We present a new approach for the development of structured optical fibers. It is shown that fibers having an effective gradient index profile with designed refractive index distribution can be developed with internal nanostructuring of the core composed of two glasses. As proof-of-concept, fibers made of two soft glasses with a parabolic gradient index profile are developed. Energy-dispersive X-ray spectroscopy reveals a possibility of selective diffusion of individual chemical ingredients among the sub-wavelength components of the nanostructure. This hints a postulate that core nanostructuring also changes material dispersion of the glasses in the core, potentially opening up unique dispersion shaping possibilities.
© 2015 Optical Society of America
Optical fibers with engineered sub-wavelength features forming the core, have evolved into a distinct field in structured fiber optics . Depending on the involved technology, different structures have been demonstrated, including fiber tapers and sub-micron scale wires, with either solid core or air core [2,3]. High mode confinement in such nanostructured optical fibers or wires favors processes and properties, which in larger form-factor fibers are either not observed or negligible. These include strong coupling of acoustic and light waves , light trapping and field enhancement in air-cores  or increased blue-shifting of supercontinuum generation due to tapering-related modulation of confinement loss along the fiber . Dispersion shaping by tapering of chalcogenide glass fibers has also been demonstrated in context of enhancing the redshift of supercontinuum spectral limit toward the mid-infrared . It has only recently been shown that correct description of the Kerr nonlinearity in subwavelength feature size fibers requires, that both the electric and magnetic field vectors of the propagating mode, and the transverse distributions of linear and nolinear refractive indices are taken into account . With this approach, new nonlinear optical processes have been identified, such as fiber geometry-dependent inhibition of soliton self-frequency shift .
The fabrication technology of sub-wavelength feature size fibers has proved more challenging, than state-of-the-art photonic crystal fiber drawing technology. Reported reasons included various deformations and structure collapse during thermal processing . The arbitrarily most straightforward method of drawing a nanostructured optical fiber – that is directly from a prior-stacked preform – was demonstrated with fabrication of suspended core-type fibers, in which the solid nano-wire core had a diameter of 0.48 µm . A regular lattice fiber with a 20 nm air-core was later demonstrated, as well .
Here, we report for the first time on the designing and fabrication of an all-solid glass fiber with a homogeneous cladding and a nanostructured gradient index core. The refractive index has been designed by a layout of stacked glass rods, made from two thermally matched borosilicate glasses, with a refractive index contrast. The concept of a nanostructured gradient index core is based on an approach for developing of nanostructured gradient index lenses introduced by Hudelist et al. . The concept was verified for various types of non-guiding microoptical components, such as elliptical microlenses or anisotropic components [13,14], however for the first time here it is considered as an optical fiber. The fabricated fiber structures had unexpected dispersion properties. The dispersion in the demonstrated proof-of-concept series of fibers evolved from anomalous to all-normal dispersion with decreasing of the core size. This is unlike in typical photonic crystal fibers where in general, decreasing of the core diameter is accompanied by a blue-shift of the zero-dispersion wavelength (ZDW) and an increase of dispersion in the anomalous range of values, as well as by a positive dispersion slope in the near-infrared . The evolution of dispersion profile from anomalous values with a zero dispersion wavelength, to an all-normal dispersion profile for smaller nanostructured core diameters was confirmed with generation of supercontinuum spectra. Energy-dispersive X-ray spectroscopy measurements (EDS) were also performed and revealed a possibility of selective diffusion of individual chemical ingredients among the sub-wavelength components of the nanostructure. We claim that this process modifies the material dispersion of the glasses in the core, when the feature size of its structure elements decreases to the nanoscale. The reversed dependence of the dispersion profile on the core geometric dimension can be reconstructed numerically, when the material dispersion contribution is changed due to the selective diffusion of the chemical elements in the core glasses.
