Fiber_Optics_Physics_Technology

What little loss remains in optical fibers is indeed fundamental to fused silica, as detailed in Chap. 5. There have been approaches to reduce loss even further by using other glass types. On theoretical grounds, chalcogenides, fluorides, and halides hold promise to have dramatically lower loss figures than fused silica. Unfortunately, such theoretical considerations never made it into a realization. Production of such fibers is fraught with problems arising from their chemical nature: It is extremely di cult to obtain good purity of a highly reactive substance. Today significant progress in that direction is not anticipated.

Our quick survey would not be complete without mentioning optical nonlinearity. Since the early 1980s, researchers have investigated the nonlinear properties of optical fiber. The term refers to the situation that some optical property of the fiber, such as the refractive index, depends on the intensity of the light wave passing through it. Nonlinearity does not occur in copper cables (at least not to any noticeable degree, anyway), but clearly manifests itself in fibers. This was considered a nuisance for a long time, but today it is increasingly realized that it is precisely the exploitation of nonlinear e ects that allows a new generation of fiber-optic transmission systems, which turns out to be vastly superior to previous technology in its data-carrying capacity. We mention here only in passing the concept of solitons, special light pulses that maintain their shape not in spite of the presence of nonlinearity but due to its presence. In Chaps. 9 and 10, we will discuss nonlinearity and solitons in greater detail.

In some sense, today’s fiber-optic networks have many aspects in common with the telegraph networks of earlier days: either has both attenuation and dispersion; these two represent the biggest practical problems. One can beat attenuation by inserting repeater stations into the fibers at intervals of 50 or 100 km or so. The novelty in fiber optics is that there is nonlinearity, and it causes e ects unknown to electrical systems engineers. Meanwhile, however, the first commercial systems exploiting and embracing nonlinearity and solitons have taken up service, and it can be anticipated that more is yet to come.

We must also point out now that optical telecommunication is by no means the only field of application of fibers. Beyond their enormous data-carrying capacity and great reach, they represent other specific properties that make them attractive for use in data acquisition systems.

One of these properties is the enormous savings in weight, as compared to copper wire. One does not so much realize it by comparing the densities (copper: 8.9 kg/dm3, fused silica: 2.2 kg/dm3) because equal volumes are hardly a relevant basis for comparison. There are protective jackets around both kinds of cable, both for mechanical protection and electrical insulation. These jackets represent the lion’s share of the cable’s mass (bare fiber weighs in at just 30 mg/m). In a realistic comparison between, let us say, fiber-optic cable and coaxial cable for use for transmission in the megahertz regime over a few kilometers, it is a rule of thumb that 1 g of fiber cable replaces 10 kg of electrical cable. (Both reach and data rate of fiber can be scaled up much higher than that of coaxial cable, though.) This represents an immediate advantage where weight limitation is an important requirement: on board of vehicles, ships, aircraft, and spacecraft.

In connection with reduced weight, there is also reduction of space requirement. This is important in cable ducts in inner cities that are crowded already;

any new installation has to find a way to squeeze in. A fiber-optic cable can replace one or several coaxial cables, upgrade the data rates, and save space at the same time. It is of course better to replace an existing cable in a duct with an upgrade than to install new ducts. Just imagine a work crew digging up Broadway in Manhattan to place more ducts – this is not an option.

As a further distinctive property, fiber-optic cables are immune to electric or magnetic field interference. This is frequently a definitive advantage in industrial installations. Even in close proximity to high-voltage installations, etc., there is no interference picked up by the fiber. This feature sets it apart from electric conductors.

Moreover, glass is chemically quite inert. As long as the fiber’s protective jackets are also made of inert materials, fiber-optic cables can be deployed in chemically hostile environments where metallic parts would quickly corrode. This is attractive for applications in the chemical industry.

And, finally, a fiber-optic cable guarantees a perfect electrical insulation between transmitter and receiver. The same thing can be achieved for electric cables by other means, the so-called optocouplers, but in a manner of speaking, a fiber is an optocoupler stretched long. Di erent fluctuating ground potentials are therefore no longer a concern when subsystems are connected with fiber optics. This is more than a small benefit when there is a potential risk from combustible fumes that one might find, e.g., on oil-drilling rigs. The combination of these properties leads to a fiber-optic sensor technology, which will be discussed in Chap. 12.

Chapter 2

Treatment with Ray Optics

Calculations in technical optics are often done with a technique called raytracing. This is a treatment of optical systems in the framework of ray optics. It provides a particularly clear, if incomplete, view of the properties of optical systems. Strictly speaking, light propagation needs to be treated by taking the wave nature of light into account. The di erence is that waves give rise to di raction and interference phenomena which are disregarded in ray optics. Whenever the geometrical dimensions of the problem are so small as to become comparable to the wavelength of light, the ray optic treatment breaks down. This is the case in single-mode fibers.

