We study novel designs of hollow-core antiresonant fibers comprising multiple materials in their core-boundary membrane. We show that these types of fibers still satisfy an antiresonance condition and compare their properties to those of an ideal single-material fiber with an equivalent thickness and refractive index. As a practical consequence of this concept, we discuss the first realization and characterization of a composite silicon/glass-based hollow antiresonant fiber.
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After almost two decades of improvement in fiber technology, the development of hollow-core optical fibers (HCs) [1,2] is still very active. In particular, the use of hollow fiber structures comprising only a limited number of detached glass tubes within an outer glass jacket is gaining significant interest [3,4]. The use of this fiber type has resulted in HCs with relatively low attenuation in the visible [5,6], near [7–9], and mid-infrared spectral ranges , combined with ultra-large transmission bandwidths [5,8,9]. Possible applications of these hollow antiresonant fibers (ARFs) range from high-power laser delivery  to gas-based laser sources  and telecommunications .
Several modifications of this basic fiber design have been proposed [5,11–15] in order to further reduce their level of leakage loss or increase their birefringence. However, all of the previous designs and fabrication proposals have concerned ARFs made of a single material (typically silica, even though other glass materials have also been considered [16,17]). In this Letter, we seek to explore a novel form of this ARF type by using, for the first time (to our knowledge), multiple materials for the fiber cladding. We numerically study the transmission properties of these composite-material antiresonant fibers (CM-ARFs) by correlating the composite-material membrane properties to that of a “single equivalent membrane,” with an identical effective thickness and refractive index. We apply this concept to the design of a novel form of ARF by adopting a hybrid semiconductor/glass-core-boundary membrane. As in previous works on semiconductor optical fibers [18,19], the inclusion of a semiconductor is desirable in order to realize functionalized devices. For example, a light induced refractive index change may be adopted for all optical fiber modulation . We numerically demonstrate that, in contrast to previous structures with silicon in the cladding area , this novel type of silicon antiresonant fiber is predicted to have very low attenuation (). Finally, we report on the first fabrication and characterization of a silicon/borosilicate based ARF.
Figure 1 shows a reproduction of a silica-based ARF ( at ) already fabricated in Ref.  with 10 cladding tubes and an original thickness of the cladding tubes (in white). The core radius is 47 μm. An additional internal membrane (in red) is added corresponding to a material with refractive index .
The dependence of leakage loss on the additional thickness , shown in Fig. 1 at a wavelength of 2.7 μm, clearly demonstrates the antiresonant properties of this CM-ARF. In the following, we will refer to an “antiresonant layer” as that additional membrane with a thickness corresponding to the minimum leakage loss of the single-layer ARF (see Fig. 1).
Figure 2(a) shows the evolution of the leakage loss when additional antiresonant glass membranes (2t, 3t, or 5t) are added to the basic structure. This behavior is almost identical to that of fiber designs shown in Fig. 2(b) where the thickness of the initial single-silica membrane is simply increased 2, 3, or 5 times (red, black, and blue curves). In particular, the fiber designs of (a) and (b) have the same resonant wavelengths and the same minimum leakage level. This is not surprising since the designs of Fig. 2(b) can be simply seen as multiple layers [of the type (a)] with the same refractive index for the alternating layers (). By using the basic formulation of the resonant wavelength , it is possible to derive that the frequency spacing between two resonant frequencies is2 of a different number of resonant wavelengths associated with the different number of antiresonant layers in the considered structures. The small differences between the spectra of Figs. 2(a) and 2(b) are associated only with the different optical couplings between the fundamental-like modes transmitted in the fiber core and the different cladding modes present in the two structures .
We can further extend the analogy between Figs. 2(a) and 2(b) by correlating the behavior of a CM-ARF made of two materials (with refractive index and , and thickness and ) to that of a single-material ARF with an equivalent refractive index and thickness . We define3): 3). As an example and validation of this equivalence, we have considered the case of two materials with and (, , ). By using Eqs. (2)–(5), it is possible to obtain and . By looking at Fig. 3, we can see that the leakage loss of the CM-ARF (blue line) and the equivalent ARF (red line) overlap in most of the considered spectral range. A slight difference between the two spectra is more evident at longer wavelengths where the fundamental mode interacts more strongly with the fiber-cladding modes. The behavior of the equivalent structure is the same even when the fiber is bent with a bend radius greater than 10 cm.
