If we consider only the SMF fiber, and include the effect of amplification 5 times , we can estimate the threshold power for SPM  . If we do so, we find that after about 10 dBm average power, SPM becomes a limiting effect. We need to investigate if this is the case, and how the residual system dispersion effects it. Figure 1 shows the eye diagrams for two different residual dispersion values and three different signal powers. This simulation shows that effect of SPM can be reduced by not completely compensating the dispersion and leaving some residual dispersion in the system.
Notice how power increase results closes the eye in the case of zero residual dispersion. Let us now consider a multi-channel system with 8 channels. For this example, the project layout is shown in Figure 2.
The first channel is at In this example, we set the sample per bit parameter to, so as to eliminate effect in fibers. For illustrative purposes, we have set the maximum nonlinear phase shift parameter of the fibers to mrad. This is done to get a fast result. To get more accurate results, this parameter should be set to a lower value. Simulation results are shown in Figure 3.
For an eight-channel system, the threshold power is approximately 10 dBm per channel . The simulation also shows that nonlinear effects can be reduced by local dispersion and better performance is obtained with nonzero residual dispersion .
As a result, the total polarization P induced by electric dipoles is nonlinear in the electric field E. Self-Phase Modulation SPM Self-phase modulation refers to the self-induced phase shift induced by the optical field during its propagation in optical fibers. Higher intensity portions of optical pulse encounter a higher refractive index of the fiber compared with the lower intensity portions while it travels through the fiber. This temporally varying index change results in temporally varying phase change.
Different parts of the pulse undergo different phase shifts due to the dependency of phase fluctuations in intensity. This results in frequency chirping. Hence, SPM results in broadening the spectrum of the pulse keeping the temporal shape unaltered . Self-phase modulation plays the role in soliton generation, optical switching, pulse compression. All rights reserved by www.
This book covers the recent progress in fiber-optic communication systems with a main focus on the impact of fiber nonlinearities on the system performance. Review. 1. Impact of Nonlinearities on Fiber Optic. 2. Communications. 3. Mário Ferreira. 4. I3N-Institute of Nanostructures, Nanomodelling and.
Koshy, Pratheesh P presented theoretical and simulation studies of fiber nonlinearities. They have investigated power effects on simulation of optical communication systems with self-phase modulation using OptiSystem. They have found that by increasing the input optical power, self-phase modulation grows. The eye diagram is the methodology used to evaluate the performance of the system .
They obtained simulation results as shown below. Thus by increasing the input power, SPM grows and depletes the signal. Cross-Phase Modulation XPM The cross-phase modulation occurs because the nonlinear refractive index seen by an optical beam depends on the intensity of that beam and the intensity of the other copropagating beams.
In fact, XPM converts power fluctuations in a particular wavelength All rights reserved by www. The results of XPM may be asymmetric spectral broadening and distortion of the pulse shape. For increased wavelength spacing, pulse overlaps for such a short time that XPM effects are virtually negligible. Optical switching, pulse compression, pulse retiming can be done through the XPM phenomenon. Murdas et al.
The dependency of XPM on input power and channel spacing has been verified. Results show that increasing the input power leads to growing XPM effect at constant channel spacing and at low channel spacing the XPM effect is significant . User-defined bit sequence generators, optical Gaussian pulse generators are used to provide signals on two channels. Multiplexer, fibers are also used for designing the system. Eye diagrams are used to evaluate the performance of the system. The important parameters of eye diagram are Q factor and BER.
Simulation done is shown as follows. Fiber length is 50 km. BER is 0. Thus, BER increases with increasing pump power while the Q-factor decreases with power. Hence it can be concluded that XPM effect increases with increase in input power and this degrades the system performance. Then result obtained is shown in figure 5. Q factor obtained at GHz channel spacing is 6. Optical phase conjugators provide a mechanism for compensating for non-linear effects associated with optical signals i. Optical phase conjugation works on the principle of spectrum inversion.
Basically, as an optical signal travels through the optical fiber it experiences optical phase shifts introduced both by itself and by adjacent optical channels. In the spectral domain, these non-linear effects change the frequency content of the signal. Such phase shifts and frequency components are added with signs determined by the intensity edge slope. If such a signal passes through a device i. If the first and second portion of the optical fiber the first portion being before the conjugator and the second portion after the conjugator are roughly equal in length, dispersion and optical power, complete cancellation of the non-linear effects can be achieved in theory.
Optical phase conjugation can also be used to cancel dispersive effects in optical fiber. Early applications of optical phase conjugators were for compensating linear dispersion. The early work considered only the linear dispersive signal distortion, which could be compensated by positioning the OPC in the center of the span. Subsequent applications included compensating intra-channel distortion, such as SPM, induced by Kerr effect in the fiber, by positioning the OPC in the center of the span.
