For a suspended core nanofiber, the holey region is expected to be as large as possible to propagate the light at wavelengths as long as possible. Additionally, a large holey region is significant for its applications in sensors. However, the fabrication of nanofiber with large holey region is still a challenge so far. In this paper a method, which involves pumping positive pressure of nitrogen gas in both the cane fabrication and fiber-drawing processes, was proposed. A suspended core nanofiber, with a core diameter of around 480 nm and an unprecedented diameter ratio of holey region to core (DRHC) of at least 62, was fabricated in the length of several hundred meters. Owing to the large holey region, the confinement loss of the suspended core nanofiber is insignificant when the wavelength of light propagated in it is 1700 nm. For this fabrication technique, the nanowire length, fabrication efficiency, and the uniformity in the diameter are much superior to those of the nanowires fabricated in other ways. Finally, single mode third harmonic generation was observed by this nanofiber under the pump of a 1557 nm femtosecond fiber laser. This work shows the prospect of fabrication of nanostructured waveguide in glass materials by an inflation technique.
©2010 Optical Society of America
For a certain waveguide the high nonlinearity owes to the strong confinement of light. A large index contrast can results in a strong confinement. The strength of confinement can reach its maximum in visible or near infrared range when the dimension of waveguide is in nanoscale. Nanowire waveguides have attracted much attention in recent years because of their impressive applications in microscale and nanoscale photonic devices [1–5]. The ability to manipulate pulses of light within sub-micrometer volumes is vital for highly integrated light-based devices such as optical computers, to be realized . Nanowires by silica glass [7,8], lead silicate glass , and chalcogenide glass  have already been demonstrated. The popular fabrication methods of them can be classified into three categories. The first is by drawing or electrospinning nanowires from bulk glass [11,12]. The second is by tapering the microstructured fiber to decrease the core diameter from microscale to nanoscale . The third is by the scheme of suspended core nanofiber, which is characterized with a suspended core in the diameter of several hundred nanometers embedded in the fiber with a usual outside diameter [14,15].
For the first method, the nanowires are exposed to the environment. The degradation in surface for these nanowires is a problem which has not been solved well so far. Because nanowires have a large ratio between surface and volume, the effect of degradation in surface is much more pronounced than in usual optical fibers. In an environment of conventional optics laboratory the naked nanowire degrades day by day, and it can fail totally after several tens of days [16,17]. Imbedding the nanowire into a polymer coating material is a solution to this problem. However, the coating materials, which have refractive index higher than that of air, will result in a decrease in confinement. In the latest report, a silica aerogel, which has a refractive index close to 1, was used as a coating material. However, this aerogel is brittle, hygroscopic, decomposable in the water, and shrunken in the air .
For the second method, one problem is that at the temperature of tapering the microstructure is subject to deformation due to the additional pressure which arises from surface tension. The smaller holes the tapered fiber has, the more possibility the deformation has, because the additional pressure is converse to the hole size. Usually when the core is tapered to nanoscale, the holes are also reduced to a comparatively small size, so sometimes the holes almost collapse in the tapering process even if they were sealed . Reference  showed that in the tapering process of a silica holey fiber the holes shrank with the reduction of core size and finally one of them disappeared. Moreover, even if the microstructure is reproduced well in the tapered nanofiber and the numerical aperture (NA) is kept roughly the same as the original fiber, in most of the cases the light cannot be confined tightly enough in the core. It can be qualitatively explained by the normalized frequency V = (2πr/λ) × NA which characterizes guidance in a step-index fiber. For a step-index fiber with V = 10 at 1.5 μm, when core is reduced to tenth of original size, V is 1, which is a value too small to confine most of the power in the core.
The nanowire fabricated by the third method is protected from the pollution of environment by a glass cladding. Meanwhile the strength is improved greatly. Moreover, because it can be drawn from preform continuously, the length, uniformity in core diameter, and efficiency of fabrication are much better than those of nanowires by the method of directly drawing or tapering. However, until today it is still a challenge to fabricate a suspended core nanofiber which has a holey region large enough to ensure a low confinement loss at long wavelengths. In this paper, we present the significance of the size of holey region for the propagation capacity of the suspended core nanofiber, and propose a fabrication technique for the nanofiber with extremely large holey region. It involves pumping a positive pressure of nitrogen gas in both the cane fabrication and fiber-drawing processes. A around 480 nm suspended core nanofiber with an unprecedented large holey region was demonstrated, and single mode third harmonic generation was observed by this nanofiber under the pump of a 1557 nm femtosecond fiber laser.