2. Nanostructured gradient index fiber design and fabrication
The structure of the fiber core has been designed for a parabolic refractive index profile with a symmetry axis along the fiber’s optical axis. The refractive index in this structure varies between 1.5273 (cladding) and 1.5581 (center of the core). The designed layout of the core is shown in Fig. 1(a). It is composed of a large number (7000-8000) of rods made of two borosilicate soft glasses: grey colored areas mark aggregations of the high index glass rods, and the white spacings represent the low index glass rods. The entire hexagonal structure was completed to circular using the low index glass rods. Circular stacked core structure was inserted into a low index glass tube before drawing of the final fibers at a fiber drawing tower. For core dimensions such, that the individual glass rods are sub-wavelength in size, the global refractive index profile in this structure has a parabolic profile as shown in Fig. 1(b). Refractive indices, thermal and rheological properties of the used soft glasses are listed in Table 1 and their chemical compositions are given in Table 2.
The actual stacked structure of the preform for the fiber core is shown in Fig. 1(c). The left-to-right diagonal of the hexagon is 6 cm wide and consists of 100 glass rods. The diameter of each rod was about 0.6 mm. The drawn sub-preform, about 2 mm wide, is shown in Fig. 1(d). This sub-preform was used for drawing of the final nanostructured core fibers, after inserting into low index glass tubes serving as cladding. A family of fibers has been drawn with geometrical parameters summarized in Table 3. Cladding tubes used during the technological process had different outer diameters, which is reflected by outer diameters of the fibers. This detail did not influence the dispersive properties of the fabricated samples in any noticeable way. Typical images of the structures, obtained using scanning electron microscopy (SEM) are shown in Fig. 2. The hexagonal shape of the core was maintained in all the fibers. Nanostructure topology of the core was discernible only in the fiber with the largest core (fiber #1). It was much less clear or completely indistinguishable in the remaining fibers. This limitation stems from the fact, that in the range of dimensions of our samples, it was difficult to find a compromise in the thickness of the conductive layer sputtered on the fiber, which would allow to observe the material contrast and at the same time prevent charging of the sample.
3. Results and discussion
Chromatic dispersion of the fibers was determined with linear simulations using finite element method. We assumed core sizes between 3 and 7 µm. Each glass rod has been approximated by a hexagon, divided into six equal elements by the calculation mesh. Results of the simulations are shown in Fig. 3(a). The ZDW of the theoretical dispersion profiles blue-shifts with decreasing core dimension, which is consistent with results reported earlier for “classic” soft glass photonic crystal fibers . Dispersion of the fibers was measured using a modified Mach–Zehnder interferometer technique . It enables to work with short fiber samples, which was important, since attenuation of the fabricated fibers measured within 1500-1600 nm was 2.0-2.5 dB/m. Lengths of the fiber samples used in the dispersion measurements were typically around 30 cm. Recorded dispersion profiles are shown in Fig. 3(b). The profiles evolve from anomalous range of values for the fiber with the largest core and a ZDW at about 1320 nm (fiber #1), to an all-normal dispersion profile for fibers with smaller cores, beginning with fiber #4. Location of the ZDW in the fibers is red-shifting with decreasing of the core size. This trend has been reported previously for structures with sub-wavelength size of the entire core area, either in nano-air-hole guiding fibers  or a tapered fiber with six subwavelength air holes . Both these fibers differ from our design in the way, that their entire core areas are sub-wavelength. In our fibers, the smallest core dimension was 2.8 × 3.2 µm, therefore the fiber cores were not sub-wavelength in size, although their entire layout was nanostructured. We also measured the mode field diameters in fibers 2, 4 and 6. The diameters measured respectively at the wavelengths of 1064 nm and 1550 nm were: 4.6 µm and 8.7 µm (fiber #2), 2.2 µm and 4.0 µm (fiber #4), 2.1 µm and 5.3 µm (fiber #6). Nonmonotonic evolution of the mode diameter at 1550 nm was expected, because the mode begins to expand as the core diameter decreases in size closer to the wavelength of the propagating mode. Considering both the core sizes and the measured mode diameters, the observed reversed trend of evolution of the dispersion profiles with decreasing core size in our fibers, cannot be explained on the grounds of sub-wavelength confinement of the guided mode.
