The dispersion of an optical fiber is the time scattering of the spectral or mode components of an optical signal. The main reason for the dispersion is the different speeds of propagation of the individual components of the optical signal. Dispersion manifests itself as a broadening, an increase in the duration of propagating through the fiber
optical impulses.
In the general case, the specified value of the optical pulse broadening ∆δ is determined directly by the values of the root-mean-square duration at the transmitting δin and δout, respectively:
In turn, dispersion creates crosstalk, leads to intersymbol interference and, accordingly, errors in signal reception, which limits the transmission rate in the line or, in other words, the length of the regeneration section (RU).
Intermode dispersion
Intermode dispersion is characteristic only for multimode optical fibers. It arises in multimode fibers due to the presence of more mod c different times propagation and different path lengths that individual modes travel in the fiber core (Fig. 1.10 - 1.11).
The bandwidth of typical gradient multimode optical fibers is characterized by the broadband factor ∆F, MHz-km, the value of which is indicated in the passport data at wavelengths corresponding to the first and second transparency windows. Typical bandwidths of typical multimode optical fibers are 400...2000 MHz-km.
The implementation of high-speed multimode FOL requires the use of single-mode lasers as radiation sources for optoelectronic modules of the OSB, providing a data transfer rate of more than 622 Mbps (STM-4). In turn, the main factor in the distortion of optical signals of single-mode OSBs propagating through the fibers of multimode FOLs is no longer multimode dispersion, but differential mode delay (DMD). DMD is random in nature and depends directly on the parameters of a specific source-fiber pair, as well as on the conditions for introducing radiation from the laser output into the linear path of a multimode FOL. Therefore, in the passport data on new type multimode optical fibers - fibers optimized for operation with lasers - in addition to the values of the coefficient of broadband, which allows estimating the amount of intermode dispersion when transmitting signals of multimode SOS over multimode FOLs, additional information obtained as a result of DMD measurements during the fiber manufacturing process is also indicated, for example, the limiting ECU length of single-mode Gigabit Ethernet SOS.
Obviously, intermode dispersion does not appear in single-mode optical fibers. One of the main factors of distortion of signals propagating through single-mode optical fibers are chromatic and polarization mode dispersion.
The chromatic dispersion Dch is due to the finite width of the laser emission spectrum and the difference in the velocities propagated by the individual spectral components of the optical signal. Chromatic dispersion is composed of material and waveguide dispersion, and manifests itself in both single-mode and multimode optical fibers:
Material dispersion
The material dispersion Dmat is determined by the dispersion characteristics of the materials from which the core of the optical fiber is made - quartz and dopants. The spectral dependence of the refractive index of the core and cladding material (Figure 1.24) causes changes with wavelength and propagation velocity.
Quite often, this dependence is described by the well-known Sellmeier equation, which has the following form:
(1.28)
Where Aj and Bj are the Sellmeir coefficients corresponding to a given type of material, dopant and its concentration.
Rice. 1.24. Spectral dependence of the refractive index of pure quartz (solid curve) and quartz doped with 13.5% germanium (dashed curve)
Obviously, this characteristic for quartz fibers can be considered unchanged. The material dispersion is characterized by the coefficient Dmat ps/(nmkm), which is determined from the known relationship:
 |
As an example, in fig. 1.25 shows the spectral characteristics of the material dispersion coefficients of pure quartz and quartz doped with 13.5% germanium.
Obviously, the nature of the manifestation of material dispersion depends not only on the width of the radiation spectrum of the source, but also on its central operating wavelength. So, for example, in the region of the third transparency window λ=1550 nm, shorter waves propagate faster than longer ones, and the material dispersion is greater than zero (Dmat>0). This range is called the area of normal or positive dispersion (Fig. 1.26 (b)).
In the region of the first transparency window λ=850 nm, on the contrary, longer waves propagate faster than shorter ones, and the material dispersion corresponds to a negative value (Dmat<0) Данный диапазон называется областью аномальной или отрицательной дисперсии (рис. 1.26 (в)).
Rice. 1.26. Chromatic dispersion: (a) pulse at the FOL input; (b) normal
dispersion; (c) anomalous dispersion; (d) region of zero dispersion.
