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Abstract
Suspended-core fibers (SCFs) with a submicron diameter hole in the core offer interesting new possibilities in dispersion management, light confinement, and nonlinear applications. We discuss the geometric demands and options of fused silica-based nanohole SCFs suitable for all-normal dispersion (ANDi) and compare them to the possibilities provided by photonic crystal fibers (PCFs). We show that nanohole SCFs extend the options PCFs provide, enabling ANDi further into the near infrared. In addition, fabrication conditions are evaluated, a reliable fabrication scheme is outlined, and ANDi nanohole SCFs are demonstrated.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Recently, optical fibers providing all-normal dispersion (ANDi) have attracted particular attention. The reason for that is the fascinating possibility for spectrally flat, pulse-preserving, octave-spanning, low noise, and coherent supercontinua [1–9], which has led to interesting applications [2,6,10,11].
With the growing number of applications grows the interest for tailored fiber-based ANDi supercontinua addressing the needs of particular applications. For instance, finite width supercontinua with a high power spectral density are attractive for various applications in the fields of spectroscopy and microscopy, and they typically utilize only a fraction of the spectrum and the power of what is provided by up-to-date commercially available supercontinuum sources. For this purpose, neither a high nonlinearity nor a very broad low dispersion range is ideal. Both conditions tend to reduce the available power spectral density in a predefined range by transferring optical power into unused spectral ranges when the pump power is scaled up.
Regarding low nonlinearity and high power-handling capability, pure fused silica is typically the most suitable choice and hence the focus of this work.
For fibers based on pure fused silica, photonic crystal fibers (PCFs) have been until now the only serious option [12]. They can provide ANDi for various pump wavelengths covering nearly the entire transmission range of fused silica from visible to near-infrared wavelengths. PCFs, albeit their high dispersion flexibility, are almost exclusively used at 0.8 and 1.0 µm pump wavelengths [1–8]. Longer pump wavelengths starting at 1.3 µm and upward are typically utilized based on soft glass fibers [13,14] (1.3 µm pumping, [15]; 1.5 µm pumping, [16,17]; 2.7 µm pumping, [18]). The reason is that PCFs that are dispersion optimized for pump wavelengths larger than 1 µm are hard to use due to the gradual disappearance of the light-guiding property, as detailed later in this paper.
This work presents an alternative pure fused silica fiber structure capable of providing ANDi in the near-infrared wavelength range while maintaining light guidance: nanohole suspended-core fibers (SCFs). SCFs without nanohole in the core are known to provide ANDi for a very small core diameter of approximately 0.5 µm but only in the vicinity of 500 nm wavelength with very limited tuning capability [12,19,20]. They have not gained practical relevance for ANDi supercontinuum generation up to date.
Recently, a microstructured fiber based on ZBLAN containing six nanohole cores was demonstrated to provide ANDi [21]. This raised the question of whether fused silica-based nanohole SCFs are a reasonable alternative to PCFs to provide ANDi in the near-infrared wavelengths range. Here, we discuss the options of tailoring fused silica nanohole SCFs for ANDi supercontinuum generation.
2. FIBER DESIGN
Fig. 1. SCF example cross sections covering (a) the entire air hole region and (b) the core region. The design parameters $t$ (strut thickness), $D$ (incircle core diameter), and $d$ (hole diameter) are highlighted in (b).
Fig. 2. Impact of (a) the core diameter $D$, (b) the hole diameter $d$, and (c) the strut thickness $t$ on the dispersion for $n\; = \;{4}$ struts. In (a), $d\; = \;{0}$ and $t\; = \;D/{6}$. In (b), $D\; = \;{1}\;{\rm \unicode{x00B5}{\rm m}}$ and $t\; = \;D/{6}$. In (c), $D\; = \;{1}\;{\rm \unicode{x00B5}{\rm m}}$ and $d\; = \;{200}\;{\rm nm}$. (d) The number of core modes as a function of strut thickness $t$ for $D\; = \;{1}\;{\rm \unicode{x00B5}{\rm m}}$ and $d\; = \;{230}\;{\rm nm}$.
Based on these parameters, the modal properties are simulated with a finite element method (COMSOL Multiphysics) and the dispersion parameter in units of ps/nm/km, hereafter referred to as dispersion, is calculated. Figure 2 displays the impact of the individual design parameters on the dispersion. The core diameter $D$ defines the region where the dispersion curve has its maximum [Fig. 2(a)]. The smaller the core diameter is, the smaller is the maximum dispersion wavelength (MDW), the wavelength that corresponds to the local maximum of the dispersion curve. A core diameter in the range from 0.6 to 2 µm addresses a comparable range regarding the MDW.
