THE UNIVERSITY OF HULL
Department of Physical Sciences (Physics)
Level 6 Examination
May 2008
Laser Physics and Devices
Monday 12 May 2008, 13.30 to 15.30
2 hours
Answer THREE questions, TWO from section A and ONE from
section B.
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 04332
CONTINUED
Page 1 of 7
SECTION A: LASER PHYSICS
1.
(i) Taking gain and loss into account show how the intensity of a laser beam
varies on one round trip in an optical cavity. Define what is meant by the laser
threshold and, hence derive an expression for the threshold gain in terms of
the cavity loss.
[6 marks]
(ii) Show how the steady-state gain of an ideal 4 level laser changes with
pump rate when it is pumped from below to above the threshold for lasing.
[5 marks]
(iii) Show the phase requirements to achieve a self-reproducing wave in an
optical cavity. Hence, define the set of longitudinal modes q and show that q
corresponds to the number of half wavelengths contained in the cavity.
[5 marks]
(iv) A HeNe laser of gain length 0.2 m has a threshold gain coefficient of
5.15  10-2 m-1 and mirror reflectivities of 100% and 98%. Calculate the
threshold gain coefficient if the reflectivity of the latter mirror is changed to
97%.
[4 marks]
2.
(i) Discuss how quantum theory can be used to determine the homogeneous
linewidth of an atomic transition. Establish the relationship between the
homogeneous linewidth and the lifetime of the contributing atomic states.
What factors determine the lifetime of the states?
[7 marks]
(ii) Discuss why single longitudinal mode lasing is normally found with a
homogeneously broadened gain medium whereas multimode lasing is
possible if the gain medium is inhomogeneously broadened. Illustrate your
answer with sketches showing the gain spectra, the sets of longitudinal and
lasing modes below, at and above threshold in both cases.
[9 marks]
(iii) Calculate the homogeneous linewidth of a Nd3+ laser transition in YAG if
its coherence (dephasing) time is 1  10-12 s. Why is the measured transition
linewidth larger than this calculated value? Suggest why the measured
linewidth of Nd3+: YAG is smaller than that of Nd3+:glass.
[4 marks]
Module 04332
CONTINUED
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3.
(i) Define the Q or quality factor of an optical cavity. Suggest a method to
reduce the Q factor of an operating laser.
[3 marks]
(ii) Describe qualitatively how the
(a)
(b)
(c)
cavity loss,
amplifier gain and
laser output power
vary with time when a laser is Q switched. Illustrate your answer with a
suitable figure.
[6 marks]
(iii) Discuss how an electro-optical modulator can be used to Q switch a laser.
Explain why a “Brewster” plate is required in the cavity and indicate the
timescale of operation of the modulator. What modifications would be required
if you wanted the electro-optical modulator to mode lock rather than Q-switch
the laser?
[7 marks]
(iv) A Nd3+:YAG crystal with a spontaneous radiative lifetime of 550 s is
used in a Q switched laser. Estimate the maximum effective pumping interval
of the Q switch. Justify your answer by considering how the population density
changes with time during pumping of the laser.
[4 marks]
Module 04332
CONTINUED
Page 3 of 7
4.
(i) Define what is meant by
(a)
(b)
(c)
the beam waist,
the Rayleigh range, and
the complex radius of curvature
of a Gaussian optical beam. Show that at a large distance z from the beam
waist, the beam has a spherical wavefront of radius z. Find the beam
divergence in terms of the beam size at its waist.
[10 marks]
(ii) A collimated Gaussian beam from a HeNe laser with a spot size of
1  10-3 m is focused into a transparent gas sample of length 5  10-2 m. What
should the size of the focused spot be in order to maximise intensity whilst
ensuring that it is roughly uniform over the length of the sample. Find the focal
length of the focusing lens needed to satisfy this condition.
[6 marks]
(iii) Explain why blue lasers have replaced near-infrared lasers for some
optical data storage applications e.g. high definition video.
[4 marks]
Module 04332
CONTINUED
Page 4 of 7
SECTION B: LASER DEVICES
5.
(i) Use an energy level diagram to discuss the excitation mechanisms of an
Argon Ion laser. In your discussion suggest why Argon ion lasers have
relatively low gain coefficient.
[6 marks]
(ii) Attached on a separate sheet is a schematic of an Argon Ion laser. Label
the various parts of the laser on the schematic, which you should submit with
your answer book. Explain how the laser is designed to cope with high
operating temperatures. Discuss any other special features included to
optimise efficiency.
[8 marks]
(iii) Both the Argon ion and Helium Neon lasers have Doppler broadened
spontaneous emission lines. Suggest why the emission line of the former is
significantly broader than that of the latter.
[2 marks]
(iv) The spectral linewidth of an Argon ion and Helium Neon laser is 3.6 109
Hz and 1.5 109 Hz respectively. Estimate the maximum number of lasing
modes for both lasers, each having a cavity length of 0.1 m. Hence suggest
why a short HeNe laser is less stable than an Argon ion laser of the same
length.
[4 marks]
Module 04332
CONTINUED
Page 5 of 7
6.
(i) Give an account of the mechanisms that lead to population inversion and
laser action in
(a) discharge excited CO2 (Carbon Dioxide) lasers,
(b) KrF (Krypton Fluoride) excimer lasers.
You should include suitable energy level diagrams to support your answer.
[9 marks]
(ii) Sketch and detail the main design features of a typical excimer laser
system including the type of excitation circuit this might use.
[4 marks]
(iii) For the KrCl excimer laser system with the properties summarised below
(a) Estimate the potential maximum efficiency of the laser.
(b) Determine the pump power density (Wm-3) needed to attain laser
action in a 0.5m long discharge if mirrors with power reflection
coefficients of 0.98 and 0.8 are available. State any assumptions
made. (You may assume the gain coefficient is given by the product of
stimulated emission cross-section and population inversion).
[7 marks]
Emission wavelength = 222nm
Average energy for upper state formation = 13eV
Upper laser state lifetime = 1.2ns
Cross section for stimulated emission = 1.8  10-20m2
Distributed loss = 0.015m-1
c = 3  108ms-1, h = 6.6  10-34Js, e = 1.6  10-19C
Module 04332
END
Page 6 of 7
PLEASE ATTACH THIS PAGE TO YOUR ANSWER BOOK
Schematic Diagram of an Argon Ion laser (Question 5)
Module 04332
Page 7 of 7