Novel design method of wide-band bend insensitive optical fiber compatible with SMF properties

American Journal of Modern Physics and Application 014; 1(): 1-19 Published online January 0 01 (http://www.openscienceonline.com/journal/ajmpa) Novel design method of wide-band bend insensitive optical fiber compatible with SMF properties S. Makouei Faculty of Electrical and Computer Engineering University of Tabriz Tabriz Iran Email address makouei@tabrizu.ac.ir To cite this article S. Makouei. Novel Design Method of Wide-Band Bend Insensitive Optical Fiber Compatible with SMF Properties. American Journal of Modern Physics and Application. Vol. 1 No. 014 pp. 1-19. Abstract We have developed a novel single-mode optical fiber design method with graded index refraction in core region which exhibits ultra low bending loss and high effective area over S+C+L communication bands. In this approach the MFD of the structure is controlled strictly and bend reduction process is done by evolutionary Genetic Algorithm. The procedure is based on expanding the fundamental mode field distribution with weighted Gaussian terms which is capable to set the MFD in the desired predefined values. Owing to direct control on MFD value this method is absolutely appropriate to design bend insensitive fiber for FTTH application. Meanwhile designed structures have same dispersion properties with SMF and follow ITU-T G.6.D standard. This fact indicates that the designed structures are applicable not only for FTTH networks but also high bit rate WDM transmission where conventional step index single-mode fiber is applied. Keywords Bending Loss MFD Effective Area Dispersion FTTH Genetic Algorithm 1. Introduction Since the late 1980s the interest in the development of broadband service platforms (the Information Super Highway) has significantly increased the activities in network architectures such as Fiber to the Home(FTTH) and Fiber to the Curb (FTTC).Bend insensitivity and splice loss have become the most attractive feature of an optical fiber according as Fiber to the home(ftth) service attracts high attention [1].The fiber should probably be curved strongly at the corner of walls or in ducts and the bends can be small as mm to 1mm and therefore a severe power penalty is caused. Bending loss of less than 0.1dB/turn will ensure robust network performance under practical bending conditions []. Due to sharp bends in FTTH type optical communication system the conventional single-mode fibers (SMF G6.D) that use the uplink and the downlink with 1.31µm and 1.µm wavelength respectively have been replaced by the bend insensitive optical fibers (BIF) having very low bending loss [3].The fiber also should have good splice characteristics to reduce splice loss in connection by mechanical splice or connector. For this background an optical fiber with lower bending loss and reduced splice loss is required for indoor wiring. It is useful to mention that the splicing loss during splicing of bend insensitive fiber structures with the conventional SMF can be minimized by making their mode field diameters as equal as possible []. The bending loss and compatibility requirements put severe constraints on the fiber design space. In the conventional optical fiber structures there is a trade-off between bend loss reduction and mode field diameter increment. Furthermore increasing resistance against curvature makes the fiber very sensitive to nonlinear effects due to the modal effective area decrement. In this paper it is tried to propose a novel design method for bend insensitive optical fiber including significant properties for FTTH operations and overcome the trade off between the MFD and bending loss. This method is capable to gather ultra low bending loss low splice loss and high effective area simultaneously. In this approach the MFD of

16 S. Makouei: Novel Design Method of Wide-Band Bend Insensitive Optical Fiber Compatible with SMF Properties the structure is controlled strictly and bend reduction process is done without MFD reducing. In other word the bending and splice losses are optimized simultaneously. The procedure is based on expanding the fundamental mode field distribution with weighted Gaussian terms which is capable to set the MFD in the desired predefined values. Simulation outcomes indicate that optimizing bending loss in the structures which support this kind of modal field distribution could provide FTTH requirements and follow ITU-T standard for the single-mode optical fiber.. Mathematical Background The Gaussian approximation of the fundamental mode in step index and graded index optical fiber motivates us to generalize the field profile of the fundamental mode and explain it as a summation of several Gaussian functions at operation wavelength. In other words the fundamental mode field distribution is expanded by the weighted Gaussian terms. = (1) where λ op a i and ω i are operation wavelength weighting parameter and spot size of ith term respectively. The equation presented as Ψ1(r) needs correction because the refractive index of least cladding layer must be constant (like n e ) in the optical fiber and the fixed n(r) causes a modified Bessel profile for the modal