Contribution to the achievement of SDGs
by Furukawa Electric Group

PropSim v1.0: A Convenient Way to Model Light Propagation
in Optical Fibers
Zoltán Várallyay*1, Zoltán Papp*2, Bálint Várady*2, Gábor Varga*1,*2
This review is related to an old project in connection with nonlinear wave propagation in optical fibers and a newly initiated idea to revision and develop theexisting solvers. These developments mostly relate to the usability of a fiber optics software
package that was developed years before but the demand to get an easy to setup software
among those working with fiber optics is high. The necessity of fiber optics related simulations inorder to design reliable fiberoptics based devices is obvious. But the commercially available fiberoptics software tools for this purpose are not easy to handle and, in many cases, missing key
features. Our concept, to add optical components to a design easily and recognizing the effectsof the parameter settings immediately, substitutes the lack of such software tools. This project
voluntarily started as an inhouse innovation activity (IHIA) project within Furukawa Electric
Institute of Technology (FETI) Ltd. in Budapest Hungary, in the middle of the last year and still wehave a strong base of a well working code with well-established data structure which allows us to
add more complex properties to the software if required. Every element of the software is intended to be tested extensively.

ABSTRACTINTRODUCTION
1.1.INTRODUCTION
FETI is a subsidiary and research laboratory of the
Furukawa Electric Co. Ltd. (FEC) in Tokyo, Japan.
Besides automotive, AI and material related research,
many R&D projects in FETI are related to computer simulation. The type of these simulations are, for instance, thedesign and optimization of opto-electronic devices or the
calculations of complex mechanical problems or coupledphysical problems where thermal, mechanical and/or
optical properties are treated at the same time. For many
problems, we use commercially available finite element(FE) software or other type of software to speed up thedesign and optimization stage of the developments but
there exists such situation when we must develop ourown simulation code to be able to model a specific problem. This is the case with light propagation in opticalfibers too. When the Simulation Group was established in
FETI in 2000 the very first project was related to the calculations of nonlinear pulse propagation in telecommunication fibers with Wavelength Division Multiplexing(WDM) in that the multiplexed signal may reach the intensity level where self-phase modulation cannot be neglected anymore. This project at that time was a collaboration
with FITEL Photonics Lab. The calculations since thatwas developed in many directions: soliton propagation ofmodulated signals1) or compression of ultra-short, low*1*2

Simulation Group, FETI Ltd.
Budapest University of Technology and Economics

energy laser pulses in small core-area photonic crystal
fibers 2), amplification and nonlinear propagation in opticalfiber amplifiers 3), 4) including multimode amplifier modeling 5) in that not only one mode but many of them amplified at the same time and mode competition happens.
Also, fiber oscillator 6) and Raman amplification was modeled7) with the developed code, and many of these investigations were done together with our sister company:
OFS Labs in Somerset, NJ. We have already reported
these achievements and the diversity of the developed
code in a 2016 paper in Furukawa Review 8) but the written code was always in a state that could be used mostly
by its developers only. The code was written in Matlab
and any execution could be started by editing the parameter list at the beginning of a text file (Matlab file).
Sometimes with careful selection of the parameterswitches and setting certain parameters to one and others to zero in order to choose the right solvers for theintended task. This made the usage of the code difficult
or completely impossible for others. Therefore, we decided last year that we develop a graphical user interface(GUI) around the existing solvers that can solve complex
tasks and concatenate different components after eachother easily. We can claim that this attempt was successful. In this review paper, we describe the basic concept ofour development directions including the solvers as wellas the GUI and also the possibilities that can be simulated easily by anybody using the propagation simulator
that we named PropSim.

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PropSim v1.0: A Convenient Way to Model Light Propagation in Optical Fibers

THEORY
2.2.THEORY
The core of the software is the split-step Fourier (SSF)
solver that can handle many different forms of the nonlinear Schrödinger equation. We show here an exact form of
the equation that is the default settings of PropSim v1.0
in its present state 9)(1)