2. Significance of large holey region
For a certain wavelength, the nonlinearity of a free-standing nanofiber reaches the maximum when the core diameter is in optimization. The optimal diameter can be deduced by :Eq. (1) A is the optimal core area. ncore and nclad are the refractive index of the core and cladding, respectively. Since at 800 nm various lasers in CW or pulse are available commercially, we chose λ = 800 nm to calculate the optimal diameter. The composition of the tellurite glass used by us was 76.5TeO2-6Bi2O3-6ZnO-11.5Li2O (mol%). The Sellmmeier coefficients for the refractive index calculation are provided in . At 800 nm ncore is 2.038 and nclad is 1. The calculated optimal diameter is 350 nm.
For the suspended core nanofiber, because the thickness of air-cladding is finite, it is necessary to consider the influence of air-cladding thickness on the propagation capacity of the nanofiber. As shown in inset (a) of Fig. 1 , a model of an ideal suspended core nanofiber is proposed. It is characterized with a suspended core without struts to support. The diameter ratio of holey region to core (DRHC) was defined by Φ1/Φ2. Supposing the ideal suspended core nanofiber has a core diameter of 350 nm, we calculated the confinement loss by the fully vectorial finite difference method (FV-FDM). The results are shown in inset (b) of Fig. 1. For each DRHC, there is a cutoff wavelength after that the confinement loss increases sharply. With the increase of DRHC, the cutoff wavelength is shifted to longer wavelength. To propagate the light at the wavelengths as long as possible, the DRHC should be as large as possible. For the nanofiber with a DRHC of 3 or 5, the 800 nm light cannot be propagated well in it. Therefore the optimization in nonlinearity is difficult to be realized. To have an insignificant confinement loss at 800 nm, the DRHC need to be at least around 10. These analyses agree with . For the nonlinear processes such as supercontinuum (SC) generation which occur at wavelengths longer than 800 nm, DRHC of 10 is not enough and we must further increase the size of holey region.
Additionally, a large holey region is also expected by its application in evanescent fiber sensor, because it allows a longer wavelength to be propagated in the core, which means a larger proportion of power expanded in the holes. Additionally, it results that the analyte can be filled into the holes more easily .
3. Fiber fabrication and charicterization
The fabrication of suspended core nanofiber with large holey region is still a challenge today . By the usual fabrication methods for the cane, it is difficult to realize nanofiber with large holey region. For the method of stack and draw, it means that it is necessary to use capillaries with impractical thin sidewall. For the method of extrusion or ultrasonic drilling, to realize a cane, which has the struts thin and long enough for the large holey region nanofiber, is still difficult so far. In the latest report  a lead silicate glass suspended core nanofiber with the core diameter of 420 nm has the DRHC of around 10. Very recently we have reported the tellurite microstructured fibers fabricated by pumping a positive pressure of nitrogen gas into the holes of cane to overcome the surface tension and reshape the microstructure . The DRHC of a tellurite glass air-clad fiber with 1 μm suspended core was increased to 20 through the inflation of pumping pressure. However, a problem occurs when fabricating the nanofiber with large holey region in the same way, because the core and struts of nanofiber are too delicate and subtle to withstand a high pump pressure. It means that the core and struts are already collapsed and all holes form one hole before the holey region is enlarged enough.
To decrease the pump pressure used to inflate the holey region, a cane with large holes is necessary because of the following two reasons: (1). For a stable fiber-drawing process at certain temperature, the pump pressure required to counteract the surface tension of holes in the fiber is determined by :Eq. (2) △P is the pump pressure, σ is the surface tension, R is the radius of hole in the cane. Sf and Sp are the speeds of fiber-drawing and preform-decline (Preform includes the cane and the jacket tube, which are introduced in the section of fiber fabrication experiment) respectively, and are constant for a stable fiber-drawing process. From Eq. (2) it can be found for a larger hole size R, a smaller pump pressure is required to counteract surface tension. Consequently the final pump pressure for inflation decreases. (2). For a stable fiber-drawing process, if the proportion among the microstructures of preform could be reproduced accurately by the fiber, the hole size of fiber should be:Eq. (3) r0 is the reproduced size of fiber hole. Supposing there were two preforms, which have the same characterized sizes except for the hole radius R of cane. The preform with larger R has a larger reproduced size r0. To inflate r0 to a certain hole size r1, the pump pressure required by the preform with larger R should be lower than that required by the one with small R, because for the latter the microstructure needed to be reshaped heavier. Here r1/r0 can be used to show the extent of reshaping.
