Design of the photonic crystal demultiplexers for ultrashort optical pulses using the gap-maps analysis

Transcription

1 Design of the photonic crystl demultiplexers for ultrshort opticl pulses using the gp-mps nlysis I. A. SUKHOIVANOV *, I. V. GURYEV, O. V. SHULIKA, A. V. KUBLYK, O. V. MASHOSHINA, E. ALVARADO- MÉNDEZ, J. A. ANDRADE-LUCIO FIMEE, University of Gunjuto, Slmnc, 36790, Mexico L. Photonics, Ntionl University of Rdio Electronics, Khrkiv, 61166, Ukrine In the work, the new method for the design of the wvelength division multiplexer on the sis of 2D photonic crystl integrted circuit for the ultr-short pulses chnnel seprtion is proposed nd investigted. The method is sed on the nlysis of full photonic ndgp mps tht llows defining the ultr-short pulse demultiplexer prmeters selection. For the method pprotion, there ws synthesized the device in which the widend filters re used for the chnnel seprtion. As it ws expected, the device effectively seprtes 50 fs pulse chnnels with 1.31 nd 1.55 microns wvelengths. The otined spectrl chrcteristics nd pulse pttern responses vlidte the efficiency of the proposed method nd the pplicility of such devices to the integrted photonic informtion processing circuits. Keywords: Photonic crystl, WDM, Ultr-short pulse, Photonic ndgp mp 1. Introduction Tody semiconductor electronics fced the chllenge of the impossiility to improve the integrted devices performnce tht is connected with the mount of the logicl elements size to its prcticl minimum nd with incresing of electricl power requirements [1]. One cn expect improving in this re if turn to development of principlly new wys for the dt hndling, such s photonic crystl devices [2, 3]. Photonic crystls (PhCs), the structures with periodiclly chnging refrctive index (RI), cn e used for cretion of the lterntive opticl informtion processing devices. Due to their properties s well s structure peculirities such s strict periodicity, the effect of strong light locliztion in the defect region of the structure ppers [4]. The theoreticl nd the experimentl investigtions demonstrte tht the PhCs cn e pplied to the wide-perture single-mode lsers [5], wvelength filters[6], opticl wveguide structures nd shrp ends [7], wvelength division multiplexing (WDM) system devices [8, 9], splitters nd cominers [10]. Thus, there is the possiility to uild the full functionl opticl processor on the single PhC structure y the vrition of the prmeters of PhC nd y the introducing the nonliner elements [2]. Such opticl devices promised to e compct, nd cn hve high-performnce. One of the possile wys which is needed to e used to chieve the mximl performnce of opticl informtion processing device is the full utiliztion of the opticl wveguide ndwidth. In order to mximize the informtion density in single physicl chnnel the timedivision multiplexing (TDM) nd the WDM technique cn e used in prllel [11]. To effectively relize the TDM it is convenient to use the ultr-short pulses (USP) technique [12]. However, USPs hve very wide spectrum. For instnce, the 100 fs USP with Gussin shpe hs the spectrum width out 60 nm. The distnce etween chnnels in dense WDM systems is usully less thn 0.2 nm [13]. Thus, it is impossile to use them for the USP chnnels seprtion. As is known, wvelength filters of opticl rnge sed on one-, two- nd three-dimensionl photonic ndgp (PBG) structures [8], [14-16] cn e creted y the proper geometricl nd physicl prmeters selection. As for opticl frequency filters nd moreover for demultiplexers, they cn e sed on the one-dimensionl PhCs [9] in comintion with opticl circultors [17]. These demultiplexers consist of circultors plced one y one with precisely tuned Brgg reflectors etween them. Such technology llows to seprte frequency chnnels with less thn 100 GHz distnce. The demultiplexer cn lso e relized using the high-q nnocvities sed on 2D PhCs [18]. However, none of such devices meet the requirements which re necessry for the USP demultiplexing. So the im of the work consists in the development of the method tht llows creting the devices on the sis of the 2D PhC which cn provide wvelength demultiplexing of the pulse pttern with wide chnnels spectr. The structure of pper is s follows. In the Device design section, the method for the design of the demultiplexer tht uses widend filters on the sis of the PhC s the wvelength filters ws considered. Such devices llow demultiplexing the USP it pttern. There ws proposed the method for designing of such devices y the nlysis of PBG mps. In the Method exmintion section, we synthesized the device for the seprtion of USP chnnels with wvelengths 1.31 nd 1.55 µm using the proposed method. The otined device chrcteristics vlidte the high-efficiency of the wvelength chnnel seprtion s well s the possiility of using such devices

