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INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2012 - 2013

SEMESTER II MAIN EXAMINATION

FACULTY OF ENGINEERING

ELECTRICAL AND ELECTRONICS ENGINEERING

FOURTH YEAR ETE SEMESTER II (PART-TIME)

EEE 3422 – FIBER OPTIC COMMUNICATION

DATE: ……………..

TIME: 2 HOURS

MAXIMUM MARKS = 60

INSTRUCTIONS

1. This paper contains ONE (1) question in SECTION A and THREE (3) questions in SECTION B 2. Answer

- ALL questions in SECTION A and

- any TWO (2) questions from SECTION B 3. No written materials allowed. 4. Write all your answers in the answer booklet provided. 5. Do not forget to write your Registration Number.

6. Do not write any answers on this question paper.

KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY

INSTITUT DES SCIENCES ET TECHNOLOGIE

Avenue de l'Armée, B.P. 3900 Kigali, Rwanda

Reg. No:…………………………….

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SECTION A (Compulsory)

Question 1 (20 Marks)

a) State three disadvantages of Optical Fiber Communications. (3 marks)

b) Give 2 examples of dopants which:

(i) Increase the refractive index of the core (1 example). (1 mark)

(ii) Decrease the refractive index of the cladding (1 example). (1 mark)

c) Compare a single-mode step index fibers and multimode step index fibers while used as an

optical channel. (5 marks)

d) Compare the light emitted from LASERs and LEDS. (2 marks)

e) With the aid of a block diagram, discuss the function of the major elements of an optical fiber

transmitter. (4 marks)

f) Design a bus optical network topology and explain its working principle. (4 marks)

SECTION B (Attempt any two questions)

Question 2 (20 Marks)

a) Using simple ray theory, design a mechanism for the transmission of light within an optical

fiber. Briefly discuss with the aid of a suitable diagram what is meant by the acceptance angle for

an optical fiber. Show how this is related to the fiber numerical aperture and the refractive

indices for the fiber core and cladding. (5 marks)

b) Briefly describe the two processes by which light can be emitted from an atom. Discuss the

requirement for population inversion in order that stimulated emission may dominate over

spontaneous emission. Illustrate your answer with an energy level diagram. (7 marks)

c) Derive the expression for the output photocurrent of a basic coherent detector in both

heterodyne and homodyne detection. (8 marks)

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Question 3 (20 Marks)

a) Discuss the mechanism of optical feedback to provide oscillation and hence amplification

within the laser. (4 marks)

b) A D-IM analog optical fiber link of length 2 Km employs an LED which launches mean

optical power of 10 dBm into a multimode optical fiber. The fiber cable exhibits a loss of 3.5

with splice losses calculated at 0.7 In addition, there is a connector loss at the

receiver of 1.6 dB. The p-i-n photodiode receiver has a sensitivity of 25 dBm for an SNR of 50

dB and with a modulation index of 0.5. It is estimated that a safety margin of 4 dB is required.

Assuming there is no dispersion-equalization penalty:

(i) Perform an optical power budget for the system operating under the above conditions and

ascertain its viability.

(ii) Estimate any possible increase in link length which may be achieved using an injection laser

source which launches mean optical power of 0 dBm into the fiber cable. In this case, the safety

margin must be increased to 7 dB. (8 marks)

c) Compare orthogonal frequency division multiplexing (OFDM) with conventional frequency

division multiplexing (FDM). (8 marks)

Question 4 (20 Marks)

a) Derive an expression for the coupling efficiency of a surface-emitting LED into a step index

fiber, assuming the device to have a Lambertian output. Determine the optical loss in decibels

when coupling the optical power emitted from the device into a step index fiber with an

acceptance angle of 14°. It may be assumed that the LED is smaller than the fiber core and that

the two are in close proximity. (10 marks)

b) Explain the Four-channel OTDM fiber system. (10 marks)

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MARKING SCHEME

Question 1

a) State three disadvantages of Optical Fiber Communications. (3 marks)

b) Give 2 examples of dopants which:

(i) Increase the refractive index of the core (1 example). (1 mark)