field distribution in the cladding region. Due to this fact the assumption of fundamental mode field distribution is extended to below model: = < $ ()! " > where r e and K 0 are core radius and modified Bessel function of the zero order. A e and γ e are defined as follows: =. % &'( )* + - 1 3 + + " =4 7 8! / (3) where k 0 is the wave number in vacuum and β is the propagation constant which defined by k 0 n eff.the MFD of optical fiber is related to the field distribution in fiber and it provides useful information about joint microbending and macrobending losses. The MFD is defined as [4]: :;< =8 > A? @ A > B CD* C* B @ By substituting the expanded fundamental mode field distribution in Eq. (4) we have: :;< =8 which means that: > E % &'( )* *+. - A E @F> G + 1 3 + @ *+ > E )H * *+. &'()* - A E @F> B C C* IG +1 3 + JB @ *+ (4) () :;< =K L 4. (6) Eq. says that by core radius (r e )increasing the modified Bessel terms of numerator and denominator would be negligible and the MFD would be only related to a i and ω i which are the expanded field s parameters. In other respects in these circumstances the MFD could be set by the core field profile parameters and there is not any relation with propagation constant. It sounds that direct control on MFD value without any modal analyses is feasible. In the meantime it is anticipated that the MFD value is led to the spot size of the term which has greater weight. For example in the case of two term fundamental mode field distribution expansion in the core layer the MFD is defined by: :;< =4 I% 0 0 F% JFN%0 % I $ 0 O J % 0 F% F PH 0H 0 Q I$ 0 O J (7) where L RL = 0 0 F $. In order to estimate the core refractive index profile which supports the predefined mode distribution the expanded fundamental mode field distribution is entered to scalar wave equation [4]. @? + @? @ @ +TU8! 7 4 V W X=0. (8) The evaluated profile for the refractive index is: [ 7 = \ which means that: H _ ` ]^F )`* _)* `a+b a H +b _ )* a [ Z c 7 > < $ (9) 7 =d e L 4 < 7 > $ (10) It is clear that the refractive index of the core is graded type and maximized in the core center. The maximum value of the extracted refractive index is defined by: 7 f%& = `H ^F H c (11) For the predefined expanded fundamental field distribution the MFD and proportional refractive index could be estimated as (β r e )parameter pairs. In order to guarantee the single-mode operation the modal analysis of the optical fiber with the estimated refractive index profile is necessary to investigate the number of guided modes in the extracted optical fiber structure. The concept to consider is that the core field distribution at the wavelengths apart from

American Journal of Modern Physics and Application 014; 1(): 1-19 17 operation wavelength (λ op ) is not predefined expanded weighted Gaussian. Therefore the modal analysis of estimated graded index optical fiber can be done by piecewise constant representation of the graded index profile that resembles a staircase. According to the LP approximation the guided modes and propagating wave vectors can be obtained by using transfer matrix method (TMM) []. In this approach the refractive index of optical fibers with an arbitrary but axially symmetric profile is approximately expressed by a staircase function One of the applications which need strong control on MFD and bending loss values is FTTH. Designing bend insensitive fibers for FTTH contains important technical challenges. The first challenge is to reduce the bending loss to meet the requirements of harsh end copper cable-like handling conditions. It is manifestly clear that the optical fiber loses the power by radiation if its axis is curved. The second challenge is to meet the demands of backward compatibility with the standard single-mode fibers imposed by the telecom industry standards [3 6]. It is useful to mention that the splicing loss during splicing of bend insensitive fiber structures with the conventional SMF can be minimized by making their mode field diameters as equal as possible [3].Using the method introduced and discussed by Jun-ichi Sakai et al. [7] the radiation loss owing to the uniform bending can be obtained. In this method it is supposed that the field near the inner layers in the curved fiber is almost similar to that in the straight one. This approximation is greatly accurate to evaluate the radiation losses in single-mode optical fiber. The radiation loss α due to uniform bending is presented in [7] and related to the following parameters: h = i * i j =h L 4. (1) The calculated bending loss can be converted to units of db/turn using the relationship: l7m nopp q ml trs7u=6.8 y z 10 l7m nopp ml/8} (13) where R b is radius of curvature in millimeter. In order to decrease bending loss the field distribution tail in the cladding region must be vanished rapidly. This behavior correlates with the case that the MFD is not related to propagation constant due to imperceptible effect of modified Bessel terms in Eq. ().Mentioned descriptions indicate that optimizing bending loss coefficient not only results in increment of resistance against curvature but also prepares the MFD to be set at the desired value. The mathematical backbone of the design procedure is presented in this part. It is clear that the refractive index profile MFD and bending loss are linked together and designing bend insensitive optical fiber appropriate for FTTH applications is possible by a search in the acceptable values for core radius (r e ) and effective refractive index (n eff ). The simulation results reported in next part would show that there is a severe control on the MFD. Also minimizing α leads to the fiber structures which have appreciable characteristics for FTTH operation. 