At some point in the spectrum, called the point of zero material dispersion λ0, a coincidence occurs, while both short and long waves propagate at the same speed (Fig. 1.26 (d)). So, for example, for pure quartz SiO2, the point of zero material dispersion corresponds to a wavelength of 1280 nm (Fig. 1.25).
Distinguish mode dispersion, which is caused by a large number of modes in the optical fiber and the chromatic dispersion associated with the incoherence of light sources actually operating in a certain range of wavelengths.
Consider the propagation of the light beam along the multimode fiber. In this case there are two modes, the two beams. The first extends along the longitudinal axis of the fiber, while the other is reflected from the interfaces of media. Thus the path of the second light beam is greater than the first. As a result, when the two beams carrying the electromagnetic energy are added together, compared oblique beam with an axial beam is the time delay, which is calculated by the following formula:
c– speed of light
l– fiber length
n 1
,
n 2– refractive indices of the core and shell
Gradient mode dispersion of optical fibers, usually two orders of magnitude lower than those fibers with a step refractive index profile. Due to the smooth change of the refractive index of the core of an optical fiber decreases the path of the second beam along the fiber. Thereby reducing second time delay relative to the first beam.
The single mode optical fiber mode dispersion, and no increase in pulse duration is determined by the chromatic dispersion, which, in turn, divided into material and waveguide.
Material dispersion phenomenon is called the absolute dependence of the refractive index n material wavelength of light ( n =ϕλ()). The waveguide dispersion coefficient is determined by the dependence of the phase β and of the frequency ( β=ϕ ω() ).
Pulse broadening due to chromatic dispersion is calculated using the formula:
m– pulse broadening due to material dispersion, ps;
τ B– broadening of the pulse due to the waveguide dispersion, ps;
∆λ
– the spectral width of the radiation source, nm;
M(λ) is the coefficient of specific material dispersion, ps / nm km;
B(λ)– a coefficient of the waveguide dispersion, ps / nm km.
Consider the effect of material and waveguide dispersion in single-mode fiber. As seen from the graph, an increase in the wavelength dispersion of the material decreases, and at a wavelength of 1.31 m it becomes equal to zero. The wavelength in this case is considered a zero-dispersion wavelength. At the same time more than 1.31 micron dispersion becomes negative. Unbiased waveguide dispersion of fibers is a relatively small value and is in the range of positive numbers. In the development of optical fiber dispersion-shifted, which is based on the waveguide component, trying to compensate for the dispersion of the material to longer wavelengths, ie, a third transparent window (λ = 1.55 m). This shift is carried out reduction of the core diameter, increasing Δ and using the triangular shape of the refractive index profile of the core.
In the propagation of polarized light wave along the optical fiber polarization dispersion occurs. The light wave from the standpoint of the wave theory is a constantly changing magnetic and electric field vector which is perpendicular to the propagation of electromagnetic (light) waves. An example of a light wave may be natural light whose direction of electric vector varies randomly. If the radiation is monochromatic and vectors oscillate with a constant frequency, they can be represented as the sum of two mutually perpendicular components of x and y. The ideal optical fiber is an isotropic medium in which the electromagnetic properties are the same in all directions, for example refractive indices. Media with different refractive indices in two orthogonal axes x and y are called birefringent. Thus in this case, the fiber remains single mode for as two orthogonally polarized modes have the same propagation constant. But this is true only for ideal optical fiber.
In a real optical fiber two orthogonally polarized modes have non-identical propagation constants, so that there is a time delay occurs and the broadening of the optical pulse.
The broadening of the pulse due to polarization mode dispersion (PMD) is calculated as follows:
Therefore, the polarization mode dispersion is manifested only in the single-mode optical fibers with netsirkulyarnoy (elliptical) core and, under certain conditions becomes comparable with chromatic. Therefore, the resulting dispersion single mode optical fiber is determined by the following formula:
Dispersion significantly limits the bandwidth of optical fibers. The maximum bandwidth on the optical line 1 km calculated by the approximate formula:
τ - pulse broadening, ps / km.
