CHARACTERIZATION OF PHOTONIC CRYSTAL FIBERS FROM FAR FIELD MEASUREMENTS

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1 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 3 CHARACTERIZATION OF PHOTONIC CRYSTAL FIBERS FROM FAR FIELD MEASREMENTS Shailendra. Varshney and R..Sinha* Dept. of Applied Physics, Delhi College of Engineering Faclty of Technology, niversity of Delhi, Bawana Road, Delhi 4, India *Tele: dr_rk_sinha@yahoo.com; skvarshney_@yahoo.co.k Abstract e report an online method for characterization of Photonic Crystal Fibers PCFs from its far field measrements. PCF is analyzed sing effective index method to obtain its far field radiation patterns. It is shown that the normalized freqency V eff, Core diameter d co, air hole spacing Λ, air hole diameter d and effective cladding index and hence nmerical apertre of PCF can be obtained from its far field measrements. ey words: Photonic Crystal Fiber, Far field, Effective index method I. INTRODCTION A considerable amont of interest has been generated in Photonic Crystal Fibers [-3] PCFs de to their nsal wavegiding properties like, single mode operation at any wavelength [4], large mode area [5] & manageable dispersion properties [6] etc. Photonic Crystal Fibers are single material optical fibers with a periodic array of air holes rnning down its length. Sch fibers gide light de to a central defect created at a design state. One of the important characteristics of PCFs is single mode operation over an entire range of operating wavelengths, which is, expected to be exploited in varios commnication and sensing applications in the near ftre. The other interesting featres are control of dispersion in PCFs. As a reslt, PCF can be designed i to exhibit zero dispersion at any wavelength in both Infra-Red & ltra-violet regions ii provide nearly zero ltraflattened dispersion in the range of.3-.7 µm and iii a very high negative dispersion [7-9]. These characteristics of PCF make them sefl candidate for Dense avelength Division Mltiplexed DDM and Dispersion compensation applications. Therefore, with a view of wide applications of PCFs in both existing and ftristic optical fiber networks, an online method for characterization of these fibers is reqired to be developed. This will help to estimate the design parameters air hole diameter, air hole spacing, core diameter and V eff etc. of PCF. The far field radiation pattern of the fndamental mode has been sccessflly sed to characterize single mode step index as well as graded index fibers [,]. Frther this techniqe has also been extended in characterization of, step index symmetric slab wavegides [] & practical integrated optical wavegides [3,4]. Copyright SBMO ISSN

2 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 33 Varios grops have modeled Photonic Crystal Fibers by different nmerical tools [5-] for determining the wavegiding parameters for lightwave propagation in sch fibers. Effective index method is one of them and is sed to calclate the effective index i.e. n eff of the infinite periodic photonic crystal cladding. The effective normalized freqency i.e. V eff of the fiber and dispersion of lightwave signal propagating throgh PCF has been reported in the literatre sing effective index approach. Herein, we describe the development of analytical formlae and a method to characterize PCF from its far field radiation pattern similar to single mode step index fiber sing effective index approach. II. EFFECTIVE INDEX METHOD This method is sed to determine the cladding mode field by solving the scalar wave eqation within a simple cell centered on one of the holes as shown in fig. a. The hexagonal shape of the cell has been approximated by a circlar one as shown in Fig. b in order to make a general circlar symmetric mode soltion. The soltions in the air hole and silica region is given by Ψ = A I R ; R= r/a air hole region; R> Ψ = B R+ C Y R silica region ; R< where a being the radis of the air hole,, Y and I are the Bessel fnctions of first kind, second kind and modified Bessel fnction of first kind of order zero respectively. sing bondary condition at the edges, the eigen vale eqation is obtained as where B and C are the constant and is given as and with the parameters, and as follows B +CY = A I + I B = I Y Y [ + I ] [ Y Y ] A I C = 3 = k a n s n eff = k a n eff n a Copyright SBMO ISSN

3 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 34 = k b n s n eff Here n s, n a and n eff are the refractive indices of pre silica, air and effective index of the cladding respectively. Therefore, by solving the eigen vale eqation given by, effective index defined by propagation constant of fndamental space filling mode β FSM as n eff = β FSM /k, where k is free space propagation constant of light with wavelength λ. The wavegide consists of a core and a cladding region that have refractive indices n co and n cl respectively as shown in Fig b. The core is pre silica bt the refractive index of microstrctred cladding region is given by propagation constant of the lowest order mode that propagates in the infinite cladding material. Now from the knowledge of cladding index n cl = n eff and known vale of core index vale n co =.45 i.e. n silica, the propagation constant & hence the modal index of gided wave of PCF is obtained similar to step index fiber having core index n co, core radis, ρ, and cladding index n cl =n eff.. PCF as a Step Index Fiber The fndamental mode soltion for the strctre as shown in Fig. b is written as Ψ = A R R< = B R R> 4 The constants A and B can be fond by applying bondary conditions. Therefore the soltion as given by eq.4 can be rewritten as, Ψ = = R R 5 where R = r/ρ, and ρ.64 Λ [7], Λ is the separation between two air holes called as air hole spacing or pitch = k ρ n s n e = k ρ n e n cl Copyright SBMO ISSN

