Introduction
The further improvement of the telecommunications networks has enlarged the need of the optical signal processing. The link lengths have grown to thousands of kilometers with no need to convert optical signals back and forth to electric form, and transmission speeds of terabits per second are today feasible. This ever-growing demand for the high-speed communication has forced to use higher bit rates and transmission powers. One interesting aspect of optical fibers system is their broad bandwidth compared to other media, such as radio waves and twisted-pair wires. Still, an optical fiber system is not ideal; it acquires some unwanted characteristics. Dispersion and nonlinearity are the major limiting factors in an optical fiber communication system. Fiber dispersion causes different spectral components of a signal to travel at different speeds. Hence, for a given transmission distance different spectral components arrive at the destination at different times. This results in a pulse broadening effect when a pulse propagates along an optical fiber. However, the situation is different when the nonlinearity and dispersion are considered together. In some situation, the nonlinearity could counteract the dispersion. In addition, when multiple channels are considered, the fiber nonlinearity results in interactions among channels. Nonlinear effects have become important at high optical power levels and have become even more significant since the development of erbium-doped fiber amplifier (EFDA) and wavelength division multiplexed (WDM) systems. By increasing the capacity of the optical transmission line, which can be done by increasing channel bit rate, decreasing channel spacing or the combination of both, the fiber nonlinearities come to play even more decisive role.
Aim
The aim of this work is to build up a simple and accurate measurement setup for maintenance measurement’s in multimode optical fiber transmission lines measuring and analyzing for insertion loss in the fiber line
1 Optical Fiber Communication System Concept
Optical communication systems differ in principle from microwave systems only in the frequency range of the carrier wave used to carry the information. The optical carrier frequencies are typically ∼200 THz, in contrast with the microwave carrier frequencies (∼1 GHz). An increase in the information capacity of optical communication systems by a factor of up to 10,000 is expected simply because of such high carrier frequencies used for light wave systems. This increase can be understood by noting that the bandwidth of the modulated carrier can be up to a few percent of the carrier frequency. Taking, for illustration, 1% as the limiting value, optical communication systems have the potential of carrying information at bit rates ∼1 Tb/s. It is this enormous potential bandwidth of optical communication systems that is the driving force behind the worldwide development and deployment of light wave systems. Current state-of-the-art systems operate at bit rates ∼10 Gb/s, indicating that there is considerable room for improvement. [1]
Fig. Generic optical communication system [1]
The application of optical fiber communications is in general possible in any area that requires transfer of information from one place to another. However, fiber-optic communication systems have been developed mostly for telecommunications applications. This is understandable in view of the existing worldwide telephone networks which are used to transmit not only voice signals but also computer data and fax messages. [1]
1.1 Transmission Characteristics of Optical Fibers
Optical-fiber systems have many advantages over metallic-based communication systems. These advantages include interference, attenuation, and bandwidth characteristics. Furthermore, the relatively smaller cross section of fiber-optic cables allows room for substantial growth of the capacity in existing conduits. Fiber-optic characteristics can be classified as linear and nonlinear. Nonlinear characteristics are influenced by parameters, such as bit rates, channel spacing, and power levels. [2]
Fiber Attenuation
Attenuation is a decrease of signal strength during transmission, such as when sending data collected through automated monitoring. Attenuation is represented in decibels (dB), which is ten times the logarithm of the signal power at a particular input divided by the signal power at an output of a specified medium. Attenuation can be caused by absorption, Scattering and Radiative losses (bending losses)
Fig. Attenuation in an optical fiber
Optical Fiber Dispersion
When a short pulse of light travels through an optical fiber its power is “dispersed” in time so that the pulse spreads into a wider time interval. [4] There are three basic sources of dispersion in optical fibers: modal dispersion, material dispersion and waveguide dispersion.
