Fundamentals of optical fibers

Introduction

Optical fibers are now key components of highcapacity telecommunication networks. They are the result of 30 years of work by major glass and telephone companies. Millions of kilometers are produced every year at a very low cost (2-3 ¤ cents). They are a good example of an industrial success story, combining a challenge, doubts, errors, and luck.

The concept of an optical fiber is probably very old, and the transmission of light through glass rods and filaments was already known by the glass makers of ancient Mediterranean civilizations. In 1870, the British scientist John Tyndall1 published the first scientific record of light guiding. In the 1950s, active research was carried out by Kapany with regard to transmitting images through bundles of various types of glass fibers.2 Between 1951 and 1966 most theoretical and experimental questions were addressed, laying the basis for the approaches to follow.3 Over the next 20 years, the key issue remained the manufacture of ultra-high-purity silica fibers. A milestone was reached one day in 1980 when the attenuation of a glass fiber was lowered to 20 dB/km, comparable to the damping an electric current undergoes in a copper wire. This was due to the use of the vapor phase deposition process which had been further improved, resulting in a spectacular decrease in fiber loss.4

The development of optical telecommunications has stimulated the use of optical fibers in other fields, such as manufacturing, sensing, instrumentation, imaging, and medicine.5 In addition to standard telecommunication fibers, a wealth of special fibers has been developed for applications as diverse as metal welding, spectroscopy, imaging, la-

ser surgery, non-invasive optical diagnosis, etc. In the long term, it cannot be excluded that important fiber applications will emerge in fields other than telecommunications.

What is an optical fiber?

Fiber structure

An optical fiber is a waveguide: a beam of light launched at one end of an optical fiber travels down the output with negligible loss. This is illustrated in Figure 1. The optical fiber is made from two transparent materials, usually types of glass: the core and the surrounding cladding. The cross-section of most optical fibers is cylindrical, but other geometrical forms (rectangular, flower-shaped, D-shaped, honeycomb, etc.) have been developed to meet particular needs. A light beam that enters the fiber core is refracted according to Snell’s law:

θo, θi, n0, and n1 are, respectively, angle of incidence, angle of refraction, refractive index of air, and refractive index of core.

As long as the input angle is smaller than the limiting value θc, the refracted beam is totally reflected at the interface between the core and cladding glasses.

Provided that the condition for light guiding is fulfilled n2 < n1, (n2 is the refractive index of cladding), and as long as the incident angle is smaller than a critical value θc, the refracted beam is totally reflected at the interface between the core and the cladding. The incident angle θc corresponds to the

Fig. 1. Light propagation in an optical fiber.

maximum angle of total reflection at the core/cladding interface and therefore only depends on n1 and n2:

This sin θc value is usually referred to as the numerical aperture (NA) of the fiber. The larger NA, the larger the light gathering power of the fiber. Typical values of NA are 0.12 for telecommunication fibers, 0.20 or larger for instrumentation fibers.

It should be noted that the retina of the human eye is made up of a large number of rods and cones having, to a large extent, the structure of an optical fiber: a dielectric cylindrical rod, a few micrometers in diameter, surrounded by a dielectric layer of slightly lower refractive index.6

Light guiding has also been demonstrated with metal pipes in which light is reflected onto the walls. However, a fraction of the beam is lost at each reflection on the metallic surface. Even with mirror quality polish, the beam is strongly attenuated after a few hundred reflections. In comparison, the damping undergone at each reflection of a beam zigzagging in a glass fiber is negligible.

Single mode and multimode optical fibers

A beam that propagates in an optical fiber is only allowed to travel a finite number of pathways, the so-called modes. The number of modes allowed depends on the geometry of the fiber, its numerical aperture, and the wavelength of the light beam. Analytical descriptions of the modes are derived from Maxwell’s laws in the weakly guiding approximation, which is the case for fibers of relatively low numerical aperture.

In a multimode fiber, low order modes correspond to beams propagating along the fiber axis, while higher modes are characterized by larger θo angles. Path lengths are different for the various modes, and are shorter for the lower modes that require a shorter time to reach the fiber output. For this reason, the temporal width of light pulses is enlarged after transmission through a multimode

fiber. The different modes can easily be seen when an helium-neon laser is coupled to a multimode fiber: the output beam is no longer homogeneous and gives a set of distinct spots when shone on a white screen.

