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Introduction
This section will examine the theory of transmission of information over optical fibers. It covers in detail all of the relevant theory behind fiber optic transmission. The section begins with the fundamental concepts of the behavior of light and then moves into the more complex issues of light transmission in optical fibers.
Areas to be covered in this section include fundamental principles and the basic mathematical representation of light transmission down a glass fiber, modes of light transmission, construction of a fiber, transmission capacities and limitations, fabrication processes and future developments.
1. Fundamental principles of operation
11 Introduction
The fundamental principle behind communicating through optical fibers is that electromagnetic energy is tunneled down a tube of glass from a transmitter to a receiver. The tube of glass acts like a pipe that ducts all the electromagnetic energy from one point to another. The electromagnetic energy that is used in this transmission system is in the near visible light section of the electromagnetic spectrum. Therefore, glass is the ideal medium to duct this electromagnetic energy, as light passes through glass with low levels of attenuation.
FIG. 1 Illustration of electromagnetic energy passing through a glass
duct: Glass Duct (Optic Fiber); Electromagnetic Waves
1.2 Reflection, refraction and diffraction
The following is a brief revision of some fundamental principles of physics. Reflection, refraction and diffraction are the three main effects that cause changes to the direction of an electromagnetic wave (this includes light, radio waves, x-rays, gamma rays etc). We will be concentrating on the specific behavior of light for the purpose of this.
Reflection
This is where a light ray that is traveling through a medium of a particular density strikes a medium of different density to the one in which it is traveling and partially or totally bounces off the interface of the two mediums.
FIG. 2 Illustrating reflection [Medium of density x Reflected Incident
ray Some rays continue through Medium of density y]
Refraction
This is where a light ray totally or partially passes into a medium of different density from the one in which it is traveling and changes direction slightly, compared to its direction in the previous medium. A small amount of the energy is also reflected at the interface as shown in FIG. 3.
FIG. 3 Illustration of refraction
Diffraction
This is where a light ray passes over an obstacle and changes direction slightly towards the obstacle. A similar phenomenon is noted when ripples of water strike a protruding rock or piece of land and then move around the rock or land with a slight change of direction towards it.
FIG. 4 Illustration of diffraction
1.3 Reflective index
Light by nature, travels at different speeds in different mediums. The denser the medium the slower will be the speed at which the light travels. A measure of these factors has been established, which relates directly to both the density of the material and the speed of light through the material. This is referred to as refractive index. This measure for any material is made relative to the speed of light in a vacuum (the vacuum is often referred to as free space). The following formula describes this relationship.
Refractive Index N of a Medium = spd. of light in a vac. / spd. of light in a med.
N = 3× 10^8 meters per sec./ Actual speed of light
N = C/ V
The higher the refractive index of a material, the denser that material is. As a ray of light passes from one medium to another, where each medium has a different refractive index, the angle of refraction will differ from the angle of incidence. A ray of light passing into a medium of lower refractive index will leave at an angle greater than the angle of incidence. A ray of light passing into a medium of higher refractive index will leave at an angle less than the angle of incidence. This is illustrated in FIG. 5.
FIG. 5a Ray passing from high N1 to low N2
FIG. 5b Ray passing from low N2 to high N1
In that case, θ1 is the angle of incidence and θ2 is the angle of refraction.
Some typical examples of refractive index are listed below:
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Vacuum 1.0000
Air 1.0002
Water 1.333
Fused Silica 1.452
Crown Glass 1.517
Dense Flint Glass 1.655
Diamond 2.421
Ethyl Alcohol 1.360
Silicone 1.405
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As a note of interest, x-rays always have a refractive index less than air in glass and therefore bend away from the normal when traveling from air into glass, rather than toward the normal as the light ray.
1.4 Snell's Law
A Dutch astronomer and mathematician by the name of Willebrod van Roijen Snell described a relationship in 1621 that relates to the refraction of light traveling through different mediums. The relationship is expressed as follows:
N1 * sin(θ1) = N2 * sin(θ2)
Where N1 and N2 are the refractive indices of medium 1 and medium 2 respectively; (θ1) and (θ2) are the corresponding angles of incidence or refraction in the respective mediums.