Modal dispersion
Modal dispersion occurs only in Multimode fibers. It arises because rays follow different paths through the fiber and consequently arrive at the other end of the fiber at different times. Mode is a mathematical and physical concept describing the propagation of electromagnetic waves through media. [3] In case of fiber, a mode is simply a path that a light ray can follow in travelling down a fiber. The number of modes supported by a fiber ranges from 1 to over 100,000. Thus, a fiber provides a path of travels for one or thousands of light rays depending on its size and properties. Since light reflects at different angles for different paths (or modes), the path lengths of different modes are different. The spreading of light is called modal dispersion. [3] Modal dispersion is that type of dispersion that results from the varying modal path lengths in the fiber. Typical modal dispersion figures for the step index fiber are 15 to 30 ns/ km. This means that for light entering a fiber at the same time, the ray following the longest path will arrive at the other end of 1 km long fiber 15 to 30 ns after the ray, following the shortest path. [3]
Material Dispersion (Chromatic dispersion)
Different wavelengths also travel at different velocities through a fiber, in the same mode, as n = c/v. where n is index of refraction, c is the speed of light in vacuum and v is the speed of the same wavelength in the material. The value of v in the equation changes for each wavelength, Thus Index of refraction changes according to the wavelength. Dispersion from this phenomenon is called material dispersion, since it arises from material properties of the fiber. Each wave changes speed differently, each is refracted differently. White light entering the prism contains all colors. [3]
Waveguide dispersion
Waveguide dispersion occurs because dissimilar spectral components of a pulse travel with different velocities by the essentials mode of the fiber. It is because of axial propagation constant β being a function of wavelength due to the existence of one or more boundaries in the structure of the fiber. Without such boundaries, the fiber reduces to a equivalent medium, the essentials mode becomes a uniform plane-wave, and the waveguide dispersion effect is eliminated.
1.2 Light Propagation in Optical Fiber
In its simplest form an optical fiber consists of a cylindrical core of silica glass surrounded by a cladding whose refractive index is lower than that of the core. [1] Because of an abrupt index change at the core–cladding interface, such fibers are called step-index fibers. In a different type of fiber, known as graded-index fiber, the refractive index decreases gradually inside the core. [1]
An optical fiber consists of core surrounded by cladding. Step-index fiber is the simplest form of an optical fiber. It has the refractive index ncore for the core and slightly lower refractive index ncladding for the cladding. [1]This makes possible to realize long optical transmission paths through total internal reflection from the interface of the core and the cladding.
Fig Schematic illustration of the refractive index profiles of (a) step-index (b) depressed cladding (c) graded-index fibers [1]
Nowadays, in order to eliminate cladding modes, njacket is often made higher than ncladding.
The material of low loss fibers is silicon dioxide (SiO2), which can be doped with different compounds to change the refractive index. For example, germanium dioxide (GeO2) and phosphorus pentoxide (P2O5) can be used to increase the refractive index of the core. For reducing the refractive index, it is possible to use materials such as boron (B) and fluorine (F). Additional dopants can be used for specific applications. Dopants such as erbium chloride (ErCl3) and neodymium oxide (Nd2O3) and compounds consisting of ytterbium, praseodymium and thulium are used. These rare-earth elements are often used for optical amplifiers and fiber lasers.
Propagation of light
If light propagates in a medium, its speed is reduced. The speed is affected by such factors as purity and structure of the material. The speed of light, c, inside a medium is defined through the refractive index n as
c=c_0/n (1.1)
where c0 = 2.99792458·108 m/s is the speed of light in vacuum.
In an optical fiber, light propagates partly in the core and partly in the cladding. Therefore, the propagation constants, βi, of a mode of the fiber satisfy the condition k0ncladding < βi < k0ncore, where k0 is the wavenumber in vacuum. Instead of the propagation constant of the mode, we can use effective index neff = βi / k0. The effective index of the mode lies between the indexes of the core and cladding. For the monochromatic wave in a single-mode fiber, the effective index is analogous to the refractive index and it can be replaced in Eq. 1.1 to obtain the speed of light inside the single-mode fiber. As the light propagates along the fiber it is attenuated. The output power, PT, after the length L will be: P_T= P_0 e^(-αL) (1.2) where α [1/m] is an attenuation constant representing total losses of the fiber, and P0 is the input power. It is customary to express αdB in units of dB/km. The conversion can be done with a relation α= ln(〖10〗^(α_dB/10) )/1000 [1/m]. (1.3) The optical power is often given in units of dBm instead of watts. This makes it possible to do relative calculations only by subtracting and adding powers. The dBm-unit is defined as the power related to 1 milliwatt in decibel-units. This relation between W and dBm can be written as P[dBm]=〖10log_10〗((P[W])/(〖10〗^(-3) W)) (2.4) 1.3 Type of Fiber Fiber is classified into different types (multimode or singlemode) based on the way in which the light travels through it. The fiber type is closely