2.1 Causes and types of dispersion
The main reason for the occurrence of dispersion in the fiber is the incoherence of the radiation source (laser). An ideal source radiates all the power at a given wavelength λ 0 , however, in reality, the radiation occurs in the spectrum λ 0 ± Δλ (Fig. 2.1), since not all excited electrons return to the same state from which they were removed during pumping.
Fig.2.1. Real laser radiation
The refractive index is a frequency-dependent quantity, that is, n is a function of λ: n = f (λ), see Fig. 2.2.
Fig.2.2. The dependence of the refractive index on the wavelength
Therefore, when a signal consisting of a mixture of wavelengths λ 0 ± Δλ propagates, parts of the signal travel at different speeds, and dispersion occurs:
λ ± Δλ → n ± Δn → c /(n ± Δn) → v ± Δv → Δτ.
This kind of dispersion is called material dispersion.
The transverse propagation constant of the wave (along the fiber radius) also depends on the wavelength, that is, the mode area and the area of that part of the cladding that is captured by the mode area that goes beyond the core boundaries depend on the wavelength. The propagation of light along the boundary part of the shell with the core proceeds at a higher speed than along the core, which contributes to the change in dispersion. This dispersion is called waveguide dispersion. Both of these dispersions, material and waveguide, are collectively referred to as chromatic dispersion. They add up arithmetically. Figure 2.3 shows the dependence of the material and waveguide dispersion and their sum on the wavelength. For a standard single-mode fiber at λ = 1300 nm, these dispersions are equal and opposite in sign, and the total dispersion is zero.
Fig.2.3. Wavelength dependence of material and waveguide dispersion in a standard single-mode fiber (nm)
In multimode fiber, in addition to chromatic dispersion, there is also intermode dispersion. If there are several modes, then each one propagates along the fiber with its own speed, which can differ significantly from each other. Figure 2.4 shows the graphs of the phase velocities of some modes.
Rice. 2.4. Plot of phase velocities of some modes as a function of frequency.
If the parameters of the fiber change, for example, the diameter of the core changes by chance, the modes change and the modes exchange energy. Intermode dispersion is an order of magnitude greater than chromatic dispersion, which has led to the development of single-mode cables in which there is no intermode dispersion. Table 2.1 shows an approximate ratio of dispersion types for different types of fibers.
Table 2.1. Relationship between different types of dispersion
The total dispersion is defined as the square root of the sum of the squares of the chromatic and intermodal dispersions:
(2.1)
Material and waveguide dispersions are calculated by the formulas
τ mat = ∆λ∙ М(λ)∙ L (2.2),
τ vv = ∆λ∙ В(λ)∙ L (2.3),
where ∆λ is the laser radiation bandwidth, nm;
М(λ) and В(λ) – specific material and waveguide dispersions, ps/(nm·km);
L is the length of the line, km.
The values M(λ) and B(λ) are given in reference books.
τ Σ \u003d [τ mm 2 + (τ mat + τ vv) 2] 1/2
Table variant. 2.1. Approximate dispersion values for different fiber types
2.2. Polarization Mode Dispersion (PMD)
Light is an oscillation transverse to the direction of light propagation (Fig. 2.5). If the end of the field vector describes a straight line, then such a polarization is called linear, if a circle or an ellipse, then circular or elliptical. Most people, with rare exceptions, do not feel the polarization of light, only a few (for example, Leo Tolstoy) clearly distinguish between polarized and non-polarized light. A conventional integrated light receiver (diode) also responds only to the intensity of the wave, and not to its polarization. However, some optical devices, such as certain types of amplifiers, have a polarization dependent gain.
Rice. 2.5. Types of linear polarization
In addition, vector polarization is of great importance in the processes of reflection and refraction, since the Fresnel coefficients characterizing the amplitudes of the reflected and refracted waves generally depend on the direction of the polarization vector (Fig. 2.6). Figure 2.6 shows how a mixture of rays of parallel (dash) and perpendicular (dot) polarizations is reflected with respect to the propagation plane when passing through the horizontal separation plane. It can be seen from the figure that at a certain angle (Brewster angle) all reflected waves have perpendicular polarization, and refracted waves have parallel polarization.
Rice. 2.6. Reflection of waves of different polarization.
