Single-nanoweb suspended twin-core fiber for optical switching.
All-optical networks (AON) [1, 2], which have attracted considerable attentions for their manageability [3,4], transparency [5-8], and flexibility [9-13], are considered to be the candidates for the future communication networks invariably by scholars. As an important supporting technology of optical communication systems, optical switching is taken account for the key-enabling function for the deployment of the developing all-optical networks and many efforts have been made on trying to accomplish it. As far as we know, the technologies to realize optical switching include optical microelectro-mechanical systems (MEMS)-based switching [14-16], thermal optical switching [17,18], electro-optic switching [19-21], opto-optical switching [22-25], acousto-optic switching  technologies and other technologies integrating some of them . However, much of the optical switches are still predominantly performed electrically in recent applications. With the emergence and development of the microstructure fiber (MSF) which has shown a great success to achieve unique properties such as high birefringence [28-36], flattened dispersion [37-40], large negative dispersion [41,42], high nonlinearity [43, 44], endless single mode  and so on, there emerges a new opportunity for the exploration of optical switching technology that it is possible to make the optical fiber be an optical switch. Recently, a type of nanomechanical optical fiber  has been proposed and demonstrated, which has two fiber cores independently suspended within the fiber. Based on sub-micron mechanical movements, the nanomechanical fiber shows the optical switching between the two fiber cores, which clearly shows the possibility to achieve an optical switching device with advantages such as fiber compatibility, compared with the traditional optical switches. However, the demonstrated nanomechanical optical fiber in Ref.  has a complex structure and needs to break the fiber cladding to achieve the mechanical movements of the fiber cores, which limits its practical applications.
In this paper, we propose a suspended twin-core fiber (STCF) based on a single-nanoweb structure for optical switching. It utilizes an ultrathin silica lamina suspended in air and attached to the inner wall of a glass fiber capillary, and there are two solid fiber cores near the central part of the nanoweb. The force applied to the proposed STCF is used to achieve optical switching. The mode coupling between the two fiber cores is sensitive to the pressure-induced index change, which provides a one-to-one correspondence (within a half period) between the force and the transmittivity of one core into which the broadband light is injected. The performances of optical switches based on STCFs with different structure parameters are presented.
2. STRUCTURE AND PERFORMANCE
The geometry structure of the cross-section of the proposed STCF is shown in Figure 1. There is an ultrathin glass membrane suspended in air and attached to the inner wall of a glass fiber capillary. The external diameter of the capillary is (D), in our simulations, which is kept being a constant of 125 [micro]m. The radius of the capillary's inner ring is (R). Figure 1(b) shows the enlarged view of the center structure of the nanoweb with the twin cores. The thickness of the nanoweb is (d). The radius of the twin cores is (r). The distance between the centers of the two fiber cores is (H). We use a full-vector finite-element method (FEM) to analyze the influence of the force applied to the proposed STCF and also investigate the guided modes.
In the pressure analysis, two pieces of iron are adopted to imitate a fiber clamp in actual applications, and placed on the direction of the nanoweb. When the fiber clamp is under force, the force applied to the STCF will lead to not only the pressure-induced refractive index change, but also the pressure-induced structure deformation. In terms of the contribution to the light guiding and mode coupling, the role of the pressure-induced structure deformation is so small  that we usually ignore it. According to the well-known photoelastic effect, the refractive index of the silica under the force is given by the equations 
[n.sub.x] = [n.sub.0] - [C.sub.1][[sigma].sub.x] - [C.sub.2]([[sigma].sub.y] + [[sigma].sub.z]) (1)
[n.sub.y] = [n.sub.0] - [C.sub.1][[sigma].sub.y] - [C.sub.2]([[sigma].sub.x] + [[sigma].sub.z]) (2)
[n.sub.z] = [n.sub.0] - [C.sub.1][[sigma].sub.z] - [C.sub.2]([[sigma].sub.x] + [[sigma].sub.y]) (3)
and the pressure-induced refractive index change is
[DELTA][n.sub.x] = [n.sub.x] - [n.sub.0] = [C.sub.1][[sigma].sub.x] - [C.sub.2]([[sigma].sub.y] + [[sigma].sub.z]) (4)
[DELTA][n.sub.y] = [n.sub.y] - [n.sub.0] = [C.sub.1][[sigma].sub.y] - [C.sub.2]([[sigma].sub.x] + [[sigma].sub.z]) (5)
[DELTA][n.sub.z] = [n.sub.z] - [n.sub.0] = [C.sub.1][[sigma].sub.z] - [C.sub.2]([[sigma].sub.x] + [[sigma].sub.y]) (6)
where [[sigma].sub.x], [[sigma].sub.y] and [[sigma].sub.z] are the stress components, and [C.sub.1] = 6.5 x [10.sup.-13] [m.sup.2]/N and [C.sub.2] = 4.2 x [10.sup.-12] [m.sup.2]/N are the stress-optic coefficients of pure silica. Thus, through the FEM analysis we can know the refractive index change of the silica under different force. Note that, in the process of calculations, z-direction is usually ignored since it almost makes no difference to the polarized mode of the optical fiber.