To further support the dispersion measurement results shown in Fig. 3(b), we performed a simple supercontinuum generation experiment. Spectral range in the dispersion measurement was limited to 1700 nm with the setup at our disposal, however it can be assumed that fibers #3 and #4 should most closely represent a “border-point” situation between a ZDW fiber and an all-normal dispersion fiber. Supercontinuum spectra, measured under pumping with a femtosecond fiber laser operating at 1560 nm (Menlo C-fiber: 90 fs pulse duration, 100 MHz) are shown in Fig. 4. Both sets of spectra show features of an all-normal dispersion broadening around the pump wavelength. In the case of fiber #4, the spectrum is contained within roughly 1400-1800 nm. Spectra recorded in samples with different lengths are similar. The slight decrease of spectral width with increased fiber length stems from attenuation. This also means that the broadening process occurs fast along the propagation, which is typical for femtosecond-pumped, normal-dispersion supercontinuum [15,18]. In the spectrum recorded for fiber #3, an extended range of wavelengths is observed beyond 1800 nm, up to 2000 nm. This part of spectrum is also very sensitive to fiber loss, with a 100 nm decrease of redshift of the spectral edge for fiber lengths between 25 and 200 cm. These features are assigned to solitons, which are generated as soon as the redshifted edge of spectrum crosses into anomalous dispersion. Soliton self-frequency shift (SSFS) in the anomalous dispersion range then results in the extended spectral width in fiber #3 over fiber #4.
In order to investigate the possible reason behind the unexpected red-shift of the ZDW in our fibers, we measured concentrations of chemical elements in the nanostructured core area. In the process of drawing at the tower, glass is heated and diffusion of chemical compounds occurs. This results in different than designed refractive index distribution in the core of the fiber. We estimated the weight percentage of elements in the fiber core using energy-dispersive X-ray spectroscopy (EDS) on a SEM. The concentration characteristics measured along the core diameter of a) sub-preform and b) fiber #3 are shown in Fig. 5. For clarity we also included corresponding SEM images of the scanned profiles. It can be easily seen, that after one drawing process high and low refractive index borosilicate rods in the sub-preform still have different chemical compositions. NC34 glass (high index) inclusions have lower amount of silicon (Si) and oxygen (O) than the NC21 (low index) glass. Unlike the NC21 glass, the NC34 inclusions contain around 11.5% of barium (Ba). However, in the final fiber, individual layout components of the nanostructure are no longer distinguishable. Barium atoms concentration corresponds well to desired parabolic profile of the refractive index. This confirms that stacked glass rods with appropriate distribution can give an arbitrary effective gradient index function. Also, concentration distribution profiles of Si and O are much more smooth and the shapes of curves correlate negatively with the amount of barium. However, one must be aware that the spatial resolution of EDS technique is limited by interaction volume of the beam electrons . Although the overall profile of distribution of elements matches the design, it does not mean, that in the nanoscale the distribution of individual types of atoms remains the same as in the stacked preform. Therefore the nanostructured fiber cannot be simply modelled as a stack of two types of glass rods, even if uniform diffusion is taken into account. Based on our results, we postulate that an individual diffusion of certain kinds of atoms, leading to subtle changes of composition of glass, results in a completely different material dispersion profiles of the individual elements comprising the nanostructured core. Such a scenario is also consistent with the experimentally observed red-shift of ZDW in our nanostructured fibers, as opposed to the expected blue-shifting of ZDW with decreasing core size. To support this claim, we performed simulations for a nanostructured gradient index fiber structure, in which the material dispersion was optimized to match the measured dispersion characteristics of fiber #1 (Fig. 3(b)). In our numerical model, the lateral refractive index profile changes along the diameter according to the real Ba concentration and to the refractive index at the center of the core, in a similar way to the high index glass (NC34). This assumption is supported by the fact, that the concentration of the heaviest elements, which determine the refractive index, is not changed in the center of core between the preform stage and final fiber (Fig. 5). As the background glass for gradient index profile, we used the low index glass (NC21). Afterwards we used previously calculated material dispersion to calculate dispersion characteristics of fibers with different diameters. Out of the different profiles of gradient index investigated, a reasonable reconstruction of the experimentally observed evolution of dispersion with the core size was obtained for a refractive index distribution shown in Fig. 6(a). Corresponding dispersion profiles, show in Fig. 6(b), follow the same trend of red-shifting ZDW with decreasing core size, starting with a ZDW at about 1300 nm for 6.9 µm core, to an all-normal dispersion profile for core areas smaller than 4 µm in diameter. Slight differences between this simulation and experimental results in Fig. 3(b) are assigned to limited precision of establishing the core size of the smaller core fibers due to decreasing SEM image contrast with decreasing sample size.