(ii) Decrease the refractive index of the cladding (1 example). (1 mark)

c) Compare a single-mode step index fibers and multimode step index fibers while used as an

optical channel. (5 marks)

d) Compare the light emitted from LASERs and LEDS. (2 marks)

e) With the aid of a block diagram, discuss the function of the major elements of an optical fiber

transmitter. (4 marks)

f) Design a bus optical network topology and explain its working principle. (4 marks)

Solution 1

a) Disadvantages of Optical Fiber Communications

(3 marks)

b) (i) Dopants such as GeO2 and P2O5 increase the refractive index of silica and are suitable for

the core. (1 mark)

(ii) Dopants such as B2O3 and fluorine decrease the refractive index of silica and are suitable for

the cladding. (1 mark)

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c) The single-mode step index fiber has the distinct advantage of low intermodal dispersion

(broadening of transmitted light pulses), as only one mode is transmitted, whereas with

multimode step index fiber considerable dispersion may occur due to the differing group

velocities of the propagating modes. This in turn restricts the maximum bandwidth attainable

with multimode step index fibers, especially when compared with single-mode fibers.

(2 marks)

However, for lower bandwidth applications multimode fibers have several advantages over

single-mode fibers. These are:

(i) The use of spatially incoherent optical sources (e.g. most light-emitting diodes) which cannot

be efficiently coupled to single-mode fibers;

(ii) Larger numerical apertures, as well as core diameters, facilitating easier coupling to optical

sources;

(iii) Lower tolerance requirements on fiber connectors.

(3 marks)

d) A laser emits a relatively narrow angular spread of Light while a LED transmits light within a

relatively wide cone (2 marks)

e) The principal components of a general optical fiber transmitter for either digital or analog

transmission are shown in the system block schematic of Figure 1.

Figure 1: The principal components of an optical fiber transmitter

The transmit terminal equipment consists of an information encoder or signal shaping circuit

preceding a modulation or electronic driver stage which operates the optical source. Light

emitted from the source is launched into an optical fiber incorporated within a cable which

constitutes the transmission medium.

(4 marks)

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f) The representation of a bus structure is shown in Figure 2.

Figure 2: Example of a bus structure with optical amplifiers and one OADM

A number (n) of WDM channels emitted from the M-Tx enters the OADM. A subset (n*) of

WDM channels is dropped and added by the OADM. The number n* of dropped and added

channels may range between 0 and n.

When n* = n, all WDM channels are dropped and added. If n* = 0, then no channel is added or

dropped, i.e. the OADM is just a through-way network element. This scheme can be generalized

by incorporating a sequence of optical amplifiers and optical add/drop multiplexers (OADMs).

(4 marks)

Question 2

a) Using simple ray theory, describe the mechanism for the transmission of light within an

optical fiber. Briefly discuss with the aid of a suitable diagram what is meant by the acceptance

angle for an optical fiber. Show how this is related to the fiber numerical aperture and the

refractive indices for the fiber core and cladding. (5 marks)

b) Briefly describe the two processes by which light can be emitted from an atom. Discuss the

requirement for population inversion in order that stimulated emission may dominate over

spontaneous emission. Illustrate your answer with an energy level diagram. (7 marks)

c) Derive the expression for the output photocurrent of a basic coherent detector in both

heterodyne and homodyne detection. (8 marks)

Solution 2

a) An optical fiber consists of a very thin fiber at its centre known as Core of refractive index n1

surrounded by a coaxial middle region which is made of material less dense than the core

material known as Cladding of refractive index n2 (n1 > n2).

If the light enters in such a fiber at an angle θ greater than the critical angle at the interface core-

cladding, it will undergo total internal reflection and is reflected at the same angle to the normal.

The light will then be contained within the fiber and will propagate to the far end by a series of

reflections.

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Acceptance angle and Numerical Aperture

Consider a meriditional ray (ray that passes through the axis of the fiber core).

The light rays contained within the core having a full angle of are accepted and transmitted

along the fiber.

The Acceptance angle is expressed as:

√

The numerical aperture NA of the fiber is defined as the sine of the acceptance angle.

√

Let

( )( )

As

Δ→ Normalized difference between the refractive indices of core and cladding

√

√

If √

(5 marks)

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b) This emission process can occur in two ways:

(i) By spontaneous emission in which the atom returns to the lower energy state in an entirely

random manner;

(ii) By stimulated emission when a photon having an energy equal to the energy difference

between the two states (E2 − E1) interacts with the atom in the upper energy state causing it to

return to the lower state with the creation of a second photon.

