Simulation of Fiber Optic Links

S-108.3110 OPTICAL COMMUNICATIONS1/17

Simulation of fiber optic links

Laboratory exercise

1.Simulation of fiber optic links......

1.1.Optical transmitter......

1.2.Optical fiber......

1.3.Receiver and bit-error rate......

1.4.Eye diagram......

2.Simulation program......

2.1.GOLD......

2.2.Labview®

Reference:......

Appendix I......

Simulation procedure......

Appendix II

answer sheet......

1.Simulation of fiber optic links

Simulation is a valuable tool in modern engineering because it can be used to predict different physical phenomena in a cost effective way. In this exercise we will go through the physical modeling and simulation of a fiber optic link. Using a good simulation tool it is possible to test different link configurations and to predict the effects of optical components along the link.

In this lab work a simulation program called GOLD (Gigabit Optical Link Designer) is used. This program uses LabVIEW®as an interface. Before the results given by the simulation program can be understood, a brief look into the methods and models of the optical components used in the link is needed. A short theoretical review is also presented but the student is encouraged to look for more detailed information from refs[1,2], course book [3] and/or other course material.

1.1.Optical transmitter

Transmitter of the fiber optic communication system is usually a semiconductor laser which is intensity modulated. Modulation can be realized by directly modulating the bias current of the laser or by using an external intensity modulator. The performance of the directly modulated laser is limited by frequency chirping, which indicates the change of the operating wavelength with intensity.

When optical fiber is used as transmission line, chirping and chromatic dispersion will broaden the pulses in time domain and induce errors in the detection. The advantage of external modulators is that they have practically no chirp and the extinction ratio (between on ‘1’ and off ‘0’) can be made very high compared with directly modulated laser. Typically used external modulators are Mach-Zehnder interferometer and electro-absorption modulator. In this simulation Mach-Zehnder type is used.

Another important parameter of optical transmitter is its linewidth. A signal travels through fiber at a group velocity defined as

,(1)

where ω is the angular frequency of the signal and β is the propagation constant. As a result different frequency components travel with different speeds. So the narrower the bandwidth of the source is the less frequency components there are to cause dispersion.

The dispersion (intra-modal) of particular media is usually characterized by the dispersion parameter D which consists both material and waveguide dispersion factors.

(2)

This dispersion parameterD can also be used to calculate the pulse broadening in time domain ΔT per unit length L per unit of spectral bandwidth Δλ:

.(3)

1.2.Optical fiber

The most commonly used optical fiber in the communication systems is a single-mode-fiber where only one electrical field mode is propagating. Important fiber parameters are its loss, dispersion, dispersion slope and nonlinearities.

The mathematical model for the fiber transmission can be derived from Maxwell’s equations by considering an electrical field inside the fiber. However, thatis quite complicated and beyond the scope of this course. The student can look for the detailed derivation for example from refs. [1, 2]. Here we just state the final result called nonlinear Schrödinger equation:

(4)

where A is the propagating electrical field, β1, β2 and β3 are dispersion parameters, α [dB/km] is the power attenuation and γ [1/W/km] is the nonlinear parameter.

Eq. (4) can reliably be used to model the propagation of the pulse envelope in an optical fiber. However, it has some limitations:

It can be used only for slowly changing signals. Typically for pulse widths over 1 ps. This is not a problem in a conventional optical communication system because the pulse width e.g. in high-speed 10 Gbit/s systems is 100 ps.
It is a scalar equation and hence models only one polarization state of the light. All polarization dependent effects such as polarization mode dispersion and polarization dependent loss are neglected.
It can not model scattering induced nonlinearities such as stimulated Raman or stimulated Brillouin scattering.

For arbitrary waveforms the solution of equation (4) is very difficult and some numerical techniques e.g. split-step Fourier method must be applied. However, if only the dispersion properties of the fiber are examined and the power in the fiber is not very high, it is possible to omit the nonlinear term from the right-hand side of the nonlinear Schrödinger equation. When this simplification is made, the equation can be solved analytically for the output optical field. The solution for optical field is given by an inverse Fourier transform

, (5)

where A(0,ω) is the optical spectrum at the input of the fiber.

The most important fiber parameters are summarized in Table 1 for two telecommunication wavelengths.

Table 1: Typical parameters for a single mode fiber.

Wavelength λ / 1550 nm / 1300 nm
Attenuation α / 0.25 dB/km / 0.45 dB/km
Dispersion D / 17 ps/(nmkm) / ∼ 0 ps/(nmkm)
Dispersion slope D2 / 0.08 ps/(nm2km) / 0.08 ps/(nm2km)
Nonlinear coefficient γ / ~ 2 /W/km / ~ 2 /W/km
Refractive index n / 1.45 / 1.45
Effective area Aeff / 80 µm2 / 80 µm2

1.3.Receiver and bit-error rate

Figure 1: Probabilities of zero and one states.

