45, 500 December 006 Bandwidth analysis of long-period fiber grating for high-order cladding mode and its application to an optical add-drop multiplexer Yue-Jing He National Cheng Kung University Department of Electrical Engineering Tainan 70 Taiwan Yu-Lung Lo National Cheng Kung University Department of Mechanical Engineering Tainan 70 Taiwan E-mail: loyl@mail.ncku.edu.tw Jen-Fa Huang National Cheng Kung University Department of Electrical Engineering Tainan 70 Taiwan Abstract. The spectrum bandwidth of long-period fiber grating LPG for various high-order cladding modes are analyzed in detail by two-mode coupled-mode equations and applied to design narrow bandwidth optical add-drop multiplexer OADM based on two parallel LPGs. In addition, in order to obtain the maximal power transmission, we further derive the structure parameters of OADM such as the distance between two parallel fibers and the length of two long-period fiber gratings according to four-mode coupled-mode equations. As far as this OADM structure is concerned, it is obvious that LPG will dominate the entire bandwidth if LPG has enough narrow bandwidth in comparison with the coupler. In other words, we can easily use LPG to estimate the bandwidth of OADM before starting to design it. In order to survey the feasibility of the above statement, the spectrum bandwidths of LPG and OADM for the various bandwidth of high-order cladding modes are compared and analyzed. Utilizing the four steps proposed in this paper, the numerical results have demonstrated that we can use the high order cladding mode =5 to design the OADM that possesses narrow FWHM 0.4 nm and meets the DWDM system. 006 Society of Photo-Optical Instrumentation Engineers. DOI: 0.7/.40495 Subject terms: dense wavelength division multiplexing DWDM; optical add-drop multiplexer; long-period fiber grating; coupler. Paper 0603 received Mar. 9, 006; accepted for publication May 4, 006; published online Dec. 3, 006. Introduction It is well-known that long-period fiber grating LPG written periodically by ultraviolet light into the core of an optical fiber can couple the power among the co-propagating modes. The coupling between core mode HE and cladding modes has been used extensively as band rejection filters, gain flatteners, and dispersion compensators. 3 So far, all the researches about the spectrum of LPG has emphasized the coupling between core mode HE and loworder cladding modes such as Refs. 4 7. Obviously, it seems impossible to use LPG to design wavelengthdivision multiplexing WDM components. The most critical component for developing a wavelength-division multiplexing system is the optical adddrop multiplexer. A simple OADM device that adds and/or drops a designed channel provides a building block of the complicated optical fiber communication system. Over the past several decades, many types of OADMs have been proposed, such as the well-known structure that consists of a fiber Bragg grating and two optical circulators OCs, 8,9 a Mach Zahnder structure that relies on the interference between two lights reflected by Bragg gratings, 0, and the configuration based on a null coupler with a tilted grating in the waist. In 000, a simple architecture that consists of two parallel long-period fiber gratings was proposed by K. S. Chiang et al. 3 This device is actually based on the mode 009-386/006/$.00 006 SPIE coupling by properly designing the period of LPG and the power coupling between two parallel and identical optical fibers. As excellent as this structure is, it has two serious drawbacks. One is a too wide FWHM 0 nm, and the other is that it is very difficult to use four-mode coupledmode equations to study the bandwidth characteristics before starting to design this OADM. According to the fundamental property of mode, the high-order cladding mode is more sensitive to the variation of wavelength than the low-order mode. 7,4 In other words, the high-order cladding mode can depart from the phasematching condition more rapidly than the low-order mode when the wavelength changes. This simple concept implies