Therefore, from the above equation the following is arrived at:
N1 / N2=sin(θ2)/sin(θ1)=C2/C1
where C1 and C2 are the speeds of light in medium 1 and medium 2 respectively.
1.5 Internal reflection
When light is traveling from one medium into a medium of different density, a certain amount of incident light is reflected. This effect is more prominent where the light is traveling from a high-density medium into a lower density medium. The exact amount of light that is reflected depends on the degree of change of refractive index and on the angle of incidence.
If the angle of incidence is increased, the angle of refraction is increased at a greater rate. At a certain incident angle (θC), the refracted ray will have an angle of refraction that has reached 90° (that is, the refracted ray emerges parallel to the interface). This is referred to as the 'critical angle'. For rays that have incident angles greater than the critical angle, the ray is internally reflected totally. In theory, total internal reflection is considered to reflect 100% of the light energy but in practice, it reflects about 99.9% of the incident ray. This is illustrated in FIG. 6.
FIG. 6 Illustration of critical angle
The critical angle (θC) is given by:
(θC) = arc sin
where total internal reflection occurs, the angle of incidence equals the angle of reflection.
1.6 External reflection
When a light ray is traveling in a medium and strikes an interface with a denser medium at greater than the critical angle, the same effect occurs as internal reflection but to a lesser degree. This is referred to as external reflection. Total external reflection only occurs when the angle of incidence equals 90 degree.
1.7 Construction of an optical fiber
An optical fiber consists of a tube of glass constructed of a number of layers of glass, which when looked at in profile, appear to have a number of concentric rings. Each layer (or ring) of glass has a different refractive index. From the previous discussion, it can be seen that to send light down the center of these concentric glass tubes, it is a requirement that total internal reflection occurs. This will duct the light through the fiber.
To achieve total internal reflection the outer glass rings require a lower refractive index than the inner glass tube in which the light is traveling. FIG. 7 illustrates the construction of a typical optical fiber. The cladding diameter and sheath diameter illustrated in this figure, are accepted as standard for most fibers used world-wide, with the core diameter and refractive indices varying depending on the type of fiber (discussed in the following sections).
FIG. 7 Construction of an optical fiber
The core and the cladding will trap the light ray in the core provided the light ray enters the core at an angle greater than the critical angle. The light ray will then travel down the core of the fiber, with minimal loss in power, by a series of total internal reflections. FIG. 8 illustrates this process.
FIG. 8 Light ray traveling through an optical fiber
It would, in theory, be possible to simply have a tube of glass of uniform refractive index acting as the core, with air acting as the outer cladding. This is possible as air has a refractive index lower than glass. This type of implementation does not generally work well because an unprotected core that is covered in scratches, dirt, and oil will appear to have an irregular cladding, with a higher refractive index at these irregular points than the core. Therefore, a lot of light will not be reflected and will be radiated out of the glass.
This is illustrated in FIG. 8a.
FIG. 8a Problems associated with a glass-air interface In reality, the
transmission of light down a fiber is far more complex than has been described
because light actually travels in a three-dimensional stepped helical manner
in glass. The mathematics required to precisely analyze this transmission phenomenon
is extremely complex, of no real practical value, and beyond the scope of this
guide. This guide will analyze the transmission of light in optical fibers
in a two dimensional manner. The core is generally constructed of germania-doped
silica glass. The cladding is generally constructed of near pure silica glass.
The cladding therefore has a lower refractive index than the core (the more
impurities there are in glass, the higher the density of that glass). The sheath
is generally constructed of ultraviolet cured plastic, which provides protection
against abrasion and external forces. The sheath will also be color coded in
a similar manner to multi-core copper cables to enable the user to distinguish
between fibers.
1.8 Fresnel reflection
When light enters the core of a fiber and strikes the cladding at an angle less than the critical angle, then most of the light energy is refracted into the cladding and is lost (as is desired). A very small amount of light will be reflected back into the core. This reflected light is referred to as 'Fresnel reflected' light. It is generally less than 4% of the total incident light energy (calculated using the formula given in section 5.1.5) and therefore generally not powerful enough to carry a spurious signal to the other end of the fiber. This is illustrated in FIG. 8b.
