After optical signals travel a certain distance through optical fiber, they undergo attenuation and distortion, causing the input and output optical signal pulses to differ. This manifests as amplitude attenuation and waveform broadening of the optical pulses. The cause of this phenomenon is the presence of loss and dispersion within the optical fiber. Loss and dispersion are the most important parameters describing the transmission characteristics of optical fibers, limiting the transmission distance and capacity of the system. This section primarily discusses the mechanisms and characteristics of optical fiber loss and dispersion.
★Characteristics of optical fibers(part 2)
Loss characteristics of optical fiber
Optical fiber loss leads to signal attenuation, hence optical fiber loss is also called attenuation. As the distance increases in optical fiber, the intensity of the light signal decreases, as follows: P(z) = P(0) /10 - (4) where P(z) is the optical power at transmission distance z; P(0) is the optical power input into the optical fiber, i.e., the optical power injected at z=0; α(λ) is the optical fiber attenuation coefficient at wavelength in dB/km; and L is the transmission distance.
When t = L, the fiber attenuation coefficient is defined as
α(λ) = (10/L) lg[P(0)/P(L)]
When the working wavelength λ is dB, if the attenuation coefficient is measured in units of dB per kilometer, then A(λ) (unit is dB) is expressed as:
A(λ) = 10 lg[P(0)/P(L)]
Optical fiber communication has developed alongside continuous improvements in optical fiber manufacturing, specifically the reduction of fiber loss. Fiber loss is one of the main factors determining the relay distance in an optical fiber communication system. Many factors contribute to fiber loss, primarily absorption loss, scattering loss, and additional loss, and the mechanisms underlying these losses are quite complex. The following discussion uses silica optical fiber as an example to illustrate the various causes of loss.
Absorption Loss
Absorption loss mainly includes intrinsic absorption, impurity absorption (OH radicals), and structural defect absorption. Intrinsic absorption includes infrared and ultraviolet absorption.
Infrared absorption is the absorption of light energy caused by molecular resonance when light passes through quartz glass composed of SiO2. For example, the absorption peaks of Si-O are at 9.1 μm, 12.5 μm, and 21.3 μm, and the absorption loss of optical fiber is as high as 10 dB/km at 9.1 μm. Ultraviolet absorption is the energy absorbed when electrons are excited to transition to higher energy levels by light waves. This absorption occurs in the ultraviolet region and is therefore usually called ultraviolet absorption. Glass materials contain transition metal ions such as iron and copper, as well as OH- ions.Impurity absorption is the loss caused by the absorption of light energy by electron steps generated by ion vibrations under light wave excitation. For example, at 1.39 μm, the attenuation is 60 dB/km when the OH- ion concentration is 1 × 10⁻⁶.
Scattering loss
Scattering loss is the loss that radiates light energy out of the optical fiber in the form of scattering. It is caused by the non-uniform density within the fiber. The main types of scattering loss in optical fibers include Rayleigh scattering, Mie scattering, stimulated Brillouin scattering, stimulated Raman scattering, additional structural defects and bending scattering, and leakage scattering.
During optical fiber manufacturing, the thermal motion of molecules in the molten glass causes fluctuations in density and refractive index within its structure, which in turn causes light scattering. Scattering caused by particles much smaller than the wavelength of light is called Rayleigh scattering; scattering caused by particles of the same wavelength as light is called Mie scattering.
Rayleigh scattering is the primary cause of fiber loss. Rayleigh scattering exhibits a property of being proportional to 1/λ of the short wavelength, i.e., αR = K/λ. The proportionality constant K is related to the glass structure and composition. Generally, the higher the glass transition temperature and the more complex its composition, the greater the Rayleigh scattering loss.
Rayleigh scattering is influenced by the intensity of the incident light. Stimulated Brillouin scattering and stimulated Raman scattering, on the other hand, occur when the light energy density exceeds a certain high value and are produced by the interaction between light and the medium.
Additional losses
Additional losses (or application losses) are losses originating from external sources, such as those caused by fiber twisting or lateral pressure during construction, installation, and operation, resulting in macro-bending and micro-bending of the fiber.
