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1 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY Loss Characteristics of Single-HE 11 -Mode Bragg Fiber Guangyu Xu, Wei Zhang, Yidong Huang, Member, IEEE, and Jiangde Peng Abstract The loss characteristics of two kinds of typical single- HE 11 -mode Bragg fibers based on PES/As 2 Se 3 and Si/SiO 2 - multilayer claddings are analyzed theoretically. The available lowest loss levels and corresponding structure parameters of the two single-he 11 -mode Bragg fiber are optimized to show the feasibility of the low-loss single-he 11 -mode Bragg fiber design under the two material systems. The influences of structure parameters on the loss characteristics are analyzed in detail. For PES/As 2 Se 3 Bragg fiber, a loss level as high as db/km is expected at wavelengths from 0.85 to 2.94 µm dueto thelarge absorption loss. To extend the limitation, lower loss cladding material should be investigated. For Si/SiO 2 Bragg fiber, low-loss single-he 11 -mode propagation can be achieved by the materials if fabrication improvement can support long fabricated fiber length. Index Terms Bragg fiber, modal loss, photonic band gap, single mode. I. INTRODUCTION BRAGG FIBER has recently attracted much interest for its capability to control the light by wavelengthscale microstructure [1]. Potential applications of Bragg fiber have been demonstrated experimentally by the Massachusetts Institute of Technology (MIT) in CO 2 laser transmission, nearinfrared-response applications, and transverse resonant cavities [2] [4], where multimode Bragg fibers with a large core (radius R several tens of lattice period a) are preferred. Some fiber fabrication techniques have been reported [1], [5]. In the field of optoelectronics, single-mode transmission is a basic requirement for fibers used in optical signal transmission and realizing various functions, which can be achieved in the largecore Bragg fiber using TE 01 mode by the modal filter effect [6]. As an example, dispersion compensation schemes based on single-te 01 -mode transmission in multimode Bragg fiber has been proposed and investigated in recent years [7] [8]. However, the ringlike distribution of the TE 01 mode will limit its applications due to the coupling problem between the Bragg fiber and traditional single-mode sources, components, and fibers, where field distributions are mainly Gaussian-like. Manuscript received April 29, 2006; revised August 25, This work was supported in part by 973 Program of China under Contract 2003CB and by Science Foundation of Beijing under Contract G. Xu was with the Department of Electronic Engineering, Tsinghua University, Beijing , China. He is now with the University of California, Los Angeles, CA USA ( guangyu@ee.ucla.edu). W. Zang, Y. Huang, and J. Peng are with the Department of Electronic Engineering, Tsinghua University, Beijing , China ( zwei@mail. tsinghua.edu.cn; yidong@tsinghua.edu.cn; pengjd@mail.tsinghua.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT Fig. 1. Scheme of typical single-mode Bragg fiber. Fiber parameters: n 1 =2.822, n 2 =1.621, n c =1.0, d 1 /a =0.5, and R/a =1.6. Inset: Cross section of Bragg fiber. Recently, single-he 11 -mode Bragg fiber with a small core (radius R several lattice period a) has emerged [9] and become interesting in some potential fiber devices such as the bistable optical switch and cutoff solitons [10] [11]. According to the metal waveguide model [12], the fundamental mode (HE 11 ) in Bragg fiber has Gaussian-like field distribution, which would match traditional optoelectronic systems well. One possible limitation of single-he 11 -mode Bragg fiber is the modal loss. Unlike the multimode Bragg fibers, the field in single-he 11 -mode Bragg fiber extends more to the fiber cladding due to the small core. Therefore, not only the radiation loss due to finite number of layers but also the absorption loss due to lossy cladding materials has to be considered. Hence, investigating the modal loss with the real lossy materials would be helpful in low-loss single-he 11 -mode Bragg fiber designs. In this paper, the loss characteristics of two typical kinds of single-he 11 -mode Bragg fibers with different material selections are investigated theoretically. One has PES/As 2 Se 3 multilayer claddings with a hollow core [2]; the other has Si/SiO 2 multilayer claddings with a solid SiO 2 core [9]. Dominating loss mechanisms and the influence of fiber structure parameters of the two kinds of Bragg fibers are analyzed numerically. The available lowest loss levels and corresponding structure parameters of the two single-he 11 -mode Bragg fibers are optimized to show the feasibility of the low-loss single-he 11 -mode Bragg fiber design under the two material systems /$ IEEE

