Highly Birefringent Elliptical-Hole Microstructure Fibers With Low Confinement Loss

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 21, NOVEMBER 1, 2012 3381 Highly Birefringent Elliptical-Hole Microstructure Fibers With Low Confinement Loss Wenbin Liang, Ningliang Liu, Zhihua Li, and Peixiang Lu Abstract A novel kind of elliptical-hole highly birefringent microstructure optical fibers (MOFs) with two defects and six rings is analyzed and proposed. Simulation results show that geometrical birefringence of this elliptical-hole MOF is two times higher than that of the circular-hole ones, which found to be about 3.5 10. The polarization beat length of such fiber is calculated to be 0.44 mm. Besides, this kind of MOF with two defects can couple with single mode fibers efficiently and the confinement loss is almost near zero when the cladding ring number reaches 6. Such proposed fiber with high birefringence and low confinement loss can find really potential applications in the fields of light transmission and optical sensing. Index Terms Bend loss, birefringence, confinement loss, microstructure optical fibers (MOFs). I. INTRODUCTION I N recent years, there has been a significant interest in microstructure optical fibers (MOFs) [1] [4] since they can be feasibly designed and realize various peculiar properties, such as endlessly single mode [5], chromatic dispersion controllable [6], high birefringence [7] [10], nonlinear property [11], and so on. Among this, highly birefringent fibers have attracted scientific attention now as they can be used as a polarization-maintaining optical fiber in long distance communications, optical fiber sensing, and designing of special laser systems. Generally speaking, there are two kinds of birefringence, including geometrical birefringence and stress birefringence. The former is mainly formed in the designing process and the latter is in the fabrication process. In this paper, we take the former into consideration. Conventional polarization-maintaining fibers based on single mode fibers (SMFs) or multimode fibers (MMFs) can realize high geometrical birefringence; however, their transmission properties are strongly influenced by stress perturbation which is a limitation. And then, many schemes have been proposed in order to enhance the geometrical birefringence. With the development of MOFs in recent years, the high birefringence can be also obtained by changing the symmetry of designed Manuscript received May 12, 2012; revised August 07, 2012; accepted August 28, 2012. Date of publication September 07, 2012; date of current version October 19, 2012. This work was supported by the National Natural Science Foundation of China under Grant 60925021, Grant 61138006, and Grant 11074085. (Corresponding author: Z. Li.) The authors are with the Wuhan National Laboratory for Optoelectronics, School of Physics, Huazhong University of Science & Technology and the Key Laboratory of Fundamental Physical Quantities Measurement of Ministry of Education, Wuhan 430074, China (e-mail: lizhihua@mail.hust.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2012.2217314 structure of those MOFs. One way is to enlarge some of the air holes in the MOF to raise the asymmetry [12]. Another way is to replace circular air holes in cladding with elliptical ones [13] [15]. Consequently, some MOFs can realize very high geometrical birefringence by different air-hole arrangement. Conventional polarization-maintaining fiber can obtain a birefringence of order [16] [19], but MOF can realize one order more than that [8],which seems to be very attractive for the high birefringence applications. In this study, four types of highly birefringent MOFs based on elliptical holes and circle holes are modeled and analyzed with the finite element method (FEM), respectively. The birefringent characteristics and transmission losses are studied theoretically. By comparison and analysis among the four models, we choose the Type-4 model with elliptical holes and two defects as the birefringence-optimized model. Then, we studied the transmission characteristics of Type-4 model in detail. Simulation results show that this kind of MOF with six rings can be used as a polarization-maintaining optical device in fiber optical communication systems, sensing applications, and other relevant fields because of its high birefringence, low confinement loss, low bend loss, and efficient coupling to SMFs. II. THEORETICAL MODELS In this paper, four models of highly birefringent MOFs were proposed and analyzed. In Fig. 1(a) (marked as Type-1), the triangle lattice MOF has a pitch (center-to-center distance between the holes) of m, a hole diameter of m for the small holes, and m for the large holes. The substrate is silica and its refractive index is set to be 1.44403 at 1550 nm. The small and big holes