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In this paper we report on limits related to the development of optical fibers with glass subwavelength inclusions incorporated into the core. We present the fabrication of a photonic crystal fiber made of an in-house developed silicate NC21 glass with a subwavelength-size high refractive index inclusion in the core made of lead silicate SF6 glass. The core has a diameter of 2 µm, while the diameter of the inclusion varies from 0 to 800 nm. Using energy-dispersive X-ray spectroscopy technique we show a dramatic change in the inclusion profile and its composition caused by a non-uniform diffusion of chemical molecules during the stack-and-draw fiber fabrication process. Therefore, the effective refractive index and the material dispersion of the final fiber are significantly different than for bulk glasses, which leads to an alteration of optical properties of the final fiber. A unique non-monotonic characteristic of the effective material dispersion is used to reproduce the fiber dispersion characteristic.
© 2015 Optical Society of America
1. Introduction
Photonic crystal fibers (PCF) with subwavelength inclusions in the core are an interesting new class of optical fibers. The introduction of inclusions in the core, such as holes or rods made of different glasses, dramatically alters the guiding properties of such fibers. The concept of engineering dispersion properties in PCFs with a single air-hole in the core was introduced and modelled by Saitoh et al. [1] The paper demonstrated zero dispersion wavelength (ZDW) tailoring performed for a fiber with a flat dispersion profile and low confinement losses. Later, subsequent successful developments of this type of fibers were reported, where modification of the dispersion was also observed. Field intensity enhancement in the core of the fiber coupled with long interaction length which together give rise to nonlinear effects were presented in PCFs made of either silica [2,3 ] or soft glasses [4]. It was also shown analytically and numerically that a dielectric inclusion made of a tellurite glass in the core of a PCF creates a new type of nonlinearity which strongly depends on the geometrical parameters of the fiber design and the specific dispersion of the core material [5]. Moreover, subwavelength-size single air holes in the core can also be used for spectral tunneling of solitons [6] and for the enhancement of cylindrical birefringence [7]. Structuring the core of a PCF may also lead to a stable soliton self-frequency shift and subpetahertz sideband generation through four-wave mixing [3]. The concept of the manipulation of fiber properties by modifying the core has also been demonstrated for sensor applications [8,9 ]. A highly doped area in the core was used to enhance the nonlinearity of a PCF, which enabled efficient broadening of the supercontinuum spectrum [10]. Recently, the concept of a fiber for mid-IR with a microporous PCF based on chalcogenide glasses was introduced and modelled by Ung and Skorobogatiy [11], where the possibility of a red-shift of the ZDW to 10.6 µm was shown. A PCF with nano-size air-holes in the core for the blue extension of a supercontinuum generation was also proposed [12]. PCFs with an inclusion in the core based on soft glasses were developed and shown to enable the generation of supercontinuum [13–15 ]. It is expected that PCFs with a structured core will find applications in metrology, optical telecommunication and nonlinear optics.
Dispersion properties of a single-mode fiber are determined by the properties of the fundamental mode and are usually described in terms of the effective refractive index. In particular, ZDW is determined by geometrical and material properties of a fiber for both classical step-index and photonic crystal fibers [16]. Subwavelength modification of the internal core structure, especially the introduction of air holes as well as high-refractive index inclusions, results in a ZDW shift only towards longer wavelengths [17]. Therefore, the existence of solitons has a short wavelength limit [6]. The most important consequences of this constraint are related to nonlinear applications of fibers and limit efficient generation of a supercontinuum in the visible wavelength range in the anomalous dispersion regime since the pump wavelength is usually matched to the location of the ZDW of nonlinear fibers [18].
In this paper we propose to incorporate a subwavelength high-index inclusion in a core of a PCF to tailor its dispersion properties and shift the ZDW. We show a high sensitivity of dispersion characteristics to parameters of the inclusion in the core and the possibility of engineering the location of the ZDW in a broad range of wavelengths, while maintaining a small mode area of the fundamental mode. We also report that the development of PCFs with a structured core using the stack-and-draw technology must take into account diffusion and evaporation of chemical molecules when processing submicron-size objects.