FIG. 8b Fresnel reflection
2. Light transmission nature of glass
From the discussion of frequency spectrum in Section 2, it is noted that visible light covers a broad range of frequencies. Transmission down optical fibers is generally in the near infrared band of frequencies. In this range of frequencies, the optical fiber exhibits the lowest signal attenuation. FIG. 9 illustrates typical attenuation characteristics of glass that is used in fiber optics. Note that this curve does vary to some degree depending on the type of glass used for the manufacture and the type and degree of impurities infused into it.
FIG. 9 Typical attenuation responses for a fiber
From this diagram, it can be seen that there are three dips in the attenuation curve at 0.85 µm, 1.3 µm and 1.55 µm. These are referred to as 'operating windows'. These are the gaps of bandwidth at which transmission down an optical fiber can take place and provide reliable communications over relatively long distances due to the low attenuation. The various types of losses that are noted in FIG. 9 will be discussed in detail in section 7.
The 0.85 µm window was the first to be used for fiber optic communications because the transmission sources and the receiving detectors were easy to manufacture and very efficient. It is still the preferred wavelength of operation for systems operating over short distances because the transmitting and receiving equipment is relatively inexpensive. A typical range of attenuation figures for an optical fiber at this wavelength is 2 to 3.2 dB per km. For the majority of fiber optic systems, the 1.3 µm window is the preferred window of operation because the overall losses are much lower than the 0.8 µm window. A typical range of attenuation figures for an optical fiber at this wavelength is 0.3-0.9 dB per km. Although the light sources are readily available, they are expensive and difficult to manufacture. Hence, this wavelength is generally used for high speed data and long distance telecommunications applications.
The third window, which operates at 1.55 µm, exhibits less loss than the second window. A typical range of attenuation figures for an optical fiber in this band is 0.15-0.6 dB per km. The trade off unfortunately is that the transmitting and receiving devices are not as advanced or as efficient as those operating in the 1.3 µm window. It is anticipated that recent technological developments will make this the most popular window of operation in the future.
A technology known as wave division multiplexing (WDM) is allowing multiple wavelengths to be simultaneously transmitted down the fiber at the same time. Normally there are multiple wavelengths close to either the 1.3 µm or 1.55 µm wavelengths. This technique effectively multiples the single wavelength data rate bandwidth by the number of wavelengths being transmitted.
3. Numerical aperture
Previous sections of this section have discussed the process of light traveling through an optical fiber. This section will discuss the requirements for transmitting into an optical fiber.
As was discussed in section 1.7, it is a requirement for light to successfully travel down an optical fiber, it must enter the fiber and reflect off the cladding at greater than the critical angle. Due to the refractive changes to the direction of the light as it enters the core of a fiber, there is a limit to the angle at which the light can enter the core to successfully propagate down the optic fiber. Any light striking the cladding at less than the critical angle will go straight through into the cladding and be lost. This is illustrated in FIG. 10.
FIG. 10 Light entering the core of a fiber
Since the fiber is cylindrical, there will be a geometrical cone at the entrance to the fiber. For light entering the core within this cone, all the light rays will strike the cladding at greater than the critical angle and will therefore allow successful transmission down the fiber. This is referred to as the 'acceptance cone' and is illustrated in FIG. 11.
FIG. 11 Cone of acceptance of an optic fiber.
The half angle (θ1) of this acceptance cone is referred to as the 'acceptance angle'. The value of the acceptance angle will depend on the refractive indices of the core, cladding and air (air having a refractive index of 1) or whatever material the source of light is. A light ray entering the core at an angle greater than θ1 will disperse into the cladding. A light ray coming in at an angle of exactly θ1 will strike the core/cladding interface at angle θc (critical) and will leave parallel to the interface.
A measurement is used to specify the light collecting ability of a fiber. This is referred to as the 'numerical aperture' (NA). NA is the sin of the acceptance angle, that is:
NA = sin (θ1)
It can also be expressed as a factor of the refractive indices of the fiber.