The impact of the hole diameter $d$ is shown in Fig. 2(b). Its main purpose is to effectively shift the dispersion downward into the normal dispersion range. A large dispersion range is covered with small changes in the hole diameter. This shift is accompanied by a redshift of the MDW.
The impact of the strut thickness $t$ is shown in Fig. 2(c). It shows a similar influence on the dispersion as the hole diameter but with a much smaller magnitude. This opens up the possibility to optimize the strut thickness toward another critical fiber property: the mode count. The core modes were determined by comparing the mode field diameter of all calculated modes to the core diameter. Modes with a field diameter comparable to the core diameter are guided in the core. Modes located in the struts show a mode field diameter significantly larger than the core diameter.
The impact of the strut thickness $t$ on the number of core modes is shown in Fig. 2(d). At a small strut thickness of $t\; = \;{150}\;{\rm nm}$, eight polarization modes are guided in the core. With increasing strut thickness, the struts behave like a modal filter, a concept similarly known and exploited for single-mode PCFs [22]. Once the struts are thick enough for the higher-order modes to match their effective index, they spread into the struts. As a result, all but the two fundamental polarization modes can be delocalized from the fiber core with proper sizing of the strut thickness. We checked this behavior at both ends of the considered wavelength range, and as a ballpark estimate the SCFs are single mode at their MDW for strut thicknesses $t\; \gt \;{0.4}D$.
Fig. 3. Overview of the ANDi tunability for (a) single-mode nanohole SCFs with $n\; = \;{3}$ struts in comparison to (b) PCFs. (b) is taken from Ref. [12]. Note the different wavelength axes. When optimized for longer wavelengths, SCFs exhibit a perpetual redshift of the local ANDi maximum, whereas PCFs exhibit an onward flattening of the long wavelength dispersion edge and eventually a transition to anomalous dispersion. At the short wavelength edge, nanohole SCFs show a shoulder formation due to the adaption of the mode field to the central hole.
Fig. 4. (a) Exaggeration of the ANDi shoulder formation around 800 nm wavelength for large core diameters in combination with large hole diameters for $n\; = \;{3}$ struts. With increasing hole size, the dispersion resembles that of a small core size comparable to a single corner of the core. (c) The geometry of the core area with $d\; = \;{1100}\;{\rm nm}$ and (c) the modal distribution of one fundamental polarization mode at 800 nm wavelength.
3. ALL-NORMAL DISPERSION SCFs AND COMPARISON TO PCFs
Based on these considerations, we calculated a series of single-mode ANDi SCF geometries [Fig. 3(a)], which covers the transmission range of fused silica. This range is similar to the one addressed with ANDi by PCFs [Fig. 3(b)]. Nevertheless, there are a couple of noteworthy differences.
At the long wavelength side, nanohole ANDi SCFs maintain the local maximum, which can be continuously shifted to 2 µm and beyond. This is in contrast to PCFs, which exhibit an onward flattening of the long wavelength edge of the dispersion, which eventually transitions into anomalous dispersion. This transition is accompanied by the disappearance of the dispersion maximum, whose redshift is therefore limited to wavelengths around 1.3 µm.
At the short wavelength side, nanohole ANDi SCFs exhibit the formation of a shoulder in the dispersion curve. This reduces the dispersion for smaller wavelengths $ \lt \;{1}\;{\rm \unicode{x00B5}{\rm m}}$ when the overall design is optimized for larger pump wavelengths $ \gt \;{1.5}\;{\rm \unicode{x00B5}{\rm m}}$. The reason for this shoulder formation is that small wavelengths start to resolve and in consequence omit the large central core hole by an adaption of the mode field. This shoulder formation can be exaggerated with larger core holes, as demonstrated in Fig. 4. The field retracts from the hole into the high index corners of the core. This allows resembling the dispersion behavior of a submicron core of, e.g., 700 nm in diameter by a much larger one of 1800 nm in diameter.