The causes of fiber loss are summarized in Figure：
| Category | Sub-Category | Details / Description |
|---|---|---|
| Absorption Loss | Intrinsic Absorption | • Infrared absorption • Ultraviolet absorption |
| Extrinsic Absorption | Caused by impurities such as Fe, Cu, transition metals, and vibrational absorption of OH⁻ | |
| Scattering Loss | Linear Scattering | |
| - Rayleigh scattering | Scattering by particles much smaller than the optical wavelength | |
| - Mie scattering | Scattering by particles comparable in size to the optical wavelength | |
| Nonlinear Scattering | ||
| - Stimulated Brillouin scattering | Occurs when optical power density exceeds a lower threshold | |
| - Stimulated Raman scattering | Occurs when optical power density exceeds a higher threshold | |
| Additional Loss | - | Loss caused by microbending, macrobending, stretching, compression, and mechanical deformation |
Dispersion characteristics of optical fibers
In physics, dispersion refers to the phenomenon where light of different colors is dispersed after passing through a transparent medium. A beam of white light is split into a seven-color band after passing through a prism. This is because glass has different refractive indices for different colors (different frequencies or different wavelengths). The longer the wavelength (or the lower the frequency), the lower the refractive index of the glass; the shorter the wavelength (or the higher the frequency), the higher the refractive index. In other words, the refractive index of glass is a function of the frequency (or wavelength) of the light wave. When white light composed of different colors is incident at the same angle θ, according to the law of refraction (n = sinθ/n²), different colors of light will have different angles of refraction due to the different n² values, thus separating the different colors of light, resulting in dispersion. Since n = c/n (where c is the speed of light, c = 3 × 10⁻⁶ m/s), it is clear that different colors of light travel at different speeds within the glass.
In optical fiber propagation theory, the meaning of the term "dispersion" has been broadened. In optical fibers, signals are carried and transmitted by light waves of many different modes or frequencies. When the signal reaches the terminal, the different modes or frequencies of light waves experience transmission delay differences, causing signal distortion. This phenomenon is collectively called dispersion. For digital signals, dispersion causes pulse broadening after propagating a certain distance through the fiber. In severe cases, consecutive pulses will overlap, forming intersymbol interference. Therefore, dispersion determines the transmission bandwidth of the optical fiber and limits the system's transmission rate or repeater distance. Dispersion and bandwidth are the same characteristic of optical fibers described from different perspectives.
Based on the causes of dispersion, optical fiber dispersion is mainly divided into: modal dispersion, material dispersion, waveguide dispersion, and polarization mode dispersion, which will be introduced below.
Mode Dispersion
Modal dispersion generally exists in multimode fibers. Because multiple modes coexist in a multimode fiber, and the group propagation speeds of different modes along the fiber axis are different, they will inevitably arrive at the terminal at different times, resulting in a time delay difference and forming intermodal dispersion, thus causing pulse width broadening. The pulse broadening due to modal dispersion is shown in Figure 2-10. For an ideal single-mode fiber, since only one mode (fundamental mode - LP or HE mode) is transmitted, there is no modal dispersion, but polarization mode dispersion exists.
Now, we estimate the maximum modal dispersion of a step-index multimode fiber. The modal dispersion of a step-index multimode fiber is shown in Figure 2-11. In a step-index multimode fiber, the two fastest and slowest propagating rays are the ray ① propagating along the axis and the ray ② incident at a critical angle of 0°, respectively. Therefore, the maximum mode dispersion in a step-index multimode fiber is the time difference between the time taken by ray ② (Tmax) and the time taken by ray ① (Tmin) to reach the terminal, ΔTmux: ΔTmux = Tmax / Tmin
According to geometric optics, in an optical fiber of length L, let the speeds of light rays ① and ② along the axial direction be c/n and sinθ·c/n, respectively. Therefore, the modal dispersion of the optical fiber is...
In weakly guided optical fibers (fibers where ni and ni differ very little), A = (ni - n)/n. If Δ = 1%, ni = 1.5 for silica optical fibers, and the fiber length is 1 km, then the maximum intermodal dispersion ΔTm can be calculated as 50 ns. Therefore, it is evident that the longer the fiber length, the more severe the intermodal dispersion; and the greater the relative refractive index difference Δ, the more severe the intermodal dispersion.
