THE UNIVERSITY OF HULL
Department of Physical Sciences (Physics)
Level 6 Examination
May 2008
Advanced Optical Physics
Tuesday 27 May 2008, 13.30 to 15.30
2 hours
Answer THREE questions, ONE from each section.
Do not open or turn over this exam paper, or start to write anything until told
to by the Invigilator. Starting to write before permitted to do so may be seen
as an attempt to use Unfair Means.
Module 04309
CONTINUED
Page 1 of 6
SECTION A: OPTICAL COMMUNICATIONS
1.
(i) Give a short account of the advantages gained from using an optical
communications link and the relative merits of fibre versus free-space
propagation.
[5 marks]
(ii) A 15 km long fibre used in a digital communications link has the following
properties
Core refractive index = 1.480
Cladding refractive index = 1.477
Core diameter = 7m
Attenuation = 3 dBkm-1
 2n
Dispersion parameter =  2 2 = 1  10-2

(a) Determine the numerical aperture (NA) of this fibre and estimate the
shortest wavelength for which it could be classed as being ‘single mode’.
(b) Calculate the power at the exit of the fibre if 50mW of optical power is
launched into its core. From this result find the signal current if the receiver
uses a detector that has a responsivity of 80AW-1.
(c) Based on the signal current in (b) use the graph below to determine the
maximum allowable noise current, , in the detector if the bit-error-rate is not
to exceed 1 in 108.
(d) Estimate the fibre bandwidth if it is limited by material dispersion and the
source has a relative spectral linewidth of / = 5  10-5. You can assume
the spread of group delay is given by
 2n 
 2
.
 c
[12 marks]
(iii) What factors will determine whether a diode laser or a light emitting diode
(LED) source is selected for a fibre communications link?
[3 marks]
8
-1
[c = 3  10 ms ]
continued overleaf
Module 04309
CONTINUED
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Question 1 continued
2.
(i) Describe the structure and properties of the three main types of optical
fibre that are available for use in communications, and compare their relative
advantages and limitations.
[6 marks]
(ii) Explain what is meant by the term modal dispersion and why this is
significant in an optical waveguide. Prove that for a step-index waveguide
modal dispersion results in a length-bandwidth product given by
cn 2
n1 n1  n 2 
where n1 and n2 are the core and cladding refractive index respectively.
[6 marks]
(iii) An ultra-short laser pulse is coupled into a 100 mm long slab waveguide
and on emerging from the guide is found to have temporal width of 4  10-11 s.
Assuming for this guide the equation in (ii) is applicable and n1  n2, determine
(n1 - n2).
[3 marks]
(iv) Outline the principle of the fibre Bragg grating (FBG). An FBG of 2 mm
length and 533 nm grating period is formed in a fibre core that has a refractive
index of 1.51. Determine the wavelength of its reflection peak and its
wavelength resolution.
[5 marks]
8
-1
[c = 3  10 ms ]
Module 04309
CONTINUED
Page 3 of 6
SECTION B: PHOTONICS MATERIALS AND DEVICES
3.
(i) With reference to a semiconductor, describe an exciton. What is meant by
the binding energy of an exciton? Explain why organic semiconductors have
much bigger binding energies than inorganic semiconductors.
[7 marks]
(ii) Use a configurational coordinate diagram to explain how the absorption
and emission lines of an organic semiconductor are broadened by vibration.
In your answer, refer to the Franck Condon principle and explain why the
emission spectrum is found at lower energy than the absorption spectrum.
[8 marks]
(iii) The binding energy of an exciton is
(a)
(b)
5 meV in GaAs, and
500 meV in an organic semiconductor.
What fraction of excitons are ionised (unbound) at 2K and 300K in both
material systems?
[5 marks]
(kT at 300 K is 26 meV)
Module 04309
CONTINUED
Page 4 of 6
4.
(i) Describe what is meant by a photonic crystal. Show how the photonic
crystal may be of one, two or three dimensions.
[5 marks]
(ii) Consider a medium consisting of a stack of layers of low dielectric constant
1 sandwiched between layers of high dielectric constant 2. Each layer has
the same thickness a/2, x is the direction of the stack and x = 0 is positioned
in the centre of a layer with dielectric constant 2. Give a qualitative
explanation why the two optical waves with phases given by sin(x/a) and
cos(x/a) are not degenerate (of equal energy) in the medium. Hence explain
how a 1 dimensional photonic band-gap develops in the medium.
[6 marks]
(iii) Describe a photonic crystal optical fibre. Outline some applications where
its structure offers key advantages compared to standard optical fibres.
[6 marks]
(iv) For light of wavelength 1.3µm the refractive index of AlxGa1-xAs varies with
x according to n = 3.45 - x(0.49).
You are asked to design a multilayer film of GaAs layers sandwiched between
AlxGa1-xAs layers to reflect light of wavelength 1.3 m. Each of the GaAs and
AlGaAs layers has a thickness of 0.192 m. What value of x do you choose to
maximise reflectivity?
[4 marks]
Module 04309
CONTINUED
Page 5 of 6
SECTION C: NONLINEAR OPTICS
5.
(i) An intense beam of frequency 1 and a weak beam of frequency 2, with
1> 2, are incident on a noncentrosymmetric material. Use energy level
diagrams to describe all the possible optical generation processes resulting
from second order polarisation of the medium. Show how energy and
momentum are conserved in each case. Explain how one particular process,
e.g. second harmonic generation, can be preferentially selected.
[8 marks]
(ii) Discuss the operation of an optical parametric oscillator as a coherent
tunable light source. Explain how the wavelength of the source is tuned and
why a threshold pump irradiance is required before oscillation.
[7 marks]
(iii) In a second harmonic generation experiment, light of intensity
1  1010 W m-2 and wavelength 694.3 nm from a ruby laser is incident on a
quartz crystal of length 1 mm. The refractive index of quartz is 1.4554 at
694.3 nm and 1.4766 at 347.2 nm. A second harmonic beam is generated
with an output intensity of 104 W m-2. Calculate what the output second
harmonic intensity would be if perfect phase matching were achieved.
[5 marks]
6.
(i) Show that the third order polarisation of a medium in response to an
incident beam of frequency  has components at  and 3.
[3 marks]
(ii) Explain the terms “self-phase modulation” and “group velocity dispersion”.
Explain how self-phase modulation results in a frequency chirp across a short
optical pulse.
[7 marks]
(iii) What is an optical soliton? Describe how it can be produced in an optical
fibre. Is soliton propagation possible at all optical frequencies in a fibre? How
is soliton propagation affected by small variations in the intensity of the pulse?
[6 marks]
(iv) An optical pulse of peak intensity 1  109 W m-2 with a temporal pulse
width (full width at half maximum) of 2 ps is incident onto an optical fibre of
length 10 km. The wavelength of light is 1.5 × 10-6 m. Estimate the frequency
spread of the pulse at the output of the fibre resulting from self-phase
modulation, stating all assumptions made.
[4 marks]
[Nonlinear refractive index coefficient, n2(glass) = 3  10-20 m2W -1 ]
Module 04309
END
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