The established analogy between a composite-material and a conventional single-material ARF suggests that only the overall optical path travelled by light at the core boundary is relevant for antiresonance guidance. This opens up the possibility to exploit the properties of additional materials deposited on the basic optical fiber matrix in order to activate and functionalize its behavior, for example, via the free carrier plasma-dispersion effect, in which the change of refractive index and absorption resulting from a change in the concentration of free carriers by photo-excitation can be used in silicon-based, all-fiber integrated modulators to achieve intensity or phase modulation . As a first step of this “active hollow-core waveguide” concept, we have investigated the feasibility of a particular form of CM-ARF, in which the core-boundary membrane is made of a composite hybrid semiconductor/glass material. Semiconductor optical fibers  have received great attention in recent years because of the prospect for integration of the existing optical fiber infrastructure with the novel silicon photonics platform . Since the first inclusions of semiconductors within optical fibers , progress in the area has seen some demonstrations of optical devices . Although potentially these structures may provide unique characteristics, their use is currently limited by the very high attenuation observed to date in these fibers (of order 1 dB/cm). Here we show that this problem can be mitigated by filling semiconductors within ARFs. Figure 4 shows a typical section of a borosilicate-based ARF  filled with amorphous hydrogenated silicon (a-Si:H) by using a high-pressure chemical vapor deposition (HPCVD) method .
The CM-ARF of Fig. 4(a) was obtained after a deposition of 48 h at a temperature of 400°C and has three layers of material [silicon (white)/borosilicate (gray)/silicon (white)]. The Si layer thickness was measured using the SEM to be close to 300 nm.
We then tested several types of ARFs by using the same HPCVD technique and modifying the temperature profile along the fiber samples, as well as the filling time. The fiber shown in the inset of Fig. 4(b) (core diameter and glass layer thickness of 1 μm) was coiled in a furnace at a temperature of 450°C and filled for only 4 h in order to obtain a very thin a-Si:H layer thickness. A length of 35 cm of this fiber was obtained and tested.
We could reveal the presence of a thin layer of a-Si:H by means of Raman spectroscopy. Figure 4(b) shows the Raman shift spectrum taken using the sample in the inset [shown in its longitudinal section (A) and transversal section (B)] and using an optical pump at a wavelength of 0.63 μm. The Raman shifts at the points centered on the external and internal sides of the cladding tubes confirm the presence of a-Si:H .
The spectrum of the signal transmitted through the considered 35-cm-long sample is shown in Fig. 5 together with the near-field intensity profile recorded by an infrared camera. In the considered spectral range (0.7–1.6 μm), the CM-ARF has two transmission windows (just above 0.8 μm and around 1.2 μm) and presents several peaks probably related to the coupling of the fundamental-like mode (in the inset) to the cladding modes, in both the two high refractive index () layers.
In Fig. 6(a), we have compared this measured transmission spectrum (blue solid line) with that of 7 meters of the same ARF without any silicon filling (green solid line; glass thickness is 1 μm, and glass dispersion is taken into account) and the calculation of the leakage loss for both the filled CM-ARF (black dotted line) and the unfilled ARF (red dotted line). Our simulations show how the addition of the internal and external silicon layers to the original ARF results in a red-frequency shift of the entire transmission spectrum. Figure 6(b) shows what would be the effect on the leakage loss of a variation of the coating thickness of , proving that the fiber attenuation levels would be kept similar, but there would be a shift of the resonant wavelength ().
In order to show the impact of the optical absorption of the a-Si:H layers on the fiber performance, we have compared in Fig. 7 the attenuation components of the CM-ARF. The fiber attenuation related to the presence of a glass (red line) and silicon (green line) material absorption is obtained as the product between the optical mode overlap on each material and their intrinsic absorption. Concerning this last quantity, we have measured the borosilicate glass absorption to be maximum 140 dB/m, and we have assumed a high absorption of the amorphous silicon material of 100 dB/cm.
The results show that, for the considered fiber, the leakage loss (blue line) is the most important contribution to the total attenuation of the CM-ARF and demonstrates the negligible impact of the absorption of the deposited semiconductor. As shown in Fig. 7, levels of attenuation as low as 0.1 dB/m or less may be obtainable in long CM-ARFs.
In conclusion, in this work we have demonstrated that CM-ARFs have the same characteristics of single-layer ARFs. We have formulated an equivalence between single-layer and CM-ARFs. By using this concept, we have fabricated and characterized the first silicon-based ARF, showing the potential of this platform for the realization of semiconductor-based devices with low attenuation. The exploration of this new avenue of research may lead to the implementations of novel forms of composite (glass/semiconductor) devices based on HC optical fiber technology with intriguing prospects in the broad fields of optical sensing, communications, light, generation and manipulation. (Datasets at http://doi.org/10.5258/SOTON/D0046.)
Engineering and Physical Sciences Research Council (EPSRC) (EP/I01196X/1, EP/I035307/1).
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