2 360 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007 Fig. 2. Single-HE 11 -mode region of typical Bragg fiber. Light and dark regions are TE and TM photonic band structures of Bragg fiber cladding, respectively. Two lowest order modes TM 01 and HE 11 are shown in the band gap above the radiation line. II. MODELING LOSS CHARACTERISTICS OF SINGLE-MODE BRAGG FIBERS The scheme of a typical single-mode Bragg fiber is shown in Fig. 1. Here, n c, n 1, and n 2 are refractive indexes of the core region, high-index, and low-index cladding layers, respectively. Here, d 1 and d 2 are the thicknesses of high-index and low-index cladding layers, respectively. The lattice scale a equals to the sum of d 1 and d 2. R is the radius of the inner core region. The modal characteristics of Bragg fiber are calculated by the transfer-matrix method [13] [14]. This method expands the field components as a linear combination of Bessel functions: E z (r) H θ (r) H z (r) E θ (r) i th layer =[M i (r)] A i B i C i D i (1) where E and H are the electrical and magnetic field components of the guiding mode in Bragg fibers. Here, i denotes the layer number; A, B, C, and D are the expansion coefficients. M(r) is a Bessel matrix for a finite number of layers. r, θ, and z are three variables of the cylindrical coordinate. Using the continuous conditions across the layer interfaces, the modes can be determined by solving the eigen equation of the effective mode index. The real and imaginary parts of the effective mode index denote the propagation constant and loss of the mode of Bragg fibers, respectively. Since the imaginary part is much less than the real part, the real part of the effective mode index is expected to be close to that of the Bragg fiber with infinite layers. Using it as the initial value, the complex effective mode index of the Bragg fiber with finite layers can be calculated [14]. This method contains no approximation; therefore it could give an accurate imaginary part of the modal index, which is essential for the loss characteristics. Fig. 2 shows the propagation constants of the lowest two modes (TM 01 and HE 11 ) in a typical Bragg fiber. The parameters used in calculation are n 1 =2.822, n 2 =1.621, Fig. 3. Normalized HE 11 -mode components H z and E θ along radial direction at 1.55 µm forω = 0.22 (normalized by 2πc/a). Inset: Electrical-field time-average energy intensity distribution of HE 11 mode. n c =1.0, d 1 /a =0.5, and R/a =1.6. It is clear that the region between the normalized cutoff frequencies of the two modes supports single fundamental mode guiding. Calculations show that the two cutoff frequencies increase with decreasing d 1 /a and R/a, giving the relations of the single-mode region with the cladding parameters and core size. Another factor impacting the single-mode region is the photonic band structure of Bragg fiber, which is also shown in Fig. 2 under the infinite periodic multilayer approximation of the cladding [15]. The single-mode region of HE 11 is also limited by both TE and TM photonic band gaps above the radiation line. Low-loss single-he 11 -mode propagation should be achieved near the center of the first band gap. Fig. 3 shows the distribution of normalized field components H z and E θ of HE 11 -mode in the radial direction of the fiber cross section at 1.55 µm. The calculation is given under the same parameters in Fig. 2 for a frequency ω =0.22 (normalized by 2πc/a). The electrical-field time-average energy intensity distribution of HE 11 mode (x polarization) is shown in the inset. About 87% of the modal power is distributed in the core region; others extend to the fiber cladding. In