2 s elements of the integrted informtion processing opticl devices. 2. Device design The integrted opticl device cn e sed on two types of 2D PhC. The first type uses the PhC structures hving the ckground refrctive index (RI) less thn elements RI nd the second one is vice-vers. In the first cse the structure is dielectric rods (DR) type nd in the second cse is perforted memrnes. In oth cses the degrees of freedom llowing the PBG mnging re the geometry vritions while the constnt RI contrst nd the RI contrst vrition when the geometry remins constnt. The comintion of two mentioned wys s well s introducing the nonliner opticl effects cn proly llow new possiilities. In most cses in equl conditions, the DR structures hve lrger PBG res existing t technologiclly convenient geometric prmeters when r vlue is essentilly lower thn 0.5. Although the cse of holes in high index medium is still oviously more importnt in prctice, one cn meet difficulties with device reliztion using memrnes. The reson is tht in perforted sls in most cses the PBG is formed t region of r ~ 0. 5, tht cn result in prolems when producing such structures. The exception is the PhC sls with tringulr lttice. Moreover, s the dditionl computtions hve shown, perforted memrnes hve the PBGs much nrrower thn the dielectric rods t the sme geometric prmeters. In cse of perforted memrnes, the PBG chieves its mximum t the rnge of r etween 0.5 nd 0.6. This ctully corresponds to cse of the DR ut with the distorted rods shpe. For instnce, the cse of circulr holes with r = 0. 6 is nothing else thn the cse of rods with the shpe of concve squre s it is shown in Fig. 1. Therefore, we restricted our nlysis to the DR structures rrnged in squre nd tringulr lttice. However, the method proposed here is generl nd does not introduce ny specil ssumptions. So, it cn e successfully pplied to 2D PhC sls s well. wveguides re used. However, ecuse of the wide USP spectrum, filters must hve low qulity nd therefore wide trnsmittnce spectrum. Tht s why the structures like dd-drop multiplexers using microresontors nd point defects [6,18] re inpplicle. In this cse, it is necessry to use low-q insertions which spectr do not override ut lie inside the ndwidth of min chnnel. The ckground PhC should form the ndgp s lrge s possile to support USP propgtion in W1 wveguide. In order to otin corresponding prmeters vlue it is not enough just compute the PhC nd structure. So the first design step is the computtion of the PBG mp, which cn e otined oth y the vrition of the geometry while the RI contrst remins constnt nd y the vrition of the RI contrst while constnt geometry. However, from the technologicl point of view, it could e esier to fricte the structure with vrition of geometry prmeters thn other one. In ddition to this, while performing n explortory nlysis we found tht geometry design is more suitle. Reltive frequency ( ω /2 π c) Reltive frequency ( ω /2 π c) r / n Fig. 1. Identity of sl PhC to dielectric rods in cse of r > 0.5. The two-chnnel demultiplexer considered here is T- or Y-splitter formed in W1 wveguide (1 defect line in the PhC). For the effective USP wvelength chnnels seprtion, the defects of specil form in secondry Fig. 2. TM Bndgp mps for the squre lttice PhC for different rdius-to-pitch rtio (), nd for vrition of the difference of refrctive indices of rod nd ckground mterils (). The results otined using plne-wve expnsion method [19] for the squre lttice of rods with circulr section emedded in ir re shown in Fig. 2 we see tht in

