Simulation study of the Self Phase Modulation effect in 30 km optical
link of a metropolitan backbone network
Agbéssignalé LATO*, Barèrèm-Mêlgueba MAO
Laboratoire de Physique des Matériaux et Composants à Semi-Conducteurs (LPMCS)
Université de Lomé
01 BP 1515 Lomé 01 Togo
ABSTRACT
This study investigates the impact of Self Phase Modulation (SPM) on optical signals under varying input power
levels, different modulation formats and fiber parameters in a 30 km optical link, representative of a typical metropolitan
backbone network. The increasing intensity of light signals in fiber networks introduces nonlinear optical effects and can
significantly impair signal quality. Among these nonlinear phenomena, the Self Phase Modulation (SPM) effect induced
by nonlinear refraction, results from the interaction between the optical pulses transmitted and the nonlinear response of
the propagation medium. It causes phase and frequency distortions and produces a broadening of the signal spectrum.
In this paper, through numerical simulations we analyse the evolution of optical pulses under the influence of SPM effect
propagating in a single mode fiber. We consider a 30 km optical link of a metropolitan backbone network with its real-
parameters. The results reveal critical thresholds for signal degradation and demonstrate the interplay between SPM-
induced spectral broadening and dispersion. We observe the broadening of the signal spectrum as the injected power
increases independently of the modulation format. The findings provide valuable insights into optimizing metropolitan
optical networks, ensuring robust performance under high data rates traffic conditions.
Keywords: Optical fiber, Nonlinear effect, Self-Phase Modulation (SPM), Optical transmission
1. INTRODUCTION
Optical communication systems play a vital role in ensuring high-speed data transmission across regions. The
demand for bandwidth-intensive applications, such as cloud computing, Internet of Things (IoT), 5G deployment and
online conferencing continues to grow, optical fiber networks are increasingly relied upon to provide reliable, high-capacity
data transport [1]. The self-phase modulation (SPM) effect is one of the most significant nonlinear phenomena that can
affect data transmission across a long-haul fiber optic link. SPM induced by nonlinear refraction, represents a significant
challenge for the quality and reliability of optical transmission
We have undertaken a deep analysis of SPM effect [2,3], using numerical simulations to assess its impact in 30 km optical
link of a metropolitan backbone network. The main objective was to understand how the nonlinear characteristics of the
optical fiber influence the signal quality and the overall performance of the communication system. To carry out this study,
we have to use mathematical models to solve numerically [4] the light propagation equation through an optical fiber known
as the Nonlinear Schrödinger Equation (NLSE). By simulating the optical signal propagating through the fiber over 30 km,
we are able to observe how the SPM effect affects the phase of the signal, leading to distortions and spectrum broadening.
Our results reveal that the SPM effect can cause significant signal distortion [5], which limits the data transmission capacity
over long-haul link. Particularly, we observe the deterioration of signal’s quality as the optical power is increasing. It leads
to an important transmission error and the decreased effective data rate. In this paper, we investigate by simulation and
then examine the impact of nonlinear SPM effect of a 192.1 THz (1560.606 nm) light source propagation in ITU-T G.652.D
single mode fiber. A comparative analysis is made through several optical signals such as: Gaussian, Return to Zero (RZ),
Non-Return to Zero (NRZ) and 64-QAM; at the rate of 10 Gbps, 100 Gbps and 400 Gbps by varying their optical power
levels. A broadening of the signal spectrum (broadening order of ) as the injected power increases (20 dBm, 25
dBm, 30 dBm and 35 dBm) independently of the modulation format is observed. By simulating various input power levels
and fiber parameters, we aim to identify optimal operating conditions that minimize the adverse effects of SPM and ensure
reliable data transmission.