that it is possible for LPGs to possess narrow bandwidth as an FBG. In this paper, we will use two-mode coupled-mode equations to analyze and quantify the spectrum bandwidth of LPG for various high-order cladding modes in detail. According to the analytic result and the requirement for the bandwidth, the proper high-order cladding mode is determined to design narrow-bandwidth OADMs based on two parallel LPGs. So far as the design of an OADM is concerned, the bandwidth and the transmission power are two main criteria on judging the entire performance. Therefore, in order to obtain the maximal power transmission, we will derive the structure parameters of an OADM such as the distance be- 500- December 006/Vol. 45
tween two parallel fibers and the length of two long-period fiber gratings according to four-mode coupled-mode equations and propose four design steps. Due to the difference in the structure, it is no doubt that OADM is different from LPG in the spectrum bandwidth even if they are designed on the same cladding mode. However, it is obvious that LPG will dominate the bandwidth of OADM if the cladding mode, which we determine at first, has enough narrow bandwidth in comparison with the coupler. In other words, it is possible only to use LPG to estimate the bandwidth of OADM before starting to design it. We will compare the spectrum of LPG and OADM for the various bandwidths of high-order cladding modes to survey the deviation of the estimation. In addition, we will also analyze the insertion loss, the homo-dye crosstalk, and the hetero-dyne crosstalk of this OADM in detail according to the obtained spectrum. Bandwidth Analysis of LPG for High-Order Cladding Modes As a uniform long-period fiber grating is induced in the fiber core, the two-mode coupled-mode equations that describe the coupling between the core mode HE and the co-propagating cladding mode can be written as follows: da co z dz da c z dz with = i co co A co z + ik cl coa cl z exp i co cl, = ik cl co A co zexp i co cl + i cl cl A cl z, co co = w 0n 0a rer 0 co E co r + E co E co E co z E co z drd, cl cl = w 0n a rer 0 0 cl E cl r + E cl cl E E z cl E z cl drd, k cl co = w 0n a rer 4 0 0 co E cl r + E co cl E E co z E cl z drd, 4 where A co z is the amplitude of the core mode HE, A cl z is the amplitude of the cladding mode, co co is the dc coupling coefficient of the core mode HE, cl cl is the v dc coupling coefficient of the cladding mode,k cl co is the AC coupling coefficient between the core mode HE and cladding mode, is the UV-induced refractive-index variation, and is the period of LPG. 3 Fig. AC coupling coefficients k co a,cl a for 66 cladding modes. Note that throughout this paper, the three-layer cylindrical optical fiber is described by the following parameters: n =.447,n =.44,n 3 =.000 air, a =4.65 m, and a =6.5 m. In addition, the long-period fiber grating is assumed to be a circularly symmetric index perturbation, so that the coupling interaction only occurs between HE and the cladding modes with azimuthal order l=. 4 After solving the dispersion relations of the cladding modes with the above parameters, there are as many as 66 cladding modes at the operating wavelength =550 nm. In Fig., we show the AC coupling coefficient k cl co for the 66 cladding modes and choose some high-order cladding modes =99, 5, and 53 to study the bandwidth characteristic of LPG. Utilizing the boundary condition of LPG, A co z=0= and A cl z=0=0, the bar and cross-power transmission can be derived from Eq. and written as follows: 5 t = = A co z /A co 0 = cos kcl co + ˆ z ˆ + kcl co k cl co + ˆ sin + ˆ z, 5 t = A cl z /A co 0 = with k cl co k cl co kcl co + ˆ sin + ˆ z, 6 ˆ = n co n cl + co co cl cl, 7 where ˆ is the general dc self-coupling coefficient, n co is the effective refractive index of the core mode HE, and n cl is the effective refractive index of the cladding mode. From Eq. 6, the bandwidth of the resonance is given by twice the change in wavelength that causes the general dc self-coupling coefficient ˆ to vary from ˆ =0 to a value of either ±ˆ zero =±/L k co a,cl a for the bandwidth between the first zeros on either side of the resonance. In addition, in order to couple completely a core mode to the cladding mode, which we desire, at the operating wavelength, the period and length of long-period fiber grating should be properly designed by 500- December 006/Vol. 45