3 cse of geometry vrition the centrl ndgp frequency cn e chnged in the rnge of nd in cse of index contrst vrition this rnge of Besides, in cse of index contrst vrition the high-frequency edge of the ndgp chnges much slower then the lowfrequency one tht results in nonvnishing PBG within the resonle limits of index contrst which corresponds to the ctul mterils. Therefore, the contrst design is unsuitle for T- or Y-junctions. However, it my e pplied to produce sequentil filtering. The otined PBG mp llows quick selection of the elements size nd lttice constnt of the 2D PhC which provides the lrgest ndgp for the structure. This corresponds to r 2 verticl line on Fig. 3. Then the edge frequencies Ω 1 nd Ω 2 corresponding to ndgp edges of the ckground PhC cn e found s cross-points of r = r nd PBG re edges, s verticl stright line 2 shown in Fig. 3. Further we find the correspondence etween the Ω 2 nd the short-wvelength prt of trnsmittnce spectrum of min. When we know the edge frequency Ω 2, USP spectrum width, nd the centrl USP wvelength, we re le to compute the lttice constnt of the ckground PhC. The reltive sizes of insertions in the secondry wveguides re defined y the cross-points of the horizontl line ( r ) = ΩC Ω nd the PBG re edges, where Ω C is the centrl reltive frequency corresponding to the center of the primry wveguide ndwidth. We fix the lttice constnt to e equl for oth ckground PhC nd defects. This could e convenient for friction process, ut it is not requirement. The ctul sizes of the insertions cn e found vi its reltive sizes nd lttice constnt of the ckground PhC found t previous steps. Finlly we should tune fine the defect sizes. We compute the trnsmittnce t the corresponding wvelengths through the defects while rdii of defects re vrying in smll rnge round the vlues otined y the descried method. The otined rdius with mximum trnsmission is utilized. We pply the method proposed for synthesis of the two-chnnel PhC demultiplexers for the USPs with centrl wvelengths of λ1 = 1. 31µ m nd λ2 = 1. 55µ m. The results re presented in the next section. Fig. 4. Results of FDTD simultion of wvelength chnnel splitting: () source wvelength λ = 1.55 µm, () - source wvelength λ = 1.31 µm. Fig. 3. The scheme for selection of geometric prmeters using ndgp mp Fig. 5. Trnsmission spectr of the filters in secondry wveguides of the demultiplexer sed on squre lttice (), nd tringulr lttice () PhCs.

4 3. Method exmintion Numericl simultions were mde for structures with squre nd tringulr lttice. For the squre lttice cse, the ckground refrctive index is n 1 = 1 ; the rod refrctive index is n r = 3. Following the method descried we found for the squre lttice cse the lttice constnt is = 0.563µ m ; the rods rdii re r1 = ; r2 = 0. 2 ; r3 = For tringulr lttice cse, ckground refrctive index is n 1 = 1; the rod refrctive index is n r = 3 ; the lttice constnt is = 0.65µ m; the rods rdii re r1 = ; r2 = ; r3 = The computtions were crried out using the FDTD method [20-22]. The field ptterns re shown in Fig. 4 for the cse of squre lttice structure. The filter in the left chnnel of the device fully reflects the rdition with 1.31 µm wvelength nd the filter in the right chnnel the rdition with 1.55 µm wvelength. To exmine this precisely we computed trnsmittnce spectr of secondry wveguides in squre nd tringulr lttices, which re shown in Fig. 5. We cn see tht in cse of squre lttice the trnsmittnce for the chnnel 1.55 µm is etter thn for 1.31 µm chnnel. For the cse of tringulr lttice the PhC the sitution is much etter the trnsmittnce peks for different wvelengths re lmost identicl. We will illustrte fine-tuning y the exmple of squre-lttice structure. The Fig. 6 shows the dependence of the trnsmittnce on the rod rdius t the wvelengths λ = 1. 55µm nd λ = 1. 31µ m. These chrcteristics hve good defined mxim. We took corresponding rdii s finl vlues to form incretions in secondry wveguides. Finl vlues re r1 = , r2 = Fig. 7. Trnsmittnce spectr efore nd fter the tuning. Squre lttice Output power 1,0 0,8 0,6 0,4 0,2 0,0 Chnnel 1.55 µm Chnnel 1.31 µm Lunched pulse Time, fs 1,0 0,8 Chnnel 1.55 µm Chnnel 1.31 µm Lunched pulse Output power 0,6 0,4 0,2 0, Time, fs Fig. 8. The pulse pttern responses of the demultiplexer sed on the squre lttice PhC. () source wvelength λ = 1. 55µm ; () source wvelength λ = 1. 31µ m. For comprison djcent chnnels re shown. Fig. 6. Tuning chrcteristics of the filters for λ = 1. 55µm () nd λ = 1. 31µ m (). For comprison djcent chnnels re shown. The Fig. 7 shows the comprison of initil T-structure to the fine-tuned one y trnsmittnce spectr. As one cn see tuning provide etter spectr. To estimte demultiplexer properties in the time domin we compute its response on pulse pttern t different wvelengths, which re shown in Fig. 8. It should e mentioned tht the ttenution of the pssed pulse equls pproximtely 60% in oth cses of squre nd tringulr lttice. But the rodening is lmost sent, so