related to the diameter of the core and cladding. [5] Fig. Type of Glass fiber [5] Multimode fiber, due to its large core, allows for the transmission of light using different paths (multiple modes) along the link. For this reason, multimode fiber is quite sensitive to modal dispersion. The primary advantages of multimode fiber are the ease of coupling to light sources and to other fiber, lower cost light sources (transmitters), and simplified connectorization and splicing processes. However, its relatively high attenuation and low bandwidth limit the transmission of light over multimode fiber to short distances. [5] 1.5 Fig. Composition of multimode fiber [5] 1.3.1 Step-Index Multimode Fiber Step-index (SI) multimode fiber guides light rays through total reflection on the boundary between the core and cladding. The refractive index is uniform in the core. Step-index multimode fiber has a minimum core diameter of 50 µm or 62.5 µm, a cladding diameter between 100 and 140 µm, and a numerical aperture between 0.2 and 0.5. Due to modal dispersion, the drawback of step-index multimode fiber is its very low bandwidth, which is expressed as the bandwidth-length product in MHz.km. A fiber bandwidth of 20 MHz.km indicates that the fiber is suitable for carrying a 20 MHz signal for a distance of 1 km, a 10 MHz signal for a distance of 2 km, a 40 MHz signal for a distance of 0.5 km, etc. Step-index multimode fiber is surrounded by a plastic coating and is used mostly for short distance links that can accommodate high attenuations. [5] 1.6 Fig. Light propagation though step-index multimode fiber [5]
1.3.2 Graded-Index Multimode Fiber
The core of graded-index (GI) multimode fiber possesses a non-uniform refractive index, decreasing gradually from the central axis to the cladding. This index variation of the core forces the rays of light to progress through the fiber in a sinusoidal manner. [5] The highest order modes will have a longer path to travel, but outside of the central axis in areas of low index, their speeds will increase. In addition, the difference in speed between the highest order modes and the lowest order modes will be smaller for graded-index multimode fiber than for step-index multimode fiber. 1.7 Fig.Light propagation through graded-index multimode fiber Typical attenuations for graded-index multimode fiber: 3 dB/km at 850 nm 1 dB/km at 1300 nm Typical numerical aperture for graded-index multimode fiber: 0.2 Typical bandwidth-length product for graded-index multimode fiber: 160 MHz.km at 850 nm 500 MHz.km at 1300 nm Typical values for the refractive index: 1.49 for 62.5 µm at 850 nm 1.475 for 50 µm at 850 nm and 1.465 for 50 µm at 1300 nm
1.3.3 Singlemode Fiber
The advantage of singlemode fiber is its higher performance with respect to bandwidth and attenuation. The reduced core diameter of singlemode fiber limits the light to only one mode of propagation, eliminating modal dispersion completely. With proper dispersion compensating components, a singlemode fiber can carry signal of 10 Gbit/s, 40 Gbit/s and above over long distances. The system carrying capacity may be further increased by injecting multiple signals of slightly differing wavelengths (wavelength division multiplexing) into one fiber. [5] The small core size of singlemode fiber generally requires more expensive light sources and alignment systems to achieve efficient coupling. In addition, splicing and connectorization is also somewhat complicated. Nonetheless, for high performance systems or for systems that are more than a few kilometers in length, singlemode fiber remains the best solution. The typical dimensions of singlemode fiber range from a core of 8 to 12 µm and a cladding of 125 µm. The typical core-cladding angle is 8.5°. The refractive index of singlemode fiber is typically 1.465 1.8 Fig.The composition of singlemode fiber [5] Since the small core diameter of singlemode fiber decreases the number of propagation modes, only one ray of light propagates down the core at a time.
1.3.4 Mode Field Diameter
The mode field diameter (MFD) of singlemode fiber can be expressed as the section of the fiber where the majority of the light energy passes. The MFD is larger than the physical core diameter. That is, a fiber with a physical core of 8 µm can yield a 9.5 µm MFD. This phenomenon occurs because some of the light energy also travels through the cladding.[5] 1.9 Fig. The mode field diameter (MFD) of single mode fiber [5] Larger mode field diameters are less sensitive to lateral offset during splicing, but they are more sensitive to losses incurred by bending during either the installation or cabling processes. Effective Area Effective area is another term that is used to define the mode field diameter. The effective area is the area of the fiber corresponding to the mode field diameter. 1.10 Fig.The effective area of single mode fiber The effective area (or mode field diameter) has a direct influence on non-linear effects, which depend directly on the power density of the light injected into the fiber. The higher the power density, the higher the incidence of non-linear effects. [5] The effective area of a fiber determines the power density of the light. For a given power level, a small effective area will provide a high power density. Subsequently, for a larger effective area, the power is better distributed, and the power density is less important. In other words, the smaller the effective area, the higher the incidence of non-linear effects. The effective area of a standard singlemode fiber is approximately 80 µm and can be as low as 30 µm for compensating fiber. The effective area of a fiber is often included in the description of the fiber’s name, such as Corning’s LEAF (for large effective area fiber).