Fig. First zeros bandwidth for high-order cladding modes =99, 5, and 53: a general dc self-coupling coefficient ˆ and b cross-power transmission. Fig. 3 Transmission spectrum for high-order cladding modes =97, 98, 99, 00, 0, and 0: a general dc self-coupling coefficient and b bar power transmission. = co co cl cl + /n co n cl, L = 8. 9 k cl co So as to quantify specifically the relation between the order of cladding mode and first zero bandwidth, Fig. a shows the first zeros bandwidth for high-order cladding modes, =99, 5, and 53. In addition, the cross-power transmission corresponded to Fig. a is shown in Fig. b. Note that in Eqs. 5 and 6, the name, dc coupling coefficient, follows Ref. 5 rather than Ref. 6, although the concept to quantify first zeros bandwidth is the same as Ref. 6. As shown in Fig., the higher the order, the narrower the first zeros bandwidth. This arises mainly because the variation in general dc self-coupling coefficient of high-order cladding mode is larger than the low-order cladding mode with the change of wavelength, or the highorder cladding mode is much more sensitive to wavelength than the low-order cladding mode. In Fig., we can clearly find that the high-order cladding mode =99, =5, and =53 possesses first zeros bandwidth about.6 nm, 0.7 nm, and 0.3 nm, respectively. Obviously, it has proved the correction of the statement that it seems possible for LPG to possess narrow bandwidth as FBG. Based on the consideration of the narrow bandwidth, in the remainder of this paper, we will use these three cladding modes to observe the spectrum characteristic of LPG and complete the design of OADM. Utilizing Eq. 7, we can also analyze the position where resonance occurs, ˆ =0, and the results are shown in Fig. 3a when LPG is designed for cladding mode =99, Fig. 4a when LPG is designed for cladding mode =5, and Fig. 5a when LPG is designed for cladding mode =53. For reasons of completeness, we plot the bar power transmission spectrum corresponding to Fig. 3a, Fig. 4a, and Fig. 5a in Fig. 3b, Fig. 4b, and Fig. 5b, respectively. 3 Operating Principle and Design of OADM The optical add-drop multiplexer consists of two similar optical fibers fibers a and b, which are placed in close proximity with d, and two long-period fiber gratings LPG and LPG, which are periodically written by ultraviolet light into the core layer of fibers a and b, as shown in Fig. 6. When we properly design LPG at a desired wavelength, the launched light at the input port of fiber a can be converted from the core mode into the cladding mode that we desire. Then, this cladding mode propagates in fiber a and excites the identical cladding mode supported by fiber b through the evanescent field between the two similar fibers. The cladding mode propagating in fiber b can be transformed to the core mode by writing LPG, whose period and length are the same as LPG s, into the core 500-3 December 006/Vol. 45
Fig. 4 Transmission spectrum for high-order cladding modes =3, 4, 5, 6, 7, and 8: a general dc self-coupling coefficient and b bar power transmission. Fig. 5 Transmission spectrum for high-order cladding modes =5, 5, 53, 54, 55, and 56: a general dc self-coupling coefficient and b bar power transmission. layer of fiber b. Obviously, the resonant wavelength core mode will be dropped at the drop port of this structure, and the other nonresonant wavelengths core mode will remain in fiber a, since their evanescent fields decay rapidly so as not to extend to fiber b. Similarly, the launched light at the add port of fiber b can be added to fiber a because of the symmetry of this structure. The coupled-mode equations that can describe the coupling among these four modes are written as follows 3 : A co a z = ik co a,cl a A cl a zexp iz, 0 A cl a z = ik co a,cl a A co a zexpiz + ic cl a,cl b A cl b z, k co a,cl a = w 0n a rer 4 0 0 co a E cl a r + E co a cl a E k co b,cl b = k co a,cl a, E z co a E z cl a drd, co a,co a = w 0n a rer 0 0 co a E co a r + E co a co a E E z co a E z co a dr d, 5 6 7 A cl b z = ik co b,cl b A co b Zexpiz + ic cl a,cl b A cl a z, A co b z = ik co b,cl b A cl b zexp iz, 3 with = co a cl a + co a,co a cl a,cl a c cl a,cl a / OADM, 4 Fig. 6 Schematic diagram of optical add-drop multiplexer. 500-4 December 006/Vol. 45
