Table Of ContentOTHER TITLES IN THE SERIES
IN NATURAL PHILOSOPHY
Vol. 1. DAVYDOV—Quantum Mechanics
Vol. 2. FOKKER—Time and Space, Weight and Inertia
Vol. 3. KAPLAN—Interstellar Gas Dynamics
Vol. 4. ABRIKOSOV, GOR'KOV and DZYALOSHINSKII—Quantum Field Theoretical
Methods in Statistical Physics
Vol. 5. OKUN'—Weak Interaction of Elementary Particles
Vol. 6. SHKLOVSKII—Physics of the Solar Corona
Vol. 7. AKHIEZER et al—Collective Oscillations in a Plasma
Vol. 8. KIRZHNITS—Field Theoretical Methods in Many-body Systems
Vol. 9. KLIMONTOVICH—The Statistical of Non-equilibrium Processes in a Plasma
Vol. 10. KURTH—Introduction to Stellar Statistics
Vol. 11. CHALMERS—Atmospheric Electricity (2nd Edition)
Vol. 12. RENNER—Current Algebras and their Applications
Vol. 13. FAIN and KHANIN—Quantum Electronics, Volume 1—Basic Theory
Vol. 14. FAIN and KHANIN—Quantum Electronics, Volume 2—Maser Amplifiers
and Oscillators
Vol. 15. MARCH—Liquid Metals
Vol. 16. HORI—Spectral Properties of Disordered Chains and Lattices
Vol. 17. SAINT JAMES, THOMAS and SARMA—Type II Superconductivity
Vol. 18. MARGENAU and KESTNER—Theory of Intermolecular Forces
Vol. 19. JANCEL—Foundations of Classical and Quantum Statistical Mechanics
Vol. 20. TAKAHASHI—An Introduction to Field Quantization
Vol. 21. YVON—Correlations and Entropy in Classical Statistical Mechanics
Vol. 22. PENROSE—Foundations of Statistical Mechanics
Vol. 23. VISCONTI—Quantum Field Theory, Volume 1
Vol. 24. FURTH—Fundamental Principles of Theoretical Physics
Vol. 25. ZHELESNYAKOV—Radioemission of the Sun and Planets
Vol. 26. GRINDLAY—An Introduction to the Phenomenological Theory of Ferro-
electricity
Vol. 27. UNGER—Introduction to Quantum Electronics
Vol. 28. KOGA—Introduction to Kinetic Theory Stochastic Processes in Gaseous
Systems
Vol. 29. GALASIEWICZ—Superconductivity and Quantum Fluids
Vol. 30. CONSTANTINESCU and MAGYACI—Problems in Quantum Mechanics
Vol. 31. KOTKIN and SERBO—Collection of Problems in Classical Mechanics
Vol. 32. PANCHEV—Random Functions and Turbulence
Vol. 33. TALPE—Theory of Experiments in Paramagnetic Resonance
Vol. 34. TER HAAR — Elements of Hamiltonian Mechanics, 2nd. Edition
POLARIZED LIGHT
and
OPTICAL MEASUREMENT
D. CLARKE, M.Sc, Ph.D., A.InstP.
Department of Astronomy, University of Glasgow
J. F. GRAINGER, B.Sc, Ph.D.
Physics Department, University of Manchester
Institute of Science and Technology
P E R G A M ON P R E SS
OXFORD NEW YORK TORONTO
SYDNEY BRAUNSCHWEIG
Pergamon Press Ltd., Headington Hill Hall, Oxford
Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford,
New York 10523
Pergamon of Canada Ltd., 207 Queen's Quay West, Toronto 1
Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street,
Rushcutters Bay, N.S.W. 2011, Australia
Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig
Copyright © 1971 D. Clarke and J.F. Grainger
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior permission of
Pergamon Press Ltd.
First edition 1971
Library of Congress Catalog Card No. 70-143590
Printed in Germany
08 016320 3
Preface
ALL light is polarized to some extent and anyone who works in the
field of optical measurement must have a conceptual understanding of
the phenomenon. The need for this is obvious if he is directly con-
cerned with measuring polarizational information, but it is also neces-
sary in any field where light is being measured, in order to be sure
that the results really represent what the experimenter thinks they
do.
Most undergraduate courses in optics include a rudimentary treat-
ment of polarization, but it is usually insufficient for application to
anything other than the simplest problems. This book is designed to
give research workers and postgraduate students the necessary under-
standing of the phenomenon and its role in optical measurement.