are both filled with air. The outer diameterofthemofsis125 m. The parameters we choose are the optimized values. Through a large number of calculations and comparison, we mainly took the high birefringence and confinement loss into consideration. Meanwhile, we also took into account the previous work and the manufacturing difficulty. In Fig. 1(b) (marked as Type-2), the structure of the MOFs changes from single defect to double defects with other parameters unchanged except for the position of the defects. Fig. 1(c) (marked as Type-3) and (d) (marked as Type-4) shows the models we have optimized. In these models, we changed the big circular holes into elliptical holes to enhance the geometrical birefringence. The geometrical parameters are identical to the aforementioned except for the parameters of big holes. Here, we define ellipticity as. We can conclude that the birefringence is much larger when [9]. In Fig. 1(c) and (d), the ellipticity is 2/3, and m. 0733-8724/$31.00 2012 IEEE

3382 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 21, NOVEMBER 1, 2012 Fig. 1. Cross section of four rings: (a) circular holes with one defect; (b) circular holes with two defects; (c) elliptical holes with one defect; (d) elliptical holes with two defects. The origin of the coordinates is at the center of the MOFs. Generally speaking, the modal birefringence and the polarization beat length are defined as follows [8]: (1) where and are the propagation constants of the two modes, and are the refractive indices of the two orthometric X- andy-directions. From (1) and (2), we can calculate the form birefringence and polarization beat length. III. CALCULATIONS AND ANALYSIS Based on the four models described previously, we calculate the effective indices and the distributed electric fields of the MOFs of Type-1 and Type-3 using FEM (COMSOL Multiphysics) with perfectly matched layers. Fig. 2 shows the dispersion and the modal birefringence of the MOFs of Type-1 and Type-3, respectively. From Fig. 2(a), we can see that the effective refractive index of Y-polarization is always larger than X-polarization during wavelength range of 0.8 1.8 m. This phenomenon is easily to be understood since the small holes of the MOFs are arranged along the Y-axis. With the circular holes changed to elliptical holes, the effective indices of both X-polarization and Y-polarization of Type-3 and Type-4 are lower than that of Type-1 and Type-2 as a whole. This is because the air area is larger when the circular holes changed to elliptical holes, which would decrease the effective index of fundamental mode. Fig. 2(b) shows the modal birefringence of the four-ring MOFs of one defect with elliptical and circular holes, respectively. With the increase of operating wavelength, the modal (2) Fig. 2. (a) Dispersion curves of the fundamental bound modes of four-ring circular- and elliptical-hole MOFs with one defect. (b) Modal birefringence of four-ring circular- and elliptical-hole MOFs with one defect. birefringence of both X-polarization and Y-polarization is enlarged gradually, but the enlarging of Y-polarization is much faster than X-polarization. So the birefringence of MOF Type-3 at the operating wavelength is much larger than Type-1. It can be explained by two reasons [9]. One is that the ellipse area is larger than the circle, which increases the air filling ratio as a result. The other is that the ellipticity. We can conclude that the birefringence of Type-3 is much larger than Type-1. The modal birefringence of Type-1 and Type-3 at 1550 nm are and, respectively. With the increasing wavelength, the birefringence magnifies gradually. Fig. 3 shows the dispersion curves of the fundamental bound modes and the modal birefringence of the four-ring MOFs with two defects. The modal birefringence of Type-2 and Type-4 are and, respectively. The other characteristics of dispersion and birefringence of these two kinds are similar to Type-1 and Type-3. Since the modal birefringence of Type-1 and Type-2 are much smaller than Type-3 and Type-4, we discuss these two types in the following. Fig. 4(a) (c) shows the fundamental bound mode distributions of the four-ring MOFs with one, two, and three defects, respectively. Through careful calculations, this kind of

