# Hollow-Core Optical Fibers for Telecommunications and Data Transmission
## 7 Selected Properties of HCFs
### Latency vs. Temperature and Strain  
The latency of conventional single-mode solid-core fused silica optical fiber is affected by temperature, due to the thermo-optic coefficient of glass and fiber expansion as well as the tensile strain in the fiber. Both effects are strongest in aerial cables subjected to a wide range of temperatures (e.g., \(-40\ldots\)+70 \({}^{\circ}\)C), vibrations, and variable tensile loads from wind or ice. Fiber optic cables in front haul links at radio sites are predominantly installed on masts or other structures exposed to the elements and solar radiation.  
The common solid SMF conforming to ITU-T Recommendation G.652 [29] shows a linear increase in latency with temperature; the temperature coefficient of latency is \(\approx\)37.4 ps/km\(\cdot\)K at 1550 nm for Corning SMF-28e+ fiber [30]. The same parameter for an HC-PBGF with 29.2 \(\upmu\)m core diameter and 21.4 \(\upmu\)m MFD was 2.0 ps/km\(\cdot\)K [85].  
Variations in latency have two sources. One is the increase in fused silica's refractive index with temperature, 11\(\cdot\)10\({}^{-6}\)/K, producing a latency change of \(\approx\)35 ps/km\(\cdot\)K. The second is the change in fiber length with temperature: \(\approx\)0.55\(\cdot\)10\({}^{-6}\)/K for bare fiber and \(\approx\)2.0\(\cdot\)10\({}^{-6}\)/K for fiber in 250 \(\upmu\)m primary coating. Due to the decrease in the glass refractive index with strain (elasto-optic effect), the relative change of latency is approx. 80% of the applied strain: \(\approx\)0.44\(\cdot\)10\({}^{-6}\)/K (\(\approx\)1.4 ps/km\(\cdot\)K) for bare fiber and \(\approx\)1.6\(\cdot\)10\({}^{-6}\)/K (\(\approx\)5 ps/km\(\cdot\)K) for primary coated fiber found in a typical loose-tube cable.  
Only the second mechanism of latency variations is observed in HCF, as the gas inside has negligible variations in the refractive index with temperature and pressure. Typically, only 0.003% (30 ppm) of light in NANF propagates in glass [85], and there is almost no change in the effective refractive index with fiber strain; latency changes almost exactly in proportion to fiber length. The calculated temperature coefficient of HCF is \(\approx\)0.55\(\cdot\)10\({}^{-6}\)/K (\(\approx\)1.75 ps/km\(\cdot\)K) for bare fiber and \(\approx\)2.0\(\cdot\)10\({}^{-6}\)/K (\(\approx\)6.4 ps/km\(\cdot\)K) for fiber in primary coating, if the glass/polymer cross-section ratio is identical to one in SMF. The low value reported by [PERSON] et al. [84] was measured for a fiber in a thin coating, e.g., 10 \(\upmu\)m thick.  
Due to the reasons stated above, SMF subjected to tensile strain exhibits a 20-25% smaller variation in latency compared to HCF, whose latency is directly proportional to physical length.  
When both SMF and PCF are encased in similar primary coatings made of dual layer epoxy-acrylate materials, the latency in HCF will be approx. 6 times less sensitive to temperature (18 times with thin coating), but approx. 1.25:1 more sensitive to tensile strain. For stable latency, a good protection of HCF against strain and thin coating is desired.  
Figure 19: The 90\({}^{\circ}\) rotational (**a**) symmetry in NANFs: (**a**) un-symmetrical fiber with six nested tubes, (**b**) less un-symmetrical fiber with seven nested tubes; (**c**) symmetrical fiber with eight nested tubes. Yellow lines indicate orthogonal polarizations of light.  
The measurements and modeling of comparative sensitivity of transmission delay to temperature in SMF-28 and fused silica PBGFs (Blaze Photonics HC-1550-02 and Crystal Fibre AIR-10-1550), all in typical acrylate primary coatings with outer diameters of 250 \(\upmu\)m, 220 \(\upmu\)m and 270 \(\upmu\)m, respectively, revealed similar difference, approx. 4:1 and 5:1 [86]. This indicates that the sensitivity of the delay to temperature reflects the longitudinal expansion of HCF in a particular coating, regardless of the type of photonic cladding.