NOVEL BAND-REJECT FILTER DESIGN USING MULTILAYER BRAGG MIRROR AT 1550 NM Krshanu Nandy 1, Suhrd Bswas 2, Rahul Bhattacharyya 3, Soumendra Nath Saha 4, Arpan Deyas 5 1,2,3,4,5 Department of Electroncs of Communcaton Engneerng, RCC Insttute of Informaton Technology, Canal South Road, Kolkata-700015 {krshrcc91, suhrdbswas3, rahulrcct91}@gmal.com 4 soumendra91@yahoo.com, 5 deyas_arpan@yahoo.co.n ABSTRACT Novel band-reject flter s proposed usng multlayer Bragg mrror structure by computng reflecton coeffcent at 1550 nm wavelength for optcal communcaton. Dmenson of dfferent layers and materal composton are modfed to study the effect on rejecton bandwdth, and no. of layers s also vared for analyzng passband characterstcs. GaN/Al x Ga 1-x N composton s taken as the choce for smulaton purpose, carred out usng propagaton matrx method. Refractve ndces of the materals are consdered as functon of bandgap, operatng wavelength and materal composton followng Adach s model. One nterestng result arses from the computaton that band-reject flter may be converted nto band-pass one by sutably varyng rato of thcknesses of unt cell, or by varyng Al mole fracton. Smulated results can be utlsed to desgn VCSEL mrror as optcal transmtter. KEYWORDS Bragg mrror, Reflecton coeffcent, Multlayer structure, Band-reject flter 1. INTRODUCTION Bragg reflectors have already attracted nterest of researchers for ther possble novel applcatons as optcal transmtter [1-2], LED [3], reflectvty modulators [4], solar cell [5]. Hghly transparent delectrc materals are requred are used to construct Bragg mrrors n order to mnmze the loss due to optcal absorpton [6-8]. It s a structure formed from multple layers of alternatng materals wth perodc varaton of refractve ndex, where each layer boundary causes a partal reflecton of an optcal wave. For waves whose wavelength s approxmately four tmes the optcal thckness of the layers, reflectons then combne wth constructve nterference, and the layers act as a hgh-qualty reflector. For desgn of such hghly reflectng multlayer structure usng delectrc materals, ts reflectvty plays a crtcal role along wth dsperson and phase [9]. By sutably choosng the refractve ndces of the consttutng layers along wth dmenson of slabs, requred flter characterstcs can be obtaned from reflecton coeffcent profle; when computed for the desred frequency regon. Dependng on the poston of passband, t can be utlzed as band-reject or bandpass flter, dependng on the requrement for optcal communcaton purpose. In ths paper, reflectvty of multlayer Bragg mrror s computed usng propagaton matrx method at 1550 nm consderng GaN/Al x Ga 1-x N materal composton. It s observed that by sutably choosgn dmenson of slabs and Al mole fracton of Al x Ga 1-x N layer, the structure can be Rupak Bhattacharyya et al. (Eds) : ACER 2013, pp. 419 425, 2013. CS & IT-CSCP 2013 DOI : 10.5121/cst.2013.3239
420 Computer Scence & Informaton Technology (CS & IT) used as band-reject or bandpass flter. Rsults can be utlzed to desgn multlayer VCSEL structure. 2. MATHEMATICAL MODELLING We consder the smplest three layers havng refractve ndces as shown n Fg 1: Fgure 1: Three-layer nterface wth r. as n 1, n 2, n 1 We consder wavevectors k 0, k 1, k 2 defned as n terms of wavelength, and assume normal ncdence of lght on the structure. For wave at meda nterface havng propagaton constant k 1 and k 2 respectvely, satsfacton of boundary condtons gve the followng equaton- A 1 2 1 1 2 2 2 exp(-k z) + A exp(k z) = B exp(-k z) + B exp(k z) 1 (1) Then nterface matrces can n general be represented as- D 1 = k 1 k (2) where 2π k = n (3) λ Consderng propagaton matrces as P 1, P 2, P 3 ; we can wrte t n general- exp( jk d ) 0 P = (4) 0 exp( jkd ) Gan can be calculated as- ( D P ( D ) ) D P ( D ) 1 ( ) 1 G = + 1 + 1 + 1 (5) 3. MATERIAL PARAMETER Several models already have been reported to calculate refractve ndex but up to now Adach s model s consdered most accurate model. Several research groups have proposed own values of Adach s fttng parameters that gve dfferent level of accuracy for a range of composton of Al n ntrde alloys. The contnuous equaton to calculate the refractve ndex for all ntrdes materal proposed by Adach and later smplfed [10-11] s gven below:
Computer Scence & Informaton Technology (CS & IT) 421 n( E) = A hω E g 2 2 hω 1+ E g hω 1 + E g B where E g s the bandgap energy of the materal, ω s the frequency of the laser emsson and A and B are the fttng parameters. For smulaton purpose, we have consdered GaN/Al x Ga 1-x N composton. 4. RESULTS & DISCUSSION Usng the equatons, reflectance of Bragg s mrror s computed for multlayer structure by varyng thcknesses and materal composton of the layers, as well as no of layers also. Fg 2a shows the reflecton coeffcent of 11-layer structure centered at 1.55 µm, and by sutably choosng the rato of thckness of the unt cell and also materal composton, reflectvty can be made unty near the desred frequency range of nterest. Hence t can be consdered as a band-reject flter for nose. It s also observed that by ncreasng no. of layers, bandwdth slghtly ncreases; and reflectvty at passbands monotoncally decreases followng exponental nature. Ths s plotted n Fg 2b. Fgure 2a: Reflecton coeffcent wth wavelength centered at 1.55 µm for 11-layer Bragg mrror structure Fgure 2b: Reflecton coeffcent wth wavelength centered at 1.55 µm for 20-layer Bragg mrror structure
422 Computer Scence & Informaton Technology (CS & IT) If materal composton s changed for that multlayer structure keepng no. of layers constant, then t s observed that wth ncreases of Al mole fracton, rejecton bandwdth at the desred central wavelength ncreases,.e., flter becomes wdeband one. Ths s shown n Fg 3b & Fg 3c respectvely. Interestngly, t can also be observed that reducton of Al percentage changes the nature of the flter, and t becomes bandpass one. Ths observaton s plotted n Fg 3a. Fgure 3a: Reflecton coeffcent wth wavelength centered at 1.55 µm for 11-layer Bragg mrror structure wth Al 0.4 Ga 0.6 N/GaN composton Fgure 3b: Reflecton coeffcent wth wavelength centered at 1.55 µm for 11-layer Bragg mrror structure wth Al 0.6 Ga 0.4 N/GaN composton
Computer Scence & Informaton Technology (CS & IT) 423 Fgure 3c: Reflecton coeffcent wth wavelength centered at 1.55 µm for 11-layer Bragg mrror structure wth Al 0.7 Ga 0.3 N/GaN composton By varyng the dmenson of dfferent layers keepng no. of layers and materal composton constant, t s observed that ncreasng the wdth of ether of the layer ultmately shft the predetermned flter bandwdth from the desred optcal communcaton wavelength and hence optmzaton of layer thckness s very much essental. In Fg 4a, reflecton coeffcent s plotted wth varaton of Al x Ga 1-x N layer thckness. It s observed that the flter characterstcs for 11- layer structure wth Al 0.6 Ga 0.4 N/GaN composton s optmzed for 3.5 µm wdth, and decreasng or ncreasng the dmenson converts t n a bandpass flter. Ths effect s smulated consderng the GaN thckness as 2.7 µm. Now keepng thckness of Al 0.6 Ga 0.4 N layer as 3.5 µm, f wdth of GaN layer s vared, then also flter characterstc changes; as evdent from Fg 4b. Fgure 4a: Reflecton coeffcent wth wavelength centered at 1.55 µm for 11-layer Bragg mrror wth Al 0.6 Ga 0.4 N/GaN composton for dfferent thckness of Al 0.6 Ga 0.4 N but constant GaN thckness
424 Computer Scence & Informaton Technology (CS & IT) Fgure 4b: Reflecton coeffcent wth wavelength centered at 1.55 µm for 11-layer Bragg mrror wth Al 0.6 Ga 0.4 N/GaN composton for dfferent GaN thckness of but constant Al 0.6 Ga 0.4 N thckness 5. CONCLUSION Throughout the smulaton work, flter property of multlayer Bragg mrror structure s analyzed by means of reflecton coeffcent at 1550 nm. Dmenson of dfferent layers and materal compostons are vared to observe the effect on optcal property. Numbers of layers are vared to observe the varaton of wdth of desred regon. In ths work we consdered the dependence of refractve ndces of dfferent layers on materal composton and frequency of nterest. Propagaton matrx method s consdered for materal analyss. Optmzed profle s generated for the structure combnng the effect of number of layers, ther dmenson and materal composton. Results are very helpful to analyze vertcal cavty surface emttng laser analyss. REFERENCES [1] M. Achtenhagen, N. V. Amarasnghe, L. Jang, J. Threadgll, P. Youn, (2009), Spectral Propertes of Hgh-Power Dstrbuted Bragg Reflector Lasers, Journal of Lghtwave Technology, vol. 27, pp. 3433-3437. [2] M. Achtenhagen, N.V. Amarasnghe, G.A. Evans, (2007), Hgh-power Dstrbuted Bragg Reflector Lasers Operatng at 1065nm", Electronc Letters, vol. 43. [3] D. Wang, I. T. Ferguson, J. A. Buck, (2007), GaN-based Dstrbuted Bragg Reflector for Hgh- Brghtness LED and Sold-State Lghtng", Appled Optcs, vol. 46, pp. 4763-4767. [4] J. Y. Tsa, T. C. Lu, S. C. Wang, (2003), "Hgh Reflectvty Dstrbuted Bragg Reflectors for 1.55 µm VCSELs usng InP/Argap", Sold State Electroncs, vol. 47, pp. 1825-1828.
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