5 the pulses remin cler enough to e recovered successfully. The pulse pttern response for the demultiplexer sed on the tringulr lttice PhC is similr to tht of the squre-lttice PhC. The low rodening is chieved y pplying widend frequency filters. Though the employment of nrrow-nd filters provides multichnnel demultiplexing, the temporl response of the device is expected to e poor due to the very rod spectrum of USP. Thus, we consider the proposed design conception s n effective one for the high-speed opticl informtionl systems. 4. Conclusion We proposed nd exmined simple method for design of the wvelength division demultiplexers on the sis of 2D PhC for USP processing. The method is sed on the nlysis of PBG mp. The method proposed here does not introduce ny specil ssumptions nd, therefore, it cn e pplied to ny 2D PhC structure. The synthesis of the structure hs shown the efficiency of the proposed method. Spectrl chrcteristics of the proe structure revel the good wvelength seprtion for oth types of lttices, squre nd tringulr. FDTD simultions of the proe structure show effective device opertion on seprtion of 50 fs opticl pulses. Such results cnnot e chieved y using the high-q filters. The results otined in this work vlidte the possiility of using the method of the PBG mps nlysis for the synthesis of the demultiplexers for the USP wvelength chnnel seprtion in the integrted PhC circuits. References [1] K. Olukotun, L. Hmmond, Multiprocessors 3(7) (2005). [2] S. F. Mingleev, Y. S. Kivshr, J. Opt. Soc. Am. B, 19(9), 2241 (2002). [3] S. Nod, M. Imd, M. Okno, S. Ogw, M. Mochizuki, A. Chutinn, IEEE Journl of Quntum Electronics 38(7), 915 (2002). [4] K. Skod, Opticl Properties of Photonic Crystls, Springer-Verlg (2001). [5] N. Yokouchi, A. J. Dnner, K. D. Choquette, IEEE J. Sel. Top. Quntum Electron. 9, 1439 (2003). [6] Y. Akhne, T. Asno1, B. S. Song, S. Nod, Optics Express 13(4), 1202 (2005). [7] A. Lvrinenko, P. I. Borel, L. H. Frndsen, M. Thorhuge, A. Hrpoth, M. Kristensen, T. Niemi, H. M. H. Chong, Optics Express 12(2), 234 (2004). [8] S. Fn, P. R. Villeneuve, J. D. Jonnopoulos, H. A. Hus, Phys. Rev. Lett. 80, 960 (1998). [9] A. D Orzio, M. De Srio, V. Petruzzelli, F. Prudenzno, Optics Express 11(3), 230 (2003). [10] S. Kim, I. Prk, H. Lim, Proc. SPIE 5597, 29 (2004). [11] F. T. An, K. S. Kim, D. Gutierez, S. Ym, E. Hu, K. Shrikhnde, L. G. Kzovsky, IEEE/OSA JLT 22(11), 2557 (2004). [12] G. A. Keeler, B. E. Nelson, D. Agrwl, C. Dees, N. C. Helmn, A. Bhtngr, A. B. Dvid, IEEE Journl of Selected Topics In Quntum Electronics 9(2), 477 (2003). [12] Y. S. Hurh, G. S. Hwng, J. Y. Jeon, K. G. Lee, K. W. Shin, S. S. Lee, K. Y. Yi, J. S. Lee, IEEE Photonics Technology Letters 17(3), 696 (2005). [13] B. E. Nelson, M. Gerken, D. A. B. Miller, R. Piestun, C. C. Lin, J. S. Hrris, Opt. Lett. 25, 1502 (2000). [14] M. Koshi, J. Lightwve Technol. 19, 1970 (2001). [15] S. Y. Lin, J. G. Fleming, J. Lightwve Technol. 17, 1944 (1999). [16] U. Peschel, A. L. Reynolds, B. Arredondo, F. Lederer, P. J. Roerts, T. F. Kruss, P. I. L. Mgt, J. Quntum Electronics 38(7), 830 (2002). [17] B. S. Song, T. Asno, Y. Akhne, Y. Tnk, S. Nod, Journl of Lightwve Technology 23(3), 1449 (2005). [18] J. D. Jonnopoulos, R. D. Mede, J. N. Winn, Photonic Crystls: Molding the Flow of Light, Princeton University Press, Princeton (1995). [18] J. P. Berenger, J. Comput. Phys. 127, 363 (1996). [19] A. Tvélove, Computtionl Electrodynmics: The Finite-Difference Time-Domin Method Artech House, Norwood, MA, (1995). [20] K. S. Yee, IEEE Trns. Antenns Propgt., AP-14, 302 (1966). * Corresponding uthor: i.sukhoivnov@ieee.org