4 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 35 III. FAR-FIELD OF PHOTONIC CRYSTAL FIBER Since, the mode distribtion depends only on radial coordinate r of eqivalent step index fiber for a given PCF, therefore far field pattern will also be cylindrically symmetric. The modal soltion of the wave propagation throgh PCF is obtained from effective index model as given by the eqation 5. These modal fields are sed for deriving an expression for far field intensity distribtion of lightwave propagating throgh PCF The far field amplitde θ is given as [] Ψ lξ mη ξ η e ik + = C, dξ dη 6 where l = x/r, m = y/r, l & m are the direction cosines of the observation direction as shown in Fig.. Calclating the field distribtion along the x axis for which m= and l=sinθ, is given as follows: Sbstitting, Since, Eq. 4 become, = C Ψ ik ξ ξ η e l, dξdη ξ = r cos φ ; dξ = -rsinφ dφ η = r sin φ ; dη = rcosφ dφ r sinθ cosφ θ C rdrψ r e ik dφ = 7 π π i cosφ = e dφ θ πc rdrψ r k r sinθ = 8 Eq.8 represents the amplitde of far field pattern at angle θ. Again sbstitting, q = k rsinθ = π/λ r sinθ and =q ρ=k asinθ; r = ρ and making se of Eq., the far field amplitde is given as Copyright SBMO ISSN

5 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. Copyright SBMO ISSN = ρ π θ d d C 9 For θ =, far field amplitde will be, + = ρ π d d C = V eff πcρ Therefore, normalized far field amplitde ~ θ is given by ~ θ θ = + = ; For [ ] V eff + = ; For = Hence, the normalized far field intensity distribtion I θ will be given by ~ θ θ I = + = I θ ; For = [ ] + V eff ; For = where = k ρ sinθ = π/λ ρ sinθ and core radis ρ =.64Λ, where Λ is the air hole spacings and λ is operating wavelength. and are the fiber parameter for a given vale of V eff for a PCF.

6 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 37 IV. CHARACTERIZATION OF PCF Far field intensity distribtion for PCF with normalized radiation angle for different vales of normalized air hole size d/λ at a wavelength of.55 µm and.3 µm are shown in Figres 3 a and 3b respectively. It is clear from Figres 3a and 3b that there is shift in the peaks of the first lobe as observed in the far-field radiation patterns. This is becase the V eff vale changes de to change in the wavelength and normalized air hole size d/λ. This indicates that the far field radiation distribtion of PCF strongly depends on its relative air hole size. niversal crve depicting the variation of the ratio of x / h = sinθ x /sinθ h and normalized half intensity angle h = k ρ sinθ h with V eff for different strctres of eqivalent step index fibers for given PCFs are shown in Figre 4. θ x is the angle corresponding to first minima of the far field pattern and θ h represents the angle where the far field intensity drops to half of its maximm. It is here emphasized that the far field intensity distribtion of PCF is similar to that of the single mode step index fiber. However, the difference lies to the fact that in case of PCF the far field intensity distribtion is observed with effective V eff vale and not with the absolte V vale. Ths, on measring the angles θ x and θ h the ratio of sinθ x /sinθ h is obtained, from where V eff of PCF can be obtained from Fig.4. Frther with the knowledge of V eff of PCF the normalized half intensity angle h can be determined and hence the core radis ρ can be determined. Since, ρ=.64λ, therefore, air hole spacings Λ of a given PCF can be obtained. Now, with the knowledge of V eff, core radis and operating wavelength λ, the effective cladding index of PCF can be known by knowing the refractive index of core. In case of PCF, the core is pre silica and its refractive index is known at any wavelength. Hence, the effective cladding index of PCF can be estimated. Again by knowing the core index and effective cladding index, nmerical apertre i.e. n s n cl of PCF can be obtained. From Figre 5, the normalized air hole size can be estimated by knowing the effective normalized freqency of PCF from Fig. 4. Since, air hole spacing is already estimated, hence, air hole diameter can be determined. Ths, with the help of figres 3,4 and 5, all the essential design parameters of PCF can be obtained. V. CONCLSION An effective index method has been applied to characterize Photonic Crystal Fibers from its far field radiation patterns similar to the conventional step index fiber. In this method, a PCF is approximated to step index fiber. The niversal crves are obtained for different designs of PCFs, which is sed to determine the additional parameters air hole size, effective cladding index and air hole spacings of PCF. Acknowledgements The athors grateflly acknowledge the financial spport provided by All India Concil for Technical edcation A.I.C.T.E, Govt. of India for the work nder R&D project Characterization of Photonic Crystal Fibers and wavegide for Telecom & Sensing Applications Copyright SBMO ISSN