this case, the absorption loss due to the material properties is not negligible as large-core Bragg fibers. Hence, the complex material indexes are considered in the fiber loss calculation. Additional loss due to the nonuniformity of structures and the roughness of inner surface are not included. Due to the lossy cladding materials of Bragg fibers considered in this paper, the quarter wave stack (QWS) approach condition [6] [8] could not optimize the total loss (absorption loss add leakage loss), since this approach deals with only the leakage loss of Bragg fiber with lossless cladding materials. In this paper, the modal loss under a scalable structure described by (d 1 /a, R/a) is optimized by the following: 1) calculating the photonic band gap under normalized structure parameters using the refractive indexes of materials at the targeted wavelength λ 0 ; 2) calculating the modal loss curve of the HE 11 mode in the single-he 11 -mode region and finding the normalized frequency

3 XU et al.: LOSS CHARACTERISTICS OF SINGLE-HE 11 -MODE BRAGG FIBER 361 TABLE I MATERIAL REFRACTIVE INDEX ω opt of the minimum loss; 3) calculating the lattice period a opt, which is defined as the product of λ 0 and corresponding ω opt (all the structure parameters can be solved simultaneously); and 4) calculating the lowest loss value of HE 11 mode under (d 1 /a, R/a) by [14] loss(db/km) = π λ 0 ln 10 Im ( n effhe11 ) (2) where n eff is the effective mode index of HE 11. The available lowest loss levels and corresponding structure parameters can be found by analyzing the influences of the scalable structure parameters (d 1 /a, R/a) on their optimized modal loss values. III. NUMERICAL RESULTS The loss characteristics of PES/As 2 Se 3 and Si/SiO 2 Bragg fibers supporting single HE 11 mode are investigated theoretically. The material refractive indexes of cladding materials are shown in Table I [16]. The core radius R in calculation is from0.8a to 1.6a, which are numerically demonstrated to guide single HE 11 mode. The dominating loss mechanism of the two kinds of Bragg fibers are determined through Fig. 4 by the loss level versus the layer number N, since the layer number directly influences the radiation/leakage loss but has much less of an effect on the absorption loss. Considering the current fabrication level, the maximum values of N in PES/As 2 Se 3 and Si/SiO 2 Bragg fibers are limited to 70 and 30, respectively. Typical results of PES/As 2 Se 3 Bragg fiber under 1.55 µm are shown in Fig. 4(a) with d 1 /a =0.5. It can be seen that the fiber loss is always above 10 6 db/km and almost unchanged with increasing N when N>40. The inset shows that the field distribution in the cladding has almost no changes between the cases of N =40 and N =70. Large absorption loss due to the large imaginary part of refractive index [Imag (n)] of the [poly(ether sulfone) (PES)] polymer contributes to the high loss level of this fiber and dominates the total fiber loss when N>40. Typical ratio of absorption loss to the radiation loss is about 10 2 in PES/As 2 Se 3 Bragg fiber with 40 cladding layers. On the other hand, from the results of Si/SiO 2 Bragg fiber under 1.55 µm shownin Fig. 4(b), it can be seen that the fiber loss is reduced by two to three orders with each additional ten layers. The inset shows that the field distribution in the cladding has some changes from Fig. 4. Loss of HE 11 mode versus number of layers N. (a)pes/as 2 Se 3 Bragg fiber with d 1 /a =0.5 for 1.55 µm. (b) Si/SiO 2 Bragg fiber with d 1 /a =0.3 for 1.55 µm. the eighth layer between the cases of N =10 and N =20. The loss with N =30could reach less than 1 db/km under R/a =0.8. It is shown that the dominating loss of Si/SiO 2 Bragg fiber is the radiation loss, which is impacted dramatically by the layer number N. The low loss level of this fiber is due to the low material absorption and large index difference of Si and SiO 2. Hence, the difference in material characteristics leads to different dominating loss mechanisms of the two kinds of Bragg fibers. In the following, the lowest modal loss and the corresponding optimized structure parameters of the two kinds of Bragg fibers are analyzed, respectively. A. PES/As 2 Se 3 Bragg Fiber The losses of single-he 11 -mode PES/As 2 Se 3 Bragg fiber with N =40in the single-mode region under 0.85 and 1.55 µm are shown in Fig. 5, wherein Fig. 5(a) and (b) shows the results with increasing R/a from 1.0 to 2.0 and different d 1 /a. The ratio d 1 /a in calculation is selected as 0.3, 0.5, and 0.7. The