Spontaneous emission: An atom stays in the excited state about seconds and reverts to

the lower state emitting a photon of energy E2 E1 = hf. The emission of a photon by an atom

without an external agent is called spontaneous emission.

(A = Atom, = Atom in excited state)

Stimulated emission: When an atom is at the excited level E2, an interaction with a photon of

energy E2 E1 = hf induces its deexciatation to a lower energy level E1 with emission of an

additional photon of the same frequency f. Thus 2 photons instead of one move on. This

phenomenon of forced photon emission by an excited atom due to the action of external agent is

called stimulated (induced) emission.

(A = Atom, = Atom in excited state)

Figure 3: Energy state diagram showing: (b) spontaneous emission; (c) stimulated emission. The

black dot indicates the state of the atom before and after a transition takes place

Population inversion

However, to achieve optical amplification it is necessary to create a non-equilibrium distribution

of atoms such that the population of the upper energy level is greater than that of the lower

energy level (i.e. N2 > N1). This condition, which is known as population inversion, is

illustrated in Figure 4.

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Figure 4: Populations in a two-energy-level system: (a) Boltzmann distribution for a system in

thermal equilibrium; (b) a non-equilibrium distribution showing population inversion

(7 marks) c) Coherent detection principle

A simple coherent receiver model for ASK is displayed in Figure 5.

Figure 5: Basic coherent receiver model

The low-level incoming signal field eS is combined with a second much larger signal field eL

derived from the local oscillator laser. It is assumed that the electromagnetic fields obtained from

the two lasers (i.e. the incoming signal and local oscillator devices) can be represented by cosine

functions and that the angle ϕ = ϕS − ϕL represents the phase relationship between the incoming

signal phase ϕS and the local oscillator signal phase ϕL defined at some arbitrary point in time.

Hence, as depicted in Figure 5, the two fields may be written as:

(1) and

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(2) where ES is the peak incoming signal field and ωS is its angular

frequency, and EL is the peak local oscillator field and ωL is its angular frequency.

The angle ϕ (t) representing the phase relationship between the two fields contains the

transmitted information in the case of FSK or PSK. However, with ASK ϕ (t) is constant and

hence it is simply written as ϕ in Eq. (4.6).

For heterodyne detection, the local oscillator frequency ωL is offset from the incoming signal

frequency ωS by an intermediate frequency such that:

(3)

where ωIF is the angular frequency of the IF. The IF is usually in the radio-frequency region and

may be a few tens or hundreds of megahertz.

By contrast, within homodyne detection there is no offset between ωS and ωL and hence

ωIF = 0. In this case the combined signal is therefore recovered in the baseband. The two

wavefronts from the incoming signal and the local oscillator laser must be perfectly matched at

the surface of the photodetector for ideal coherent detection.

In the case of both heterodyne and homodyne detection, the optical detector produces a signal

photocurrent Ip which is proportional to the optical intensity (i.e. the square of the total field for

the square-law photodetection process) so that:

(4)

Substitution in the expression (4.11) from Eqs (4.6) and (4.7) gives:

(5)

Assuming perfect optical mixing expansion of the right hand side of the expression shown in Eq.

(4.10) gives:

Removing the higher frequency terms oscillating near the frequencies of 2ωS and 2ωL which are

beyond the response of the detector and therefore do not appear in its output, we have:

(6)

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Then recalling that the optical power contained within a signal is proportional to the square of its

electrical field strength, expression (4.11) may be written as:

(7) where PS and PL are the

optical powers in the incoming signal and local oscillator signal respectively.

Furthermore, a relationship was obtained between the output photocurrent from an optical

detector and the incident optical power Po of the form:

Hence the expression in (4.12) becomes:

(8) where η is the

quantum efficiency of the photodetector, e is the charge on an electron, h is

Planck’s constant and f is optical frequency.

When the local oscillator signal is much larger than the incoming signal, then the third a.c. term

in Eq. (4.13) may be distinguished from the first two d.c. terms and Ip can be replaced by the

approximation IS where:

(9)

Equation (4.14) allows the two coherent detection strategies to be considered. For heterodyne

detection ωS ≠ ωL and substituting from Eq. (4.8) gives:

(10) indicating that the output from the

photodetector is centered on an IF. This IF is stabilized by incorporating the local oscillator laser

in a frequency control loop. Temperature stability for the signal and local oscillator lasers is also

a factor which must be considered.