2 Nonlinearities in Optical Fibers
A silica optical fiber is strictly speaking not a linear transmission medium. At optical powers beyond 1 mW nonlinearities become more and more noticeable. We investigate several effects and their influence on optical data transmission systems. [6] If a nonlinearity is to be utilized it is beneficial to choose a small core area since this increases the power density and hence the nonlinear effect. When a nonlinearity threatens to impair transmission and this is more frequent one chooses if possible a fiber with large core area. [6] The nonlinear effects can be divided into two categories. The first type arises due the interaction of light waves with phonons. It contains two important nonlinear scattering effects called stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS). The second category of the nonlinearities contains the effects that are related to the Kerr effect, that is, the intensity dependence on the nonlinear refractive index of the optical fiber. The main effects in this category are self -phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM). The category also contains effects called modulation instability and soliton formation. These nonlinear effects are characterized and influenced by several parameters, including dispersion, effective area of the optical fiber, overall unregenerate system length, channel spacing in multi-channel systems, the degree of longitudinal uniformity of the fiber characteristics, source linewidth and intensity of the signal. Therefore, at high bit rates such as 10 Gb/s and above and/or at higher transmitted powers, it is important to consider the effect of nonlinearities. In the case of WDM systems, nonlinear effects can become important even at moderate optical powers and bit rates.
2.1 Effective Length
As the signal propagates along the fiber its power decreases because of attenuation. Modeling this effect can be quite complicated, but in practice, a simple model that assumes that the power is constant over a certain effective length, Leff, has proven to be quite sufficient in estimating the effect of nonlinearities. Most of the nonlinear effects occur in the beginning of the fiber. The principle of effective length is presented in Fig. 2.1. On the left side, power is attenuated along the whole fiber length, and on the right, side the power is assumed to be constant over the certain effective length of L_eff=1/P_0 ∫_0^L▒P_0 e^(-αz) dz=1/(-α) l⁄0 e^(-αz)=1/(-α) (e^(-αL)-1)= (1-e^(-αL))/α where α is the attenuation constant. 2.1.Fig. (a) Propagating power along the fiber length L and (b) the corresponding model for effective length
2.2 Nonlinear Refractive Index
Nonlinear interactions between light and silica fiber start to arise, when high powers are used. The response of any dielectric material to light becomes nonlinear for intense electromagnetic fields. Several nonlinear effects influence the propagation of light. [7] The total polarization P is not linear with respect to the electric field E but it can be written as P = ε 0 (χ (1) ⋅ E + χ (2) ⋅ E ⋅ E + χ (3) ⋅ E ⋅ E ⋅ E + L), (2.1) where ε0 is the vacuum permittivity and χ(j ) (j = 1,2,…) is jth order susceptibility. The linear susceptibility χ(1) represents the dominant contribution to P. It is included in the refractive index n and the attenuation constant α. The second order susceptibility χ(2) is responsible for nonlinear effects such as second harmonic generation and sum-frequency generation. However, these phenomena arise from the lack of inversion symmetry of the propagation medium molecules. As SiO2 is a symmetrical molecule, the second-order susceptibility normally vanishes. [7] The lowest-order nonlinear effects in the optical fibers originate from the third-order susceptibility χ(3), which is responsible for such phenomena as third-harmonic generation, four-wave mixing and nonlinear refraction. Most of the nonlinear effects in optical fiber arise from the nonlinear refraction, a phenomenon referring to the intensity dependence of the refractive index. The relation between the refractive index n, intensity I and power P is n=n_0+n_2 I=n_0+((n_2 )/A_eff )P, (2.2) where the first term n0 is the wavelength-dependent part of the refractive index and Aeff is the effective area of the optical fiber. The second term, nonlinear refractive index, n2, collects up intensity-dependent nonlinear effects. The most interesting effects of this group are self-phase modulation (SPM), cross-phase modulation (XPM) and four- wave mixing (FWM). Because all of the above-mentioned effects are intensity-dependent and optical fiber has relatively low value of nonlinear susceptibility χ(3), these effects are visible only at high powers.