4 362 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007 Fig. 5. Loss of HE 11 mode in PES/As 2 Se 3 Bragg fiber: (a) 0.85-µm window, (b) 1.55-µm window, and (c) d 1 /a =0.5 under different wavelength windows. different endpoints of the loss curves under different d 1 /a in Fig. 5(a) are due to the band structure variations. Under the same d 1 /a, it is shown that the loss increases at small and large R/a since the changes of R/a lead to changes of the HE 11 -mode curve, which make the lowest loss point on the mode curve move to the upper and lower edge of the cladding band gap, respectively. An optimal value of R/a exists, corresponding to the lowest loss under the same d 1 /a. On the other hand, it is noted that an optimal d 1 /a also exists under the same R/a, comparing the results under different d 1 /a. Thelowest loss generally appears when d 1 /a =0.5 under both 0.85 and 1.55 µm, while this value should be around 0.3 as QWS approach. The reason is that the modal field distributes less in the highly lossy PES layer when d 1 /a =0.5. Fig. 5(c) shows the loss under d 1 /a =0.5 versus R/a under three typical wavelengths windows. The tendencies of the loss curves under the four wavelengths are similar. Results show that fiber loss is very high ( db/km) in all the wavelength

5 XU et al.: LOSS CHARACTERISTICS OF SINGLE-HE 11 -MODE BRAGG FIBER 363 Fig. 7. Loss of HE 11 mode in Si/SiO 2 Bragg fiber: (a) 1.55-µm window and (b) d 1 /a =0.3under different wavelength windows. Fig. 6. Optimized lattice scale a opt in PES/As 2 Se 3 Bragg fiber. (a) 1.55-µm window and (b) d 1 /a =0.5under different wavelength windows. windows, even in optimized single-he 11 -mode PES/As 2 Se 3 Bragg fibers. The optimized lattice scale a opt for single-he 11 -mode PES/As 2 Se 3 Bragg fiber is shown in Fig. 6. Fig. 6(a) shows the results for 1.55 µm. Under the same R/a, both a opt and the corresponding R opt, which is defined as the product of a opt and the corresponding R/a, always increase with decreasing d 1 /a. Under the same d 1 /a, thea opt decreases with increasing R/a while the corresponding R opt increases. Fig. 6(b) shows the a opt versus R/a under d 1 /a =0.5for different wavelength windows. It is shown that the a opt almost increases linearly with wavelengths, which shows the wavelength scalability of PES/As 2 Se 3 Bragg fiber. The extremely high loss about db/km of PES/As 2 Se 3 Bragg fiber is due to the large absorption losses of PES cladding (e.g., db/m). The minimum fiber loss for 1.55 µm is 4.6 db/cm, which limits the length of devices based on PES/As 2 Se 3 Bragg fiber to the scale of 1 cm. To extend the limitation, new cladding material with lower absorption should be investigated to replace PES. Calculations show that total loss could reduce to less than 1 db/cm if the imaginary part of refractive index of the polymer layer reduces one order while the real part of the refractive index is in the range of B. Si/SiO 2 Bragg Fiber Fig. 7 shows the loss characteristics of single-he 11 -mode Si/SiO 2 Bragg fiber with N =20. The results for 1.55 µm with increasing R/a under different d 1 /a are shown in Fig. 7(a). Here, d 1 /a in calculation are selected as 0.3, 0.5, and 0.7. Comparing with PES/As 2 Se 3 Bragg fiber, Si/SiO 2 Bragg fiber has a wider region of R/a to support single-he 11 -mode propagation under the same d 1 /a due to a wider band gap. The loss increases at small and large ends of R/a like PES/As 2 Se 3 Bragg fiber. The fiber loss generally decreases when d 1 /a changes from 0.7 to 0.3 under the same R/a. It is noted that the lowest losses generally appear when d 1 /a =0.3 which is close to the value 0.24 as QWS approach, because the absorption in the Si/SiO 2 multilayer is relatively small. Fig. 7(b) shows the loss of (d 1 /a =0.3) versus R/a under three wavelength windows. The wavelengths are chosen for low absorption loss windows of Si and SiO 2. The tendencies of the loss curves under the three wavelengths are similar. The losses for 2.94 µm are lower than 1.55 µm due to the larger ratio of cladding refractive indexes n 1 /n 2 (see Table I), which have better light confinement. The losses in Si/SiO 2 Bragg fiber maintain a level of db/km when R/a < 1.3, which are about two orders smaller than PES/As 2 Se 3 Bragg fiber. The optimized lattice scale a opt for single-he 11 -mode Si/SiO 2 Bragg fiber is shown in Fig. 8. From the result for 2.94 µm shown in Fig. 8(a), it can be seen that the changes of