cl a,cl a = w 0n a rer 0 0 cl a E cl a r + E cl a cl a E E z cl a E z cl a drd, c cl a,cl b = w a b rer 4 0 d0 cl a E cl b r + E cl a cl b E E z cl a E z cl b dr, 8 9 S = c cl a,cl b, 4 Q = S + k co a,cl a, 5 Q = S + k co a,cl a. 6 From Eq., the maximum cross-power transmission which occurs when =0 is c cl a,cl a = w a b rer 4 0 d0 cl a E cl a r + E cl a cl a E E z cl a E z cl a dr, 0 where A co a z is the amplitude for core mode HE propagating in fiber a, A cl a z is the amplitude for cladding mode propagating in fiber a, A co b z is the amplitude for core mode HE propagating in fiber b, A cl b z is the amplitude for cladding mode propagating in fiber b, k co a,cl a is the AC coupling coefficient between core mode HE and cladding mode for fiber a, k co b,cl b is the AC coupling coefficient between core mode HE and cladding mode for fiber b, co a,co a is the dc coupling coefficient of core mode HE for fiber a, cl a,cl a is the dc coupling coefficient of cladding mode for fiber a, c cl a,cl b is the cross coupling coefficient between fibers a and b for cladding mode, c cl a,cl a is the self-coupling coefficient of cladding mode for fiber a, is the UV-induced refractiveindex variation, and b is the dielectric constant of fiber b. Note that in this paper we assume that the core mode HE and the cladding mode in fiber a are the same as those in fiber b, since two similar fibers are used. Utilizing the boundary condition of OADM, A co a z=0=, A cl a z =0=0, A co b z=0=0, and A cl b z=0=0, the bar and cross power transmission can be written as follows: t = z = A co a z /A co a 0 = expis zcosq z i S sinq Q z + expis zcosq z i S sinq Q z, t x z = A co b z /A co a 0 = expis zcosq z with i S sinq Q z expis zcosq z i S sinq Q z, S = + c cl a,cl b, 3 t,max =sins L OADM cosq L OADM coss L OADM sinq L OADM Q S Besides, if we further set S L OADM = and. 7 8 Q L OADM =, 9 the maximum cross-power transmission will equal. After substituting Eqs. 3 and 5 into Eqs. 8 and 9, the cross-coupling coefficient, c cl a,cl b, and the length of two LPGs, L OADM, are obtained as follows: c cl a,cl b = 3 k co a,cl a, 30 3 L OADM =. 3 k co a,cl a In other words, once the cladding mode that we use to design the OADM is determined that is, the AC coupling coefficient, k co a,cl a, is determined according to the requirement for the bandwidth, in order to obtain maximal power transmission, the cross-coupling coefficient and the length of two LPGs must meet Eqs. 30 and 3 simultaneously. Finally, we propose four steps below to design the narrow-bandwidth OADM: According to the bandwidth analysis of LPG and the requirement for the narrow bandwidth, determine which of the cladding modes will be used to design the OADM. Calculate the AC coupling coefficient of the chosen cladding mode by using Eq. 5, and then calculate the length of two LPGs by using Eq. 3. 3 Find which distance d can make the crosscoupling coefficient, calculated by Eq. 9, meet Eq. 30. 4 Calculate the period of two LPGs by OADM = co a cl a +k co a,co a k cl a,cl a c cl a,cl a. Due to the difference in the structure, it is no doubt that the OADM is different from the LPG in the spectrum band- 500-5 December 006/Vol. 45