LIANG et al.: HIGHLY BIREFRINGENT ELLIPTICAL-HOLE MICROSTRUCTURE FIBERS WITH LOW CONFINEMENT LOSS 3383 Fig. 3. (a)dispersion curves of the fundamental bound modes of four-ring circular- and elliptical-hole MOFs with two defects. (b)modal birefringence of four-ring circular- and elliptical-hole MOFs with two defects. MOF can be regarded as a SMF. We calculated the coupling efficiency between SMFs and the proposed MOFs with one, two, and three defects, respectively, by the software of COMSOL and MATLAB. The results are shown in Fig. 4(d). From Fig. 4(d), we can see that with the increase of operating wavelength, the coupling efficiency decreases as a whole. The reason is that when the wavelength is longer, the confinement ability of light in such fibers is reduced. The result also shows that the coupling efficiency of SMF to MOF with two defects is much larger than those of MOFs with one and three defects. Moreover, the coupling efficiency of MOF with three defects is a little larger than that with one defect. This phenomenon can be explained as follows: first, the light from SMF is nearly a Gaussian beam and the large aptitude area is almost confinedinthefiber center. So themodeareaofmofsinthefiber center along axis is a most important problem for coupling efficiency to the SMF. However, when the defects become three, the light confinement and intensity play a leading role. As can be seen from Fig. 4(b) and (c), the light confinement ability of MOF with three defects is weaker than that with two defects. Consequently, the coupling efficiency of MOF with two defects is stronger than that with three defects, which may be dependent on the fiber structure. Fig. 4. fundamental mode distribution of (a) four-ring MOF with one defect at 1550 nm; (b) four-ring MOF with two defects at 1550 nm; (c) four-ring MOF with three defects at 1550 nm; (d) coupling efficiency of the three structures to SMFs as a function of wavelength. Second, the two-defect symmetrical structure is not the same as the structure with one or three defects, which leads to the differences of light guiding. As the figure indicates, the coupling efficiency of two-defect MOF is the largest among three models, so we choose it as an optimized structure of highly birefringent fiber. From the aforementioned simulation results, we can choose MOF Type-4 as the optimized project. Considering that the modal birefringence in this paper is only geometrical birefringence, if we introduce stress birefringence in the fabrication process, even larger birefringence can be obtained. In the following, we typically study MOF Type-4 in detail about the small holes, confinement loss, and bend loss.

3384 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 21, NOVEMBER 1, 2012 communications. Confinement loss of MOFs can be calculated using the following formula [20]: (3) Fig. 5. (a) Birefringence of MOF of Type-4 at different wavelengths from 0.7 to 1.8 m when equals 1, 0.8, 0.6, 0.4, and 0.2 m, respectively. (b) Confinement loss of MOF Type-4 at 1550 nm when the air-hole ring number changes from2to6. In the highly birefringent MOFs of four types we proposed, the introduction of the small holes is in order to realize two functions: (a) it can increase the difference of the refractive index of the Y-axis and X-axistoobtainhighbirefringence; (b) it can confine light in the core area to decrease confinement loss. Here, we study the influence of the small-hole diameter on the modal birefringence of MOF Type-4. In Type-4, with other parameters unchanged, we alter the diameter of the small holes as 1, 0.8, 0.6, 0.4, and 0.2 m, and calculated, respectively. From 0.7 to 1.8 m, we calculated with an increment of 0.1 m and then obtain Fig. 5(a) We can know that from mto0.2 m that the birefringence of the MOF increases gradually. And we found that with the decrease of,theconfinement loss increased monotonically. This phenomenon can be demonstrated by the decreasing ability of the small air holes to confine the light. When equals 0.2 m, the radiation loss is very large. The reason is that the small hole is too small to confine the light efficiently. Therefore, we define m, and it can be fabricated with not much difficultly. Confinement loss of a fiber is another important property for guiding light, which limits the transmission distance in real fiber where is the operating wavelength given by micrometers, is the effective index of the fundamental mode, and is the imaginary part of. The propagation loss of high-order modes is much larger than fundamental mode. Furthermore, high-order modes are almost distributed in the cladding and disappear quickly in SMFs. Therefore, we can only consider the fundamental mode in the following. With (3), confinement losses of MOFs can be evaluated. The air-hole ring number of MOF is an important factor for confinement loss. In this paper, we emphasized on four-ring MOFs. But we also calculated MOF Type-4 when the air-hole ring number is 2, 3, 5, and 6, respectively. We found that from two rings to three rings, the propagation constant of fundamental bound mode changed a little and the confinement loss was a little larger. With the increase of the ring number, the confinement loss decreased gradually, as could be seen in Fig. 5(b) From Fig. 5(b), we can know that when the air-hole ring is determined, the Y-polarized confinement loss is larger than X-polarized. This phenomenon