7 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 38 One of the athors Shailendra mar Varshney also acknowledges the financial spport provided by niversity Grants Commission GC, Govt. of India. REFERENCES []. C. night, T. A. Birks, R. F. Cregan and P. St.. Rssell, Photonic crystals as optical fibers-physics and applications, Opt. Mater. Vol., 998, pp []. Broeng, D. Mogilevstev, S. E. Barko and A. Bjarklev, Photonic Crystal Fibers: A new class of optical wavegide, Opt. Fiber Technol., Vol. 5, 999, pp [3] R. Ghosh, A. mar,. P.Menier and E. Marin, Modal characteristics of few-mode silicabased photonic crystal fibers,. Opt. & Qantm Electron. Vol. 3,, pp [4] T.A.Birks,.C.night and P.St..Rssell, Endlessely single mode Photonic crystal fiber Opt.Lett [5]. C. night, T. A. Birks, R. F. Cregan, P. St.. Rssell and. P. de Sandro, Large mode area photonic crystal fiber, Elect. Lett. Vol. 34, 998, pp [6] Tanya M. Monro, D..Richardson, N.G.R.Broderick and P..Bennett, Holey Optical Fibers: An Efficient Modal Model,. Lightwave Technol., [7] A. Ferrando, E. Silvestre,..Miret and P. Andres, Nearly zero ltraflattened dispersion in photonic crystal fibers, Opt. Lett. Vol. 5,, pp [8] T. A. Birks, D. Mogilevstev,. C. night and P. St.. Rssell, Dispersion compression sing single material fibers, Photon. Technol. Lett. Vol., 999, pp [9] R.. Sinha and Shailendra Varshney, Dispersion properties of Photonic crystal fibers, sbmitted for pblication in Microwave & Optical Technology Letters [].A. Gambling, D.N. Payne, H. Matsmra and R.B. Dyott, IEE Microwave Opt. and Acost., [] A..Ghatak, R. Srivastava, I.F. Faria,.Thyagarajan and R. Tewari, Electronics Letters, Vol.9983 pp [] A.C. Bocovalas, Electronics Letters, Vol [3] A. mar and R.. Sinha, Characterization of single mode channel wavegides from far field measrements, Optics Commnications, Vol pp [4] R..Sinha and S.I.Hosain, Characterization of single mode asymmetric slab wavegide from far field intensity pattern,. Opt. Commn. Vol., 989 pp. 5-7 [5] A. Ferrando, E. Silvestre,.. Miret, P.Andres and M. V. Andres, Fll-vector analysis of a realistic Photonic crystal fiber Opt. Lett. Vol pp [6] E. Silvestre,.. Miret, P.Andres and M. V. Andres, Biothonormal-basis method for the description of optical fiber modes. Lightwave Technol. Vol pp [7] F. Brechet,. Marco, D. Pagnox and P. Roy, Complete analysis of the propagation characteristics into Photonic Crystal Fibers by the Finite Element Method,. Opt. Fiber Technology, Vol. 6 pp. 8-9 [8] M. Qi, Analysis of gided modes in photonic crystal fibers sing the finite difference time domain method, Microwave Opt. Technol. Lett. Vol. 3, pp [9] Z. Zh and T. G. Brown, Fll-vectorial finite-difference analysis of microstrctred optical fibers, Opt. Express, Vol., pp [] A. Ghatak,. Thyagarajan, Introdction to Fiber Optics, Cambridge niversity Press,, 999. Copyright SBMO ISSN

8 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 39 Λ d Fig. a Cross-section of trianglar photonic crystal with air hole diameter d and spacing between two air holes as Λ composed of hexagonal nit cell Silica b Air a b Fig. b Circlar approximation of hexagonal nit cell air in silica strctre Copyright SBMO ISSN

9 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 4 z r θ P Fig Far-field radiation pattern with observation point P and angle θ. Fig. 3a Far-field intensity pattern of Photonic Crystal Fibers having d/λ=.,.3,.4 having core radis.64λ at a wavelength of.55µm Copyright SBMO ISSN

10 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 4 Fig 3b Far-field intensity pattern of Photonic Crystal Fibers having d/λ=.,.3,.4 having core radis.64λ at a wavelength of.3µm Fig. 4 niversal crves depicting the variation of sinθ x /sinθ h and k ρ sinθ h with V eff for eqivalent step index fiber for given PCF Copyright SBMO ISSN

11 ornal of Microwaves and Optoelectronics, Vol., N. o 6, December. 4 Fig. 5: Variation of effective normalized freqency V eff as a fnction of normalized air hole size d/λ Copyright SBMO ISSN