To increase the hole size of preform as large as possible, in this research we modified fabrication techniques based on the fabrication process in : Firstly, we changed the microstructure from six holes to three holes, in this way the hole size doubled for a same holey region. Secondly, when fabricating the cane, we pumped a positive pressure into the holes to inflate them. In this way the hole size in the preform was increased greatly. Finally a nanofiber with the core diameter of around 480 nm and the DRHC of at least 62 was fabricated.
The nanofiber was made from the same tellurite glass as that which was given in calculating the optimal diameter of a free-standing nanofiber. This glass is transparent in mid infrared, and has a nonlinear refractive index higher than that of silica glass by more than one order of magnitude. The raw materials in powder were analytic grade. The cane for the fiber-drawing was fabricated by the method of cast rod in tube. A tellurite glass rod, which has a cross section in the shape of “Y” was prepared by casting the glass melt in an alloy mold and then annealing it at the glass transition temperature. It has an outside diameter of 6 mm and a core diameter of 2.5 mm. The tellurite glass tubes with the outside diameter of 12 mm were prepared by the rotational casting method. The rod was inserted into a tube with the inside diameter of 7 mm and then was elongated into the original cane in the outside diameter of 2 mm and the core diameter of 0.4 mm. The tips of three struts of the rod touched the inside surface of the tube tightly. In this way three holes was formed in the cross section of the original cane. The original cane was inserted into another tellurite glass tube with inside diameter of 3 mm and elongated into the final cane in the outside diameter of 2.7 mm and the core diameter of around 50 μm. In this elongation process, a positive pressure of nitrogen gas, 3.0 kPa, was pumped into the holes of the original cane to enlarge the holes in the final cane. The final cane was inserted into other tellurite jacket tube with the inside diameter of 4 mm, and then was fixed at the drawing tower for the fiber-drawing. The jacket tube was used to decrease the ratio of the core to cladding size. In the fiber-drawing process a positive pressure of nitrogen gas, 2.5 kPa, was pumped into the holes of the final cane. The pump pressure is much lower than that (7.8 kPa) used in  for a holey region with the diameter of 20 μm.
In Fig. 2 the fabrication process of the final cane was shown schematically. In inset f the thickness of struts is around 20 μm. In Fig. 3 the cross sections of the fiber are shown. The fiber has an outside diameter of 120 μm and a core diameter of around 480 nm. The core diameter was defined by the largest inscribed circle within the triangle core. The diameter of holey region is larger than 30 μm. The DRHC is at least 62, which is the largest value for the highly nonlinear air-clad fibers so far. The thickness of three struts is in the magnitude of several tens of nanometers. Such thin and long struts can isolate the nanowire well from the outer tellurite glass. Several hundred meter nanofiber was drawn in one time of fiber-drawing. The cross-section of the fiber was checked at various intervals along the fiber. It was found that the core diameter kept constant for the whole fiber. The aspect ratio of the suspended core is in the magnitude of 108, which is a value higher than those by direct drawing or tapering in several orders of magnitude.
To get high nonlinearity, experientially the fabricated fiber has a core diameter a little larger than the optimal size , because the nonlinearity falls off rapidly when the core diameter becomes smaller than the optimal size. Therefore, in our case to get high nonlinearity at 800 nm, the fabricated fiber has a core diameter of around 480 nm. The core diameter can be reduced further without sacrificing the size of holey region if only cane with holes large enough can be prepared.
The chromatic dispersion and calculated confinement loss were calculated by the method of FV-FDM. The simulation was based on the nanostructure of real fiber. The results were shown in Fig. 4 . The inset shows the calculated mode field at 800 nm. The wavelength of 800 nm locates in the anomalous dispersion region, and is close to the zero dispersion wavelength. It is of significance for applications such as parametric amplification and SC generation. Owing to the large holey region, the confinement loss of the suspended core nanofiber is insignificant when the wavelength of light propagated in it is 1700 nm.
The nonlinear coefficient at 800 nm, calculated by the traditional method shown in [24,25], is 22.9 W−1m−1. The tellurite glasses are the same for them. Very recently a revised calculation method for the nonlinearity of nanowire was proposed . In that method the effect of the z-component of the propagating fields is included. According to this method the nonlinear coefficient is 31.4 W−1m−1.
