Along with the attenuation coefficient of the OF, the most important parameter is the dispersion, which determines its bandwidth for information transmission.
Dispersion - this is the scattering in time of the spectral and mode components of the optical optical signal, which lead to an increase in the duration of the optical radiation pulse when it propagates along the OF.
Pulse broadening is defined as the quadratic difference between the pulse duration at the output and input of an optical fiber using the formula:
moreover, the values of and are taken at the level of half the amplitude of the pulses (Figure 2.8).
Figure 2.8
Figure 2.8 - Pulse broadening due to dispersion
Dispersion arises for two reasons: the incoherence of radiation sources and the existence of a large number of modes. The dispersion caused by the first cause is called chromatic (frequency) , it consists of two components – material and waveguide (intramode) dispersions. Material dispersion is due to the dependence of the refractive index on the wavelength, waveguide dispersion is associated with the dependence of the propagation coefficient on the wavelength.
The dispersion caused by the second cause is called modal (intermode).
Modal dispersion is characteristic only of multimode fibers and is due to the difference in the time it takes for modes to travel through the optical fiber from its input to output. AT OF with a stepped refractive index profile propagation speed electromagnetic waves with the wavelength is the same and equal to: , where C is the speed of light. In this case, all rays incident on the fiber end at an angle to the axis within the aperture angle propagate in the fiber core along their zigzag lines and, at the same propagation velocity, reach the receiving end at different time, which leads to an increase in the duration of the received pulse. Since the minimum propagation time of the optical beam occurs when the incident beam , and the maximum when , then we can write:
where L is the length of the fiber;
Refractive index of the fiber core;
C is the speed of light in vacuum.
Then the value of intermode dispersion is equal to:
Mode dispersion of gradient OFs an order of magnitude or more lower than that of stepped fibers. This is due to the fact that due to a decrease in the refractive index from the OF axis to the shell, the propagation velocity of the rays along their trajectory changes. So, on trajectories close to the axis, it is less, and more distant. Rays propagating along the shortest trajectories (closer to the axis) have a lower speed, and rays propagating along longer trajectories have a greater speed. As a result, the propagation time of the beams is equalized, and the increase in the pulse duration becomes smaller. With a parabolic refractive index profile, when the exponent of the profile is q=2, the modal dispersion is given by:
The modal dispersion of the gradient OF is several times smaller than that of the stepped one for the same values of . And since usually , then the modal dispersion of the indicated optical fibers can differ by two orders of magnitude.
When calculating the modal dispersion, it should be borne in mind that up to a certain line length, called the mode coupling length, there is no intermode coupling, and then at , the process of mutual mode conversion occurs and a steady state occurs. Therefore, at , the dispersion increases according to a linear law, and then, at - according to a quadratic law.
Thus, the above formulas are valid only for length . For line lengths, the following formulas should be used:
- for stepped light guide
- for a gradient light guide,
where is the length of the line;
The mode coupling length (steady state) is equal to km for a stepped fiber and km for a gradient one (established empirically).
Material dispersion depends on the frequency (or on the wavelength ) and the material of the OF, which, as a rule, is used quartz glass. The dispersion is determined by the electromagnetic interaction of the wave with the bound electrons of the material of the medium, which, as a rule, is of a nonlinear (resonant) nature.
The occurrence of dispersion in the material of the light guide, even for single-mode fibers, is due to the fact that the optical source that excites the fiber (light-emitting diode - LED or PPL semiconductor laser) generates light radiation having a continuous wave spectrum of a certain width (for LED it is about nm, for multimode PPL - nm , for single-mode laser diodes nm). Different spectral components of light radiation propagate at different speeds and arrive at a certain point at different times, leading to pulse broadening at the receiving end and, under certain conditions, to distortion of its shape. The refractive index varies with wavelength (frequency), with the level of dispersion depending on the wavelength range of the light injected into the fiber (typically, the source emits multiple wavelengths) as well as the center operating wavelength of the source. In region I of the transparency window, longer wavelengths (850nm) move faster compared to shorter wavelengths (845nm). In region III of the transparency window, the situation changes: the shorter ones (1550 nm) move faster than the longer ones (1560 nm). Figure 2.9
Figure 2.9 - Speeds of propagation of wavelengths
The length of the arrows corresponds to the speed of the wavelengths, the longer arrow corresponds to the faster movement.
At some point in the spectrum, the velocities coincide. This coincidence in pure quartz glass occurs at a wavelength of nm, called the wavelength of zero dispersion of the material, since . At a wavelength below the wavelength of zero dispersion, the parameter has a positive value, otherwise it is negative. Figure 2.10
Material dispersion can be determined through the specific dispersion by the expression:
.