3. Simulation Results and Discussion Based to the established formalism in previous section in this part the simulation results are presented to evaluate the efficiency of design methodology. To emphasize the advantages of design procedure suitable structures for FTTH application with acceptable MFD are introduced. For this case of application all simulations should be done at 1.µm with mm radius of curvature. The splicing loss with the conventional SMF is minimized as the MFD is optimized to be nearer to that of conventional SMF. Due to this fact the spot size of terms(ω i ) are set in the (4µm -.µm) interval [ 3].As said earlier the MFD and bending loss values are extracted for the different pairs of propagation constant and core radius. The minimizing of bending loss would be done by the aim of Genetic Algorithm optimization method [8]. According to the GA technique the problem will have two genes and their ranges are chosen conceptually. The acceptable intervals for r e and β and are respectively (µm - 1µm) and: ~7 8! 8! 7 +1 `H. %. (14) is the maximum acceptable refractive index difference which the LP approximation [4] has accuracy on it. In order to investigate the effects of weighting parameters on the bending loss and MFD each weighting parameter is varied one at a time while the others are kept constant and the bending loss minimizing has been done by the GA approach. In the first investigation the expanded mode field distribution is assumed to have two terms with ω 1 =4.µm and ω =µm spot sizes and the impact of weighting parameters on the transmission characteristics are studied. It is useful to mention that the default value of the weighting parameter (a i ) is one. The influence of weighting parameters on the MFD and corresponding optimized bending loss are illustrated in Figure 1. Marker curves are related to influence of weighting parameters on MFD. Impact of a 1 and a variations are shown by solid and dash lines respectively. It is clear that by increasing a 1 and a the MFD is led to the ω 1 and ω respectively. As it is anticipated the MFD value would be approached to the ω i spot size with increasing a i in multi-term expanded modal field distribution. This means that the weighting coefficients describe the relative importance of each subset in the expanded field distribution. Meanwhile equal weighting parameters make the MFD to be near to average of spot sizes. In the case of different weighting parameters with acceptable degree of accuracy it can be said that: :;<. %. (1). %

18 S. Makouei: Novel Design Method of Wide-Band Bend Insensitive Optical Fiber Compatible with SMF Properties The bending loss behaviors of the designed structures are extracted at 1.µm with mm radius of curvature. It is clear that by a 1 increasing the MFD decreases and this yields to higher resistance against curvature. The reverse result is shown for a increment. The concept to consider is that the MFD values are in the acceptable amount for FTTH application. In the meantime the bending loss values at the operation wavelength are ultra small which is suitable for this case of application. MFD (um) 10 9.8 9.6 9.4 0.01 0.00 is bend insensitive in S+C+L communication bands. Such a low bending loss coupled with the property of broadband bend-insensitivity in the optical fiber should find future applications in the wide band FTTH handling multiple wavelengths. The ITU-T standard for the single-mode optical fiber (SMF) has been categorized under G6.D where the zerodispersion wavelength should be about 1300-134 nm and the dispersion should not be larger than 18. ps/km/nm at 10 nm [3].It is interesting to evaluate dispersion behavior of such structures. As a study case this analysis is done for the first designed structure presented in Table 1. Zerodispersion wavelength dispersion and dispersion slope at 1.µm are 1.3 µm 16.47ps/km/nm and 0.06ps/km/nm respectively. These values are compatible with the standard SMF [3 10]. This fact indicates that the designed structure is applicable not only for FTTH networks but also high bit rate WDM transmission where conventional step index singlemode fiber is applied. 9. 30 0.01 9 0 1 3 4 6 0 Figure 1. MFD (µm) and Bending loss (db/turn) versus weighting parameter. a 1 impact (solid) a impact (dash). Table 1. MFD A eff and Bending loss behaviors in the designed fibers. a1 0. 0. 