where A denotes the complex envelope of the propagating field, z is a coordinate pointing to the direction of the
propagation (parallel with the fiber axis), T is the temporalspace, α is the attenuation in the fiber in 1/m units, βm isthe mth Taylor term of the dispersion, γ is the nonlinear
coefficient and TR is the Raman response time that is usually 2 fs for silica fibers. ω0 is the center frequency, N is
the number of the dispersion components that can be up
to 14 Taylor components but most of the cases 6-8 dispersion parameters are enough to describe the dispersion property of most of the fibers with great accuracy on
a 100-300 nm wavelength range.
For calculating the amplification, the power evaluation
equations are combined with the rate-equation as it isdescribed by Giles and Desurvire10) :(2)where uk can be -1 or +1 representing backward and forward signal directions, respectively. The k index denotes
the k th frequency component of the signal, Γ is the overlap factor of the propagating mode with the doping ions,nt is the doping concentration of the fiber in 1/m3 units, σeand σa are the emission and absorption cross-sections,
respectively, in m2 units, N2 is the ratio of the upper population while N1=1-N2 is the ratio of the base populationlevel, ν is the frequency components of the amplified
spontaneous emission (ASE), Δνk is the width of the k thfrequency component and m is the number of the polarization states of ASE and h is the Planck constant. N2 andconsequently N1 must be determined in every step of thecalculations, and this is described by a two-level rateequation working well for Ytterbium and Erbium doped
fibers. The inversion level from the rate equation insteady-state approximation (dN2/dt =0) can be calculated
as follows
The numerical solution of the nonlinear Schrödinger
equation is done by the split-step Fourier algorithm that isa spectral method to solve nonlinear partial differential
equations9). The power evaluation equation however ishandled by a 4th order Runge-Kutta method with great
accuracy as we will show later. It is a question how thetwo equations can be coupled in a solver that simulate again amplifier with nonlinearity and dispersion related
effects too. The answer is to add a gain term to the equation (1) that has a similar form than the loss term in thatsame equation. The frequency dependent gain coefficient
can be calculated from the ratio of the output and input
powers of every calculation segment. These power values
are obtained from the solution of the equation (2) and (3).
This is the method we use to model optical fiber amplifiers including not only gain but also the effects of dispersion and nonlinearity.

INTRODUCTIONTHE
SOFTWARE
3.3.INTRODUCTIONOFOF
THE
SOFTWARE
Opening PropSim software and creating a new component arrangement that is intended to be simulated can bedone by opening the Device Management menu andclicking on the Create Device menu item. This will place alight source, a passive fiber and a diagnostic element tothe user interface and small + signs appear between
them. Clicking on any plus sign will allow us to add additional components to the existing ones. This is the way
how we can build up a complete system. In Figure 1, weshow the main GUI window of the software using a few
components to model. Clicking on any of the component
will open the corresponding dialogue window to set up its
parameters. By clicking with the right button of themouse on any component, a dialogue menu will openthat will allow us to delete the actual component or shift(3)

where ζ=πReff 2nt /τ, in that Reff is the effective radius of the
doped region and τ is the fluorescence lifetime of thedoping ion. For example, τ is approximately 10 ms for
Er-doped silica fibers while it is around 2 ms for Ytterbium
doped ones.

Figure 1 The main GUI window of PropSim with a few
additional components compared to the initial state.
From left to right the components are the followings:
light source, a passive fiber, Ytterbium doped fiber,band-pass filter, passive optical fiber and diagnostic
tool.

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PropSim v1.0: A Convenient Way to Model Light Propagation in Optical Fibers

to the right or shift to the left. Clicking on the Start button
will start the simulation and the results are plotted in separate windows finally.
The basic concept of the software which interweaves thewhole design of it is that the user can recognize immediately what he or she is doing. This is apparent on theparameter setting dialogue of the light source, for example. After clicking on the light source icon on the main
GUI (most left icon in Figure 1), one can get the settings
dialogue of the light source as it is shown in Figure 2. We
selected a Gaussian pulse, and we define it in the temporalspace though the opportunity to characterize the sourcewith its spectrum is given by clicking on the Define
Spectrum checkbox. Now, in Figure 2, one can see a distorted pulse shape due to the fact that the user has justtyped a third order chirp value that causes an asymmetricbroadening in a too large extent and the temporal window
is too narrow to be able to include the pulse, therefore it
is sticking out of the range. That is crucial to make a simulation with a well characterized signal not affected by
the edge of the available space. Another issue what we
can recognize in Figure 2 that the user defines suchbroad spectral range that the shape of the spectrum cannot be perceived, and the central wavelength cannot be
seen. If the spectrum is broader than that can be visualized in wavelength units, the graph switches to the relative frequency range where the zero frequency corresponds to the central wavelength of the pulse defined
here as 1030 nm. To overcome these issues can be doneby simply clicking on the Double Temporal Window button and Halve Spectral Window button a few times. In
Figure 3, we show the result of adjusting the temporaland spectral space this way.