The stabilized IF current is usually separated from the direct current by filtering prior to

electrical amplification and demodulation.

For the special case of homodyne detection, however, ωS = ωL and therefore Eq. (4.14) reduces

to:

(11) or (12)

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where R is the responsivity of the optical detector. In this case the output from the photodiode is

in the baseband and the local oscillator laser needs to be phase locked to the incoming optical

signal.

(8 marks)

Question 3

a) Discuss the mechanism of optical feedback to provide oscillation and hence amplification

within the laser. (4 marks)

b) A D-IM analog optical fiber link of length 2 Km employs an LED which launches mean

optical power of 10 dBm into a multimode optical fiber. The fiber cable exhibits a loss of 3.5

with splice losses calculated at 0.7 In addition, there is a connector loss at the

receiver of 1.6 dB. The p-i-n photodiode receiver has a sensitivity of 25 dBm for an SNR of 50

dB and with a modulation index of 0.5. It is estimated that a safety margin of 4 dB and with a

modulation index of 0.5. It is estimated that a safety margin of 4 dB is required. Assuming there

is no dispersion-equalization penalty:

(i) Perform an optical power budget for the system operating under the above conditions and

ascertain its viability.

(ii) Estimate any possible increase in link length which may be achieved using an injection laser

source which launches mean optical power of 0 dBm into the fiber cable. In this case, the safety

margin must be increased to 7 dB. (8 marks)

c) Compare orthogonal frequency division multiplexing (OFDM) with conventional frequency

division multiplexing (FDM). (8 marks)

Solution 3

a) Optical feedback

To achieve this laser action, it is necessary to contain photons within the laser medium and

maintain the conditions for coherence. This is accomplished by placing or forming mirrors (plane

or curved) at either end of the amplifying medium, as illustrated in Figure 6.

Figure 6: The basic laser structure incorporating plane mirrors

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The optical cavity formed is more analogous to an oscillator than an amplifier as it provides

positive feedback of the photons by reflection at the mirrors at either end of the cavity. Hence the

optical signal is fed back many times while receiving amplification as it passes through the

medium.

Very high radiation density should be present in the medium. The density is made larger by

enclosing the emitted radiation in an optical resonant cavity. An optical resonant cavity is a pair

of optically plane mirrors; one of them is fully reflecting (100%) while the other is partially

reflecting (90%) and a small fraction of it is transmitted through it as a laser.

(4 marks)

b)

(8 marks)

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c) Orthogonal frequency division multiplexing (OFDM) is a multicarrier transmission technique

which is based on frequency division multiplexing (FDM). In conventional FDM, multiple-

frequency signals are transmitted simultaneously in parallel where the data contained in each

signal is modulated onto subcarriers and therefore the subcarrier multiplexed signal typically

contains a wide range of frequencies. Each subcarrier is separated by a guard band to avoid

signal overlapping. The subcarriers are then demodulated at the receiver by using filters to

separate the frequency bands.

By contrast, OFDM employs several subcarrier frequencies orthogonal to each other (i.e.

perpendicular) and therefore they do not overlap. Hence this technique can squeeze multiple

modulated carriers tightly together at a reduced bandwidth without the requirement for guard

bands while at the same time keeping the modulated signals orthogonal so that they do not

interfere with each other, as illustrated in Figure 7.

In the upper spectral diagram, 10 non-overlapping subcarrier frequency signals arranged in

parallel depicting conventional FDM are shown, each being separated by a finite guard band.

OFDM is displayed in the bottom spectral diagram where the peak of one signal coincides with

the trough of another signal. Each subcarrier, however, must maintain the Nyquist criterion

separation with the minimum time period of T (i.e. a frequency spread of 1/T) for each

subcarrier.

OFDM uses the inverse fast Fourier transform (IFFT) for the purpose of modulation and the fast

Fourier transform (FFT) for demodulation. Moreover, this is a consequence of the FFT operation

by which subcarriers are positioned perpendicularly and hence the reason why the technique is

referred to as orthogonal FDM. It may be observed that a large bandwidth saving in comparison

with conventional FDM is identified in Figure 7 resulting from the orthogonal placement of the

subcarriers.