The optical loss at 1557 nm for the fiber was measured by using the standard cutback measurement technique. A homemade femtosecond fiber laser with the peak wavelength at 1557 nm was connected with a single mode fiber (SMF) by a connector. Beam from the SMF was collimated into parallel by a lens of 0.25 NA. The parallel beam was focused and coupled into the tellurite nanostructured fiber by a lens of 0.50 NA. The coupling efficiency, defined as the launched power divided by the incident power on the lens, was about 2%. The output end of the fiber was mechanically spliced with another silica SMF by using butt-joint method. By the butt-joint method the light of cladding mode of nanofiber cannot be coupled into the SMF. The other end of the SMF was connected with the optical spectrum analyzer. To ensure the light is coupled into the core of the fiber, firstly we coupled the pulse of a 1557 nm femtosecond fiber laser into the nanofiber. When the third harmonic generation (THG) was observed (The fiber laser and THG are explained in the section of SC experiment), the CW light source replaced the femtosecond laser at the connector. The measured optical loss at 1557 nm is 8 ± 2 dB/m. The predominant loss is most likely due to the roughness of inner surface of the nanofiber .
Due to the limitation of experimental conditions, we pumped the nanofiber at not 800 nm but 1557 nm. Figure 5 shows the pulse energy dependent SC spectra measured by using a homemade femtosecond fiber laser at 1557 nm. The pulse width was 400 fs and the repetition rate was 16.75 MHz. The length of the nanostructured fiber was around 8 cm. Because the pump wavelength locates in the normal dispersion region, the visible emission could not be dispersive wave. It should be the THG of the pump laser. The frequency of THG deviates from the triple frequency of pump laser. It is a usual phenomenon for the THG generated by highly linear fibers . Possible reasons involve cross-phase modulation on the THG field from the pump pulse . The inset (a) and the inset in inset (b) show the patterns of the spatial mode for THG. It is single mode. Therefore the THG was generated under single mode non-phase matched conditions . This is different from the previous reported THG by tellurite air-clad fibers which have a larger core diameter under the same pump laser . In  the THG was induced by multimode phase matching and then was in high-order mode . According to the normalized frequency the cutoff wavelength of fundamental mode of this nanofiber is 910 nm. At 580 nm, the normalized frequency for it is 3.9, and for the fibers in  is at least 10. Hence, this nanofiber could be quasi single mode fiber at THG wavelengths, but the fibers in  are definitely multi-mode at THG wavelengths. Additionally, even if the nanofiber is multi-mode at THG wavelengths, the number of high order modes is reduced greatly than the fibers in . The phase matched conditions might not be met in so few modes, or even if be met, but the superposition of mode profiles of pump pulse and high order modes at THG wavelengths is too poor . Therefore, the THG obtained by this nanofiber is not multi-mode but single mode.
The THG by this nanofiber is more interesting than that in  because it is single mode. However, as shown in spectra it seems not as efficient as reported in . A main reason is that the coupling efficiency is too low. The efficiency of THG will increase quickly with the increasing launched power because of the third order correlation between the powers of THG and fundamental wave. To improve the coupling efficiency, this nanofiber needs to be coupled by the method of evanescent field by using a tapered silica fiber with a tip in nanoscale. The tip is inserted into the holes of nanofiber and contacted with the core in a superposition length of few micrometers. Due to the limitation of experiment conditions we did not try this experiment. The coupling efficiency can be higher than 90% theoretically .
For a suspended core nanofiber, a large holey region has important significances for its practical applications. In previous report, suspended core nanofibers with optimized nonlinearity have been demonstrated by traditional fabrication techniques . However, to obtain a fiber which has the capacity to propagate the light at wavelengths as long as possible, the DRHC is expected to be as large as possible, so new fabrication technique is required to be explored. In this report we elucidated the fabrication technique for the nanofiber with extremely large holey region. The reason why only cane with large holes can be inflated and drawn into the nanofiber with large holey region was explained, and a suspended core nanofiber, with a core diameter of around 480 nm and an unprecedented large DRHC of at least 62, was demonstrated. Compared with the free-standing nanowire, this nanofiber is protected by the cladding glass, so it has a much higher strength, and is less likely to be polluted by environment. Owing to the large holey region, the confinement loss of the suspended core nanofiber is insignificant when the wavelength of light propagated in it is 1700 nm. The fabrication efficiency, and the uniformity in the diameter are much superior to those of the nanowires fabricated in other ways. Finally, we coupled 1557 nm femtosecond laser into the nanofiber and observed single mode non-phase matched third harmonic generations.
Nanowires have fascinating applications in future compact devices. We believe we have achieved a breakthrough in the fabrication of suspended core nanofibers. Furthermore, this fabrication technology can serves as the reference for the fabrication of nanostructured waveguide in glass materials by an inflation technique.
This work was supported by MEXT, the Private University High-Tech Research Center Program (2006-2010).
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