If there are two fibers with the same core diameter but different NAs, then the fiber with the larger NA will accept more light energy radiated from a light source than the fiber with smaller NA. If there are two fibers with the same NAs but different diameters then the fiber with the larger diameter will allow more light energy into the core than the fiber with the smaller diameter. This is illustrated in FIG. 12.
NA = √(N12-N22)
=N1 sin (θ2)
FIG. 12a Fibers with different NAs but same diameters
FIG. 12b Fibers with same NAs but different diameters
As optical fibers with large NAs or diameters will accept more light than fibers with smaller NAs or diameters, the larger NA or diameter fibers will be more suitable for less expensive light transmitters such as LEDs, which are unable to concentrate their output energy into a narrow coherent beam (as do lasers) and radiate over a larger angle. However, the disadvantage of a fiber that is constructed with these parameters is that there will be a greater dispersion (spreading) of the light that is injected into the core and therefore a reduction in the fiber transmission bandwidth (discussed further in sections 5 and 6). At the other end of the scale, the fiber with a small NA or diameter will have a greater bandwidth. This is because only relatively parallel rays of light will enter the core and there will be less dispersion of the light down the core. However, the disadvantage here is that it will require a more expensive light source that provides a narrower beam of light (such as a laser) and a more precise alignment of the transmitter and the core.
4. Modal propagation of fibers
4.1 Intro
Optical fibers are classified according to the number of rays of light that can be carried down the fiber at one time. This is referred to as the 'mode of operation' of the fiber. Therefore, a mode of light is simply a ray of light. The higher the mode of operation of an optical fiber, more rays of light that can travel through the core. It is possible for a fiber to carry as many as several thousand modes or as few as only one.
The following section discusses various modes of propagation in optical fibers and the effects of modal dispersion.
4.2 Modal dispersion
It is important firstly to examine the nature and effects of modal transmission. A fiber that has a high NA and/or diameter will have a large number of modes (rays of light) operating along the length of that fiber. An omnidirectional light source (i.e. one that effectively radiates light rays equally in all directions) such as an LED will emit several thousand rays of light in a single pulse. Because the light source injects a broad angle of beam into the core, each mode of light traveling at a different angle as it propagates down the fiber will therefore travel different total distances over the whole length of the fiber. It follows therefore that it will take different lengths of time for each light ray to travel from one end of the fiber to the other. The light transmitter will launch all modes into the fiber exactly at the same time, and the signal will appear at the beginning of the fiber as a short sharp pulse. By the time the light reaches the end of the fiber, it will have spread out and will appear as an elongated pulse. This is referred to as 'modal dispersion'. This is illustrated in FIG. 13.
FIG. 13 The dispersion effect on a pulse due to multiple modes of propagation.
The light ray that travels down the center axis of the fiber is referred to as the fundamental mode and is the lowest order mode possible. The light rays that travel the shorter distances down the length of fiber are the lower order modes and the light rays that travel the longer distances down the length of fiber are the higher order modes.
If the input pulses are too close together, then the output pulses will overlap on each other, causing inter-symbol interference at the receiver. The effect of modal dispersion would rely on this development. This situation will make it difficult for the receiver to distinguish between pulses and will introduce errors into the data. This is the major factor in fiber optic cables (multimode types) that limits transmission speeds. This is illustrated in FIG. 14.
FIG. 14 Inter-symbol interference due to modal dispersion
It can be seen from this diagram that it will be difficult for the receiver to distinguish between the output pulses as they overlap on each other as they exit the fiber core (inter- symbol interference). Modal dispersion is measured in nanoseconds and is given by the following formula:
D = √(D02 -D02)
where:
D = total dispersion of a pulse
Do = pulse width at the output of the fiber in nanoseconds
Di = pulse width at the input of the fiber in nanoseconds
Modal dispersion increases with increasing NA, and therefore, the bandwidth of the fiber decreases with an increase in NA. The same rule applies to the increasing diameter of a fiber core. This is illustrated in the graphs in FIG. 15.
FIG. 15a Pulse dispersion vs the ratio of refractive indices.