The most important difference is not to be seen in the dispersion behavior but in the effective mode area of the fundamental mode at the MDW [Fig. 5(a)]. The PCF exhibits a limit of the MDW around 1350 nm due to the transition into the anomalous dispersion range thereafter. This limit is accompanied by a very strong increase of the effective mode area due to the very low air filling fraction of the hexagonal air hole lattice that surrounds the core. These small air holes allow a far-reaching penetration of the mode field into the cladding. From a practical perspective, this implies the disappearance of the light-guiding capability. In contrast, nanohole SCFs maintain a local ANDi maximum when moving to a longer wavelength. A small effective mode area is maintained as well. This clearly favors nanohole SCFs over PCFs when choosing a pure fused silica fiber for all-normal nonlinear applications at wavelengths beyond 1.3 µm.
Fig. 5. (a) Effective mode area at the MDW for nanohole SCFs and PCFs. Clearly visible is the inability of PCFs to shift the MDW beyond 1.3 µm due to the transition into the anomalous dispersion range. In addition, the effective mode area increases rapidly beyond 1 µm MDW due to the low air filling fraction required for dispersion management. Practically, this implies the loss of the guiding capability. In contrast, nanohole SCFs maintain their guiding capability and allow an MDW approaching 2 µm. (b) The strong increase of mode area is accompanied by a corresponding decrease of the nonlinear parameter.
Note that the mode area for a given fiber geometry is quite constant for all wavelengths for both PCFs and SCFs, but whereas in PCFs the mode area equally increases for all wavelengths when the MDW is shifted toward 1.3 µm wavelength, SCFs allow to keep the mode area confined.
Accordingly, the nonlinear parameter of the PCFs drops much faster when approaching longer wavelengths compared to SCFs, as demonstrated in Fig. 5(b). Although the nonlinear parameter of PCFs is quite similar to SCFs at small wavelengths well below 1 µm, it is an order of magnitude smaller already at 1.3 µm wavelength. This emphasizes the advantageous nonlinear properties of SCFs compared to PCFs in this wavelength range.
4. FABRICATION SCHEME
SCFs are typically realized by the stack-and-draw-technique [23]. In a first step, the preform is stacked, meaning that small thin-walled capillaries are fitted into a larger cladding tube. In a second step, this preform is drawn into the fiber. During this drawing step an excess pressure within the capillaries ensures their inflation, and the core forms by the collapse of the central air region and the fusion of the respective capillary wall sections (Fig. 6).
Fig. 6. From left to right: scheme of the formation of the SCF structure during fiber drawing due to the inflation of the capillaries and the collapse of interstitial air regions.
The most crucial part when fabricating nanohole SCFs is the control of the hole size. To ensure proper control, we combined pure fused silica capillaries with a strongly fluorine-doped cladding tube (Heraeus F520). The fluorine-doped cladding tube reduces the viscosity relative to the capillaries. This allows a sufficient reduction of the drawing temperature to enable a temperature range where there is only a partial collapse of the central air region, and a core hole is maintained. In high concentrations, fluorine tends to degas, which can result in bubble formation, distorted core geometries, and brittle fibers. For us a faster preform feed was sufficient to keep the furnace transition time approximately at a quarter of an hour or below to circumvent this effect.
5. REALIZED FIBERS
The advantage of the fabrication scheme explained above is that the size of the core hole can be tuned by the drawing temperature without impacting the other structural parameters. With this approach, we realized different fiber series based on both $n\; = \;{3}$ and $n\; = \;{4}$ struts.
Figures 7(a)–7(c) display example cross sections from a series of fibers that originated from a single drawing run by varying the furnace temperature. By decreasing the displayed furnace temperature from 2010°C [Fig. 7(a)] to 2000°C [Fig. 7(b)] and 1990°C [Fig. 7(c)], the central hole increases while core size and strut thickness are unaffected. Because there is no option to reliably determine the submicron hole size during fiber drawing, a predefined temperature range is covered during drawing, and the optimum ANDi geometry is determined afterward.
Fig. 7. Realized nanohole SCFs with similar incircle core diameter $D\; = \;{1.8}\;{\rm \unicode{x00B5}{\rm m}}$ and different hole sizes $d$ of (a) 260 nm, (b) 430 nm, and (c) 550 nm. The scale bars indicate a length of 1 µm. The different hole sizes originate from different drawing temperatures of 2010°C, 2000°C, and 1990°C, respectively. (d)–(f) The respective calculated dispersion. Calculations are based on the actual cross section without approximation. The two dispersion curves correspond to the two fundamental polarization modes indicating a low birefringence.