The value - specific dispersion, , is determined experimentally. With different compositions of dopants in OF, it has different values depending on (Table 2.3).
Table 2.3 - Typical values of specific material dispersion
Waveguide (intramode) dispersion – this term denotes the dependence of the delay of a light pulse on the wavelength, associated with a change in the speed of its propagation in the fiber due to the waveguide nature of propagation. The pulse broadening due to waveguide dispersion is similarly proportional to the width of the radiation spectrum of the source and is defined as:
,
where is the specific waveguide dispersion, the value of which is presented in Table 2.4:
Table 2.4
– due to the differential group delay between beams with ground polarization states. The distribution of signal energy over different polarization states changes slowly with time, for example, due to temperature changes environment, refractive index anisotropy caused by mechanical forces.
In a single-mode fiber, not one mode propagates, as is commonly believed, but two perpendicular polarizations (modes) of the original signal. In an ideal fiber, these modes would propagate at the same speed, but real fibers do not have an ideal geometry. The main cause of PMD is the non-concentricity of the fiber core profile, which occurs during the fiber and cable manufacturing process. As a result, two perpendicular polarization components have different propagation velocities, which leads to dispersion (Figure 2.11)
Figure 2.11
The coefficient of specific polarization-mode dispersion is normalized per 1 km and has the dimension . The value of the polarization-mode dispersion is calculated by the formula:
Due to its small value, it must be taken into account exclusively in single-mode fiber, moreover, when high-speed signal transmission (2.5 Gbit / s and higher) with a very narrow spectral emission band of 0.1 nm or less is used. In this case, the chromatic dispersion becomes comparable to the polarization mode dispersion.
The specific PMD coefficient of a typical fiber is, as a rule, 
.
Fiber-optic communication lines (FOCL) have long occupied one of the leading positions in the telecommunications market. Having a number of advantages over other methods of information transmission (twisted pair, coaxial cable, wireless communication ...), FOCLs are widely used in telecommunication networks different levels, as well as in industry, energy, medicine, security systems, high-performance computing systems and many other areas.
The transmission of information in the FOCL is carried out via optical fiber (optical fiber). In order to competently approach the issue of using FOCL, it is important to understand well what an optical fiber is as a data transmission medium, what are its main properties and characteristics, what are the types of optical fibers. It is these basic issues of the theory of fiber-optic communication that this article is devoted to.
Structure of optical fiber
optical fiber(optical fiber) is a waveguide with a circular cross-section of a very small diameter (comparable to the thickness human hair), through which electromagnetic radiation of the optical range is transmitted. The wavelengths of optical radiation occupy the region of the electromagnetic spectrum from 100 nm to 1 mm, however, FOCL usually uses the near infrared (IR) range (760-1600 nm) and less often visible (380-760 nm). An optical fiber consists of a core (core) and an optical cladding made of materials that are transparent to optical radiation (Fig. 1).
Rice. 1. Construction of optical fiber
Light propagates through an optical fiber due to the phenomenon total internal reflection. The refractive index of the core, typically between 1.4 and 1.5, is always slightly larger than the refractive index of the optical cladding (difference of the order of 1%). Therefore, light waves propagating in the core at an angle not exceeding a certain critical value undergo total internal reflection from the optical cladding (Fig. 2). This follows from Snell's law of refraction. Through multiple re-reflections from the cladding, these waves propagate along the optical fiber.
Rice. 2. Total internal reflection in an optical fiber
On the first meters of the optical communication line, part of the light waves cancel each other due to the phenomenon of interference. light waves, which continue to propagate in the fiber over considerable distances, are called spatial mods optical radiation. The concept of a mode is described mathematically using Maxwell's equations for electromagnetic waves; however, in the case of optical radiation, modes are conveniently understood as the propagation trajectories of allowed light waves (indicated by black lines in Fig. 2). The concept of mode is one of the main ones in the theory of fiber-optic communication.
Main characteristics of optical fiber
The ability of an optical fiber to transmit an information signal is described using a number of geometric and optical parameters and characteristics, of which the most important are attenuation and dispersion.
1. Geometric parameters.
In addition to the ratio of the diameters of the core and shell, great importance for the signal transmission process, they also have other geometric parameters of the optical fiber, for example:
- out-of-roundness (ellipticity) of the core and shell, defined as the difference between the maximum and minimum diameters of the core (shell), divided by the nominal radius, expressed as a percentage;
- non-concentricity core and shell - the distance between the centers of the core and shell (Fig. 3).