Figure 3 Corrected signal parameters for better resolution of
the spectral and temporal shapes.

The software can use Gaussian or sechant-hyperbolic
pulses (m is the order of the Gaussian shape in Figure 2
and in Figure 3), continuous wave signals and frequency
combs as possible inputs for the simulations.
1030 nm signals can be amplified well by Ytterbium
doped fiber amplifiers (YDFA), this is the reason that the
setup in Figure 1 contains an YDFA though the software
is prepared for calculating with Erbium doped fiber amplifiers (EDFA) if necessary, at around the telecommunication wavelengths. The component list contains also YDFA
and EDFA at the present state of the code they can be
set by clicking on their icons in the main GUI. The pop-up
dialogue as shown in Figure 4 is sectioned according to
the parameters of a fiber that can be simulated with ourpresent models. This includes polarization related effects,
dispersion, nonlinearity, loss and gain related parameters.
Clicking on any of the button representing the given set ofparameters will make available the corresponding parameter set. For example, clicking on the Dispersion button
will open the window shown in Figure 5. Again, this element of the GUI is designed the way that the user can
immediately check the effect of his or her parameter
input. Changing any parameter including the axis limits
will take effect immediately after hitting enter or clicking
out from the edit-box. The available tools at the upper
right corner of the graph appear when the pointer is
moved above the graph and can be used for further analysis. For example, in Figure 5, the user has just used thedata tips tool to check the zero-dispersion wavelength ofthe curve defined by the dispersion parameters.

Figure 2 Setting dialogue of the light source. Graphs
immediately show the effect of changing any
parameter of the source properties in the temporal aswell as in the spectral space.

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PropSim v1.0: A Convenient Way to Model Light Propagation in Optical Fibers

RESULTS
4.4.RESULTS
We tested the solvers from many aspects including typical dispersion and nonlinearity related solutions of analytically solvable forms of the nonlinear Schrödinger equation. Those solutions can be found in the Agrawal book 9),
for instance. We also executed simulations that calculates
super-continuum generation and good agreement was
obtained with published results. These tests are available
in the form of regular research reports. Therefore, we
think that the code can handle well the effects describedby the nonlinear Schrödinger equation. The forthcomingtask is to test the optical fiber amplifier related calculations. An extensive test is still to come but a possible test
opportunity is presented in Figure 6. In this test case, we
compare the solution of a basic arrangement, for example, in this case a signal and a forward pump situation
solved with two different numerical methods. Basically,
we want to use a fourth order Runge-Kutta method tohandle the power evaluation equations corresponds togain fibers, but we wrote another finite difference solver
and compare the two to each other. This is useful for testing purposes. If the two different numerical scheme provides the same result, we can claim that the solutions areaccurate with great probability. The Euler method is a firstorder numerical method to solve differential equations.
Therefore, the solution of the power evaluation equationis quite unstable with it at low resolution in the longitudinal direction. This is shown in Figure 6 (a) where the 10 mlong amplifier was calculated only in ten steps. But surprisingly the Runge-Kutta solver provides a stable solution even in this case at such a low resolution for the longitudinal coordinate. This accuracy is apparent checking
the results in Figure 6 (b) where the discretization is donein 100 steps. In this case, the Euler method provides thesame solution than the Runge-Kutta solver and this factindicate that our solution can be considered appropriate.
Figure 6 (c) shows the convergence of the two methods
using different number of numerical steps in the solutions. The Runge-Kutta solver for this problem is very stable. The difference between solutions with high and low
resolutions are apparent only in the third or fourth digitsof the power values. The parameters of these calculations

RK4, pump
Euler, pump

1.0

1.0

0.8

0.8

Inversion level (N2)

0.6

0.6

0.4

0.4

0.2

Power / W

Power / W

0.8

0.6

0.4

0.2

0.0

0.0

-0.2

0.0

-0.2

10

0.6

0.4

0.2

Distance / m

RK4, N2
Euler, N2

1.0

0.8

5

RK4, pump
Euler, pump

（b）

1.0

0

RK4, signal
Euler, signal

RK4, N2
Euler, N2（c）Inversion level (N2)RK4, signal
Euler, signal

（a）

0.2
0.0
0

5

Distance / m

10

1.2

1.2

1.0

1.0

0.8

Euler, Signal output power [W]

0.4

0.2

Euler, Inversion @z=L
0

10

20

30

40

0.6
0.4

RK4, Inversion @z=L

0.2
0.0

0.8

RK4, Signal output power [W]

0.6

50

60

Inversion level (N2)

Figure 5 Dispersion parameter setting dialogue for opticalfiber components including amplifiers.