can be demonstrated by the fact that ; thus, the X-polarized light is confined more intensively by the air holes. We calculated the properties of MOFs Type-4 from two rings to six rings, and found that from two rings to three rings the propagation constants have a slight change but almost invariable when the ring number is more than 3. The confinement loss of two-ring MOF is relatively large up to about 1.8 db/m and the four-ring MOF is small as 0.0652 db/m, but when the ring number reached 5 and 6, the confinement loss almost arrived zero theoretically. Of course after fabrication the practical loss will be a little larger. Therefore, this MOF with six rings can be used for light transmission or other applications with low confinement loss. In addition, bend loss is another issue that should be taken into consideration in the practical use of fibers. We discussed the bend loss of the proposed six-layer MOF here. We calculated the bend loss when the bending radius is 10, 5, and 2 cm, respectively. Results show that the bend loss is very small, and with the variation of bending radius, the bend loss almost does not change, as can be seen in Fig. 6. (Only bend loss of radius of 2 cm is plotted in Fig. 6.) However, when the wavelength increases, the bend losses of X-polarization and Y-polarization are enlarged. Obviously, the Y-polarization loss is much larger than that of X-polarization, and increases much faster. Even so, the influence of a bending direction is almost negligible when the radius changes. Besides, Fig. 7 shows the bend loss variation of the optimized MOF versus bend radius from 2 to 19 mm in the Y-direction under 1550 nm. When the bending radius is smaller than 4 mm, the bend loss increases sharply; however, the bend loss is very small (near 0.1 db/km) and changes little when the bending radius is larger than 4 mm. Besides, when the

LIANG et al.: HIGHLY BIREFRINGENT ELLIPTICAL-HOLE MICROSTRUCTURE FIBERS WITH LOW CONFINEMENT LOSS 3385 Fig. 6. Bend loss versus wavelength of an optimized six-layer model when the bending radius is 2 cm. Fig. 7. Bend loss versus radius of the optimized six-layer model at the operating wavelength 1550 nm. MOF bends along the X-axis and the bending diameter is from 2to19mm,wefoundthatthebendlossisverysmall(smaller than 0.1 db/km at both Y-polarization and X-polarization) and almost does not change. We can conclude that the bend loss is very small and nearly can be negligible at the communication window which is very suitable for light transmission. IV. CONCLUSION In conclusion, we proposed an optimized highly birefringent two-defect MOF based on elliptical and small holes with low confinement loss. The birefringence of this kind of MOF can achieve about and the polarization beat length is about 0.44 mm. 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Xu et al., Highly nonlinear all-solid photonic crystal fibers with low dispersion slope, Appl. Opt., vol. 51, pp. 1021 1027, Mar. 2012. Wenbin Liang received the Master s degree in communication and information systems at the School of Communication and Information Engineering, Shanghai University, Shanghai, China, in 2009. Since 2010, he has been working toward the Ph.D. degree in photoelectric information engineering at the School of Photoelectron Science and Engineering, Huazhong University of Science & Technology, Wuhan, China. His main interests include optical fiber communication and sensing. Ningliang Liu received the B.Sc. degree in optical information science and technology from the School of Photoelectron Science and Engineering, Huazhong University of Science & Technology, Wuhan, China, in 2006. Since 2008, she has been working toward the Ph.D. degree in physical electronics at the Huazhong University of Science & Technology. Her main research interests are optical fiber sensing and femtosecond laser micromachining.

3386 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 21, NOVEMBER 1, 2012 Zhihua Li received the B.Sc. degree in physics from Wuhan University, Wuhan, China, the Master s degree and the Ph.D. degree in physics from the Huazhong University of Science & Technology (HUST), Wuhan, in 1998, 2001, and 2004, respectively. She is currently an Associate Professor with the School of Physics, HUST. Her main research interests include theoretical and experimental research for interaction of femtosecond laser and materials. Peixiang Lu received the B.Sc. degree in physics from Beijing University, Beijing, China, and the Ph.D. degree from the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Beijing, in 1987 and 1992, respectively. He is currently a Professor with the School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science & Technology, Wuhan, China. His main research interests include ultrafast optics, femtosecond laser micromachining, and fiber laser.