2. FIBER NONLINEARITIES
2.1. Nonlinear effect
The electric field
of a light wave propagating in matter induces elementary movements of charges at the atom level
[6]. The induced dipole moments create a polarization
of the medium on the macroscopic scale. Polarization resulting
from wave-matter interaction is
. with
the linear polarization vector, and
is the nonlinear polarization
vector
In complex notation
(1)
Let a monochromatic wave whose field
given by:
()
Let the polarization at frequency , given by:
(3)
With
(4)
However
(5)
Where is the effective susceptibility
The density of the electric field is then written by:
(6)
(7)
We have:
(8)
(9)
(10)
Where is the linear refractive index and
is the Kerr coefficient
The refractive index is a function of the intensity according to (10)
2.2. Pulse propagation in the fiber
The propagation of an electromagnetic field in the optical fiber is described using Maxwell's equations [5,6]. As the
optical fiber is a non-magnetic medium, the magnetic polarization is zero. The propagation of the electromagnetic wave
in the optical fiber will be described, using only the electric field E [3] by:
(11)
2.3. Nonlinear Schrödinger equation (NLSE)
Assuming that the optical fiber maintains polarization along the fiber and adopting the slowly varying field envelope
approximation [5], the electric field can be written as:
(12)
Where , the unit polarization vector and , the central frequency of the optical pulse
We can write the polarization components as:
(13)
(14)
We obtain finally:
(15)
With
(16)
Most nonlinear effects in optical fibers are observed using short-duration optical pulses because of the dispersive effects
generated. The signal propagating in the fiber sees different refractive index depending on whether the intensity is high or
low, or there are other waves in the medium. The refractive index then depends on the intensity of the optical wave [5].
Thus, the wave which propagates in the fiber is described by the Nonlinear Schrödinger Equation (NLSE):
(17)
Where is the slowly varying envelope; is the Group-velocity Dispersion (GVD) parameter; is the fiber losses
and is the nonlinearity coefficient given by:
(18)
Where is the effective core area of the fiber
3. SELF PHASE MODULATION (SPM)
Self-phase modulation (SPM) is a direct consequence of the optical Kerr effect. Due to the intensity dependence of
the refractive index, a wave pulsation which is propagating in a nonlinear medium of length L acquires an additional
self-induced phase shift. The nonlinear phase shift is induced by the signal itself, hence the name phase self-modulation
[7].
A general description of SPM in optical fibers requires numerical solutions of the NLSE.
In fact, the phase introduced by an electric field
during the propagation of the wave in a fiber with L the length,
is given as a function of the wavelength by:
(19)
However, the variation of the phase as a function of time causes a frequency shift given by:
The self-phase modulation effect would lead to a spectral broadening of the pulse, while the temporal shape of the
pulse would not change. The frequency shift is proportional to the signal intensity, phase self-modulation manifests itself
much more when the power or intensity of the signal becomes increasingly important [8]. The effective length for a
fiber of length L becomes:
(20)
SPM gives rise to an intensity-dependent phase, but the pulse shape remains unchanged.
3.1. Simulation of the SPM effect
Here, we analytically modelled and simulated a system highlighting the impact of SPM effect in a 30 km optical link
using the Optisystem tool (see Fig.1). The 30 kilometres are corresponding to the total length of a metropolitan backbone
of a telecommunication company in Lome (Togo). The Optisystem software is an environment essentially developed for
the modelling and simulation of optical fiber transmission systems. It contains almost all the components necessary for
modelling an optical transmission chain, with real parameters. For the simulation we choose the real-world parameters that
closely reflect practical scenarios of the metropolitan backbone networks such as: Single Mode Fiber (SMF) G.625.D of
ITU-T, fiber splices and connectors attenuation and different modulation formats: NRZ, RZ and 64-QAM in use.
Figure 1. SPM effect simulation diagram
The diagram in figure 1 above shows the simulation of SPM effect, with different source signals at different power
levels. We use the G.652.D fiber parameters of ITU-T standard and environmental parameters. We injected a gaussian
signal at the input at 192.1 THz (1560.606 nm) with a bit rate of 10 Gbps and 100 Gbps. These values correspond to those
used when operating the backbone. We varied the input power levels propagating in a 30 km length of optical fiber in order
to lay out the nonlinearities phenomena.
3.2. Results and discussions
The analysis of the impact of nonlinear effects in an optical transmission system directly involves the evaluation of
the performance of this system. Performance evaluation can be done using several factors. We used optical spectrum
analyzers at the input and output of the fiber, to understand the impact of SPM on optical transmission. We’ve also used a
comparative analyzer of the fiber input and output bit sequences to detect possible data errors during transmission. For the
overall performance of the system, we evaluated the signal-to-noise ratio (OSNR: Optical Signal Noise Ratio) [9,10] of an
input signal with different modulation formats and rates.
(a) (b)
(c) (d)
Figure 2. 30 dBm input signal of the 30 km distance fiber a-Input in frequency domain; b- output in frequency domain; c-input in time
domain, d-output in time domain
Figure 3. Input/Output bit sequences
Figure 4. Signal transmission performance in 30 km optical link using different modulation formats
Rate in Gbps
Input power in dBm
6
1
/
6
100%