[7] γ=(ω_0 n_2)/(c_0 A_eff )=2π/λ_0 n_2/A_eff (2.3) where ω0 represents the angular frequency of the light wave, c0 is the speed of light in vacuum, λ0 is the wavelength in vacuum and Aeff is the effective area of the optical fiber. In general, n2 is related to χ for linear polarization as[7] n_2=3/8n χ_xxx^((3)) (2.4) Where χ(3) is the third-order susceptibility and x represents one direction of the principal axes. The optical field is assumed to be linearly polarized, and therefore only one component of the fourth-rank tensor contributes to the refractive index. Typically, measured values for nonlinear refractive index n2 are found to vary in the range 2.2 – 3.9×10-20 m2/W for silica. Such large variation in the values of n2 can be explained by different dopants in the fiber core and cladding, such as GeO2 and Al2O3.[7] 2.2.1 Self-phase modulation (SPM) Self-phase modulation (SPM) is proportional to the optical power, to be precise, to the instantaneous power that is variable within a period of the optical wave. It can be understood as a modulation, where the intensity of the signal modulates its own phase. In the SPM, different parts of the pulse undergo optical power dependent phase shifts, leading to broadening of the pulse spectrum. [6] Nonlinear pulse propagation Pulse propagation in fibers can be described by nonlinear Schrödinger equation (NLS) ∂A/∂z+β_1 ∂A/∂t+(iβ_2)/2 (∂^2 A)/(∂t^2 )+α/2 A=iγ|A|^2 A, (2.5) where A is the pulse amplitude that is assumed to be normalized such that │A│2 represents the optical power. NLS equation includes the effects of fiber losses through α, chromatic dispersion through β1 and β2, and fiber nonlinearity through γ. The dispersion parameter, D, is related to propagation constants β1 and β2 by the relation [7]: D=(dβ_1)/dλ=-2πc/λ^2 β_2≈λ/c_0 (d^2 n)/(dλ^2 ) (2.6) where c0 is the speed of light in vacuum, λ is the wavelength in vacuum, and n is the refractive index. Nonlinear phase shift The group velocity dispersion can be neglected for relatively long pulses (T0>100ps) with a large peak power (P0>1W) [7]. As a result, the term β2 can be set to zero in Eq. 2.5 Now, the SPM gives rise to an intensity-dependent nonlinear phase shift φSPM.
First, normalized amplitude, U, is defined by [7]
A(z,T)=√(P_0 e) (_^(-αz)⁄2)U (z,t), (2.7)
where A is the slowly varying amplitude of the pulse, P0 is the peak power of the incident pulse, α represents losses, and τ is the normalized time scale proportional to the input pulse width T0. The τ is defined as
τ=T/T_0 =(t-z⁄v_g )/T_0 (2.8)
where vg is the group velocity, and T is measured pulse width in a frame of reference moving with the pulse at group velocity after pulse has propagated time t and distance z in the fiber. Now, the pulse-propagation equation [7] can be written with normalized amplitude as
∂U/∂z=〖ie〗^(-αz)/L_NL |U|^2 U (2.9)
where α accounts for fiber losses. The nonlinear length LNL is defined as [7]
L_NL=1/(γP_0 ) (2.10)
where P0 is the peak power and γ is related to nonlinear refractive index as in Eq. 2.3. Eq. 2.9 can be solved directly to obtain the general solution
U(L,T)=U(0,T) e^(iφ_NL (L,T) ) (2.11)
Where U(0,T) is the field amplitude at z = 0 and nonlinear phase shift is
φ_NL (L,T)=|U(0,T)|^2 (L_eff/L_NL ) (2.12)
with the effective length Leff defined in Eq. 6.
Eq. 2.11 shows that SPM gives rise to the intensity -dependent phase shift but the pulse shape remains unaffected. The nonlinear phase shift φNL increases with fiber length. In the absence of fiber losses α = 0 and Leff = L , the maximum phase shift φMAX occurs at the pulse center located at T = 0. With U normalized such that │U(0,0)│ = 1, it is given by
φ_MAX=L_eff/L_NL =γP_0 L_eff (2.13)
The effect of SPM to an optical signal propagating along the fiber is presented in Fig. 2.2. The frequency chirp and dispersion induce distortion to output signal.