The receiver of the optical fiber link is either a PIN- or avalanche photodiode (APD). Photodiode generates a current proportional to the optical power

.(6)

If the bits are ideal they are always correctly detected. However, there are always fluctuations in the received bit levels. These fluctuations result from noise, relaxation oscillation of the laser diode, loss, dispersion induced distortion and other imperfections. The value of the bit at zero or one state is not precisely defined, but is divided into a larger region modeled by a Gaussian distribution. This is illustrated in fig. 1.

The average received photocurrents for zero and one states are given by I0 and I1. The decision level is denoted by ID. The variances of the Gaussian distributions are given by σ1 and σ2. The noise from different sources can be analytically determined. The sources of the noise include the receiver thermal noise, shot noise of the detector, signal-ASE beat noise and ASE-ASE beat noise. The variances of these noises are given in the following form

(7)

where k is the Boltzman constant, T is temperature, Be electrical bandwidth of the receiver, q is the charge of the electron, η [mA/mW] is the responsivity of the photodetector, Ps the power of the signal, nsp is the spontaneous emission factor of the EDFA (≈ 1), and B0 is the optical bandwidth. The total noise variation is given by

. (8)

The error probability that the receiving bit is decided to be 0 when 1 is actually received is P(0/1) and, vice versa, 1 when 0 is received is P(1/0) (Fig.2). The expressions for these probabilities can be given by an integration of the Gaussian-probability

.(9)

Fig.2: Probabilities that a bit is not interpreted correctly.

The bit-error-rate (BER) is now given by

.(10)

Next we will define a Q-factor, which is used for determination of the BER. The factor for the optimal decision point is defined by

.(11)

Finally the expression for BER is given approximately as a Gaussian function

.(12)

This expression is reasonably accurate for Q > 3.

The receiver sensitivity is defined as an average received power that is required to achieve a BER of 10-9. In the simulation program user gives few important parameters: ASE noise [mW/GHz], optical- and electrical bandwidths B0 and Be and the receiver sensitivity [dBm]. The desired link configuration is then simulated and the Q-parameter is calculated from the received eye-diagram and from the given noise parameters.

1.4.Eye diagram

One powerful and very often used display of the transmitted or received signal quality is the eye diagram. Typically in test measurements the bit-patterns are pseudorandom-bit-sequences (PRBS). They consist of large string of bits, typically from 27-1 to 232-1 bits. These bits are generated such that their probability should match the probability of the telecommunication signal, which is totally random.

The eye diagram is generated with an oscilloscope by triggering the scope to the clock or a frame signal synchronized to the PSBS-sequence. Now all the bit-sequences will be imposed on top of each other and an eye like diagram is displayed (Fig. 3).

Figure 3: Detected bits are overlaid to form an eye-diagram.

The eye opening is a useful parameter in determining the degradations of an optical link. Eye-opening penalty(EOP) is defined as a required increase in received power (in dB) to maintain the desiredBER.

(13)

In this equation P0 is the received power without the impairment and P1is the received power with the impairment.This is visualized in Fig. 4. There are also many other things that can be read from the diagram as can be seen from Fig.5. [5]

Fig.4: The eye-opening penalty.

Fig.5: Interpreting an eye-diagram.

2.Simulation program

2.1.GOLD

GOLD (Gigabit Optical Link Designer) is a computer software which has been designed to simulate a wide variety of optical transmission systems. It can be used to investigate the impact on the transmission from various effects such as fiber dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) accumulated from optical amplifiers. As a user interface GOLD uses LabVIEW®.

The GOLD libraries contain several optical components:

Optical sources (such as a monochromatic tunable source, a semiconductor laser, an optical impulse source)
Optical amplifiers (EDFA)
Optical components (delays, switches, couplers, modulators)
Optical filters (a Fabry-Perot filter, fiber Bragg grating)
Optical fibers (linear, nonlinear, nonlinear including Raman scattering)
Optical instrumentation (spectrum analyzers, power meters, photo detectors)
Electrical components and instrumentation
Utilities (file storage and retrieval)

GOLD operates in the frequency domain (for high speed) and therefore requires the signal to be periodic. It provides estimations of the bit-error-rate (BER) and allows investigation of polarization effects for linear fibers. Finally, the software only includes forward traveling waves; reflections from one component back into another are not taken into account.

2.2.Labview®

The interface for the simulation program GOLD is LabVIEW® which is a graphical programming language for controlling instruments and handling data. The purpose of this simulation work is not to learn to use the LabVIEW®, only a brief introduction is given.

There are two separate LabVIEW® windows associated with each simulation: a block diagram window where the desired system (the actual physical configuration) is constructed by selecting components and wiring them together, and a front panel window which displays the simulation results e.g. in the form of a graph. The example of these windows is given in figures 6 and 7 where a simple optical link is illustrated.

Fig.6: Block diagram window of the simple fiber optic link.