Fig. 8. Realized polarization maintaining ANDi SCFs. (a) and (b) Scanning electron images and (c) and (d) corresponding calculated dispersion, respectively. The two dispersion curves correspond to the two fundamental polarization modes. Scale bars indicate a length of 1 µm. The legend shows the polarization direction with respect to the long core axis.
The dispersion corresponding to these cross sections is displayed in Figs. 7(d)–7(f). The dispersion was calculated based on the actual cross section of the fibers without idealizing approximation by the design parameters introduced above. We assume the calculated dispersion to be a quite accurate representation of the actual dispersion due to the accurate knowledge of the material dispersion of fused silica, which is very well documented [24], and the refractive index distribution, which is precisely know by the scanning electron microscopy images. Compliance of simulated with actual dispersion properties of silica-air-microstructured optical fibers is consistently reported [25].
The dispersion curves shown here confirm the correlations and results presented in Fig. 2. When there is no or a very small hole, the dispersion covers both the normal and anomalous range. With increasing hole size, anomalous dispersion values are gradually reduced until normal dispersion is reached and an ANDi profile is constituted.
The two dispersion curves correspond to the two fundamental polarization modes and indicate a low birefringence. An unintentional or low birefringence is known to impact the ANDi supercontinuum generation process and the resulting polarization state [4]. These effects are suppressed in fibers having a birefringence $ \gt {10^{ - 4}}$.
Whereas preforms based on three capillaries favor non- or weakly birefringent SCFs, preforms based on four struts can be used to realize birefringent ANDi nanohole SCFs. An asymmetry in the preform, e.g., by different capillary outer diameters or wall thicknesses, leads to an asymmetric and birefringent core. Figure 8 shows fibers that support the realization of linear polarized suspended-core sources. Figure 8(a) shows a fiber whose core axes have a ratio of approximately 2/3. This fiber has a birefringence of ${\Delta }n = 1.3 \cdot {10^{ - 3}}$ at 1 µm wavelength. Dispersion calculations of the two polarization modes in Fig. 8(c) reveal that one polarization direction experiences ANDi, and the other experiences two dispersion zeros. In the more pronounced case of Fig. 8(b), the core axes have a ratio of approximately 1/2. Here, both polarization directions experience ANDi but for strongly different pump wavelengths around 800 nm $( {{\Delta }n = 4.1 \cdot {{10}^{ - 3}}} )$ and 1.5 µm $( {{\Delta }n = 2.3 \cdot {{10}^{ - 2}}} )$. When the polarization is aligned along the long core axis, the MDW is also shifted to longer wavelengths, and when the polarization is aligned along the short core axis, the MDW is shifted to shorter wavelengths. Hence, the polarization dependence reflects the impact of the core size as discussed above.
6. SUMMARY AND CONCLUSION
We demonstrated the capabilities of nanohole suspended-core optical fibers based on fused silica to provide ANDi. They can provide ANDi from 600 nm upward to above 2 µm wavelengths.
Compared to PCFs based on fused silica, nanohole SCFs have the advantage of maintaining a convex ANDi profile and their guiding capability when optimized for wavelengths above 1.3 µm. In contrast, PCFs lose both their ANDi property by the transition to anomalous dispersion and their guiding capability, demonstrated by the rapid increase of the effective mode area.
It was shown that the mode count of nanohole SCFs is easily influenced by the thickness of the suspending struts with minor impact on the dispersion and that as a rough estimate a strut thickness equal to 40% of the core diameter leads to single-mode SCFs.
A fabrication technique was outlined based on the combination of fused silica capillaries fitted into a highly fluorine-doped cladding tube. Various non- to low birefringent SCFs based on three suspending struts and highly birefringent fibers based on four struts exhibiting ANDi were demonstrated.
In conclusion, nanohole SCFs are a promising concept for ANDi fibers extending the PCF capabilities further into the near infrared. The maintained convex ANDi in combination with a strong increase of the dispersion magnitude at the long wavelength side assists the concentration of generated supercontinua. An extension into the absorption range of fused silica, which starts beyond 2.2 µm wavelengths, is prevented. The optical power stays confined in the vicinity of the ANDi maximum, which assists the formation of energy-efficient finite width supercontinua with a high power spectral density.
Funding
Bundesministerium für Bildung und Forschung (03WKCV02F).
Acknowledgment
Funding in the framework of the BMBF initiative “Wachstumskern Tailored Optical Fibers” is gratefully acknowledged (https://tailored-optical-fibers.net/).
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