1 4 6 MFD (µm) 9.81 9.68 9.1 9.3 9.1 9.1 Aeff(µm ) 7.44 73.40 70.88 68.41 66.46 6.64 Bend loss 4.7e-3 4.4e-3 1.76e-3 1.11e-3 7.19e-4 6.80e-4 (db/turn) *a =1 in all cases. As a case study the results related to the influence of a 1 weighting parameter are gathered in Table1. It is clear that the proposal of expanding the modal field distribution in the core region has made a remarkable breakthrough in the fiber design domain. Owing to this new method intense control on the MFD is achieved and bend insensitive optical fiber with large effective area is introduced. In the paper reported by Pramod R. Watekar et al. [9] the bending loss was about 0.4 db/turn at 1.µm at the bending radius of mm. In the other work reported by S. Matsuo et al. [10] the bending loss was 0.0 db/turn at the bending radius of 10mm. So by notice on previous works it is clear that the designed structures have significant potential to be used in FTTH application. In the meantime the bending loss is found to be in the range of 6.9e-4 to 7.4e-3 db/turn for the entire band of 1. µm to 1.60 µm for mm of curvature at the first case of Table 1 which has higher bending loss value at operation wavelength (worst case) and its curve is presented in Figure.According to results reported in [9] the bending loss was in the range of 4e-3 to 1.6e- db/turn in forgoing wavelength interval for 10 mm of bend radius. It is evident that the structures not only have ultra low bending loss at λ op but also Dispersion (ps/km/nm) 0 10 0-10 1.1 1. 1.3 1.4 1. 1.6 1.7 1.8 0 Wavelength (um) Figure. Dispersion (ps/km/nm) and at mm radius of curvature versus wavelength (µm). MFD (um) 9.8 9.6 9.4 9. 9 8.8 8.6 Figure 3. MFD (µm) versus weighting parameter a 1 impact (solid) a 3 impact (dash). In order to show generality of the gained results we assumed the expanded fundamental mode field distribution with three terms ω 1 =4µm ω =4.µm and ω 3 =µm.as said earlier these values are chosen in the manner that the 0.008 0.006 0.004 0.00 8.4 a1 Impact a3 Impact 8. 0 4 6 8

American Journal of Modern Physics and Application 014; 1(): 1-19 19 extracted MFD be appropriate for FTTH application. The default value of the weighting parameters is one. The effect of weighting parameters on the MFD is illustrated in figure 3. The influence of a is not presented because the average of ω 1 and ω 3 (with equal weight) is ω. In this case the a variation could not change the MFD or other structure characteristics severely. It is obvious that like former conclusion by a i increasing the MFD is led to corresponding spot size. The bending loss behavior of the designed structures at 1.µm with mm radius of curvature is presented in Figure 4. It is clear that the bending loss values at the operation wavelength are less than 0.1dB/turn which is absolutely appropriate for FTTH application. References [1] Kuniharo Himeno Shoichiro Matsuo Ning Guan and Akira Wada Low-Bending-Loss Single-Mode Fibers for Fiber-tothe-Home J. Ligthwave Technology Vol. 3 pp. 3494-3499 00. [] Pramod R. Watekar SeongminJu and Won-Taek Han Single-mode optical fiber design with wide-band ultra low bending-loss for FTTH application J. Opt. Express Vol. 16 pp. 1180-118 008. [3] Pramod R. Watekar SeongminJu and Won-Taek Han Near zero bending loss in a double-trenched bend insensitive optical fiber at 10nm J. Optics Express Vol. 17 pp. 01-0166 009. 10-10 -3 a1 Impact a3 Impact [4] Ghatak A. and Thyagarajan K. 00 Introduction to fiber optics Cambridge University Press. [] M. Shenoy K. Thygarajan and A. Ghatak Numerical analysis of optical fibers using matrix approach J. Lightwave Technology Nol. 6 pp. 18-191 1988. [6] Jinkee Kim David W. Peckham Alan H. McCurdy John M. Fini Peter I. Borel KariofilisKonstadinidis Peter Weimann Richard Norris Fengqing Wu Robert Lingle David J. Mazzarese John George and Andrew Oliviero Bend Insensitive Fibers for FTTH and MDU Proc. Of SPIE V. 7134 008. 10-4 0 4 6 8 Figure 4. versus weighting parameter a 1 impact (solid) a 3 impact (dash). 4. Conclusion The proposal of the novel design method for wide-band bend insensitive single-mode optical fibers appropriate for indoor wiring in FTTH is presented. The procedure is based on expanding fundamental mode field distribution with weighted Gaussian terms. Simulation results show that the MFD can be managed by the aim of weighting parameters. As a study case simulation results show bending loss of 4.7 10-3 db at 1.µm for single turn of mm radius and the MFD and effective area are 9.81µm and 7.44µm respectively. Furthermore designed structures have same dispersion properties with SMF and its optical properties follow ITU-T G.6.D recommendation. [7] Jun-ichi Sakai Tatsuya Kimura "Bending loss of propagation modes in arbitrary index profile optical fibers "J. Applied Optics Vol. 17 pp. 1499-106 1978. [8] T. Baeck F. Hoffmeister and H. P. Schwefel An Overview of Evolutionarv Algorithms for Parameter Optimization J. Evol. Comput. Vol. 1 pp. 1-4 1993. [9] Pramod R. Watekar SeongminJu Young Sik Yoon YeongSeop Lee Jinhan Kim and Won-Taek Han Ultra-low Bending Loss of 0.007dB/loop for 10mm of Bending Diameter at 10nm in the Double Trenched Bend Insensitive Optical Fiber The European Conference on Lasers and Electro-Optics and the XIth European Quantum Electronics Conference (CLEO/Europe-EQEC) Munich Germany14-19 June 009 CE.P.7 pp. 1-1 009. [10] S. Matsuo T. Nunome T. Yoshida T. Hamada and K. Himeno Design Optimization of Trench Index Profile for the same dispersion characteristics with SMF OFCNFOEC 007 paper JWA.