Signal output power / W

Figure 4 Parameter settings dialogue for the Ytterbium doped
fiber amplifier.

0.0

Number of steps

Figure 6 Comparison of the RK4 and Euler methods. (a) low resolution calculations with 10 steps, (b) high resolution calculations with
100 steps and (c) convergence of the two methods as function of the step size.

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PropSim v1.0: A Convenient Way to Model Light Propagation in Optical Fibers

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Table 1

Parameter list of the test simulations in an EDFA
system calculating with only forward direction signal
and pump.
Parameter nameParameter value

Units

Signal input power

1

mW

Signal wavelength

1550

nm

Overlap factor of the signal

0.6―

Emission cross-section @1550 nm

3.602

x10 －25 m2

2.848

－25

Absorption cross-section @1550 nm
Forward pump power

x10

1475

nm

Overlap factor of the forward pump

0.63

―

Emission cross-section @1475 nm

0.6076x10 －25 m2

Absorption cross-section @1475 nm

2.213

x10 －25 m2

Fiber length

10m

Number of steps

-10
-20
-30

1520

1540

m

Forward pump wavelength

Fluorescence lifetime

0

2

W

Er-concentration in the glass

Input signal
Output signal
Forward ASE
Backward ASE

10

-40

1

Effective radius of the doped region

Spectral power / dBm

are collected in Table 1 that are essentially the same as
for the forthcoming simulation example.

3.45

µm

15 × 10 24

1/m3

10.8

ms

10 － 100

In Figure 7, we show a typical computation example or
usage of an EDFA simulation with input signals having
equally spaced spectral spikes (frequency combs). The
length of the fiber is 10 m and a forward and backward
pump are injected both ends of the fiber. The backward
pump is a 400 mW CW light source at 1475 nm and theforward pump is a 250 mW CW light at the same wavelength. The doping concentration is selected to be
15∙10 24 1/m3 and the emission and absorption cross-sections are the cross-section values of a typical Er 3+-doped
Aluminum-Phosphate fiber (Shown also in Table 1).
Results looks reasonable, for example, the spectral features of the signal channels follow the spectral propertiesof the forward and backward ASE, but we note that thissetting is too complicate to test with analytical solution.
The next step in our amplifier development plan to makean extensive test for the amplifier gain simulations that
one can done the easiest way by using literature data.

1560
1580
Wavelength / nm

1600

1620

Figure 7 Modeling the spectral behavior of an EDFA around
1555 nm wavelength range using bidirectional
pumping at 1475 nm.

CONCLUSION
5.5.CONCLUSION
We developed here in FETI within the framework of an
IHIA project (project# 211009) a software tool named
PropSim that can be used for general optical fiber related
investigations including telecommunication related tasks
or laser science related researches. The software is easy
to handle and indicates the effect of the selected parameters instantaneously. Additional modules and components can be added to the code due to the well-designed
data structure behind the scenes that can make PropSim
a versatile fiber optics simulator. At the moment, the nonlinear Schrödinger equation and the power evaluation
equations for gain fibers are treated by the code reliably
but some tests are still needed.
We must note that this is not the first software tool withhigh versatility developed in FETI. The software named
CRTD is a complex laser diode simulation tool used forthe design of DFB and DBR based lasers and also SOA
applications. In connection with this development aknow-how was made recently titled “CRTD simulation
tool to design and optimize wavelength tunable laser
diodes for telecom applications”.
Another inhouse developed software is called OptiCo.
OptiCo is a software tool, that was developed for laserto-fiber coupling simulations. The core is based on the socalled “wave propagation method” that is more accurate
for non-paraxial systems than most beam propagation
method (BPM) based software and requires less resources than full-wave solvers. Thanks to its modularity andgraphical user interface, it became a frequently used
design tool for micro-optics modules at multiple locationsof the Furukawa Electric Group.
Now, PropSim could also become a software tool thatcan be used in FEC and OFS, despite the non-userfriendly version of it existed and used for long time. If wehave the opportunity to make further developments on
the PropSim code, this software may become an evenmore mature and essential tool to design state-of-the-art
fiber optic devices.
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PropSim v1.0: A Convenient Way to Model Light Propagation in Optical Fibers

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