The number of different modes depends on core size, NA, and wavelength of the light. Single mode propagation is observed when the core diameter is small enough: this is the case for telecommunication fibers operating at 1.5 µm in which the core size is less than 10 µm. Single mode fibers are not only used for telecommunications, but also for special sensors and interferometric devices. However, light insertion in a small core is difficult, especially when coupled to an external laser source. An additional limitation is caused by the high energy density in the fiber core.

Graded index fibers make up the third group of optical fibers. The interface between core and cladding glass can be described as a thick tube in which the value of the refractive index decreases continuously from n1 to n2. This design partly compensates for the path differences between the high and low modes. As a consequence, the beam shape is closer to the gaussian profile than in a simple multimode fiber.

Evanescent waves

It may seem useless to have a cladding glass in an optical fiber since most transmissions take place in air that has a refractive index close to 1, which ensures light guiding. Indeed, there are numerous examples of single index fibers. However, these have serious limitations. The main reason lies in the refraction process at the interface between the two media of the respective refractive indices n1 and n2. Although geometry suggests that a light beam is entirely confined in a fiber core, Maxwell’s relationships show that electric and magnetic fields enter the cladding zone, with two major consequences: they may be subject to physical interactions leading to optical absorption, and they may escape into the outer medium when some conditions are fulfilled. In practice, optical losses are generated at contact points between bare fibers and

holders; image transmission through bundles of single index fibers suffers from crosstalk between the adjacent fibers. Thus, it is necessary to insulate each fiber with optical cladding, the thickness of which depends on light wavelength and propagation modes. In multimode fibers, low modes are confined to the core, while higher modes penetrate deeper into the outer cladding.

Optical transmission

The major requirement of an optical fiber is its ability to transmit light with minimal attenuation. Normal optical components have a thickness of less than 1 cm, and the emphasis is on glass homogeneity rather than on high transparency. Specifications for optical fibers are more severe since thickness is exactly fiber length, i.e., meters or kilometers. The expression of transmitted light follows Beer’s law:

Fig. 2. Evolution of the theoretical losses of pure silica versus wavelength.

where Io and It are the respective intensities of the incident and transmitted beams, x is the path length, and α the absorption coefficient. If a given transmission factor is required, the value of α should be 100,000 smaller for a 1-km fiber than for a 1-cm window. The α value of the fibers is expressed in decibels per meter or kilometer, dB/m or dB/km. For example, the transmission factor of a two-meter long fiber with a 0.5 dB/m attenuation is 80%, as 1 dB loss corresponds to 80% transmission.

Intrinsic losses

An ideally pure material has a transparency range which is limited by three loss mechanisms: electronic absorption in the UV-visible spectrum, lattice vibrations in the infrared, and Rayleigh scattering. This is exemplified by Figure 2 which shows the typical V shape of the theoretical losses of pure silica. Each material has a specific curve which correlates closely with its chemical composition and structure. The transparency range of silica and other oxide glasses encompasses the visible and near-infrared spectrum. Other materials are required for use at wavelengths greater than 2 µm.

Extrinsic losses

Real materials contain a set of impurities and defects that limit their performance. Large optical absorption arises from transition metal impurities (Cr, Fe, Co, Ni, Cu, rare earths), even at the subppm level. Anionic impurities such as hydroxyls OH or complex anions (sulphates, phosphates, etc.) are another source of optical losses. Finally, local defects, such as inclusions and bubbles, induce light scattering. The resulting absorption coefficient may be expressed as:

where K is a constant, and exponent n can have different values: n = 0, corresponding to wavelength independent scattering, for defects larger than the wavelength, n = 4 for much smaller defects, and n = 2 (Mie scattering) for intermediate defects.

Defects may be randomly distributed along the fiber, more abundant in the cladding or at the core/ cladding interface. Both defects and residual impurities have been drastically reduced in silica fibers, by means of vapor phase processes. Fiber quality is more difficult to achieve in multicomponent and exotic glasses.

Insertion losses

Coupling light from an external source, e.g., a laser, to an optical fiber can be tricky, especially when a high coupling efficiency is desirable. Coupling is carried out using a focusing lens or a mirror. In addition to Fresnel losses at the input end, part of the beam will escape into the cladding if the spot size or the angle of the focused beam is too large. The problem is less severe in multimode fibers because the core diameter may be large (e.g., > 100 µm). However, the beam profile at the output may be irregular, the more so as some propagation modes change when the fiber is moved.

Power transmission

Optical fibers are currently in use for laser power transmission, especially with industrial Nd:YAG lasers operating at 1.06 µm. The maximum power density is limited by fundamental phenomena, and there is a damage threshold for a given material at a given wavelength. In practice, this threshold is larger than current requirements, but various de-

fects or external factors may promote fiber failure upon laser exposition.