6 364 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007 Fig. 8. Optimized lattice scale a opt in Si/SiO 2 Bragg fiber. (a) 2.94-µm window and (b) d 1 /a =0.3under different wavelength windows. a opt and corresponding R opt with the structure parameters are similar with those in PES/As 2 Se 3 Bragg fiber. Fig. 8(b) shows the a opt (d 1 /a =0.3) versus R/a under three wavelength windows. The a opt has an approximately linearly increase with the wavelengths like PES/As 2 Se 3 Bragg fiber. The single-he 11 -mode bandwidths of Si/SiO 2 Bragg fiber are given in Fig. 9. Typical results for the 1.55-µm windoware shown in Fig. 9(a). It can be seen that bandwidth decreases at the small and large ends of R/a. In addition, the largest bandwidth decreases with increasing d 1 /a. The sharp reduction of bandwidth curve under d 1 /a =0.3 with increasing R/a is due to the changes of the cutoff frequency of the TM 01 mode. The bandwidth is always larger than 80 nm when R/a > 0.9, which covers the whole C-band. Fig. 9(b) shows the bandwidths (d 1 /a =0.3) versus R/a under three wavelength windows. It is shown that the bandwidth increases with the wavelengths. Large bandwidth over 100 nm can be achieved in all the wavelength windows. The loss of Si/SiO 2 Bragg fiber is mainly due to the radiation losses, which is about db/km with d 1 /a =0.3. The losses that are less than 0.06 db/cm at 1.55 µm and 0.03 db/cm at 2.94 µm can be achieved by optimizing structure parameters, respectively. When the layer number increases to 30, the losses could even be less than 2 db/km under 1.55 µm. The single-he 11 -mode bandwidth is maintained above 80 nm when R/a > 0.9 in all the wavelength windows. Both the loss levels and the bandwidths are sufficient for applications of single-mode fiber devices at these wavelengths. Fig. 9. Single-HE 11 -mode bandwidth in Si/SiO 2 Bragg fiber: (a) 1.55-µm window and (b) d 1 /a =0.3under different wavelength windows. IV. DISCUSSIONS Numerical results in the previous section have shown the loss characteristics of two kinds of single-he 11 -mode Bragg fibers based on different materials. In this section, the influences of several first layers to the loss characteristics are presented; the feasibility of the two kinds of fibers is also discussed according to the structure parameter requirements by simulation and current fabrication level. A. Optimization of Several First Layers For PES/As 2 Se 3 Bragg fiber, the dominating loss mechanism is absorption loss in highly lossy claddings. Fig. 10 shows the losses when the widths of first three layers (set as defect layers) are separately changed. Parameters are chosen at λ 0 =1.55 µm with R/a =1.6 and d 1 /a =0.5, which means d 1 = d 2 = d 0 =0.5a. Here, ω opt is taken as 0.22 through the calculation since the defect layer does not change significantly. Results show that only the first defect layer could reduce the loss, but it is still as high as 10 5 db/km. Coupling of cladding mode might even happen if the defect layer changes significantly, which will bring additional losses. Therefore, changing several first layers could not significantly reduce the total losses. Instead, the available method to reduce losses in PES/As 2 Se 3 Bragg fiber is to search low-loss cladding material. For Si/SiO 2 Bragg fiber, optimized widths of layers should generally follow the QWS condition since the absorption loss