He, Lo, and Huang: Bandwidth analysis of long-period fiber grating... Fig. 7 Cross power transmission of OADM and LPG for high-order cladding modes = 99,5, and 53 at operating wavelength 0 = 550 nm. width even if they are designed on the same cladding mode. However, if the cladding mode, which we determine first, has enough narrow bandwidth in comparison with the coupler, it is obvious that LPG will dominate the bandwidth of OADM. In Fig. 8, we compare the cross-power transmission of OADM and LPG on high-order cladding mode = 99, 5, and 53. Obviously, the difference between LPG and OADM in the FWHM can almost be neglected. In other words, we can estimate the bandwidth of Fig. 9 Cross and bar power transmission of high-order cladding modes = 5 and 6 when the parameters are designed for cladding mode = 5: 共a兲 LPG and 共b兲 OADM. OADM before starting to design the OADM by calculating the bandwidth of LPG. Besides, Figs. 7 and 8 also prove that LPG is capable of designing the narrow FWHM OADM. Based on the same concept, we can anticipate that the OADM designed at the cladding modes = 99, 5, and 53 will, respectively, possess the spectrum similar to Figs. 4 6. In Figs. 7 0, we show the cross and bar power transmission of LPG and OADM for the design at the high-order cladding modes = 99, 5, and 53. According to conservation of energy, the total power of cladding modes at z = LOADM can be obtained by 关t=共z = LOADM兲 + tx共z = LOADM兲兴, and it will be regarded as the insertion loss of OADM. As shown in Figs. 8共b兲, 9共b兲, and 0共b兲, the highorder cladding mode = 54 possesses the highest insertion loss at the center wavelength. According to the definition of Eq. 共兲, it is obvious that the magnitude of bar power transmission at z = LOADM will result in the homo-dyne crosstalk. As shown in Figs. 8共b兲, 9共b兲, and 0共b兲, the highorder cladding mode = 54 possesses the largest homodyne crosstalk at the center wavelength. In terms of the hetero-dyne crosstalk in this OADM, we can find the interference between high-order cladding mode = 99 and 00 is lowest as shown in Fig. 0共b兲. Finally, based on the above analysis, we choose the high-order cladding mode = 5 to design the OADM. Fig. 8 Cross and bar power transmission of high-order cladding modes = 99 and 00 when the parameters are designed for cladding mode = 99: 共a兲 LPG and 共b兲 OADM. 4 Conclusions In this paper we analyze the spectrum bandwidth of LPG for high-order cladding modes = 99,5, and 53 in detail 500-6 December 006/Vol. 45共兲
References Fig. 0 Cross and bar power transmission of high-order cladding modes =53 and 54 when the parameters are designed for cladding mode =53: a LPG and b OADM.. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, Long-period fiber gratings as band-rejection filters, J. Lightwave Technol. 4, 58 65 996.. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, and P. J. Lemaire, Long-period fiber-grating-based gain equalizers, Opt. Lett., 336 338 996. 3. D. Stegall and T. Erdogan, Dispersion control with use of longperiod fiber gratings, J. Opt. Soc. Am. A 7, 304 3 000. 4. T. Erdogan, Cladding-mode resonances in short and long period fiber grating filters, J. Opt. Soc. Am. A 4, 760 773 997. 5. T. Erdogan, Fiber grating spectra, J. Lightwave Technol. 5, 77 94 997. 6. T. Erdogan and D. Stegall, Impact of dispersion on the bandwidth of long-period fiber-grating filters, OFC, 80 8 998. 7. D. B. Stegall and T. Erdogan, Dispersion control with use of longperiod gratings, J. Opt. Soc. Am. A 7, 304 3 000. 8. Y. K. Chen, C. J. Hu, C. C. Lee, K. M. Feng, M. K. Lu, C. H. Chang, Y. K. Tu, and S. L. Tzeng, Low-crosstalk and compact optical adddrop multiplexer using a multiport circulator and fiber Bragg grating, IEEE Photonics Technol. Lett., 394 396 000. 9. A. V. Tran, W. D. Zhong, R. C. Tucker, and R. Lauder, Optical add-drop multiplexers with low crosstalk, IEEE Photonics Technol. Lett. 3, 58 584 00. 0. F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, and J. Albert, Highreturn-loss narrow-band all-fiber bandpass Bragg transmission filter, IEEE Photonics Technol. Lett., 394 396 000.. T. Erdogan, T. A. Strasser, M. A. Milbrodt, E. J. Laskowski, C. H. Henry, and G. E. Kohnke, Integrated-optical Mach Zehnder adddrop filter fabricated by a single UV-induced grating exposure, Appl. Opt. 36, 7838 7845 997.. C. Riziotis and M. N. Zervas, Design considerations in optical add/ drop multiplexers based on grating-assisted null couplers, J. Lightwave Technol. 9, 9 04 00. 