Bending Orientation Insensitive Large Mode Area ... - IEEE Xplore

Bending Orientation Insensitive Large Mode Area Photonic Crystal Fiber With Triangular Core Volume 5, Number 4, August 2013 Xin Wang Shuqin Lou Wenliang Lu

DOI: 10.1109/JPHOT.2013.2271720 1943-0655/$31.00 Ó2013 IEEE

IEEE Photonics Journal

Bending Orientation Insensitive LMA PCF

Bending Orientation Insensitive Large Mode Area Photonic Crystal Fiber With Triangular Core Xin Wang, Shuqin Lou, and Wenliang Lu School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China DOI: 10.1109/JPHOT.2013.2271720 1943-0655/$31.00 Ó2013 IEEE

Manuscript received May 28, 2013; revised June 23, 2013; accepted June 25, 2013. Date of publication July 4, 2013; date of current version July 10, 2013. This work was supported in part by the National Natural Science Foundation of China under Grants 61177082 and 61205074 and in part by the Beijing Natural Science Foundation under Grant 4122063. Corresponding author: S. Lou (e-mail: shqlou@bjtu. edu.cn).

Abstract: In view of the feasibility of fabrication and application, a bending orientation insensitive large mode area photonic crystal fiber with triangular core is proposed. This fiber structure breaks the limit of bend orientation angle and realizes single mode operation under any bending orientation angle at the bending radius of 30 cm. The mode field area of the fundamental mode at the wavelength of 1.064 m achieves 1386 m2 at the straight state and 1154 m2 at a bending radius of 30 cm, respectively. The decrement of the mode field area at the bent state is only 16.85% compared to that at the straight state. The large mode area at the bent state, small decrement of the mode field area, and low sensitivity of bending orientation make the fiber of great potential in compact high power fiber lasers. Index Terms: Bending orientation insensitive, large mode area, photonic crystal fiber.

1. Introduction Fiber lasers have been under intensive study due to the advantages of compact structure and high beam quality. Recently, fiber lasers have entered the realm of kilowatt power with diffraction-limited beam quality [1]. However, challenges still exist especially in the way to deal with fiber nonlinearity induced by the high power. Fibers with large mode area (LMA) provide the most effectively solution to the issue because the fiber nonlinearity is inversely proportional to mode field area. To ensure high beam quality and stability of the laser output, it is very important for LMA fiber to operate at single mode. In compact high power laser system, a method of coiling is generally adopted to help the fiber maintain single mode operation and make laser miniaturization [2], [3]. Therefore, LMA fibers which can be single mode operation at bent state are of great significance in practical applications. As for conventional LMA fibers, there are two limits to obtain single mode operation and low bending loss simultaneously. Since the normalized frequency increases with the core diameter and numerical aperture (NA), LMA fibers with large core diameter should reduce the NA to ensure single mode operation. For instance, when the core diameter is 30 m, in order to ensure single mode operation, the NA should be reduced to 0.027 [2]. However, the lowest NA which can be reliably fabricated with conventional fiber manufacturing technique is 0.06 [1]. On the other hand, conventional fibers with low NA are sensitive to bending. For the core diameter of 30 m, even at a bending radius as large as 50 cm, the bending loss is as high as 3.3 dB/m [2]. Therefore, for the