Dispersion engineering may be achieved by integrating a subwavelength structure only inside the core, without the need to use a photonic lattice as a cladding. Therefore, dispersion engineering may be obtained in a step-index fiber with a nanoinclusion in the core. This simplifies the drawing process and integration with standard fibers.
Embedding a subwavelength inclusion in a PCF core and engineering dispersion properties may lead to the integration of multiple small cores in a single fiber, where each core with different dispersion is used to stimulate the generation of supercontinuum. The interaction between spectra generated in highly coupled cores may in turn contribute to an enhancement of the bandwidth of supercontinuum generated in such a structure.
2. Concept and numerical modelling of a PCF with a subwavelength inclusion in the core
First, an ideal PCF structure was investigated numerically. A commercial mode solver based on the finite difference method was used to perform the modelling [19]. The cladding of the fiber is composed of seven rings of holes in a glass, ordered in a hexagonal lattice with the lattice constant Λ = 1.8 μm and the relative air-hole size d/Λ = 0.91, where d is the diameter of the holes. The core is created by replacing the central capillary with a tube in which a glass subwavelength inclusion in form of a rod is embedded in the center. The inclusion is made of a glass of a higher refractive index than that of the background glass. The schematic of the fiber with the first three rings of holes of the cladding is shown in Fig. 1 . An in-house developed silicate NC21 glass [20] was used as the background glass and SF6 glass was used as the inclusion [21]. The core has the diameter of 2 µm, while the inclusion diameter dincl varied in the range of 0–800 nm.
Fig. 1 Schematic of an ideal PCF structure with a subwavelength inclusion in the core and with three rings of air-holes in the cladding.
For a PCF without an inclusion in the core only the fundamental mode can be excited effectively, assuming a linearly-polarized Gaussian beam at the wavelength of 800 nm. This mode has the mode area of 2.12 μm2. It is expected that the embedment of an inclusion which has a higher refractive index than that of the background glass in the core decreases the fundamental mode area, which in turn leads to an increase of the nonlinear coefficient of the fundamental mode. The fundamental mode area as a function of the diameter of the inclusion is shown in Fig. 2 . For the inclusion diameter in the range of 400–680 nm, the mode area remains lower than 0.4 μm2 for the wavelength of 800 nm, which allows to obtain a desirable high energy density. At the same time the mode area of higher order modes is similar to the case when the core does not have any inclusion. This allows to spatially separate different optical modes supported by the fiber.
Fig. 2 The fundamental mode area as a function of the diameter of the inclusion for the numerically modelled fiber and the wavelength equal to 800 nm; In the inset, the relative intensity of the maximum (no inclusion) and minimum (inclusion diameter of 500 nm) fundamental mode area is shown.
The ZDW of the fundamental mode is highly sensitive to parameters of the inclusion, especially to the diameter and the material dispersion characteristic of the glass used. It is shifted approximately 1.8 μm towards longer wavelengths when the diameter of the inclusion changes from 0 (no inclusion) to 800 nm, as shown in Fig. 3 . Thus, it is possible to engineer the dispersion of the fiber while maintaining a small fundamental mode area. Based on these calculations, the final inclusion diameter of 400 nm was chosen for a follow-up development stage.
Fig. 3 Dispersion characteristics of photonic crystal fibers with the hexagonal lattice constant Λ = 1.8 μm and the relative air-hole size d/Λ = 0.91 with a high refractive index subwavelength inclusion in the core of the diameter in the range of 0–800 nm.