2.2 Fig. Frequency chirp and dispersion induce distortion to output signal. Four curves are input power PIN(t), SPM induced phase shift φ(t), frequency chirp f(t) and output power POUT(t).
2.2.2 Cross-Phase Modulation (XPM)
In systems with multiple wavelength channels, consequent effects of intensity-dependent phase shift can be affected by the signals in the other channels. In this effect called cross-phase modulation (XPM), the intensity of a second channel modulates the phase of the first channel. Therefore, XPM is always accompanied by SPM and occurs, because the nonlinear refractive index seen by an optical signal in a nonlinear medium depends not only on its own intensity, but also on the intensity of the other propagating signals. This phase modulation broadens the signal spectrum.
When a signal at wavelength λ1 is overlapping another signal at wavelength λ2, signals are interfering. This is shown in Fig. 2.3, where interfering pulse is causing a red shift to the overlapped signal’s trailing edge and later blue shift to the leading edge. This can be understood, if the leading edge is considered to carry red shift components and the trailing edge blue shifted components, respectively, when the spectrum of the signal pulse is shifted towards red, the spectrum of the interfering pulse is shifted towards blue.
2.3. Fig. The effect of XPM to signal pulse in the different points of overlapping
In Fig. 2.4, the spectra of the interfering pulses are investigated, before and after overlapping each other. A spectrum where an unmodulated pulse coincides with modulated pulse is presented. After pulses have overlapped each other, the phase of the first channel has been modulated by the second channel.
Fig. The effect of XPM to unmodulated signal’s spectrum
The effects of XPM can be significantly reduced by increasing the channel spacing in WDM systems. Because of the fiber chromatic dispersion, the propagation constant βi becomes rapidly different so that the pulses corresponding to each other on individual channels rapidly walk away from each other. Because this walk-off phenomenon, the pulses which were overlapping at the beginning of the fiber will be separated after some time. Therefore, they are not able to interact with each other anymore. If the dispersion over the used wavelength range does not vary significantly (e.g. in dispersion shifted fibers), then the walk-off effect is small and different wavelengths travel approximately at the same speed. Thus, XPM can be a significant problem in high-speed WDM systems using dispersion shifted fibers.
2.3 Nonlinear Scattering
The nonlinear scattering effects in optical fibers are due to the inelastic scattering of a photon to a lower energy photon. The energy difference is absorbed by the molecular vibrations or phonons in the medium. In other words, one can state that the energy of a light wave is transferred to another wave, which is at a higher wavelength (lower energy) such that energy difference appears in form of phonons. [7]
Nonlinear scattering contains two important phenomena caused by interaction of light with phonons. The first one is stimulated Brillouin scattering (SBS) and the second one is stimulated Raman scattering (SRS). Both of these phenomena are related to vibrational excitation modes of silica and transfer energy from the optical field to the nonlinear medium. The nonlinear scattering effects start to influence the signal close to their threshold power.
SBS occurs when an intense light beam scatters from an acoustic phonon. SRS takes place when optical phonon is involved. Different phonons cause some basic differences between the phenomena. A fundamental difference is that SBS occurs mainly in the backward direction while SRS can occur in both directions.
2.3.1 Stimulated Raman Scattering (SRS)
Stimulated Raman scattering (SRS) is a nonlinear process that can also be exploited in Raman amplifiers and tunable Raman lasers. It can also severely limit the performance of multichannel light wave systems by transferring energy from one channel to the lower frequency neighboring channels. If a small fraction of power is transferred from one optical field to another due to the spontaneous Raman scattering, the phenomenon is called the Raman effect. Raman effect can be described quantum-mechanically as scattering of a photon by one of the molecules to lower-frequency photon, while the molecule makes transition to a higher energy vibrational state. Incident light acts as a pump for generating the frequency-shifted radiation called Stokes wave. In a case of an intense pump wave SRS can occur, when Stokes wave grows rapidly inside the medium such that most of the pump energy is transferred to it.
Fig. Raman-gain spectrum for fused silica as a function of the frequency shift at pump wavelength λpump = 1μm
When a monochromatic light beam propagates in an optical fiber, spontaneous Raman scattering (Fig. 2.6(a)) occurs. It transfers some of the photons to new frequencies. The scattered photons may lose energy (Stokes shift) or gain energy (anti-Stokes shift). If the pump beam is linearly polarized, the polarization of scattered photon may be the same (parallel scattering) or orthogonal (perpendicular scattering). If photons at other frequencies are already present, then the probability of scattering to those frequencies is enhanced. This process is known as stimulated Raman scattering (Fig 2.6(b)).