In classical single-mode fiber, the only mode is the HE 11 wave. However, if the polarization is taken into account, then the fiber contains two mutually orthogonal modes corresponding to the horizontal and vertical axes x and y. In a real situation, the fiber is not always an ideal circle in cross section, but often represents a small ellipse due to certain features of the technology. In addition, during the winding of the cable and during its laying, asymmetric mechanical stresses and fiber deformations occur, which leads to birefringence. The refractive index will change due to the additional voltage, and the propagation velocities of orthogonal modes in different areas will differ from each other, which will introduce different time delays in the propagation of orthogonal modes. The pulse as a whole will experience a statistical broadening with time, which is called polarization mode dispersion (PMD). Since the PMD in different sections of the line is different and obeys statistical laws, the root-mean-square summation is usually used, and the PMD is calculated using the formula
Information on the OF is transmitted in the form of short optical pulses. The pulse energy is distributed among all guided modes. The velocities of all modes along their trajectory in a stepped OF are the same. However, the time it takes for them to travel 1 km of the SV will vary. At the output of the OF, the pulses of individual modes, which arrived at different times, are added, forming a wider optical pulse compared to the input one (Fig. 2.1).
Rice. 2.1. Trajectories of meridional rays in OF with a stepped refractive index profile.
The phenomenon of pulse broadening in a multimode optical fiber is called intermode dispersion, which is characterized by the value D m , measured in ns/km. If the dispersion value is known, then the momentum broadening Δt in the OF of length L in the first approximation is determined by the expression:
The upper estimate of the intermode dispersion value: the smallest trajectory and the smallest propagation time t min has a beam propagating along the OF axis.
The greatest trajectory and the longest propagation time t max has a beam propagating along the optical fiber, reflecting from the interface between the core and the shell at an angle of total internal reflection.
Then . (2.4)
Dispersion limits the rate of information transfer over the OF.
Rice. 2.2. Dependence of the intermode dispersion on the relative difference between the refractive indices of the core and cladding.
The intermode dispersion value [ns/km] is related to the concept of fiber broadband or specific bandwidth B[MHz km]
The bandwidth value for stepped multimode silica fibers is limited to 20-50 MHz km.
For gradient multimode fibers, the bandwidth is in the range of 200 - 2000 MHz km.
A radical way to reduce dispersion is to switch from multimode transmission to single mode.
For the first time, single-mode transmission in stepped index fiber was achieved by reducing the core radius to 5 µm. Such fibers are called standard single-mode fibers.
An important normalized parameter for single-mode fibers is the diameter w or the radius r n m of the mode spot (field), which characterizes the loss when light enters the fiber and is used for calculations instead of the radius or diameter of the core, its value depends on the type of fiber and the operating wavelength and lies in within 8..10 microns (in fact, it is 10-12% larger than the core diameter).
For a single-mode OF, the intensity distribution of the mode field can be approximated by a Gaussian curve:
Rice. 2.3. Determination of the mode field diameter.
On fig. 2.4. Shown are the expression-calculated modal field distributions for a standard fiber at wavelengths that are commonly used for communications.
Rice. 2.4. Mode field distribution of the fundamental mode in a standard fiber.
Since the speed of light propagation in the OF depends on the radiation wavelength λ, different spectral components of the signal propagate at different speeds.
Rice. 2.5. Radiation spectrum of the source.
Chromatic dispersion consists of two components: material and waveguide:
As a physical quantity, it is measured in ps / (nm km) and means pulse broadening in a 1 km long fiber with a signal spectrum width of 1 nm (taking into account the transmission rate and the spectrum width of the radiation source).
Material dispersion is due to the dependence of the refractive index of quartz n (both phase and group) or the speed of propagation of light in quartz on the wavelength (Fig. 1.10) and is proportional to the second derivative of the refractive index with respect to the wavelength:
Rice. 2.6. The emergence of material dispersion.
On fig. 2.7 shows the dependence of the material dispersion on the wavelength. It can be seen that the material dispersion has a sign and at a wavelength of zero material dispersion λ = λ 0 mat passes through 0.