3. Development of a PCF with a nanostructured core
We have developed a PCF with a high refractive index inclusion in the core. The fiber is made of NC21 silicate glass (55% SiO2, 1% Al2O3, 26% B2O3, 3% Li2O, 9.5% Na2O, 5.5% K2O, 0.8% As2O3) synthesized in-house. Bulk NC21 glass refractive index is described using the following Sellmeier coefficients: B1 = 1.15672327, B2 = 0.1496439, B3 = 1.37076559, C1 = 0.00611444 μm2, C2 = 0.02546248 μm2, C3 = 122.5877913 μm2. Nonlinear Kerr refractive index of NC21 glass is close to that of pure silica and has been measured as 1.1 × 10−20 m2/W at 1240 nm [20]. The inclusion was made of SF6 glass which is a standard lead silicate Schott glass [21]. The measured thermo-physical properties of both glasses are presented in Table 1 . Characteristic glass temperatures were derived on the basis of the observation of the shape of the sample in a Leitz II A-P heat microscope (sample dimensions 4 mm × 4 mm × 4 mm, rate of increase of temperature 10 °C min–1).
Table 1. Measured thermo-physical properties of the SF6 and NC21 glasses.
The fiber was developed using the stack-and-draw technique. Both glasses are thermally matched and can be jointly processed. The temperature of the drawing process was set at 750 °C. SF6 glass has lower viscosity that NC21 glass at this temperature. As a result, SF6 is softer and heavy metal components have a tendency for higher diffusion rate. Figure 4 and Fig. 5 present scanning electron microscope (SEM) images of the subpreform and the final fiber, respectively. During the fiber drawing stage the hexagonal air-holes transform into circular ones. The final fiber has the core whose diameter equals 1.90 ± 0.08 μm. Photonic lattice of the cladding consists of 7 rings of air-holes, with the lattice constant Λ = 1.71 and the relative air-hole size d/Λ = 0.9. According to the SEM image shown in Fig. 5(b), the total diameter of the inclusion equaled approximately 490 nm (a diameter at full-width half maximum FWHM of 400 nm). We verified the uniformity of the drawn fiber over a distance of 20 m. In particular, the inclusion keeps the total diameter of 490 nm with an accuracy of approximately ± 10 nm.
The fiber’s attenuation characteristic was measured using the cut-back technique and is shown in Fig. 6 . Typical loss level in the considered wavelength range between 0.75 μm and 1.65 μm was 6–7 dB/m. These are typical losses for lead-oxide based glasses [20]. The absorption peak near 1.4 μm is related to OH ions absorption.
4. Mode dispersion measurements and modelling
The dispersion characteristics for the fundamental mode and for the second guided mode of the fiber with a 490 nm inclusion in the core was measured with white light interferometric method using unbalanced Mach-Zehnder interferometer [22]. In this method, series of spectral patterns are recorded. As a result, an interference pattern in the spectral domain was obtained, with a characteristic wide fringe pattern at the wavelength for which the interferometer was compensated. Changing the length of the reference arm, we were able to measure an optical path difference between the measurement and the reference arm in a wide spectral range, and then to determine the chromatic dispersion of the fiber. The characteristics are shown in Fig. 7 . The method allows to determine the dispersion characteristics with a very high precision [22]. It also enables to distinguish between the dispersion characteristics of the fundamental mode (FM) and the higher order modes (HOM). The FM and HOM have different propagation constants. Therefore, for a fixed position of mirrors in the reference arm of the Mach-Zehnder interferometer we can observe two separated interference patterns. Moreover, the modes have different dispersions and moving the mirror causes an independent movement of the patterns. The discrimination between the FM and HOM dispersions is further simplified for longer wavelengths, where the FM has a higher pattern contrast due to the cut-off of the HOMs.
Fig. 7 Dispersion characteristics for the experimentally measured modes (dotted lines) and for the modelled fundamental modes for PCFs without an inclusion (ideal or based on SEM image), with a step-index inclusion of diameter equal to 400 nm and for the uniform model of diffusion.