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application of high power, LMA fibers with conventional structure should be kept in straight state to avoid significant bending loss. Photonic crystal fibers (PCFs) provide an effective solution to the contradiction between large mode field area and low bending loss. Due to the flexible design of structure, NA of the PCF is precisely controlled by varying the core size and hole pitch. Various novel LMA PCFs with low bending loss have been proposed [5]–[10], but they are either not strictly single mode operation at bent state [5]–[10] or of great difficulty to fabricate [4], [5], [10]. Recently, PCFs with asymmetric structure which can achieve single mode operation at the bent state have attracted intensive attention. In 2010, Napierala put forward a novel asymmetric-cladding structure firstly, which contains two sizes of air holes [11]. However, an issue of bending orientation angle is introduced due to the asymmetric structure. The bending orientation angle must be exactly controlled to prevent the leakage of the fundamental mode. Due to the torsion is unavoidable during the process of coiling, bending orientation angle is a vital factor of determining whether the LMA fibers are suitable for practical application in compact high power fiber laser system. In literature [11], there are two kinds of structures reported, their mode field areas at straight state are 1342 m2 and 2524 m2 , respectively. While at bent state, mode field areas are decreased to 657 m2 and 1065 m2 with the corresponding bending orientation angles are 5 and 3 , respectively. These imply that the two kinds of structures are extremely sensitive to bend orientation. In 2011, Napierala reported and fabricated an asymmetric structure LMA PCF with double lattice constant [12]. The mode filed areas are 1454 m2 at straight state and 655 m2 at bent state. Since the bending orientation angle is 7 , this kind of fiber is still extremely sensitive to bending orientation. With further research, Chen and Zhang proposed a novel type of LMA PCF whose cladding is composed of two types of low-index rods with different periods and diameters. The bending orientation angle can be extended to 45 at the bending radius of 30 cm [13]. Nevertheless, this fiber is not single-mode guided at bent state. In this paper, we propose a solution to the limit of bending orientation angle with a novel triangular-core LMA PCF. The employment of uniform size of circle air holes arranged in the array of hexagonal lattice ensures that the fiber is easy to fabricate with the method of stack and draw. This kind of structure makes a breakthrough in bending orientation angle and realizes single mode operation at any bending orientation at the bending radius of 30 cm. At the wavelength of 1.064 m, this fiber achieves a mode filed area of 1386 m2 when it is kept straight. As a bending radius of 30 cm is applied, the mode field area is 1154 m2 , which only decreases by 16.85% compared to the straight state. Bending loss of the fundamental mode is 0.087 dB/m while bending losses of the second order modes are higher than 1.5 dB/m. The loss difference between the fundamental mode and the second order modes is large enough to ensure that the fiber conforms to the single mode operation conditions [4]. Large mode area at bent state, small decrement of mode field area and low sensitivity of bending orientation make the fiber much more conductive to practical applications of compact high power fiber laser.

2. Structure and Principles Fig. 1 illustrates the cross section of the proposed bending orientation insensitive LMA PCF. In the view of the feasibility of fabrication [19], we employ uniform circle air holes and a few fluorine-doped rods arranged in hexagonal lattice. As shown in Fig. 1, the gray background represents silica-host background with a refractive index of 1.45 at the wavelength of 1.064 m. The core is formed by the omission of three center air holes (dotted circles in Fig. 1). In order to enlarge the mode field area, the inner air holes are replaced by fluorine-doped rods (dark gray circles in Fig. 1). There are three rings of air holes (white circles in Fig. 1) in the cladding, which ensures that the light can be well confined in the core. The diameters of the fluorine-doped rods and air holes are denoted by d0 and d1 , respectively. is the hole pitch. As one of the methods to simulate the properties of PCF, the finite-element method (FEM) [14], [15], is the most widely used for modeling complex fiber structures, especially for PCF with various refractive index distribution. In this paper, we adopt a full-vector FEM combined with perfectly matched layers (PML) [16] boundary conditions to analyze the properties of our proposed LMA PCF.


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Fig. 1. Cross section of the proposed bending orientation insensitive LMA PCF.

With the anisotropic PML, Maxwell vector equation can be expressed as 5 ð½s1 5 E Þ k02 n2 ½sE ¼ 0 0 1 sy =sx 0 0 B C sx =sy 0 A ½s ¼ @ 0 0

0

(1) (2)

sx sy

where E is the electric field vector, k0 ¼ 2= is the wavenumber in the vacuum, is the operating wavelength, n is the refractive index, ½s is the PML matrix, sx and sy are the PML parameters. To investigate the mode properties of PCF, the refractive index distribution of the fiber cross section is of vital importance. When the fiber is bent, it can be simulated as a straight fiber with an equivalent refractive index distribution formula [17] x cos þ y sin nðx ; y Þ ¼ n0 ðx ; y Þ 1 þ (3) R where n0 ðx ; y Þ is the initial refractive index profile when the fiber is straight, x and y is the position across the fiber cross section, R is the bending radius and is the bending orientation angle illustrated in Fig. 1. We take the center of the equilateral triangle as the origin of coordinates in order to make sure that the fiber structure has rotational symmetry. represents the angle between the bending orientation and the þx axis. Mode field area (MFA) and confinement loss (CL) are two key parameters for LMA PCF. MFA and CL can be expressed as RR 2 jE j2 dxdy MFA ¼ RR (4) jE j4 dxdy 20 20 ImðÞ ¼ k0 Imðneff Þ CL ¼ (5) ln10 ln 10


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Fig. 2. Impact of the diameter of air holes (a) and the hole pitch (b) on the bending characteristics. FM represents fundamental mode, SM-1 and SM-2 represent two different second order modes, and MFA represents the mode field area of fundamental mode.

where ¼ k0 neff is the propagation constant and neff is the effective index of the corresponding mode. In this paper, we employ the mode loss requirement that the confinement loss of the fundamental mode should be lower than 0.1 dB/m while the loss of second order mode is higher than 1 dB/m to ensure single mode operation [4].