When a force of 1 N is applied to a 10-cm STCF with parameters of D = 125 [micro]m, R = 50 [micro]m, d = 1 [micro]m, r = 1 [micro]m, and H = 3 [micro]m, the calculated [[sigma].sub.y] in the STCF is shown in Figure 2(a). Note that the calculated [[sigma].sub.x] is much smaller than [[sigma].sub.y] in the twin-core region and it is 0 in the rest part of the nanoweb, thus it is ignored for the pressure-induced index change. One can very clearly see the amplification effect of the proposed structure, that is to say, a force of 1 N applied to the STCF results to a high stress up to about 6.3 Mpa in the nanoweb of the STCF. According to Eqs. (4) and (5), it's easy to describe the distribution of the pressure-induced refractive index change along the y direction, which is shown in Figure 2(b). For example, the pressureinduced index change is [DELTA][n.sub.x] = 20.2 x [10.sup.-6] and [DELTA][n.sub.y] = 3.1 x [10.sup.-6] in the center of the fiber cores, which shows that the x-polarized light has a stronger response to the force applied to the STCF.
It is mentioned above that the guiding light in the proposed STCF will be influenced by the pressure-induced refractive index change. To make it unequivocal, we simulate the guiding modes in the twin-core region and acquire the effective refractive indices of the even mode and the odd mode. Figures 3(a) and (b) show the mode profiles of the electric field for the even mode and the odd mode, respectively, and meanwhile describe their normalized electric field distribution along the y direction. Note that the operation wavelength [lambda] is set at 1550 nm, and a 10-cm STCF with parameters of D = 125 [micro]m, R = 50 [micro]m, d = 1 [micro]m, r = 1 [micro]m, and H = 3 [micro]m is employed. The calculated effective refractive indices of the even mode and the odd mode are [n.sub.e] = 1.36493 and [n.sub.o] = 1.36122. According to the mode coupling theory, the optic power transferred from one fiber core to the other fiber core after a length Z along the STCF is given by 
p([lambda], Z) = [sin.sup.2] ([absolute value of ([n.sub.e]-[n.sub.o]] Z * [pi]/[lambda]) = [sin.sup.2]([DELTA][n.sub.eo]Z * [pi]/[lambda]) (7)
and the coupling length is given by 
[L.sub.c] = [lambda]/(2[absolute value of ([n.sub.e]-[n.sub.o]]) (8)
Note that the coupling strength is usually expressed by the coupling length or the coupling coefficient. The relation between them also has shown in .
[L.sub.c] = [lambda]/4[k.sub.12] (9)
According to Eqs. (7) and (8), we can get a function of the optical transmittivity dependent on Z and [L.sub.c]
p(Z,[L.sub.c]) = [sin.sup.2](Z * [pi]/2[L.sub.c]) (10)
When the x-polarized laser light with the wavelength of 1550 nm is injected into one fiber core of the STCF without applied force, we can calculate transmittivity for another fiber core of the STCF according to Eq. (9). Figure 4 shows transmittivity when the length of the STCF is in the range around 10 cm. One can see that after only 0.22 mm, the light of this core can be transferred to the other one completely. Therefore we can use the length of its integral multiple to initialize the optical switching device.
Figure 5 shows the (x-polarized) transmission of the STCF with the length of 9.96 cm and 5.03 cm at a force range from 0 to 950 N. Here, we define a switching force ([DELTA]F) that is a force applied to the STCF to switch guided light from one fiber core to the other. One can distinctly see that for the STCF with same structure parameters, longer the fiber is, smaller the switching force is needed, in the case of the incident light with a fixed wavelength. And the switching force of the STCF with the length of 9.96 cm is 148 N. Mechanical strength of fiber has been commonly mentioned in the experiments of fiber pressure sensing .
For the given length of the proposed STCF, small [DELTA]F is expected to achieve optical switching in practical applications, which actually pushes us to design a STCF with high force sensitivity. Therefore, here we investigate STCFs with different parameters for optical switching. Note that, in the following discussions, a 10-cm STCF with parameters of D = 125 [micro]m, R = 50 [micro]m, d = 1 [micro]m, r = 1 [micro]m, and H = 3 [micro]m is used as the reference for which [DELTA]F of 148 N is needed to achieve optical switching.
