ENG227 Electromagnetics and Communication Technology
Assignment 2
This assignment is worth 12.5% of the total unit. This is an individual
assignment. If you found guilty of plagiarism, a failure grade will be awarded.
The due date of this assignment is 20 th October 2019. Please submit your answers
in a single pdf file via Learnline (in the “Submit Here” tab). Late submissions incur
a 10% penalty per day.
Question 1
Consider the design of an optical fibre.
The fibre has a core refractive index of 1.47. The radius a and the relative refractive
index difference are to be selected to make this a single mode fibre.
Sketch a design characteristic of refractive index difference versus core radius for
the fibre representing the conditions for single mode propagation at a wavelength of
1.3 m.
Determine whether this fibre remains single-mode at a transmission wavelength of
0.85 m when its core radius is 4.5 m.
Question 2
The Gaussian approximation for the electric field distribution of the fundamental
mode in a single-mode fibre takes the form:
E(r) = Eo exp (-r2/wo2)
where wo is the spot size. The approximate expression for the spot size over the
range 1<V<2.5 is given by
wo/a = 0.65 + 1.619V-3/2 + 2.879V-6
Sketch the field profile E(r)/Eo versus r/a over the range 0 to 3, for values of
normalized frequency V = 1.0, 1.5, 2.0, 2.5. Comment on the field profile as the
normalized frequency is reduced significantly below 2.4 and suggest what this
indicates about the distribution of the light within the fibre.
Question 3
The velocity of light in the core of a step index fibre is 2.01108 m/s, and the critical
angle at the core-cladding interface is 80. Determine the numerical aperture and
the acceptance angle for the fibre in air, assuming it has a core diameter suitable for
consideration by ray analysis. The velocity of light in a vacuum is 2.998108 m/s.
Question 4
Optical Gain 100
Coefficient
50
(cm-1)
0
1.298 1.300 1.336 1.338
Wavelength (m)
Fig. 1
The optical gain coefficient of a semiconductor laser with 150 m cavity length is
shown in Fig. 1. The loss coefficient and the refractive index of the semiconductor
laser are 21.6 cm-1 and 3.5 respectively. Find:
(i) The minimum gain coefficient required for lasing.
(ii) The frequency separation between the longitudinal modes of the laser.
(iii) The number of longitudinal modes emitted.
Note. The power reflectivity of a surface between two materials of refractive indices
n1 and n2 is given by:
2
n − n1
R = 2
n2 + n1
Question 5
This problem concerns external modulation of a laser source. The transfer
characteristic of the electro-optic intensity modulator shown in Fig. 2 is given by
Pout = 101 + cos V (mW )
4
Evaluate the small signal gain in W/V, defined as the ratio of the detected ac optical
power PD,ac to the input RF voltage VRF, of the 30 km externally modulated fibre-optic
communication link shown in Fig 2 when the bias voltage is Vb = 2 V. Assume that the
fibre loss is 0.3 dB/km.
VRF
Bias
PD
Laser
30 km
Electro-optic Optical
Modulator Detector
Fig. 2
