2.1.1

Extrinsic

The ubiquity of fiber-based data communications is facilitated by silica’s remarkably low attenuation. While this is today considered an intrinsic property of the glass, it is only so because extrinsic sources of loss, and therefore heat, have been removed. Transition metal impurities, specifically, Cu and Fe, play the most consequential roles at communication wavelengths, which had been established in the 1970s [5,6]. To remove these extrinsic absorbers, thermodynamics in the form of vapor pressure difference between the glass (e.g., SiCl₄) and impurity (e.g., Fe₂Cl₆) precursors was employed with immediate impact. A good review of this importance, but largely forgotten amongst the current fiber community, is provided in Ref. [7]. Attenuation due to OH species in the glass have also been mitigated in long-haul fibers through judicious drying protocols involving chlorine. Modern silica fibers are essentially free of extrinsic sources of loss, hence heat generation, entirely due to the materials science of the chemical vapor deposition (CVD) process. However, as discussed in Sections 2.1.2 and 2.2, the blessings of CVD for intrinsically low loss fibers results in a curse when it comes to compositional tailorability of the fiber core [8].

2.1.2

Intrinsic

Intrinsic sources of loss in optical fibers relate to both the glass host and the active dopant (e.g., Yb, Er, Tm). As relates to the former, absorption due to electronic transitions and charge transfer at shorter wavelengths or multiphonon vibrations at longer wavelengths are the main intrinsic heat sources. While the impacts of Rayleigh scattering are captured in attenuation (e.g., cut-back) measurements, it is not, per se, an intrinsic absorption process unless the scattered light exits the fiber and is absorbed by the polymer coating. Rayleigh scattering is the principal intrinsic “loss” in silica fibers at 1 µm (Yb-doped systems), whereas Rayleigh scattering and multiphonon absorption contribute together at 1.55 µm (Er-doped systems), and multiphonon absorption dominates at 2 µm operation (Tm-doped systems), setting aside any extrinsic absorption due to the fundamental OH vibration. As noted, the CVD processes employed to fabricate modern silica-based fibers lead to base glasses that are intrinsically pure for all intents and purposes.

As relates to the active dopant, numerous phenomena contribute to heat generation including the quantum defect, multiphonon relaxations, energy transfer, and photodarkening, to name a few. The quantum defect (QD) relates to the energetic difference between the pump and emission photons and represents the theoretical minimum driver of heat generation given an otherwise lossless fiber system (i.e., not considering inefficiencies with pump diodes, coupling, etc.). While the energies of the rare-earth dopant electronic states are fairly immune to host glass composition, the spectral lineshapes can be somewhat tailored resulting in a quantum defect from Yb, for example, that can range from about 8% to less than 1% [8]. Multiphonon relaxation results from electron-phonon coupling between the excited rare-earth dopant ion and the host glass phonons. For example, the highest energy Si-O vibration in silica glass occurs at an energy of about 1100 cm^-1. Accordingly, whereas 5 phonons are required to non-radiatively relax an electron across the ⁴I_13/2 to ⁴I_15/2 energy gap in Er³⁺, which yields the 1.55 µm emission, 9 are required to bridge the ²F_5/2 to ²F_3/2 transition in Yb³⁺, which yields the 1 µm emission, for example, making Yb more radiatively efficient. In fairness, the erbium emission at 1.55 µm is also quite efficient from a practical sense, so this illustration is more for relative considerations.

Energy transfer and photodarkening may result when rare-earth ions cluster at higher dopants concentrations. A degradation in laser performance occurs via energy transfer when the excited electron migrates from dopant to dopant in close proximately, ultimately non-radiatively relaxing when it encounters an (extrinsic) impurity or (intrinsic or extrinsic) defect or color center. Photodarkening can occur when excitation energy is cooperatively upconverted and creates color centers in the glass host, leading to added attenuation over time (or optical power). As ion clustering is fundamentally thermodynamic in origin [9], it is noted here as an intrinsic source of loss, hence heat.

Lastly, it is worth noting that optical nonlinearities, such as stimulated Brillouin scattering (SBS) and stimulated thermal Rayleigh scattering (STRS [2]), can also be considered intrinsic sources of loss as they nonlinearly convert signal energy or power to other wavelengths or propagating modes that can subsequently be absorbed or facilitate other parasitic effects, such as TMI. Such nonlinearity scattering phenomena are also fundamentally thermodynamic [10].