In stimulated Raman scattering, a coincident photon at the downshifted frequency will receive a gain. This feature of Raman scattering is exploited in Raman amplifiers for signal amplification.
Fig. (a) Spontaneous Raman scattering phenomenon. (b) Stimulated Raman scattering phenomenon.
2.3.2 Stimulated Brillouin scattering (SBS)
Stimulated Brillouin scattering (SBS) can be considered classically as a nonlinear interaction between the input field and Stokes fields through an acoustic wave. The power of the input field generates the acoustic wave through the process of electrostriction. The acoustic wave in turn modulates the refractive index of the propagation medium. This power-induced index grating scatters the incoming light through Bragg reflection. Scattered light is downshifted in frequency, because of the Doppler shift associated with a grating moving at the acoustic velocity [7]
Fig. Principle of SBS.
The SBS takes place in a very narrow band width of 20MHz at 1.55μm [8]. The interaction produces the Stokes wave propagating to a direction opposite to the pump wave. The back scattered power caused by the SBS has been presented in Fig. 2.8. The peak at lower wavelength is not frequency shifted since it is caused by the Rayleigh scattering and the reflections of the connectors and splices. The power, back scattered due to SBS, is frequency shifted to higher wavelength, because of the Doppler shift. The SBS will become significant effect, when high powers are used, because it is highly dependent on the intensity.
Fig. Spectrum of reflected light from 500m long SMF with input power of 25.7dBm
In single mode fibers, the spontaneous Brillouin scattering may occur in forward direction also. The reason behind this is that there is relaxation of the wave vector selection rule due to guided nature of acoustic waves. This process is known as guided acoustic wave Brillouin scattering. In this case a small amount of extremely weak light is generated.
When scattered, wave is produced spontaneously, it interferes with the pump beam. This interference generates spatial modulation in intensity, which results in amplification of acoustic wave by the electrostriction effect (elasto-optic effect). The amplified acoustic wave in turn raises the spatial modulation of intensity and hence the amplitude of scattered wave. Again, there is increment in amplitude of acoustic wave. This positive feedback dynamics is responsible for the stimulated Brillouin scattering, which ultimately, can transfer all power from the pump to the scattered wave. [7]
Fig. (a) Spontaneous Brillouin scattering phenomenon. (b) Stimulated Brillouin scattering phenomenon.
3 Optical Fiber Measurement
3.1 Measurement of fiber mode-field distribution
Mode-field distribution is an important parameter in the specification of an optical fiber. Many practical characteristics of the optical fiber, such as the mode-field diameter, the coupling efficiency between fibers, and the effective cross-section area, are all determined by mode-field distribution. Although the core diameter can be easily determined by the geometry of the fiber, the determination of its mode-field distribution is more complex, depending on the refractive index profile as well as the wavelength of the optical signal propagating in the fiber. Mode-field distribution can be described by near-field, far-field, or a specially defined mode-field diameter. [9]
3.1.1 Near-Field, Far-Field, and Mode-Field Diameter
Because of the circular geometry of an optical fiber, the field distribution of the fundamental mode in a single-mode optical fiber is circularly symmetrical.[9] This simplifies the problem, and the fiber mode field can be specified by a single parameter known as the mode-field diameter (MFD), and the electrical field.
E(r)=E_0 exp(-r^2/(W_0^2 )) (3.1)
where r is the radius, E0 is the optical field at r ¼ 0, and W0 is the width of the field distribution. Specifically, the MFD is defined as 2W0, which is
2W_0=2((2∫_0^∞▒〖r^3 E^2 (r)dr〗)/(∫_0^∞▒〖r^3 E^2 (r)dr〗))^(1⁄2) (3.2)
Fig. 3.1 illustrates the mode-field distribution of a single mode fiber in which Gaussian approximation is used. The physical meaning of the MFD definition given by Equation 3.2 can be explained as follows: The denominator in Equation 3.2is proportional to the integration of the power density across the entire fiber cross-section, which is the total power of the fundamental mode, whereas the numerator is the integration of the square of the radial distance (r2) weighted by the power density over the fiber cross-section.Therefore MFD defined by Equation 3.2 represents a root mean square (rms) value of the mode distribution of the optical field on the fiber cross-section.[9]
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