Such simultaneous compensation of chromatic dispersion and non-linear effects e. Specifically, the 40 channels 18 are split from the 88 channels 16 prior to the OPC with the 40 channels 18 traversing the OPC while the 88 channels 16 bypass the OPC If the transmission path for the 40 channels 18 experiences substantially constant non-linear effects per unit length, the OPC may be placed approximately at the physical center of the transmission path.
Of course, if the transmission path has varying non-linear effects, then the OPC is positioned so that the accumulated non-linear effects prior to the OPC are canceled by non-linear effects after the OPC The OPC may be implemented using known techniques. For example, four-wave mixing in a highly nonlinear fiber can be used to generate the optically-conjugated wave. Another example may be the use of four-wave mixing in a semiconductor optical amplifier.
Another example may be the use of three-wave mixing in an electro-optic waveguide, as could be made with a LiNbO 3 material. Such devices typically employ a pumping light source for outputting a pumping light and a non-linear optical material for receiving signal light and the pumping light. An optical filter may be used to separate the phase conjugate light from non-phase conjugate light as desired. The OPC receives the incoming multiplexed signal and produces a conjugate signal with a spectrally inverted, shifted, and phase-conjugated characteristics.
As shown in FIG.
Chen; C. Published Date: 24th February The broad objective of this course is to provide a working knowledge of the numerous techniques and tools used to model and design the physical transport layer of fiber-optic communication networks. Except for SPM and XPM, all nonlinear effects provide gains to some channels at the expense of depleting power from other channels. Chujo, Simulating and designing Brillouin gain spectrum in single mode fibres , J. Powered by. Nonlinear effects can be classified into two categories:.
This conjugate signal is again propagated though a series of fiber links , with periodic amplification at amplifiers and dispersion compensation at DCM's The non-linear effects that are added after the OPC by the fiber links act to cancel a portion of the non-linear effects accumulated before the OPC Thus, as the signal propagates, the non-linear effects are gradually mitigated resulting in a performance improvement relative to a similar system without OPC The non-linear effects are mitigated up to the point where the nonlinear effects accumulated in front of the OPC are largely cancelled by the propagation after the OPC.
Beyond this distance, the non-linear effects start to grow again. In the optical link configuration , the dispersion compensation modules are separate components from the OPC Thus, the compensation of dispersion and optionally dispersion slope is decoupled from the compensation of non-linear effects.
This eliminates the trade-offs often encountered when attempting to correct both dispersion and non-linear effects with a common device. Accordingly, more accurate compensation of dispersion and non-linear effects may be achieved. Several non-linear effects are dependent on the power of the signal. A more accurate cancellation of non-linear effects, both due to Kerr non-linearity and due to Raman scattering, relies on a proper balance of accumulated dispersion and power in each of the optical carrier wavelengths.
Power non-uniformity may be introduced by mechanisms such as wavelength-dependent fiber loss, optical amplifier gain ripple, and stimulated Raman inter-channel power transfer. The optical link configuration shows an embodiment that includes optical power measurement OPM device and optical power spectral equalizer OSE The OPM device monitors power across channels and the OSE attenuates channel power s so that each channel has substantially equal power.
The OPM device is normally out of the optical signal path so it does not directly modify the signals. The OSE is in the optical path to achieve desired signal manipulation. All non-linear effects e. By controlling power across channels, non-linear effects accumulate in a similar manner for each channel. This facilitates compensation of the non-linear effects since each channel can be compensated in a similar manner. By controlling power across channels, more accurate compensation is achieved.
This allows the signal prior to the OPC to have substantially the same power as the conjugate signal after the OPC Accordingly, the power-dependent, non-linear effects accumulated prior to the OPC are substantially cancelled by the transmission path after the OPC The span manager communicates with the OPM devices and receives information about the state of the optical signals e. The span manager then directs the OSE's to change attenuation levels for different channels to provide substantially uniform power across channels.
The span manager may poll the OPM devices additionally to ensure that the desired result is achieved. The power management performed by the span manager may be local, on a sub-span basis or global across multiple sub-spans. Multiple OPC's may be positioned along the transmission path between the terminals 22 , 26 to prevent excessive accumulation of nonlinear impairments, especially in cases where the fiber links are substantially different, or where wavelength channels may need to be dropped or added at intermediate points.
Also shown in FIG. The signal quality may be represented by bit error rate, signal-noise ratio, etc. After OPC 1 , the signal quality increases due to the non-linear effects being applied to the conjugate signal. After some point, the non-linear effects created prior to OPC 1 are compensated and the non-linear effects begin to have deleterious effect on the signal until reaching OPC 2. At OPC 2 , the signal is subjected to conjugation and thereafter the non-linear effects experienced prior to OPC 30 2 are compensated.