2.2.1

Low reduction in modern long-haul telecom fibers

The performance of an optical fiber is dependent on both the waveguide design and the materials from which it is made. But, as noted above, glass is not “just glass” and the process by which the glass is made, specifically its time / temperature history, may also be deterministic. Here, the on-going effort to reduce attenuation in long-haul fibers, even by small fractions of a dB/km, is a good exemplar of this thermodynamic / kinetic balance. As represented well in Ref. [11], the development of “ultra-low loss” fibers (attenuation below 0.15 dB/km) was predicated on reducing the Rayleigh scattering of the pure silica glass core. This was done through thoughtfully controlling the cooling rate of the fiber to permit greater relaxation of the glass network, thus reducing the distribution of ring structures. Materially, this reduces the fictive temperature of the glass, which lessens both the compositional and density contributions to Rayleigh scattering [10]. While Rayleigh scattering is not normally a source of heat in fibers, nonetheless, that the attenuation of the pure silica core depend on cooling rate is proof-positive of kinetics at play.

2.2.2

Compositional limits in CVD optical fibers: The aluminosilicate system

A second important consideration as relates to optical fiber generally, and heat generation specifically (though, perhaps, not obviously), is the compositional limit of the core glass. As noted, the properties of glass depend on (1) its thermal history and (2) its composition. However, these two are themselves casually related. The range of glass-forming compositions can be tailored by how the glass is fabricated and processed, i.e., its time / temperature history. This is represented in Figure 1. Figure 1(a) shows the equilibrium (i.e., thermodynamic) phase diagram for the (crystalline) SiO₂-Al₂O₃ system. There is a well-defined liquidus (melting point) for each composition. Shaded in blue is one of two immiscibility regions where system will phase separate into silica-rich and alumina-rich regions. This is critical because it defines the maximum concentration of Al₂O₃ that can be added to SiO₂ and still form a homogeneous material. Figure 1(b) provides a representation of the time / temperature profile for two CVD processes (modified chemical vapor deposition, MCVD) where the doping is performed either using a solution (“solution doping”) or metal-organic chelate vapors (“chelate doping”). Clearly observed are differences in both the time and the temperature of the various process stages from the start of the preform (time = 0) to the finished collapsed rod (time where data ends). The temperature ordinate in Figure 1(b) is scaled to align with the temperature ordinate of Figure 1(a) for the reader to see how the process temperature overlay against the melting temperatures and immiscibilities. Lastly, Figure 1(c) approximately presents the maximum Al₂O₃ concentration that can be added to SiO₂ for several different processes, their maximum process temperature, as well as melting points and viscosities. Similar limits exist for other dopants into silica [8]. In truth, it is best to consider each composition a fundamentally different glass since all the thermal and physiochemical properties are different. Further, it is worth remembering that glass does not per se have a melting temperature since, above the glass transition temperature, the viscosity changes continuously with temperature. Here, too, the fact that the maximum concentration of alumina prior to phase separation is dependent on processing conditions speaks to the kinetic qualities of glass.

Figure 1.

Thermodynamic and kinetics effects in the SiO₂-Al₂O₃ system. (a) The SiO₂-Al₂O₃ equilibrium phase diagram with colored overlay of the high-silica content immiscibility region where phase separation can occur. Reproduced with annotations with permission of John Wiley & Sons and the American Ceramic Society (2022). (b) Representative time-temperature profiles for MCVD with solution doping (“solution doping”) compared to that for chelate doping (“chelate doping”). The temperature ordinate is aligned with that from (b) so one can better understand how the processes relate to the thermodynamic phases and phase behaviors. (c) A relative comparison of processing temperature as a function of permissible Al₂O₃ concentrations for various glass processes, including the liquidus temperature (red curve) and log viscosity of the melt (yellow curve with dotted data points). Underlying data from Refs. [12-16].

This is relevant to heat generation since clustering of the active rare-earth dopant facilitates energy transfer, concentration quenching, and photodarkening. While there are always glass forming limits, understanding the kinetic aspects of the material system and method of manufacturing offer tools to enhance performance.