# Hollow-Core Optical Fibers for Telecommunications and Data Transmission
## 10 Splicing and Termination of Hollow-Core Fibers
### Splicing HCF to SMF  
In terms of reducing the collapse of the cladding in HCF, HCF-SMF fusion is easier than that of two HCFs, because the arc can be offset from the fiber's contact plane, directing most of the heat towards the solid fiber free of voids prone to collapse. This arrangement reduces the maximum temperature and damage in the HCF, and its efficiency has been proven with a large variety of microstructured fibers [101; 107].  
[PERSON] et al. [100] spliced SMF to NKT HC-1550-02 HC-PBGF [35] using a conventional arc fusion splicer by pumping pressurized nitrogen into HCF, completely preventing the collapse of the photonic cladding at 165 kPa internal pressure; however splice loss was still high, 1.05 dB, despite HCF and SMF-28 having a similar MFD: 9.0 \(\upmu\)m and 10.5 \(\upmu\)m, respectively.  
The rotational alignment of fibers is not required due to the radial symmetry of SMF. However, the parameters of splice between HCF and SMF are degraded by:  
* Fresnel reflection;
* MFD mismatch of fibers (see data in Tables 2 and 3).  
Fresnel reflection at the interface between media with refractive indices n\({}_{1}\) and n\({}_{2}\) introduces the following return loss RL and reflection-related insertion loss ILR:  
\[\text{RL}=-20\text{log}[(\text{n}_{1}-\text{n}_{2})/(\text{n}_{1}+\text{n}_{2 })], \tag{10}\]  
\[\text{IL}_{\text{R}}=10\text{log}\{1-[(\text{n}_{1}-\text{n}_{2})/(\text{n}_{ 1}+\text{n}_{2})]^{2}\}\text{ [dB]}. \tag{11}\]  
For a butt-coupling between cleaved HCF (n\({}_{\text{eff}}\approx\)1.005) and SMF (n\({}_{\text{eff}}\approx\) 1.465) with identical mode field diameters, we obtain RL = 14.60 dB and IL = 0.15 dB.  
When two fibers with different mode field radii \(\omega_{1}\) and \(\omega_{2}\) are joined with perfect alignment, the joint exhibits MFD-related component of insertion loss ILM:  
\[\text{IL}_{\text{M}}=-20\text{ log}\left[(2\omega_{1}\omega_{2})/(\omega^{2} _{1}+\omega^{2}_{2})\right]\text{ [dB]}. \tag{12}\]  
ILM rises super-proportionally with the MFD ratio, as shown in Figure 21. When it is high, such as 2:1, which is typical when splicing SMF to NANF (Table 3), it is beneficial to insert a short length of fiber with intermediate MFD and make two splices instead of one (Figure 20b). While a single splice between fibers with 1:2 MFD ratio has the lowest loss, 1.94 dB, two splices between fibers with a 1:\(\surd\)2:2 MFD ratio have a combined loss of 2:\(\surd\)51 = 1.02 dB.  
ILM can also be reduced via the thermal expansion of SMF core at the tip to be joined with HCF by prolonged heating to cause a diffusion of the GeO\({}_{2}\) dopant into areas adjacent to the core, thus increasing the core's diameter and the fiber's MFD [33].  
Both components of insertion loss add up: IL = ILR + ILM.  
There is work on other techniques like the insertion of graded index (GRIN) lens between cleaved fibers, and fixing fibers via gluing instead of fusion. [PERSON] et al. [108] reported a joint loss as low as 0.30 dB between Corning SMF-28 (MFD = 10.4 \(\upmu\)m @ 1550 nm) [30] and HC-PBGF (31.4 \(\upmu\)m core diameter, MFD = 21.1 \(\upmu\)m @ 1550 nm) fibers with an MFD ratio of 1:2.03. A 0.295 mm long GRIN lens made of 62.5/125 \(\upmu\)m OM1 multimode fiber, with anti-reflection coating, served as mode size converter, with its length being critical. Its reflectivity was \(\leq-30\) dB. The same team later joined SMF-28 fiber to a six-tube NANF (MFD \(\approx\) 24 \(\upmu\)m) in a similar way, achieving a loss as low as 0.16 dB [84], of which half was attributed by the authors to the non-circular shape of the mode field in the NANF (Figure 18). This time, the GRIN lens was made of 50/125 \(\upmu\)m OM2 multimode fiber. Reflectivity was reduced below \(-40\) dB over a 60 nm bandwidth. Another MFD adaptation technique successfully tested was the inclusion of a short length of commercially available SMT-28 fiber with a core thermally expanded to MFD = 24 \(\upmu\)m; the loss of joint was 0.21 dB.