The waveguide dispersion Dv is not related to the properties of the material, but depends on the design and dimensions of the waveguide. Its appearance is due to the fact that a wave in a single-mode OF propagates partly in the core, partly in the cladding, and the refractive index for it takes the average value between the refractive indices of the core and cladding. When the wavelength changes, the depth of penetration of the field into the quartz shell changes and, consequently, the average value of the refractive index changes.
Rice. 2.7. Chromatic dispersion in standard single mode
fiber.
Rice. 2.8. The emergence of waveguide dispersion.
The waveguide dispersion is negative and decreases with increasing λ. This makes it possible, by changing the size and design of the OF, to control the dependence of Dv, and, consequently, the dependence of D xp on λ.
There is such a wavelength at which the material and waveguide dispersions are equal in absolute value and have opposite signs, that is, the chromatic dispersion is zero. This wavelength is called the wavelength of zero chromatic dispersion or simply the wavelength of zero dispersion λ 0 D .
In most single-mode OFs, the location of the axes of the highest and lowest speeds is random, and the expansion of the pulse passing through the OF increases with increasing length L in proportion to the square root of the length of the OF:
where D p is the polarization-mode dispersion.
For most single-mode optical fibers, the polarization-mode dispersion is in the range 0.02 – 0.2 ps/km 0.5 .
Before considering the concept of a chromatic dispersion analyzer, let us denote what types of dispersions are in an optical fiber, what chromatic dispersion (CD) is, what components it consists of, what methods exist for measuring it.
Types of dispersions
There are the following types of dispersions in a light guide:
modal or intermodal;
chromatic (material, waveguide);
polarizing.
Their sum forms the total dispersion in the fiber.
Chromatic dispersion
Chromatic dispersion has an impact on system performance. The phenomenon of chromatic dispersion arises due to the fact that the propagation of wavelengths in an optical fiber occurs at a slightly different speed from each other. As a result, there is a prolonged, and therefore ineffective momentum. When the CD value is too high, cross modulation and signal loss occur. At the same time, small controlled values of chromatic dispersion are needed to eliminate unwanted non-linear effects such as four-wave mixing.
For glass, which is used in the manufacture of optical fiber, an important characteristic is the dispersion of the refractive index (material dispersion). It manifests itself in the dependence of the speed of propagation of the optical signal on the wavelength. In addition, at the time of production, when drawing a quartz filament from a glass preform, various degrees of deviation occur both in the fiber geometry and in the radial refractive index profile. Geometry + deviations from the ideal profile contribute significantly to the above-mentioned dependence of the speed of propagation of an optical signal on the wavelength - this is already called waveguide dispersion.
Chromatic dispersion is the combined effect of material and waveguide dispersion.
HD is observed during the propagation of a light signal in both single and multimode fibers. But it is most clearly manifested in a single mode due to the absence of intermode dispersion in it.
Methods for measuring HD
The GOST R IEC 60793-1-42-2013 standard defines the following methods:
phase shift;
spectral group delay in the time domain;
differential phase shift;
interferometry.
Chromatic dispersion analyzer
HD analyzers can be conditionally divided into stationary and field ones.
Chromatic dispersion measurement is now becoming increasingly critical for telecom companies and service providers looking to improve their systems by upgrading their bit rates. Modern chromatic dispersion analyzers are characterized by high performance, allowing you to carry out all types of CD measurements, including in the field.
For example, EXFO's FTB-5800 Chromatic Dispersion Analyzer for comprehensive field testing of CD determines it using the method phase shift. From a source located on one side of the communication line, a modulated light signal is sent into the optical fiber. On the other side of this communication line, different wavelengths come with different phase shifts. By measuring these shifts, the corresponding time delays are calculated and the HD value is determined.
Other methods of measuring HD
There is also a method such as flight time measurement(FOTR-168). For example, the CD-OTDR measurement system is based on it, which allows the evaluation of the chromatic dispersion of individual fibers. The test uses a single fiber and multiple wavelengths, resulting in increased measurement accuracy and reduced test time.
Another method - impulse, regulated by the ITUT G650 standard. The pulse method is characterized by direct measurement of the delay of light pulses with different wavelengths when passing through an optical fiber of a given length.