Figure 3. Non-roundness and non-concentricity of the core and shell
Geometric parameters are standardized for different types optical fibre. Thanks to the improvement of manufacturing technology, the values of out-of-roundness and non-concentricity can be minimized, so that the effect of the inaccuracy of the geometry of the fiber on its optical properties is negligible.
(NA) is the sine of the maximum angle of incidence of the light beam on the end of the fiber, at which the condition of total internal reflection is satisfied (Fig. 4). This parameter determines the number of modes propagating in the optical fiber. Also, the value of the numerical aperture affects the accuracy with which the optical fibers must be spliced with each other and with other line components.
Fig 4. Numerical aperture
3. Profile of the refractive index.
Refractive index profile is the dependence of the refractive index of the core on its transverse radius. If the refractive index remains the same at all points of the cross section of the core, such a profile is called stepped . Among other profiles, the most widely used gradient profile, in which the refractive index smoothly increases from the shell to the axis (Fig. 5). In addition to these two main ones, there are also more complex profiles.
Rice. 5. Profiles of the refractive index
4. Attenuation (losses).
attenuation - is the decrease in the power of optical radiation as it propagates through the optical fiber (measured in dB / km). Attenuation occurs due to various physical processes occurring in the material from which the optical fiber is made. The main mechanisms for the occurrence of losses in an optical fiber are absorption and scattering.
a) Absorption . As a result of the interaction of optical radiation with particles (atoms, ions ...) of the core material, part of the optical power is released in the form of heat. Distinguish own takeover associated with the properties of the material itself, and impurity absorption , arising from the interaction of a light wave with various inclusions contained in the core material (hydroxyl groups OH - , metal ions ...).
b) Scattering light, that is, the deviation from the original propagation trajectory, occurs at various inhomogeneities of the refractive index, the geometric dimensions of which are less than or comparable to the radiation wavelength. Such inhomogeneities are a consequence of both the presence of defects in the fiber structure ( Mie scattering ), and the properties of the amorphous (non-crystalline) substance from which the fiber is made ( Rayleigh scattering ). Rayleigh scattering is a fundamental property of a material and defines the lower attenuation limit of an optical fiber. There are other types of scattering ( Brillouin-Mandelstam, Ramana), which appear at radiation power levels higher than those commonly used in telecommunications.
The attenuation coefficient has a complex dependence on the radiation wavelength. An example of such a spectral dependence is shown in Fig. 6. The region of wavelengths with low attenuation is called transparency window optical fibre. There may be several such windows, and it is at these wavelengths that the information signal is usually transmitted.
Rice. 6. Spectral dependence of the damping coefficient
The power loss in the fiber is also caused by various external factors. Thus, mechanical influences (bends, tensions, transverse loads) can lead to violation of the condition of total internal reflection at the interface between the core and the cladding and the escape of part of the radiation from the core. The environmental conditions (temperature, humidity, background radiation…) have a certain influence on the attenuation value.
Since the receiver of optical radiation has a certain threshold of sensitivity (the minimum power that a signal must have in order to receive data correctly), attenuation serves as a limiting factor for the range of information transmission over an optical fiber.
5. Dispersion properties.
In addition to the distance over which radiation is transmitted along the optical fiber, an important parameter is the speed of information transfer. Propagating along the fiber, optical pulses broaden in time. With a high pulse repetition rate at a certain distance from the radiation source, a situation may arise when the pulses begin to overlap in time (that is, the next pulse will arrive at the output of the optical fiber before the previous one ends). This phenomenon is called intersymbol interference (eng. ISI - InterSymbol Interference, see Fig. 7). The receiver will process the received signal with errors.
Rice. 7. Pulse overlap causing intersymbol interference: a) input signal; b) a signal that has traveled some distanceL1 over optical fiber; c) a signal that has traveled a distanceL2>L1.
Pulse broadening, or dispersion , is determined by the dependence of the phase velocity of light propagation on the radiation wavelength, as well as by other mechanisms (Table 1).