Material dispersion
Because the refractive index of optical fiber materials varies with the wavelength of light, the group velocity of different frequencies of the optical signal differs, causing a transmission delay difference, a phenomenon known as material dispersion. This dispersion depends on the wavelength characteristics of the refractive index of the optical fiber material and the linewidth of the light source.
In digital fiber optic communication systems, the output light from the actual light source is not a single wavelength but has a certain spectral linewidth. Since the refractive index of the fiber material is a function of wavelength, the propagation speed of light within it (λ) = c/n(λ) also varies with the wavelength. When a light pulse emitted by a light source with a certain spectral linewidth is incident on a single-mode fiber and propagates, light pulses of different wavelengths will have different propagation speeds, resulting in a time delay difference when they reach the output end, thus causing pulse broadening. This is the mechanism of material dispersion.
If the group velocity is known to be u = da/dB, then the group delay per unit length is T = 1/v, = n,/c. Therefore, the material dispersion of an optical fiber of length L is...
In the formula, c is the speed of light in vacuum; λ is the refractive index of the fiber core; λ is the wavelength of light; and Aλ is the spectral linewidth of the light source, where Aλ = λ - λ, representing the wavelength range centered at A. Generally, the dispersion coefficient is used to measure the magnitude of dispersion. The dispersion coefficient D (unit: ps/(nm·km)) is defined as...
It can be seen that the dispersion coefficient is the dispersion caused by a light source with a unit spectral linewidth propagating in a unit length of optical fiber. If the material dispersion coefficient of the optical fiber is known, the material dispersion can be easily calculated as ΔTm = DmAAL.
Example 2-1: Suppose that the maximum material dispersion coefficient of an optical fiber at a wavelength of 1.31m is D = 3.5ps/(nm·km). If a semiconductor laser with a center wavelength of 1.31µm is used to generate transmission light with a spectral linewidth of λ = 4nm, calculate the material dispersion caused by this light propagating in a 1km length of optical fiber.
Solution: The material dispersion of the optical fiber can be easily calculated as:
Tm = DmLΔA = 3.5ps/(nm·km) x 1km x 4nm = 0.014ns = 14ps
As seen in Example 2-1, the material dispersion is relatively small, even smaller than the modal dispersion of a step-index multimode fiber. It should also be noted that the dispersion coefficient of an optical fiber (not just the material dispersion coefficient) can be positive or negative. In optical fiber, the group delay (A) increases with the carrier wavelength; in other words, shorter wavelength light waves propagate faster.In this case, the dispersion coefficient is negative, called negative dispersion; conversely, longer wavelength light waves propagate slower than shorter wavelength light waves.
Here, the dispersion coefficient is positive, called positive dispersion. Clearly, if two optical fibers with opposite dispersion coefficient signs are fused together,the material dispersion will be improved.
waveguide dispersion
Waveguide dispersion ΔTw refers to a specific guided mode in an optical fiber. Different wavelengths have different phase constants β, resulting in different group velocities and thus dispersion. Waveguide dispersion is also related to various factors such as the structural parameters of the optical fiber and the relative refractive index difference between the core and cladding; therefore, it is also called structural dispersion.
Polarization mode dispersion
Polarization mode dispersion is a type of dispersion unique to single-mode optical fibers. Because single-mode fibers actually transmit two mutually orthogonal polarization modes, their electric fields are polarized along the x and y directions, respectively.
Fiber optic bandwidth
The dispersion and bandwidth of optical fibers describe the same characteristic. In fact, dispersion describes the extent to which a light pulse broadens along the time axis after transmission; it's a description of the fiber's characteristics in the time domain. Bandwidth, on the other hand, describes this characteristic in the frequency domain. In the frequency domain, for a modulating signal, the optical fiber can be considered a low-pass filter. When the high-frequency components of the modulating signal pass through it, they are severely attenuated. That is, if the amplitude of the input signal (modulating signal) remains constant, but only the frequency changes, the amplitude of the output signal after transmission through the fiber will change with the frequency of the modulating signal (input signal). TTU-T recommends specifying that the bandwidth of an optical fiber is [bandwidth per kilometer].