FIG. 15b Pulse dispersion vs data rates.
Cable suppliers provide a dispersion figure in the cable specification. The unit of measure will be given as pico-seconds (or nanoseconds) of pulse spreading per kilometer of fiber (ps/km). Generally, the supplier does not give this figure directly but it is easily determined from the bandwidth. For example, a 400 MHz-km bandwidth represents a maximum modal dispersion you would expect from the fiber of 1/400 MHz/km, which equals 2.5 ns/km. Section 8.3.2 describes the techniques for calculating the effects of modal dispersion on a system.
4.3 Number of modes
When the core and cladding each have a constant refractive index across their cross sectional area but the core refractive index being different to the cladding refraction index, then they behave like an optical waveguide. This is referred to as 'step index' and is discussed in the next section. In this waveguide only a specific number of modes can propagate. The number of discrete modes is determined by the following formula:
M = 0.5 [θd(NA)2] / λ
where:
d = the diameter of the fiber core
λ = the wavelength of the light
NA = the numerical aperture
It can be seen from this formula that as the diameter and the NA decrease, so do the number of modes that can propagate down the fiber. The decrease in modes is more significant with a reduction in diameter than a reduction in NA. The NA tends to remain relatively constant for a wide range of diameters. Note also that as the diameter starts to approximate the wavelength of light, then only one mode will travel down the fiber. This state is referred to as 'single mode' or 'mono mode' propagation. FIG. 16 illustrates the rate at which the number of modes increases with increasing core diameter.
FIG. 16 Number of propagation modes vs core diameter.
4.4 Leaky modes
An unusual phenomenon is noted when the NA for very short lengths of fiber is compared to the NA for very long lengths of fiber. For example, the NA of 3 meters of multimode fiber may be measured at 0.36 but for 1 km of the same cable, it may be measured at 0.3.
The reason for this spurious result is due to the way NA is measured. A certain amount of light will escape into the cladding at the point of connection with the light source and will transverse down the cladding and be detected by the receiving detector several meters away. As NA is a measure of the light acceptance ability of the fiber, it appears to have a larger NA than it actually has.
The light that enters the cladding will be very small in amplitude and will readily leak out of the cladding with any slight bends in the fiber. Therefore, the light traveling in the cladding will have significantly dispersed after 10 or 20 meters only. These are referred to as leaky modes.
4.5 Refractive index profile
The discussion so far has assumed that the refractive index of the core and the cladding are constant across their surface areas. This is the case for a lot of fibers but not all. For example, the graded index multimode fiber to be discussed in section 6.5 has a gradual changing refractive index in the core and cladding. To help distinguish between optical fibers, they are generally specified with a graphed profile of their refractive indices. FIG. 17 illustrates three examples of refractive index profiles.
FIG. 17 Examples of refractive index profiles
4.6 Multimode step and graded fibers
The term 'multimode' generally applies to fibers with a diameter of 50 micrometers or greater. Because of the relatively wide diameter of the core, multiple modes of light are able to travel down the core. As was discussed in section 4.2, allowing multiple modes of light to travel down a fiber causes modal dispersion.
The modal dispersion that occurs in a multimode fiber affects or is affected by a number of operating parameters of the fiber.
Attenuation -- Multimode fibers have a maximum operating distance of approximately 5 km.
Bandwidth -- Multimode fibers have a maximum operating data speed of approximately 2-300 Mbps.
Wavelength -- They generally operate at wavelengths of 850 nm or 1300 nm. Some fibers are available that operate at both wavelengths (different physical communications standards use different operating wavelengths). The wide diameter of the multimode fiber makes it suitable for using with LED light sources. This, in turn, makes the complete transmission system a lot cheaper than compared to fibers that have a thinner diameter and which require the use of lasers. Recently, the introduction of VCSEL lasers (refer to Section 6) has significantly reduced the cost of lasers and they are now starting to be used for high-speed data links up to 10 Gbps on multimode fiber (over distances of less than 90 meters). A further advantage with using multimode fibers is that the wider diameter makes them easier to splice and to terminate, which makes the final installed system cheaper.