Firstly, we change the radius of the inner ring of the glass capillary when other parameters of the STCF are fixed. The relationship between the switching force [DELTA]F and the radius R is shown in Figure 6. Note that all STCFs are with the same length of 10 cm for the calculated results in Figure 6. Obviously, a STCF with a larger radius R has a smaller switching force [DELTA]F. This can be understood due to the fact the larger air hole of the STCF is more sensitive to the applied force. The principle is similar with the special MSFs  with side holes which provide an internal amplification mechanism to enhance the force sensitivity. However, in practical applications, R is limited by the physical strength of the fibers. Secondly, according to the contrast of several different structures, we deploy the exploration of the role of the distance H of the twin cores. Figure 7 shows that optical switching will be more difficult when the distance of the twin cores is widening, that is due to the fact that the larger distance H results to weak mode coupling between the twin cores. The size of fiber cores also influences the property of the STCF for optical switching. For a given STCF, when we change the size of fiber cores within a certain range, there is a maximum value for [DELTA]F which is shown in Figure 8. When the twin cores are most close to each other (i.e., they are tangent), the corresponding [DELTA]F will be the minimum. Meanwhile, when r becomes smaller, a smaller [DELTA]F can also be achieved, which indicates the smaller r is preferred. Here we can find two effects for the size of the fiber cores and the mode coupling. A larger r will enhance the mode overlapping of the twin cores since they are closer to each other. While the fiber core with a small r will result to weak confinement of the mode light, and also strong mode coupling of the twin cores. Thus a suitable value of r should be chosen for practical applications of the STCF when considering the light confinement and sensitivity for optical switching. Likewise, similar behaviour can be seen for the parameter d. Figure 9 shows the switching force [DELTA]F for a 10-cm STCF with different thickness (d) of the nanoweb when other parameters are fixed. It can come to be a conclusion that the optimized thickness (d) will lead to a minimum value of the switching force [DELTA]F. When d turns to be thin, for a given force applied to the STCF, pressure-induced index change of the twin cores becomes larger due to the built-in transducing mechanism. However, the thickness (d) of the nanoweb will also influence the mode coupling, that is, the thin nanoweb will lead to a weak mode coupling of the twin cores since there is more air instead of silica material between the twin cores. Thus, we can understand the thickness (d) can be optimized to achieve minimum switching force [DELTA]F. Generally, parameters of the STCF for optical switching can be optimized to achieve a low switching force. Under the guidance of the above-mentioned discussions, we find the optimized structure of the STCF with parameters of D = 125 [micro]m, R = 50 [micro]m, d = 1 [micro]m, r = 1 [micro]m, and H = 2 [micro]m for optical switching, and the calculated switching force is [DELTA]F = 8 N. Note that we choose a fiber size same as the single mode fiber and a reasonable radius R here, and the switching force can be much smaller if we use a much larger STCF with a larger radius R.
3. DISCUSSION AND CONCLUSION
The recently designed nanomechanical optical fiber  and the proposed STCF are actually two kinds of microstructured optical fibers with a dual-nanoweb structure and a single-nanoweb structure, respectively. The proposed STCF shows several advantages. Firstly, the single-nanoweb structure is relatively simple which benefits the fiber fabrication process. Such as easily controlling the size of the twin cores and the distance between them. Special measures should be taken to control the distance of the two fiber cores for nanomechanical optical fiber with the dual-nanoweb structure in the fabrication process. Secondly, optical switching can be achieved by controlling the force applied to the external surface of the STCF, but one should break the fiber cladding of the dual-nanoweb fiber to achieve optical switching. The STCF is used as the optical switch by simply add suitable fiber clamp. Thirdly, for the proposed STCF, optical switching is achieved based on the pressure-induced index change which essentially has advantages such as high response speed and high repeatability, compared with optical switch based on mechanical movement of the dual-nanoweb fiber. There is some research work on the fiber-optic vibration sensors based on the photoelastic effect of the fiber which indicates that the response frequency of pressure applied on the fiber can at least up to 3000 Hz. According to the successful optical switching of the nanomechanical optical fiber  and the load force test in the experiment of fiber pressure sensing , we can believe that the STCF can withstand 8 N to achieve optical switching without breaking the structure. Of course, since there is a thin structure in the proposed STCF, further experimental research is still needed to make sure how much force the STCF can bear.
In conclusion, we have proposed and investigated a novel STCF based on a single-nanoweb structure, which can be used as an optical switch. Optical and mechanical properties of the proposed STCFs under different force have been numerically investigated. By analyzing the mode coupling between the twin cores, we reveal the rule of the STCF's parameters for optical switching and indicate the optimized method for achieving an optical switch with low switching force. Finally, we also discuss the advantages of the proposed STCF compared with the early reported dual-nanoweb fiber.
Received 20 May 2013, Accepted 6 July 2013, Scheduled 15 July 2013
This work was supported in part by the National Natural Science Foundation of China under project (No. 61007029), Projects of Zhejiang Province (No. 2011C21038 and No. 2010R50007) and the Program for Science and Technology Innovative Research Team in Zhejiang Normal University.
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Xiaowei Ma and Daru Chen *
Institute of Information Optics, Zhejiang Normal University, Jinhua 321004, China
* Corresponding author: Daru Chen (email@example.com).
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|Date:||May 1, 2013|
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