3. Numerical Analysis With respect to the proposed LMA PCF, structural parameters, such as the diameters of air holes and fluorine-doped rods, the refractive index of fluorine-doped rods and the hole pitch, have significant influence on the fiber properties. In order to achieve the optimum structural parameters, we investigate the impacts of these parameters on the bending properties when the fiber is bent at a radius of 30 cm. The original parameters are set as: ¼ 20 m, d1 ¼ 8 m, d0 ¼ 6 m, nf ¼ 1:448. In the process of our numerical analysis, we just change one of the parameters and keep other parameters fixed. First, the impacts of the diameter of air holes and the hole pitch on the bending characteristics are discussed. It can be clearly seen from Fig. 2(a) that the bending loss and mode field area decrease simultaneously as the diameter of air holes increases. It can be explained physically that the enlargement of air hole diameter enhances the light confinement ability and diminishes the effective modal area of the fundamental mode comparatively. It can be also used to explain the impact of hole pitch on the bending characteristics, since the enlargement of hole pitch can be regarded as the decrement of the diameter of air holes relatively. In addition, it is worth noting that there is a largest loss difference between the fundamental mode and the second order modes when the hole pitch is 20 m, which contributes to the realization of single mode operation. Then, the impacts of the refractive index and the diameter of the fluorine-doped rods on the bending characteristics are taken into consideration. It can be clearly seen from Fig. 3(a) that the bending losses decreases while the mode field area increases as the refractive index of the fluorinedoped rods nf increases. It can be explained that as the nf increases, the refractive index of the fluorine-doped rods gets closer to the fundamental modes and mode filed moves toward the right side. What confine the fundamental mode are the outer air holes, instead of the fluorine-doped rods. Meanwhile mode field area increases because of the leakage of the fundamental mode. The evolution of the pattern of the mode field with the nf can be directly observed in Fig. 4. Likewise, the decrement of the diameter of the fluorine-doped rods can be regarded as the increase of nf relatively. Numerical analysis results demonstrate that when there is only one parameter changing, d1 is in the range from 7.6 m to 8.4 m, is in the range from 19.5 m to 20.5 m, nf is in the range from 1.4465 to 1.4485, d0 is smaller than 7.6 m, bending loss of the fundamental mode is below 0.1 dB/m and bending losses of second order modes exceed 1 dB/m, indicating the fiber confirms to single mode operation.


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Fig. 3. Impact of the refractive index of the fluorine-doped rods (a) and the diameter of the fluorinedoped rods (b) on the bending characteristics. FM represents fundamental mode, SM-1 and SM-2 represent two different second order modes, and MFA represents the mode field area of fundamental mode.

Fig. 4. Mode field distribution with different nf . (a) nf ¼ 1:4465. (b) nf ¼ 1:4485.

Fig. 5. Confinement loss and mode field area of the fundamental mode as functions of wavelength.

4. Bending Properties of LMA PCF Considering the impacts of structural parameters comprehensively, we achieve the optimum structural parameters, with which the fiber can be single mode operation without the limit of bending orientation at the bending radius of 30 cm. The optimum structural parameters are: ¼ 20 m, d1 ¼ 8 m, d0 ¼ 7 m, nf ¼ 1:4474. With the optimum structural parameters, we investigate the bending properties of the LMA PCF. Fig. 5 shows the confinement loss and mode field area of the fundamental mode as functions of wavelength. At the operating wavelength of 1.064 m, the confinement loss of the fundamental mode is 2 109 dB/m and the mode field area is 1386 m2 .


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Fig. 6. Bending loss and mode field area of the fundamental mode as functions of bending radius.

Fig. 7. Bending loss (a) and mode field area (b) as functions of bending orientation angle at a bending radius of 30 cm. FM represents fundamental mode, SM-1and SM-2 represent two different second order modes, and MFA represents the mode field area of fundamental mode.