The described selective diffusion process could be considered an opportunity to extend the dispersion engineering flexibility in optical fibers, provided numerical design tools are extended with means to anticipate this effect. Otherwise, it is a limitation which introduces uncertainty of the final dispersion profile of the nanostructured core fiber concept. We note that the demonstrated family of fibers was realized as a technological proof-of-concept for the core nanostructuring. The work did not involve any optimization procedures aimed at control of the diffusion effects. Such procedures could involve either changes in the glass synthesis or in the fiber drawing process, or in both. As a general outline of possible optimization of the glass chemistry in context of diffusion control, compositions not including alkali oxides, like Li2O, Na2O, K2O, could be suggested. These could be e.g. oxide glasses based on BaO, CaO, CdO or PbO. Any candidate glasses for nonastructured core fibers have to be matched in terms of rheology and thermal expansion coefficients, must be crystallization resistant and their refractive index contrast must be high enough to enable designing of the desired refractive index profile. At the fiber drawing stage, the process parameters critical for diffusion are the number of drawing cycles, the drawing temperature and the preform feed rate. In our case, the fiber drawing included four separate drawing cycles, which was motivated by the intent to study evolution of the drawn structure at several different development phases. However, increased number of temperature cycles favoured the diffusion. Optimized preform stacking should enable reduction of drawing cycles to just two, in which the core subpreform would be stacked and drawn first, followed by drawing of the final fiber. The latter two parameters – the drawing temperature and preform feed rate – are both determined in large part by the rheology of the fiber glasses. The structure of the fiber preform can also play a role, with certain structure layouts being more susceptible to breakage during drawing, when the temperature is set too low or the feed rate is too high. There is considerable room for optimization of the fabrication procedures of the nanostructured core fibers, in context of the diffusion effects. However these problems fall out of scope of the present study.
Gradient index optical fibers with nanostructured core and a solid, homogeneous cladding were fabricated by directly drawing from a stacked preform. Although the demonstrated fibers’ gradient index profile was circularly symmetric against the optical axis, the presented approach enables arbitrary refractive index profile designs using the same technological procedure. Such freedom to design a fiber’s transverse mode structure would be an advantage for the emerging field of multimode nonlinear fiber optics . Proposed concept can also be a key enabler in shaping of birefringence properties of optical fibers. We have shown, that the physical profiles of chromatic dispersion in a fiber with nanostructured core, composed of two multicomponent soft glasses, can differ significantly from a profile predicted in linear simulations of the structure layout. Diffusion at the interfaces between adjacent glass rods could be expected. However EDS measurements revealed additionally, that various chemical elements of the glasses diffuse in the transverse plane of the nanostructured core at different rates. This results in different concentrations in the final nanostructure. We assigned this effect as the reason for the change of material dispersion of the glasses in the nanostructured core. Using numerical modelling we showed, that including this change in the simulation enables to reconstruct the experimentally observed evolution of the fiber’s dispersion profile with decreasing of the core size. Unexpected evolution of the dispersion profile in the presented fibers was observed as a type of “side effect”. The original motivation for this work was to demonstrate fiber structures with refractive index determined by an effective profile stemming from the stacked transverse layout, and not to demonstrate a specific dispersion characteristic. In spite of that, the core nanostructuring procedure enabled manipulation of the ZDW location or the dispersion sign, to a degree otherwise possible only with restricting the fiber’s effective mode area to the sub-wavelength regime [3,17]. This could be of use for example in fabrication of negative dispersion slope fibers for all-fiber optical pulse compressors  or in fiber-based parametric frequency conversion . Therefore these results call for further research on modification of the numerical procedures to include and anticipate the effect of selective diffusion phenomena at the fiber design stage, which is subject of our present study.
This work was supported by the project TEAM/2012-9/1 operated within the Foundation for Polish Science Team Programme co-financed by the European Regional Development Fund, Operational Program Innovative Economy 2007-2013.
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