Numerical modeling, analysis, and simulation of few-mode fiber.

1. Numerical Modeling, Analysis &
Simulation of Non-Linear Model of
Few Mode Fiber
Indian Institute of Technology Patna
Guided By: Prepared By:
Dr. Sumanta Gupta Tulasi Chandan
Roll:1301EE42
Electrical Engg (B.Tech)

2. Why Optical Fiber Communication ?
➢ Much lower levels of signal attenuation
➢ Provides a much higher bandwidth allowing more data to be delivered
➢ Fibre optic cables are much lighter than the coaxial cables that might
otherwise be used.
➢ Cost effectiveness.
Why Few Mode Fiber?
➢ Single-mode fiber (SMF) has been the de facto medium for high-capacity data
transmission for over three decades.
➢ However, the exponential growth of internet traffic could exhaust the available
capacity of SMF in the near future.
➢ Consequently, there has been an intense research effort in space-division
multiplexing (SDM) based on few-mode fiber (FMF) to overcome the barrier
from capacity limit of SMF is going on.

3. Fibre optic transmission system:
❖ Transmitter (light source)
❖ Fibre optic cable
❖ Receiver (Detector)
▪ The different elements of the system will vary according to the application.
Systems used for lower capacity links will employ somewhat different techniques
and components to those used by network providers that provide extremely high
data rates over long distances. Nevertheless the basic principles are the same
whatever the system.
▪ In the system the transmitter of light source generates a light stream modulated to
enable it to carry the data.
▪ This light is transmitted down a very thin fibre of glass or other suitable material to
be presented at the receiver or detector.
▪ The detector converts the pulses of light into equivalent electrical pulses. In this
way the data can be transmitted as light over great distances.

4. MODAL
MULTIPLEXER
MULTIMODE
FIBER SECTIONS
MULTIMODE
FIBER AMPLIFIER
Mode Division Multilexing:
➢ In MDM systems, each data channel is modulated onto individual mode
to increase the overall number of parallel channels, thus enabling
higher transmission capacity.

5. Impairments inside Optical Fiber :
Linear impairments:
❖ Loss
❖ Group Velocity Dispersion (GVD)
❖ Polarization Mode Dispersion (PMD)
Nonlinear impairments:
❖ Self Phase Modulation
❖ Cross Phase Modulation
❖ Four Wave Mixing (FWM)
❖ Raman Scattering
❖ Brillouin Scattering

6. Practical channel modelling for few mode fiber:
 In optical communication over FMF, all modes have different speed,
propagation, and attenuation values.
 These differences are caused by the characteristics of the optical fibers, such
as distribution of refractive index inside the fiber.
 As a result, differential mode delay (DMD) and mode dependent loss (MDL) are
uniquely observed in optical communication.

7. Split-step Fourier (SSF) METHOD:
 The entire channel is divided into statistically independent sections where each section
may represent an optical device or a span of a few-mode fiber transmission line.
 The channel propagation matrix of each section represents the channel characteristics
of its corresponding physical component.
 When the number of modes is equal to D, the channel propagation matrix of the kth
(1<=k<=K ) section represented by M k (ῳ) is given by
Mk (ω)= Vk Ʌk (ω) (Uk)*
 Where ∗ denotes Hermitian transpose. U(k) and V(k) are frequency independent unitary
matrices representing mode coupling at the input and output of the kth section,
respectively and a diagonal Ʌk (ω) with well-defined GDs.

8. Working:
Using Split-step Fourier method:
 The entire channel is divided into independent sections where each section
may represent an optical device or a span of a few-mode fiber transmission
line.
 The channel propagation matrix of each section represents the channel
characteristics of its corresponding physical component.
 When the number of modes is equal to D, the channel propagation matrix of
the kth (1<=k<=K ) section represented by M k (ῳ) is given by
Mk (ω)= Vk Ʌk (ω) (Uk)*

9. hij (t) = IFFT (M1(i, j), M2(i, j),--- MN(i, j))
Where
1. ∗ denotes Hermitian transpose.
2. U(k) and V(k) are frequency independent unitary matrices representing mode
coupling at the input and output of the kth section, respectively .
3. Ʌk (ω) is a diagonal matrix with well-defined GDs.
4. hij (t):Time domain channel impulse response
5. MN(i, j)) :Channel matrix in frequency domain

10. MODELLING OF NON LINEARITY IN FEW MODE FIBER:
Non linear Schrodinger’s Equation for few mode fiber:

11.  Where i and j are the orthogonal states of polarization of each mode μ. Aμi
(z, t), β1μi , β2μi and αμi are the slowly varying field envelope, group
velocity parameter, group velocity dispersion parameter and attenuation
parameter for the i polarization of the μ mode, respectively. γμνi j is the
nonlinear coupling parameter between the i polarization of mode μ and the j
polarization of mode ν, which depends on the nonlinear refractive index n2 of
the silica.
 The first term of the right side is responsible for modal self-phase modulation
(mSPM) of the polarization i of the mode μ. The second term results in modal
cross phase modulation (mXPM) from the same polarization (i ) of different
waveguide modes (ν _= μ). The third term results also in mXPM, but coming
from the orthogonal polarization ( j ) of the same (ν = μ) or different
waveguide modes (ν _= μ).

12. Results:
 Fig 1:Scatter plot corresponding to mode1 in a two mode system when input power =0dbm for
both the signal entering into different modes not considering nonlinearity in FMF.
 Fig 2 Scatter plot corresponding to mode1 in a two mode system when input power =0dbm for
both the signal entering into different modes considering nonlinearity in FMF.

13.  Fig 1:Scatter plot corresponding to mode2 in a two mode system when input
power =0dbm for both the signal entering into different modes and not
considering nonlinearity in FMF.
 Fig 2:Scatter plot corresponding to mode2 in a two mode system when input
power =0dbm for both the signal entering into different modes and
considering nonlinearity in FMF.

14.  Scatter plot corresponding to mode1 in the first plot and mode2 in the second plot
in a two mode system when peak input power =-5dbm for both the signal entering
into different modes and not considering nonlinearity in FMF.

15.  Scatter plot corresponding to mode1 in the first plot and mode2 in the second
plot in a two mode system when peak input power =-5dbm for both the signal
entering into different modes and considering nonlinearity in FMF.

16.  Scatter plot corresponding to mode1 in the first plot and mode2 in the second
plot in a two mode system when peak input power = 5dbm for both the signal
entering into different modes and not considering nonlinearity in FMF.

17.  Scatter plot corresponding to mode1 in the first plot and mode2 in the second
plot in a two mode system when peak input power = 5dbm for both the signal
entering into different modes and considering nonlinearity in FMF

18.  Scatter plot corresponding to mode1 in the first plot (1st line),mode2 in the second plot(1st line), mode3 in
the first plot(2nd line) and mode2 in the second plot (2nd line) in a four mode system when peak input power
for mode1= 7dbm for mode1, peak input power for mode2= 3dbm, peak input power for mode3= 0dbm for
mode3 and peak input power for mode4= -3dbm for the signal entering into different modes and considering
nonlinearity in FMF

19. THANNK YOU