Multimode fibers are constructed in three main sizes. The following section discusses the advantages and disadvantages of each. The first piece of text in each of the following three sections illustrates how the fiber is specified and next to it, the meaning of each part of the specification.
50 Micron cores
50/125/250 µm
50 µm core diameter
125 µm cladding diameter
250 µm sheath diameter
50/125/900 µm 900 µm tight buffer sheath diameter
This particular size fiber is used extensively in Europe.
Attenuation -- Compared to the other two fiber sizes discussed, this fiber experiences lower signal attenuation. But to counter this, the smaller diameter fiber does not allow as much signal energy to be coupled into the fiber from the LED.
Bandwidth -- Overall, this fiber has a higher bandwidth than the other two fibers and therefore achieves higher data rates. The higher bandwidth is due to lower modal dispersion.
N/A -- This fiber has the lowest numerical aperture of the three fiber sizes, generally around 0.2. The relatively small core size and NA result in this fiber coupling the least amount of energy from the light source. For long cable runs the lower attenuation will tend to counter this.
62.5 Micron cores
62.5/125/250 µm
62.5 µm core diameter
125 µm cladding diameter
250 µm sheath diameter
62.5/125/900 µm
900 µm tight buffer sheath diameter
This size fiber is predominantly used throughout the USA and the Asian/Australasian regions.
Attenuation
Compared to the other two fiber sizes, there is marginally more signal attenuation than the 50 µm fiber and significantly less attenuation than the 100 µm fiber.
Bandwidth
This fiber has a bandwidth that is only slightly less than the 50 µm fiber. Therefore it is used in systems that operate at the same data rates as those using 50 µm fibers.
NA
It has a relatively high NA that is close to the NA of the 100 µm fiber, generally around 0.275. The higher NA of this fiber will couple approximately 5 dB more power than a 50 µm fiber when connected to a same capacity source. This will generally counter the lower attenuation characteristic of the 50 µm fiber over distances of several kilometers and provide similar distances of transmission.
100 Micron cores
100/140/250 µm
100 µm core diameter
140 µm cladding diameter
250 µm sheath diameter
This size fiber is rarely used today in commercial or industrial data communications applications. It was one of the first fibers introduced in the market and had a large core diameter because of the limitations of early fabrication techniques.
Attenuation
This fiber exhibits attenuation characteristics approximately twice that of the 50 µm and 62.5 µm multimode fibers. This has made it unsuitable for most data communications applications.
Bandwidth
It has the lowest bandwidth of the three fiber sizes. This is generally around 20 or 30% of the other fiber sizes. Therefore it will only support relatively slow data rates.
NA
Compared to other multimode fibers, this fiber has the largest NA, generally around 0.290. This represents an extra coupling of approximately 9 dB when compared to a 50 µm cable connected to the same capacity light source. Because of its larger diameter, it is easier to splice and to couple to the transmitters and receivers. The increase in NA of this fiber is only slightly more than the 62.5 µm fiber and does not compensate for the very high attenuation and low bandwidth.
Note that it is possible to use 50 µm fiber with 62.5 µm connectors and transmitting and receiving equipment, and vice versa, because both have the same cladding diameter. There will be a small loss introduced due to the misalignment of the fiber cores.
Multimode fibers are manufactured in two types:
• Step index
• Graded index
Step index
A step index fiber consists of a glass core of constant cross-sectional refractive index, surrounded by a cladding of a different constant cross-sectional refractive index. Because of this sudden change in the refractive index light will reflect off the core/cladding interface and transverse its way down through the core. It has a refractive index profile as shown in FIG. 18.
FIG. 18 Step index fibers
The refractive index of the core (N1) is typically 1.48 and the cladding (N2) approximately 1.46. The acceptance angle (θ1) is typically around 14°. Step Index fibers exhibit significant modal dispersion. This is generally around 15 to 40 nanoseconds per kilometer and limits the transmission bandwidth to approximately 25 MHz - km. This in turn limits the digital transmission speed to not much greater than 10 Mbps/km. It is suitable for many industrial applications where only slow data rates are required but is unsatisfactory for most commercial telecommunication applications where much higher data rates are required.