The length of the fiber sample used in the measurement was about 24 cm. The ZDW of the FM is located at about 817 nm, while for the second order mode the ZDW equals 606 nm. Unexpectedly, these values are very close to those obtained numerically for an ideal structure designed without any inclusion (see Fig. 7). The ZDW of the fundamental mode in this case is equal to 790 nm. It means that we observe only a 30 nm red-shift of the ZDW due to the presence of an inclusion, instead of a 650 nm red-shift. Similar conclusions can be made for the dispersion characteristic of a structure based on the SEM image from Fig. 5(a), where the inclusion is also neglected. Although these results show that the developed structure of the photonic cladding is very similar to the ideal one, since both dispersion lines almost overlap in the whole considered wavelength range, it does not explain the huge discrepancy between the measured characteristics of the fiber and the modelled one with a 400 nm step-index inclusion in the core, determined on the basis of the SEM image (see Fig. 5).
In order to further investigate this mismatch between the modelling results and the experimental data we also considered a Gaussian profile of the inclusion instead of a step-index one. In this approach, the refractive index varied from the value for the pure SF6 glass in the center, towards the value for NC21 glass at the edge of the inclusion. The full width at half maximum of this inclusion was equal to 400 nm. Although this model should incorporate the effect of the uniform diffusion of atoms and molecules from the area of the inclusion to the NC21 core of the fiber, we found that the dispersion characteristics are still far from the measured results, which is shown in Fig. 7.
5. Analysis of chemical components distribution in the core with a subwavelength inclusion
It is well known that diffusion and evaporation of chemical molecules occur during the fiber drawing process [23,24 ]. These phenomena are usually negligible in the case of development of all-solid photonic crystal fibers, since all the glass inclusions are much larger than any expected diffusion depth. We expect that in the case of subwavelength inclusions, such processes may change both the size of an inclusion and the refractive index, and may thus dramatically influence the fiber performance. Moreover, the diffusion may vary for different glass components. It also depends on the processing temperature and the differences between the thermal properties of glasses.
Both glasses used in this work, that is SF6 and NC21, have different concentrations of chemical elements O, Si and Pb. The concentrations were measured using energy-dispersive X-ray spectroscopy (EDS) implemented in Zeiss Sigma SEM [25]. Figures 8(a) and 8(b) present the profiles of the concentration of chemical elements expressed in weight percentage, determined along the diameter of the core of the subpreform and the final fiber, respectively.
Fig. 8 The characteristics of the concentration of chemical elements along the core diameter of a) the subpreform and b) the final developed PCF.
We observe that the concentration of lead (Pb) in the area of the inclusion in the fiber drops from approx. 60% to less than 8% with respect to the central part of the subpreform core. Moreover, the inclusion is highly diffused. Its profile is not step-index, as is the case of the subpreform, but it is close to a Gaussian profile. The ratio between the inclusion and the core diameter grows from approximately 0.14 to 0.37, which indicates the spreading of Pb atoms. This behaviour can be explained in terms of different melting point temperatures of both glasses. Because the viscosity of SF6 glass is lower than that of NC21 glass at the drawing temperature, the inclusion made of SF6 glass is softer than the core made of NC21 glass. As a consequence, SF6 glass more easily penetrates its surroundings.
The EDS measurements also indicate that the concentration of oxygen (O2), silica (Si) and sodium (Na) in the center of the subpreform is much lower than for the final fiber. Indeed, the amount of these elements in SF6 and NC21 glasses is different. However, after the fiber drawing process, the contrast in the concentration of elements between the glasses drops and it is almost imperceptible for Si and Na.
The observations demonstrate a strong diffusion process in the nanoscale. They also reveal that apart from a uniform diffusion process of all components, we might also expect a non-uniform, nonselective diffusion of individual chemical ingredients in the sub-micron scale features of the fiber structure. Unfortunately, because of a carbon layer deposited on the fiber sample, EDS method does not allow to measure precisely the presence of light elements such as boron atoms in NC21 glass, and this element is thus not taken into account in the analysis [25].