7 XU et al.: LOSS CHARACTERISTICS OF SINGLE-HE 11 -MODE BRAGG FIBER 365 Fig. 10. Loss of HE 11 mode versus widths of several first layers d defect in PES/As 2 Se 3 Bragg fiber with d 1 /a =0.5 and R/a =1.6 for 1.55-µm window. Here, ω opt is taken as 0.22 throughout the calculation. in Si/SiO 2 multilayer is relatively small. Additional changes to several first layers have no goods to loss optimization, which can be proved by simulation. and radiation loss are considered. The influences of structure parameters on the loss characteristics are analyzed in detail. Influences of several first layers to the loss characteristics are presented. The feasibility of the realization of single-he 11 - mode Bragg fibers is discussed according to the structure parameter requirements by simulation and current fabrication level. For the PES/As 2 Se 3 Bragg fiber, a loss level as high as db/km is expected at wavelengths from 0.85 to 2.94 µm, mainly due to the large absorption loss in cladding materials. The large losses limit their applications only in devices shorter than 1 cm. To extend the limitation, a new cladding material with lower absorption should be investigated. Calculations show that the total loss could be reduced to less than 1 db/cm if the imaginary part of the refractive index of the polymer layer reduces one order, while the real part of the refractive index is in the range of For the Si/SiO 2 Bragg fiber, low-loss single-he 11 -mode propagation can be achieved by the materials and fabrication technology. Great effort on extending the fabricated fiber length is necessary. These results would be helpful to fiber designs and applications of low-loss single-mode Bragg fiber. B. Fabrication Limits PES/As 2 Se 3 Bragg fiber is fabricated by preform preparation and fiber drawing [1]. Samples with 260-nm lattice scale, 75-nm thickness of individual layer, and as many as 70 layers have been reported [3]. As shown in Fig. 6, the a opt of single HE 11 Bragg fibers for 1.55 and 2.94 µm are both larger than 300 nm, which is acceptable under the current fabrication level. Some efforts on the control of the cladding period under a smaller scale are needed to realize single-he 11 Bragg fibers for 0.85 µm. The large absorption loss of PES leads to a large fiber loss in our simulation, which limits its applications in devices shorter than 1 cm. Selecting lower loss cladding materials would improve this, as referred to in the previous section. Si/SiO 2 Bragg fiber is fabricated by sputtering depositions of Si and SiO 2 layers on the solid SiO 2 core drawn from a conventional single-mode fiber. Reported multimode samples have 2.5-µm core radius, 16 layers, and 0.75-µm lattice scale [9]. Current drawing techniques have fabricated low loss tapered fibers with a radius of the silica glass core below 1 µm. The thickness of cladding layers could be finely controlled by the sputtering time. Hence, the requirement of single-he 11 - mode Si/SiO 2 Bragg fiber can be satisfied through the current technique. On the other hand, great effort on fabrication technology is necessary to extend the length of fabricated Si/SiO 2 Bragg fiber. V. C ONCLUSION The loss characteristics of two kinds of typical single-he 11 - mode Bragg fibers based on PES/As 2 Se 3 and Si/SiO 2 multilayer claddings are analyzed theoretically. The optimization approach is aimed to give optimized eigen modal loss of Bragg fiber at targeted wavelengths under any scalable structure, which is described by d 1 /a and R/a. Both absorption loss REFERENCES [1] M. Bayindir, F. Sorin, A. F. Abouraddy, J. Viens, S. D. Hart, J. D. Joannopoulos, and Y. Fink, Metal insulator semiconductor optoelectronic fibres, Nature, vol. 431, no. 7010, pp , Oct [2] B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO 2 laser transmission, Nature, vol. 420, no. 6916, pp , Dec [3] K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, Hollow multilayer photonic bandgap fibers for NIR applications, Opt. Express, vol. 12, no. 8, pp , Apr [4] G. Benoit, K. Kuriki, J.