3. K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, Coupling between two parallel long-period fiber gratings, Electron. Lett. 36, 408 409 000. 4. K. W. Chung and S. Yin, Analysis of a widely tunable long-period grating by use of an ultrathin cladding layer and higher-order cladding mode coupling, Opt. Lett. 9, 8 84 004. by two-mode coupled-mode equations. According to the analytic result and the requirement for the bandwidth, the proper high-order cladding mode is determined to design narrow-bandwidth OADM based on two parallel LPGs. In addition, we also derive the structure parameters of OADM such as the distance between two parallel fibers and the length of two long-period fiber gratings to obtain the maximal power transmission by four-mode coupled-mode equations. From the spectrum of OADM obtained by the proposed four steps, we discuss the insertion loss, the homodye crosstalk, and the hetero-dyne crosstalk of the OADM in detail and prove that the deviation on using LPG to estimate the FWHM of OADM before starting to design it is acceptable as long as the FWHM of LPG that we use to design the OADM is less than 0.4 nm. The numerical results have demonstrated that we can use the high-order cladding mode =5 to design the OADM that possesses narrow FWHM 0.4 nm and meets the DWDM system. Acknowledgments The authors gratefully acknowledge the support by the Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council NSC94--E- 006-08 and NSC94-8-M-008-009 in Taiwan. Yue-Jing He was born in Kaohsiung, Taiwan, in June 975. He received his MS degree in the Department of Communication Engineering from National Chiao-Tung Taiwan University, Taiwan, in 000. He is currently working toward his PhD degree in the area of fiber-optic networking communications. His major interests are in DWDM networking devices, long-period fiber grating filter, fiber Bragg grating sensors, and multi-user communication systems. Yu-Lung Lo received his BS degree from National Cheng Kung University, Tainan, Taiwan, in 985, and the MS and PhD degrees in mechanical engineering from the Smart Materials and Structures Research Center, University of Maryland, College Park, USA, in 99 and 995, respectively. After graduation, he joined the Industrial Technology Research Institute ITRI, Opto-Electronics and Systems Laboratories, working on fiber-optic smart structures. He has been a member of the faculty of the Mechanical Engineering Department, National Cheng Kung University, Taiwan, since 996. His research interests are in the areas of experimental mechanics, fiber-optic sensors, smart structures, optical techniques in precision measurements, electronic packaging, and MEMS. He has written over 50 technical publications and filed five patent disclosures. Dr. Lo is a member of the SPIE and SEM. Dr. Lo received the First- Class Research Award by the National Science Council in Taiwan, 005 006 and Dr. Wu, Ta-You Memorial Award for young Researchers by the National Science Council in Taiwan, 00. Currently he is Vice Chair in technical division of optical methods and Secretary in the technical division of inverse problem methodologies in Society of Experimental Mechanics SEM in the USA. Also, he is Steering Committee in Society of Asian Committee for Experimental Mechanics ACEM. 500-7 December 006/Vol. 45
Jen-Fa Huang received the MASc and PhD degrees from the Department of Electrical Engineering at the University of Ottawa, ON, Canada, in 98 and 985, respectively. Since 99, he has been with the Department of Electrical Engineering at the National Cheng Kung University, Taiwan, where he is currently a conjunction professor of the Institute of Computer and Communication Engineering and the Institute of Opto-Electronic Science and Engineering. Prior to 99, he was with MPB technologies, Montreal, PQ, Canada, in the Optical Communication Laboratories working on the TAT-9 Transatlantic undersea lightwave transmission project. His research interests are mainly in the areas of optical communications, alloptical data networking, and fiber-optic sensors. 500-8 December 006/Vol. 45