6. Numerical retrieval of the effective refractive index
The subwavelength inclusion located in the core is too small to measure its refractive index experimentally. Thus, in order to estimate the refractive index distribution in the core and the influence of uniform and non-uniform diffusion processes on the optical behaviour of the fiber, we implemented a numerical retrieval method. We assumed that the refractive index characteristic changes along the diameter of the core according to the real lead concentration, and its value changes from a hypothetical glass in the center of the inclusion to NC21 at its edge. Then, the material dispersion of this postulated glass was calculated by an optimization procedure in which the numerically calculated dispersion was compared with the measured dispersion of the fundamental mode of the PCF.
In Fig. 9 the dispersion of the refractive index is plotted for SF6, NC21 glasses and also for the postulated inclusion glass. For more clarity, we also plotted refractive index values for the points in the core where the concentration of lead is two times lower (FWHM) than in the center, and the data for the elementary lead (the real part) [26]. The numerical results confirm that the values of the refractive index of the postulated glass are closer to NC21 glass than to the original SF6. Moreover, the shape of the postulated glass dispersion curve differs from both materials in the long-wavelengths range and resembles the characteristic of pure lead.
Finally, in Fig. 10 we compare the experimentally measured dispersion characteristics with the ones obtained numerically for the structure containing the postulated glass in the inclusion. Although the optimization procedure was performed only for the fundamental mode, we observe a very good agreement between numerical calculations and experimental data for the higher order mode. This result proves the correctness of our model and confirms the fact that both the material dispersion and the refractive index of the nanoscale elements might be different than that for bulk materials.
Fig. 10 Dispersion as a function of wavelength for two measured modes (dotted lines) and for modelled modes on the basis of the postulated glass.
7. Conclusion
We reported on the limits related to the development of fibers with a subwavelength inclusion in the core. We have shown numerical modelling and fabrication of a PCF made from an in-house developed silicate glass NC21, with a subwavelength inclusion in the core made from lead silicate SF6 glass that has a higher refractive index than the surrounding glass. It was numerically confirmed that the PCF structure exhibits a high sensitivity of dispersion characteristics to parameters of the inclusion in the core and enables to engineer the ZDW location in a broad range, while maintaining small fundamental mode area. The experimental results show that the profile of the inclusion in the subpreform is not maintained after the final drawing. We observed a high migration of chemical molecules in the nanoscale elements during the fiber fabrication process. Moreover, the glass did not diffuse uniformly but various chemical components diffused at different rates. As a result, the effective refractive index and the material dispersion of the subwavelength inclusion can be significantly different than it was estimated, considering a uniform diffusion between the glasses. This profoundly affects the optical performance of the final fiber. The shapes of the measured dispersion profiles cannot be explained when a uniform diffusion is assumed. Only a numerical model which takes into account different migration rates of molecules allowed to accurately reproduce dispersion characteristics for the fundamental and the higher order modes. In order to develop PCFs with a structured core using the stack-and-draw technology, one must take into account the diffusion and evaporation of both chemical elements and compounds when processing nanometric-size objects.
Our final note is that the diffusion and evaporation of chemical molecules for a given pair of glasses can be minimized by the optimization of technological parameters of the stack-and-draw method. These parameters would include the lowering of the processing temperature at all stages and the increase of the fiber drawing rate. The former leads to the lowering of the viscosity of the glass and the latter limits the time left for diffusion. An alternative approach would be the reduction of the number of drawing stages by optimizing the stacking stage. In addition, another set of thermally matched glasses can be used. In this case, a high-index glass with a higher viscosity in the drawing temperature should be used for the inclusion, and the glass with the lower viscosity as the background glass.
Acknowledgments
This work is supported by the TEAM/2012-9/1 project within the Foundation for Polish Science Team Programme co-financed by the European Regional Development Fund, Operational Program Innovative Economy 2007-2013 and by the National Science Centre research grant no. 2011/03/B/ST3/03337.
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