When the proposed LMA PCF is bent, bending loss and mode field area would vary with the change of bending radius, as shown in Fig. 6. With the decrease of the bending radius, the bending loss increases while the mode field area decreases. When the bending radius is less than 30 cm, the bending loss exceeds 0.1 dB/m and the fundamental mode would be attenuated rapidly, accompanied with a significant increase in mode field area. Bending radius of 30 cm as the critical radius is the key that we pay close attention to. When the fiber is bent at a radius of 30 cm, the bending loss of the fundamental mode is 0.087 dB/m and the mode field area is 1154 m2 , the decrement in mode field area is 16.85% compared to the straight state. Since the reported LMA PCFs with asymmetric structure are extremely sensitive to bending orientation angle, we make a breakthrough to the limit of the bending orientation. Fig. 7 shows the bending loss and mode field area as functions of bending orientation angle at the bending radius of 30 cm. As shown in Fig. 7, the bending loss of the fundamental mode is lower than 0.1 dB/m and the bending losses of second order modes are higher than 1 dB/m when the bending orientation angle varies in the range from 0 to 180 . Because the fiber structure is symmetric about x axis, so it can be concluded that the fiber conforms to the single mode operation conditions no matter what the bending orientation angle is. Moreover, it is worth noting that bending loss and mode field area appear periodic variation because of the rotational symmetry of triangle-core structure. The bending orientation angle varies 120 as a period and when is 60 , the mode field area and the loss difference between the fundamental mode and the second order modes achieve the maximum value simultaneously. Fig. 8


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Fig. 8. Mode field distribution under different bending orientation angles with the value of 20 (a), 45 (b), 60 (c), and 90 (d).

Fig. 9. Bending loss as a function of bending orientation angle at a bending radius of 30 cm when the air hole diameters change by þ1% (a) and 1% (b). FM represents fundamental mode, and SM-1 and SM-2 represent two different second order modes.

shows the mode field distribution under different bending orientation angles i.e., 20 , 45 , 60 , 90 . It can be directly observed that the mode field varies with the bending orientation angle and reaches the maximum when is 60 , which is consistent with the tendency shown in Fig. 7. In addition, from the view of practical application, the average effects of orientation drift on bending loss and mode field area are also taken into consideration. To our calculation, the average bending loss of the fundamental mode and the second order mode are 0.06 dB/m and 15.6 dB/m, the average mode field area is 1250 m2 . It means that the fiber can be robust single mode operation with a mode field area of 1250 m2 in practical application.

5. Discussion From the view of fabrication feasibility, a tolerance analysis is carried out. According to the current fabrication technology of PCFs, the fabrication accuracy of a circular air hole can be controlled within 1% [18]. Assuming that the diameters of air holes vary within 1% from the optimum parameters, numerical simulations for the deviation of the diameters of air holes are carried out, as shown in Fig. 9. It can be concluded from Fig. 9 that when the diameters of air holes are increased by 1%, the fiber still conforms to single mode operation conditions without the limit of bending orientation angle. Though the bending losses of fundamental modes are slightly higher than 0.1 dB/m when is 30 , 90 , 150 , single mode operation can also be maintained due to the large loss difference between the fundamental mode and the second order modes. On the other hand, when the air hole diameters are decreased by 1%, the fiber conforms to single mode operation conditions as changes from 30 to 90 in a period. The range of bending orientation angle is still larger than the current reported.


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6. Conclusion From the point of view of fabrication and application, we propose a bending orientation insensitive LMA PCF and investigate its bending properties. When it is at straight state and a bending radius of 30 cm, mode field areas achieve 1386 m2 and 1154 m2 at the wavelength of 1.064 m, respectively. The decrement of mode field area at bent state is 16.85% compared to the straight state. In addition to large mode area and small decrement of mode filed area at bent state, this fiber makes a breakthrough in bending orientation angle. It realizes single mode operation under any bending direction at the bending radius of 30 cm. Moreover, uniform size of air holes in the cladding reduce the difficulty of fabrication and tolerance analysis results demonstrate that 1% deviation of air hole diameters has slight effect on the bending properties. Large mode area at bent state, small decrement of mode field area and low sensitivity of bending orientation make the fiber of great potential in compact high power fiber lasers.

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