That notwithstanding, we will first present a ray-optical consideration in order to get an idea of the phenomena to be expected. When we then proceed with a wave-optic treatment in Chap. 3, it will become apparent that in fibers the main di erence consists in the fact that the direction of light propagation, which can be any direction in ray optics, is restricted to a discrete set of angles in the full picture.

2.1Waveguiding by Total Internal Reflection

Consider a light ray impinging on some boundary to an optically less-dense medium. Less dense is optics parlance and means “having a lower index of refraction.” At a suitable angle of incidence the ray will be fully reflected, instead of passing through. This process is called total internal reflection and is explained in any textbook on optics (see, e.g., [125, 65, 135]). Total internal reflection plays a role in many contexts: Prisms in binoculars or camera viewfinders use it, and it is the reason why to a diver the water surface appears like a mirror.

Call the angle of incidence α and the angle of refraction β (Fig. 2.1). At the boundary to the less-dense medium (nA < nG if we think of air and glass), the inequality β > α holds. On the other hand, β cannot exceed 90◦. This becomes clear from an inspection of Snell’s law of refraction

Figure 2.2: Total internal reflection in water lets illuminated fountains glow. Submerged lamps illuminate the fountain from below, and the water column guides it up. This picture was taken in Boca Raton, Florida, USA.

And indeed, fibers exist which consist of nothing but basically a long cylinder of glass or transparent plastic with a diameter of the order of 1 mm. They are used for some special illumination applications, like guiding light into hard-to- reach places inside some apparatus, and everybody has seen those decorative lamps in which a whole bundle of such fibers is combined. Typical optical fibers for data transmission have a somewhat more complex inner structure, though.

2.2Step Index Fiber

A frequently used type of fiber is called step index fiber. Its internal structure is as shown in Fig. 1.3: There is a core with circular cross-section, surrounded by a cladding zone with ring-shaped cross-section. The core consists of a glass with slightly higher refractive index than that of the cladding. Light is therefore guided in the core (but we will need to make this statement more precise in Sect. 3.13). The advantage of this two-layer structure over the simple version is that the fiber surface, i.e., the boundary between cladding and the outside is no longer involved in the light-guiding mechanism. In the event that the fiber surface is soiled or touches other glass, the function is not compromised. The unstructured fiber, in contrast, would su er from enormous loss. Just consider the case that a drop of oil or other liquid comes into contact with the fiber surface: if it had a refractive index comparable to that of the glass, the waveguiding by total internal reflection would break down [158].

Figure 2.3: Sketch for calculating total internal reflection.

Since the outer surface is not important for the waveguiding in step index fiber, we may simplify its discussion by pretending that the cladding diameter is infinitely wide so that no outside surface exists. Now we can discuss the largest angle with respect to the fiber axis which a ray of light may take and still be guided by the fiber (Fig. 2.3).

Near the fiber end face, we distinguish three refractive indices n, with

nK > nM ≥ nA,

where we used indices A for ambient air, K for core, and M for cladding.2 In the second relation, the equality is valid for unstructured fibers; we will concentrate on step index fibers, though.

We apply Snell’s law:

When we assume the fiber axis to be perpendicular to the front face, β +γ = π/2 and hence sin β = cos γ. Then

sin β = 1 − sin2 γ. (2.3)

The limiting angle for total internal refraction is defined by

2These indices suggest the German words Kern (core) and Mantel (cladding), respectively. We keep them from the original German edition of this book because the English words core and cladding, as they share the same initial, do not provide a better option. Conveniently, the related English words “kernel” and “mantel” also denote the central part of something and some kind of enclosure, respectively.

We may assume nA = 1 for air. Then the limiting angle αmax for rays to be guided is

αmax = arcsin n2K − n2M.

The argument of arcsin bears a special name: it is called the numerical aperture, often abbreviated as NA:

NA = n2K − n2M.

(The word “aperture” derives from Latin apertus = open and indicates some form of opening. We also find it in “aperitif,” the opening of a meal, and in “overture,” the opening of an opera or a romantic a air. “Numerical” here indicates a dimensionless number.)

Clearly, the numerical aperture is a measure of the index di erence between core and cladding. The largest acceptance angle for rays hitting the fiber face is given by sin αmax = NA, inside the fiber by sin αmax = NA/nK . Using the fact that in (linear) optics ray paths can be reversed, the acceptance cone at the same time describes the exit cone of light at the other fiber end. In Fig. 2.4, this input/output cone is schematically shown.

We use the opportunity to introduce another frequently used quantity which is also a measure of the index di erence between core and cladding:

or normalized index step.

Let us consider typical realistic numbers for single-mode fibers. We assume = 0.3%; with nK = 1.46, this implies NA = 0.11; 0.11 rad indicates an acceptance angle of about ±7◦. Rays hitting the fiber face within a cone of this angle will be guided in the fiber. Rays coming in at steeper angles will leave the core; they propagate in the cladding and move away from the axis. Ultimately they are lost for guiding: The cladding often has more loss than the core, so that part of this light is dissipated. The rest eventually reaches the outside surface where typically a plastic coating is applied for protection; the coating