Table 1. Types of dispersion in optical fiber.
| Name | Short description | Parameter |
| 1. Chromatic dispersion | Any source emits not one wavelength, but a spectrum of slightly different wavelengths that propagate at different speeds. |
Chromatic dispersion coefficient, ps/(nm*km). It can be positive (spectral components with longer wavelengths move faster) and negative (vice versa). There is a zero dispersion wavelength. |
| a) Material chromatic dispersion | Associated with the properties of the material (dependence of the refractive index on the wavelength of radiation) | |
| b) Waveguide chromatic dispersion | Associated with the presence of a waveguide structure (refractive index profile) | |
| 2. Intermode dispersion | The modes propagate along different trajectories, so there is a delay in their propagation time. |
Bandwidth ( bandwidth), MHz*km. This value determines the maximum pulse repetition rate at which there is no inter-symbol interference (the signal is transmitted without significant distortion). The channel capacity (Mbit/s) may differ numerically from the bandwidth (MHz*km) depending on the method of encoding information. |
| 3. Polarization mode dispersion, PMD | A mode has two mutually perpendicular components (polarization modes) that can propagate at different speeds. |
Coefficient PMD, ps/√km. Time delay due to PMD, rated per 1 km. |
Thus, the dispersion in an optical fiber adversely affects both the range and the speed of information transmission.
Varieties and classification of optical fibers
The considered properties are common to all optical fibers. However, the described parameters and characteristics may differ significantly and have different influence on the process of information transmission, depending on the characteristics of the production of optical fibers.
The division of optical fibers according to the following criteria is fundamental.
- Material . The main material for manufacturing the core and cladding of an optical fiber is quartz glass of various compositions. However, a large number of other transparent materials are used, in particular polymeric compounds.
- Number of propagating modes . Depending on the geometric dimensions of the core and cladding and the value of the refractive index in an optical fiber, only one (main) or a large number of spatial modes can propagate. Therefore, all optical fibers are divided into two large classes: single-mode and multimode (Fig. 8).
Rice. 8. Multi-mode and single-mode fiber
Based on these factors, four main classes of optical fibers that have become widespread in telecommunications can be distinguished:
- (POF).
- (HCS).
Each of these classes is devoted to a separate article on our website. Each of these classes also has its own classification.
Production of optical fibers
The manufacturing process of optical fiber is extremely complex and requires great precision. The technological process takes place in two stages: 1) the creation of a blank, which is a rod of the selected material with a formed refractive index profile, and 2) the drawing of the fiber in the drawing tower, accompanied by coating with a protective sheath. There are a large number of different technologies for creating an optical fiber preform, the development and improvement of which is ongoing.
The practical use of optical fiber as an information transmission medium is impossible without additional hardening and protection. fiber optic cable is a design that includes one or many optical fibers, as well as various protective coatings, load-bearing and reinforcing elements, moisture-proof materials. Because of great variety fiber optic applications Manufacturers produce a wide variety of fiber optic cables, differing in design, size, materials used and cost (Fig. 9).
Fig.9. Fiber optic cables
3.3 OPTICAL FIBER
There are four main phenomena in optical fiber that limit the performance of WDM systems - these are chromatic dispersion, polarization mode dispersion of the first and second order, and nonlinear optical effects.
3.3.1 Chromatic dispersion
An important optical characteristic of the glass used in the manufacture of fibers is the dispersion of the refractive index, which manifests itself in the dependence of the signal propagation speed on the wavelength - material dispersion. In addition, in the production of single-mode fiber, when a quartz filament is drawn from a glass preform, deviations in the fiber geometry and in the radial refractive index profile occur to some extent. The fiber geometry itself, together with deviations from the ideal profile, also makes a significant contribution to the dependence of the signal propagation velocity on the wavelength, this is the waveguide dispersion.
The combined effect of the material and waveguide dispersions is called the chromatic dispersion of the fiber, fig. 3.16.
Fig.3.16 Dependence of chromatic dispersion on wavelength
The phenomenon of chromatic dispersion weakens as the spectral width of the laser radiation decreases. Even if it were possible to use an ideal source of monochromatic radiation with zero generation linewidth, then after modulation by the information signal, the signal would be spectrally broadened, and the greater the broadening, the greater the modulation rate. There are other factors that lead to the spectral broadening of the radiation, from which the chirping of the radiation source can be distinguished.
Thus, the original channel is represented not by a single wavelength, but by a group of wavelengths in a narrow spectral range - a wave packet. Since different wavelengths propagate at different velocities (or more precisely, at different group velocities), the optical pulse, which has a strictly rectangular shape at the input of the communication line, will become wider and wider as it passes through the fiber. With a long propagation time in the fiber, this pulse can mix with neighboring pulses, making it difficult to accurately reconstruct them. With an increase in the transmission rate and the length of the communication line, the influence of chromatic dispersion increases.
Chromatic dispersion, as already mentioned, depends on the material and waveguide components. At a certain wavelength λ o chromatic dispersion vanishes - this wavelength is called the wavelength of zero dispersion.
The single-mode stepped-index silica fiber has zero dispersion at a wavelength of 1310 nm. Such a fiber is often referred to as a dispersion-unshifted fiber.
