Verlag, Berlin 276 | P a g e