In the ideal situation, all laser energy is transferred to the fiber. In actual cases, the lost energy is a source of worry, not only because the cost of the laser increases in relation to the energy produced, but also because this lost energy will finally heat the fiber or the surrounding area. The first obvious requirement is that the laser power may not enter the polymeric cladding in the coupling area. While the optical attenuation of the fiber at the laser wavelength is an important factor, it is not the most critical. Point defects with a strong absorption coefficient, e.g., carbon and metal inclusion, are rapidly heated under laser irradiation. Fibers may melt and break locally. These defects also scatter light into the cladding and polymeric coating that protects the fiber. If the scattered intensity is great, coatings may be destroyed and fibers damaged. Fiber ends are critical areas because various impurities may be deposited onto them. These impurities contain water and carbon that have an active part in the failure mechanism.

In practice, fibers for laser power transmission are optimized to minimize the absorbing defects,

and they are packaged in order to protect input and output ends from external grime and pollutants.

Fiber fabrication

Drawing a fiber from a glass rod is a simple exercise, which was already known in ancient Egypt, and is routinely achieved by glass artists or chemistry students. However, the manufacture of an optical fiber requires rigorous control for any contamination factors. Silica fibers are made by drawing high purity preforms at 2000°C using the setup schematically described in Figure 3. Preforms are rods in which the central part consists of a core glass of a higher index of refraction, while the external part is made from cladding glass. These preforms are prepared by a vapor phase process in which silicon chloride reacts with gaseous oxygen. This results in a very high purity material which contains extremely low levels of metal impurities and hydroxyl. Variations of the refractive index are achieved by modification of the vapor composition: germanium, phosphorous, and fluorine can be incorporated in this way. High quality preforms can

Fig. 4. Double crucible for drawing fibers from the glass melt.

be made by using other forms of chemical processing, for example, sol-gel. Preforms of low melting glasses can also be prepared by inserting a rod into a cladding tube or by using other classical methods of glass manufacturing. This is the case for fluoride, borosilicate, germanate, and chalcogenide glasses.

Optical fibers may also be drawn directly from the melt using the double crucible method. Both core and cladding glasses are heated in two concentric crucibles at a temperature for which melt viscosity is large enough. Then a step index fiber can be drawn from the bottom of the double crucible, as shown in Figure 4.

Special glasses are sometimes difficult to draw into fiber because of their tendency to devitrification. These problems are solved by adjustment of the composition of the glass and optimization of the process.

An external polymeric coating is applied to protect the fiber from scratching, to limit the chemical attack of water, and to increase the mechanical strength. Epoxyacrylate resins are the normal coatings, but other polymers such as silicones and polyamide can also be used. Despite their hydrophobic properties, fluorinated polymers (PTFE, FEP) do not create an efficient barrier against hydrolysis, and lead to weaker fibers.

Special techniques are used for growing sapphire

and polycrystalline fibers. While the pulling rate is much slower than for glass fibers, this is not a serious problem for short length applications. Hollow core fibers are made from capillaries internally coated with dielectrics under controlled thickness.

Choice of fiber

Material

Choosing the optimum optical fiber for a specific use may be an obvious task or a subtle exercise in the balance between various parameters: attenuation, reliability, toxicity, availability, and cost. Fibers from different materials can be used depending on choice criteria.

Silica fibers offer a unique set of advantages: lowest attenuations, good mechanical and chemical resistance, transparency range extending from 300 nm to 2 µm. Silica fibers for telecommunications are inexpensive, but the cost increases when a particular size and NA are needed, requiring the manufacture of special preforms. Special silica fibers have been developed for UV transmission, either doped with OH or made from fused quartz.

When low attenuation is not important, glass fibers made from borosilicate glass or polymer fibers (PMMA) are a cheaper alternative choice for use in the visible spectrum.

Transmission in the mid-infrared spectrum cannot be achieved with silica. This is the case at 3 µm at the emission wavelength of the Er:YAG laser. Possible choices include fluoride fibers made from fluorozirconate glass, germanate glass, and sapphire. This latter material is crystalline, which raises the problem of the optical cladding. Such fibers can be used up to 4-5 µm. Fluoride fibers have low attenuation, as shown in Figure 5.