The waveguide dispersion is primarily determined by the refractive index profile of the fiber core and inner cladding. In a fiber with a complex refractive index profile, by changing the ratio between the dispersion of the medium and the dispersion of the waveguide, one can not only shift the zero-dispersion wavelength, but also choose the desired shape of the dispersion characteristic, i.e. the form of the dependence of the dispersion on the wavelength.
The shape of the dispersion characteristic is key for WDM systems, especially over dispersion-shifted fiber (Rec. ITU-T G.653).
In addition to the parameter λ o, the parameter S o is used, which describes the slope of the dispersion characteristic at the wavelength λ o , fig. 3.17. In general, the slope at other wavelengths is different from the slope at wavelength λ o . The current value of the slope S o determines the linear component of the dispersion in the vicinity of λ o .
Rice. 3.17 The main parameters of the dependence of chromatic dispersion on the wavelength: λ o - the wavelength of zero dispersion and S o - the slope of the dispersion characteristic at the point of zero dispersion
Chromatic dispersion τchr(usually measured in ps) can be calculated using the formula
τ chr = D(λ) ∆τ L,
where D(λ)- chromatic dispersion coefficient (ps/(nm*km)) , and L- length of communication line (km). Note that this formula is not exact in the case of ultra-narrow-band radiation sources.
On fig. 3.18 separately shows the dependences of the waveguide dispersion for a fiber with unshifted (1) and shifted (2) dispersion and material dispersion on the wavelength.
Rice. 3.18 Wavelength dependence of dispersion (chromatic dispersion is defined as the sum of the material and waveguide dispersions.)
The chromatic dispersion of a transmission system is sensitive to:
increasing the length and number of sections of the communication line;
an increase in the transmission rate (because the effective width of the source generation line increases).
It is less affected by:
reduction of the frequency interval between channels;
increase in the number of channels.
Chromatic dispersion decreases with:
reducing the absolute value of the chromatic dispersion of the fiber;
dispersion compensation.
In WDM systems with conventional standard fiber (Rec. ITU-T G.652), special attention should be paid to chromatic dispersion, as it is large in the 1550 nm wavelength region.
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.
Chromatic dispersion consists of material and waveguide components and occurs during propagation in both single-mode and multimode fibers. However, it manifests itself most clearly in single-mode fiber due to the absence of intermode dispersion.
Material dispersion is due to the dependence of the refractive index of the fiber on the wavelength. The expression for the dispersion of a single-mode fiber includes the differential dependence of the refractive index on the wavelength.
Waveguide dispersion is due to the dependence of the mode propagation coefficient on the wavelength
where the coefficients M(l) and N(l) are the specific material and waveguide dispersions, respectively, and Dl (nm) is the broadening of the wavelength due to the incoherence of the radiation source. The resulting value of the specific chromatic dispersion coefficient is defined as D(l) = M(l) + N(l). Specific dispersion has the dimension ps/(nm*km). If the waveguide dispersion coefficient is always greater than zero, then the material dispersion coefficient can be either positive or negative. And here it is important that at a certain wavelength (approximately 1310 ± 10 nm for a stepped single-mode fiber) there is a mutual compensation of M(l) and N(l), and the resulting dispersion D(l) vanishes. The wavelength at which this occurs is called the zero dispersion wavelength l0. Usually, a certain range of wavelengths is indicated, within which l0 can vary for this particular fiber.
Corning uses the following method for determining the specific chromatic dispersion. Time delays are measured during the propagation of short light pulses in a fiber with a length of at least 1 km. After sampling data for several wavelengths from the interpolation range (800-1600 nm for MMF, 1200-1600 nm for SF and DSF), the delay measurements are resampled at the same wavelengths, but only on a short reference fiber (length 2 m ). The delay times obtained on it are subtracted from the corresponding times obtained on the long fiber in order to eliminate the systematic component of the error.
For single-mode stepped and multimode gradient fibers, the empirical Sellmeier formula is used: t (l) = A + Bl2 + Cl-2. The coefficients A, B, C are adjustable and are chosen so that the experimental points fit better on the t (l) curve. Then the specific chromatic dispersion is calculated by the formula:
where l0 = (C/B)1/4 is the zero dispersion wavelength, the new parameter S0 = 8B is the zero dispersion slope (its dimension is ps/(nm2*km)), and l is operating wavelength for which the specific chromatic dispersion is determined.
a) multimode gradient fiber (62.5/125)
b) single mode stepped fiber (SF)
c) single-mode dispersion-shifted fiber (DSF)
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