Fig.7: Front panel window of the simple fiber link showing laser spectrum and eye diagram after detection and filtering.

The simulation parameters (source linewidth, fiber length, dispersion parameter, etc.) can be changed by selecting Show Tools Palette from Windows menu. Tools palette has many symbols (Finger, Arrow, Letters, Wire), from these Finger allows the control of parameters and to change the scaling of figure axes, Arrow can be used to move objects and Wire to wire elements (only in Block Diagram Window).

Reference:

G. P. Agrawal, Fiber-optic communication systems, Wiley, New York, 1992.
G. P. Agrawal, Nonlinear fiber optics 3.ed, Academic Press, 2001.
R Ramaswami, S.N. Kumar, Optical Networks: A Practical Perspective 2.ed., Morgan Kaufmann, San Francisco, 2002.
G. Pendock, P Gurney, A. Lowery, Gigabit Optical Link Designer: Users manual v1.0, Virtual Photonics, 1997
E. Mutafungwa, S-72.3340 Optical Networks: Slides, TKK, Spring 2007.

Appendix I

Simulation procedure

In this lab work the student studies the effects of dispersion and loss to optical link. The student will also get an idea of computer based simulation as a powerful and cost effective design and research tool. Graphical programming interface called Labview is introduced on the way. The files needed in this simulation are located in D:\Labworks\.

Fig. 8 presents the simplified configuration of the optical link simulated in this exercise. Data source creates a PRBS (Pseudo-Random-Bit-Sequence) which is modulated into an optical signal. This signal is transmitted through linear fiber, detected and low-pass filtered. Finally the eye-opening and bit-error-rate are calculated. The purple line represents the actual optical signal.

Fig.8: Simplified layout of the link under simulation.

In this exercise it is possible to tune the linewidth of the source and change the length and dispersion properties of the linear fiber (Windows-Show Tools Palette: Finger). The purpose is to compare the performance of an almost ideal link to a link where dispersion and loss are present.

Follow these steps:

Use the assistant whenever you encounter problems!

Launch LabVIEW® if it is not already open.

Open the file D:\Labworks \Simulation.vi.

Save the file as D:\Labworks\GroupNoXX.vi.

You will see a Front panel window of this simulation. It contains five small graph windows, BER and eye-opening indicators and transmitter and fiber parameters.

Check that the initial values are as follows (change if needed by using the finger: Windows – Show Tools Palette):

Transmitter:

Linewidth (MHz):10
Bit-rate (Gb/s):10

Fiber:

Length (km):20
Loss (dB/km):0
Dispersion (ps/(nmkm)):0
Dispersion Slope (ps/(nm^2km)):0,08

Run the simulation and explore the results so that you will get an idea of the facts shown on the screen. Remember to answer the questions on the answer sheet as you work through these steps. (You can run the simulation by clicking the white arrow icon on the top left corner of the Labview window.)

Change the length of the fiber to 200km. Notice any difference? What about 2000km?

Change the length back to 20km and add some loss (0,20dB/km) to the link. What happened? How short the link has to be to get back to BER better than 10-8?

Reinitialize the values to those mentioned in step 6 and run the simulation. Add 16 ps/(nmkm) of dispersion to the link.Run the simulation a couple of times and use the values you consider to be suitable (Statistical deviation will occur because of the properties of the simulation tool). Any influence? What if you increase the linewidth of the source? (The original value of 10 MHz (~80fm) of linewidth is quite narrow. In many cases it can be order of 1-100GHz which correspond 0,008–0,8 nm in wave length.) Explain the difference. How long can the fiber be if BER is required to be better than 10-8and the bandwidth of the source is 1GHz?

Add 0,20 dB/km of loss. What is the length now? Compare the result to those from parts 9 and 10. In this case which one of these effects is more limiting? Can you think of any case where the situation could be vice versa?

Close the file (File: close).

Appendix II

Answer sheet

Date and time:

Names and student numbers:

Step 8

Is there a difference between fiber lengths of 20km, 200km and 2000km?

______

BER: ______

Eye-opening: ______

Step 9

What happens when loss is applied?

______

BER: ______

Eye-opening: ______

What is the eye-opening penalty caused by loss?______

How long the link can be if BER < 110-8 is required?______

Step 10

What happens when dispersion is applied?

______

What if the linewidth of the source is increased? Explain.

______

BER: ______

Eye-opening: ______

What is the eye-opening penalty caused by dispersion?______

Can you see the effects of dispersion in frequency domain? Why?

______

How long the link can be if BER < 110-8is required? (linewidth 1GHz)

______

Step 11

In this case, which one is more limiting; loss or dispersion? Can you think of any case where the situation could be vice versa?

______

Which one, loss or dispersion, is easier to deal with in optical systems? (Hint: Compare the effects they have on the time-domain presentation of the signal and especially on the eye-diagram.)

How can you compensate the effects of loss and dispersion?

______

Simulation of Fiber Optic Links