Other materials are required at longer wavelengths.7 Fibers made from sulphide can be used up to 8 or 9 µm, and heavy chalcogenides (Se, Te) glasses allow transmission above 10 µm. However, they still have limitations with regard to optical

Fig. 5. Optical losses from a standard fluorozirconate glass fiber (from Le Verre Fluoré SA).

losses and toxicity problems. Polycrystalline fibers made from silver halides and hollow core fibers have been developed as an alternative to these chalcogenide fibers at 10.6 µm. Even when fibers are designed for IR transmission, it is useful if they can also transmit visible light: the He-Ne laser beam at 633 nm is currently being used for alignment or for checking the delivery area.

Fiber reliability

As a general rule, the lifetime of the fiber mainly depends on chemical durability and applied stress. Failure corresponds to breaking, which happens as a crack propagating from a surface flaw. Real fibers have surface flaws resulting from their processing. The initial intrinsic strength of a fiber is related to its chemical composition, and ultimately to the chemical bond energy. Current values are 4 GPa for silica fibers and less than 1 GPa for fluoride and sulphide fibers. The initial strength decreases versus time when the fiber is subject to stress corrosion, or, put more simply, under permanent stress in a humid environment. This phenomenon has been extensively studied in silica fibers.8

As the main characteristic of a fiber lies in its flexibility, it will be moved and bent during operation. The minimum bending radius must be defined. This depends on fiber material and diameter: it is small (a few millimeters) for silica fibers, but it is larger for fluoride, chalcogenide, and polycrystalline fibers.

The aging of fibers used for laser transmission also depends on the evolution of internal and end defects under laser irradiation. This aging effect is minimized if the defect density is low enough, and if water concentration and residual stress are controlled.

Apart from worsening surface flaws, water has little influence on oxide glasses, which are insoluble and remain transparent. However, things are different for some glasses, such as phosphate and halide. The chemical action of water can weaken the fiber and reduce transmission if its ends and outer surface are corroded. Direct contact with liquid water must be avoided, and various solutions have been successfully employed in harsh environments.

Current fiber applications

Apart from their use in signal transmission for telecommunications, fibers are also being used in an increasing number of devices. The availability of non-silica fibers has expanded the field of the possible applications.9 Passive and active applications were already foreseen in the early stages of the development of fiber optics.3 The first group of

applications covers optical fiber sensors, remote chemical analysis, thermal measurements and imaging, reflectometry, optical instrumentation, and also laser power delivery. Most medical applications of fibers, with their specific requirements, belong to this group. These could be expanded very significantly when technological progress leads to the discovery of cheaper disposable fibers.

Active fibers are doped fibers from which a laser effect or amplification can be obtained. The large interaction length of the fiber, and the high energy density that can be used for optical pumping, are the main features supporting the development of active fiber devices. Another attractive point is the possibility of generating short wavelength signals using IR laser diodes as pump sources. Powerful laser fibers can be built in this way with very good beam quality, which is more difficult to achieve with semiconducting lasers. Cost aspects and reliability still limit practical applications, but significant changes are likely to occur in the comingyears. Solid-state and compact-fiber lasers could come to replace the large, noisy gas lasers.

Conclusions

Optical fiber technology has opened the door to a large number of applications, i.e. metal welding, spectroscopy, imaging, laser surgery, non-invasive optical diagnosis, etc. This is possible due to the fact that attenuation of light energy is extremely low, namely 20 dB/km, comparable to the damping an electric current undergoes in a copper wire. Here, the fiber structure and its optical performance are analyzed together with its various applications.

References

1.Tyndall J: Proceedings of the Royal Institution of Great Britain 1:446, 1854

2.Kapany NS: Fiber optics. Part 1. Optical properties of certain dielectric cylinders. J Opt Soc Am 47:413, 1957

3.Kapany NS: Fiber Optics: Principles and Applications. New York, NY: Academic Press 1967

4.Miya T, Terunume Y, Hosaka T, Miyashita T: An ultimate low loss single-mode fiber at 1.55 µm. Electronic Lett 15: 106-108, 1979

5.Katzir A: Lasers and Optical Fibers in Medicine. New York, NY: Academic Press 1993

6.Enoch JM: Wavaguide modes in retinal receptors. Science 133:1353, 1961

7.Kokorina VF: Glasses for Infrared Optics. New York, NY: CRC 1996

8.Matthewson MJ, Kurkjan CR: Environmental effect on the static fatigue of silica optical fiber. J Am Ceramic Soc 71:177-183, 1988

9.Poulain M: Fluoride glass fibers: applications and prospects. Proceedings SPIE 3416:2-12, 1998