Figure 7: Orthogonal frequency division multiplexing (OFDM) compared with conventional

frequency division multiplexing (FDM)

(8 marks)

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Question 4

a) Derive an expression for the coupling efficiency of a surface-emitting LED into a step index

fiber, assuming the device to have a Lambertian output. Determine the optical loss in decibels

when coupling the optical power emitted from the device into a step index fiber with an

acceptance angle of 14°. It may be assumed that the LED is smaller than the fiber core and that

the two are in close proximity. (10 marks)

b) Explain the Four-channel OTDM fiber system. (10 marks)

Solution 4

a) Although the possible internal quantum efficiency can be relatively high, the radiation

geometry for an LED which emits through a planar surface is essentially Lambertian in that the

surface radiance is constant in all directions. The Lambertian intensity distribution is illustrated

in Figure 8 where the maximum intensity I0 is perpendicular to the planar surface but is reduced

on the sides in proportion to the cosine of the viewing angle θ as the apparent area varies with

this angle.

Figure 8: The Lambertian intensity distribution typical of a planar LED

A further loss is encountered when coupling the light output into a fiber. Considerations of this

coupling efficiency are very complex; however, it is possible to use an approximate simplified

approach.

If it is assumed for step index fibers that all the light incident on the exposed end of the core

within the acceptance angle θa is coupled, then for a fiber in air:

(2.5)

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Also, incident light at angles greater than θa will not be coupled. For a Lambertian source, the

radiant intensity at an angle θ, I(θ), is given by (see Figure 2.7):

(2.6)

where I0 is the radiant intensity along the line θ = 0. Considering a source which is smaller than,

and in close proximity to, the fiber core, and assuming cylindrical symmetry, the coupling

efficiency ηc is given by:

(2.7)

Hence substituting from Eq. (2.6):

Furthermore, from Eq. (2.5):

(2.8)

Numerical Aperture NA = Sin (ϴA) = Sin (140) = 0.241

Coupling loss ( ) ( )

(10 marks)

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b) A block schematic of an OTDM system which has demonstrated 160 Gbit s−1

transmission

over 100 km is shown in Figure 9. The principle of this technique is to extend ETDM (Electrical

TDM) by optically combining a number of lower speed electronic baseband digital channels.

In the case illustrated in Figure 9, the optical multiplexing and demultiplexing ratio is 1: 4, with a

baseband channel rate of 40 Gbit s−1

. Hence the system can be referred to as a four-channel

OTDM system.

Figure 9: Four-channel OTDM fiber system

The four optical transmitters in Figure 5.1 were driven by a common 40 GHz clock using quarter

bit period time delays. Mode-locked semiconductor laser sources which produced short optical

pulses (around 2 ps long) were utilized at the transmitters to provide low duty cycle pulse

streams for subsequent time multiplexing.

Data was encoded onto these pulse streams using integrated optical intensity modulators which

gave return-to-zero transmitter outputs at 40 Gbit s−1

. These I/O devices were employed to

eliminate the laser chirp which would result in dispersion of the transmitted pulses as they

propagated within the single-mode fiber, thus limiting the achievable transmission distance.

The four 40 Gbit s−1

data signals were combined using an OTDM multiplexer. Although four

optical sources were employed, they all emitted at the same optical wavelength and the 40 Gbit

s−1

data streams were bit interleaved to produce the 160 Gbit s−1

signal.

At the receive terminal, the incoming signal was decomposed into the 40 Gbit s−1

baseband

components in a demultiplexer. Hence single-wavelength 160 Gbit s−1

optical transmission was

obtained with electronics which only required a maximum bandwidth of about 40 GHz, as

return-to-zero pulses were employed.

The transmitter and receiver sections shown in Figure 5.1 employed electro-absorption

modulators to provide for operation at the high transmission rate and furthermore negative

dispersion fibers were also incorporated to compensate for the positive dispersion of the standard

single-mode fiber (SSMF). Moreover, a field trial employing such transmitters and receivers at a

transmission rate of 160 Gbit s−1

over deployed SSMF has been successfully carried out.

(10 marks)