-F. Viens, J. D. Joannopoulos, and Y. Fink, Dynamic all-optical tuning of transverse resonant cavity modes in photonic bandgap fibers, Opt. Lett., vol.30,no.13,pp ,Jul [5] Y. Gao, N. Guo, B. Gauvreau, M. Rajabian, O. Skorobogata, E. Pone, O. Zabeida, L. Martinu, C. Dubois, and M. Skorobogatiy, Consecutive solvent evaporation and co-rolling techniques for polymer multilayer hollow fiber preform fabrication, J. Mater. Res., vol. 21, no. 9, pp , Sep [6] S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers, Opt. Express, vol. 9, no. 13, pp , Dec [7] S. Dasgupta, B. P. Pal, and M. R. Shenoy, Design of dispersioncompensating Bragg fiber with an ultrahigh figure of merit, Opt. Lett., vol. 30, no. 15, pp , Aug [8] T. D. Engeness, M. Ibanescu, S. G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, Dispersion tailoring and compensation by modal interactions in OmniGuide fibers, Opt. Express, vol. 11, no. 10, pp , May [9] T. Katagiri, Y. Matsuura, and M. Miyagi, Single-mode operation in silica-core Bragg fibers, presented at the Optical Fiber Commun./Nat. Fiber Opt. Eng. Conf., Anaheim, CA, Mar. 2005, Paper OWL5. [10] M. Soljačić, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. 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8 366 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 1, JANUARY 2007 [13] P. Yeh and A. Yariv, Theory of Bragg fiber, J. Opt. Soc. Amer., vol. 68, no. 9, pp , Sep [14] S. Guo, S. Albin, and R. S. Rogowski, Comparative analysis of Bragg fibers, Opt. Express, vol. 12, no. 1, pp , Jan [15] P. Yeh, A. Yariv, and C.-S. Hong, Electromagnetic propagation in periodic stratified media. I. General theory, J. Opt. Soc. Amer., vol. 67,no. 4, pp , Apr [16] Published Experimental Data of Photonic Bandgap Fibers and Devices Group. [Online]. Available: Guangyu Xu was born in Changchun, Jilin, China, in He received the B.S. and M.S. degrees in fundamental science and electronic engineering from Tsinghua University, Beijing, China, in 2003 and 2006, respectively. He is currently working toward the Ph.D. degree in electrical engineering at University of California, Los Angeles. His M.S. thesis was focused on microstructure fibers and their applications. He is currently engaged in research on nanoelectronics including nanotube and nanowire devices. Wei Zhang received the B.S. and Ph.D. degrees from the Department of Electronic Engineering, Tsinghua University, Beijing, China, in 1998 and 2003, respectively. He joined the Information Optoelectronic Technology Research Institute, Tsinghua University, in His major research interests include active and passive fiber devices and microstructure optoelectrical materials, especially microstructure fibers and their applications. He is currently with the Department of Electronic Engineering, Tsinghua University. Yidong Huang (M 98) was born in Beijing, China. She received the B.S. and Ph.D. degrees in optoelectronics from Tsinghua University, Beijing, in 1988 and 1994, respectively. Her Ph.D. dissertation was mainly concerned with strained quantum-well lasers and laser amplifiers. From 1991 to 1993, she attended Arai Laboratories, Tokyo Institute of Technology, Tokyo, Japan, while on leave from Tsinghua University. In 1994, she joined the Photonic and Wireless Devices Research Laboratories, NEC Corporation, where she was engaged in the research on semiconductor laser diodes for optical-fiber communication and became an Assistant Manager in In 2003, she joined the Department of Electronic Engineering, Tsinghua University, as a Professor. She is currently engaged in research on nanostructure optoelectronics. Jiangde Peng was born in Hunan, China, on October 26, He graduated from Tsinghua University, Beijing, China, in Since 1964, he has been with the Department of Electronic Engineering, Tsinghua University, where he is currently a Professor. He was a Senior Visiting Scholar at the Centre National de la Recherche Scientifique Laboratoire de Photophysique Moleculare, Universite d Orsay, Orsay, France, during , and at the Department of EE-Systems, University of Southern California, Los Angeles, during He has been engaged in research on active and passive fiber devices for wavelength division multiplexing optical fiber communications, with specific emphasis on fiber amplifiers and lasers. Currently, his primary research interests focus on slow light, entangled photon-pair sources, and sensors based on micronanostructure materials. Prof. Peng received the National Invention Award in He is author or coauthor of over 100 papers, 12 patents, and one textbook. He is a member of the Optical Society of China.

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