Certain parts of it, however (especially the first and last chapters),
could profitably be read by undergraduates.
It would be impossible to list all the interactions of light and matter
in which polarization is important. Nor is the book concerned with
discussing these interactions for their own sake. It is taken for granted
that there are many situations in which it is desirable to measure, con-
trol or allow for the polarizational characteristics of a beam of light
or of a measuring instrument. Interactions are only discussed in so far
as they are relevant to optical measurement.
Many of the topics discussed will already be familiar to the reader,
vii
PREFACE
but they are presented here from a polarizational standpoint and often
to a greater depth than is usual in general optical texts.
In the first chapter a self-consistent conceptual picture of the pheno-
menon of polarization is presented, in order that the theory of polariza-
tional experimentation may be understood. Mathematical methods for
describing polarized light and its interaction with optical elements are
developed.
Chapter 2 describes a number of interactions of light and matter
which are made use of in devising optical elements to be used in polar-
ization studies. These optical elements are discussed in Chapter 3.
Some of them may be new to the reader as they are not often described.
The measurement of polarization—or polarimetry in its broadest
sense—is discussed in Chapter 4 and the various techniques which are
open to the experimentalist are presented. The discussion does not go
into details of any particular Polarimeter but presents ideas and back-
ground for some of the problems an experimeter might have. Although
it has been assumed throughout that the detector is photo-electric,
the ideas referred to are not restricted to this type of detection.
Chapter 5 examines the roles which polarization plays as an in-
formation carrier or information distorter.
This book could never have been completed without the patient
understanding and help of our wives, and we should like to take this
opportunity of expressing our thanks to them.
viii
ACKNOWLEDGEMENT
P.90. Table 31. The data in this table has been taken from Jenkins &
White 'Fundamentals of Optics', Third Edition, McGraw Hill (1965).
Reprinted through permission of the publisher.
P. 175. From Opticks' by Sir Isaac Newton, Dover Publications Inc.,
New York. Reprinted through permission of the publisher.
CHAPTER 1
The Description of Polarized Light
PROGRAMME
Information about the universe is carried by electromagnetic waves. The in-
formation is contained in the transverse characteristics of the waves, as well as
in their intensity. Measurement of these transverse characteristics, or polariza-
tion as they are collectively called, is therefore important. In order to discuss
these measurement procedures, it is first of all necessary to have a clear under-
standing of the physical phenomena involved. In this chapter, a self-consistent
conceptual picture of polarization is developed.
The subject is approached phenomenologically, by considering the behaviour
of ordinary light when subjected to certain simple experiments. These show the
incoherence of orthogonally resolved components of unpolarized light, a fact
which is found to be the key to the understanding of the statistical nature of the
radiation processes—whether these are thought of from a classical or quantum
standpoint.
Based on this understanding, mathematical methods are then developed for
the description of the polarization characteristics of light.
1.1. Introduction
Our knowledge of the world around us is built up from signals trans-
mitted to our brains from sensory cells. These signals are the result
of the interaction of the external universe and the sensory cells. Ex-
perimental science through the ages has developed devices for extend-
ing the scope and sensitivity of the senses. In all cases, these devices
produce stimuli which we can sense, their magnitudes being related in
1
POLARIZED LIGHT AND OPTICAL MEASUREMENT
a known way to the original stimulus. For example, our ability to assess
temperature directly is very limited both in range and sensitivity. How-
ever, small changes in temperature or very high or low temperatures
(of which, even if the observer were able to survive, he would be un-
able to make an assessment) may be measured by a transducer depen-
dent upon a known variation with temperature of some displayable
quantity. The display must then interact with one or other human
sense and convey the information to the brain. Almost always, this
last link in the chain is visual.
In this book we shall concern ourselves with some of the physical
phenomena which are known to us directly through the sense of sight
or its extensions by instruments. The eye, in giving us a sense of colour,
is sensitive only to a limited range of frequencies in the electromagnetic
spectrum. The range of signal strengths which can be accommodated
is also limited. The transducing instruments allow us to determine
colour quantitatively and to accommodate a greater range of signal
strengths and frequencies. However, as a result of the transverse nature
of electromagnetic waves, light has another characteristic, to which the
eye is not normally sensitive.! It is perhaps because of this that the
effects of this other characteristic on some optical measurements are
sometimes overlooked, or the information carried by it is wasted.
Two apparently identical beams of light, having the same frequency
range and intensity distribution within that range, can nevertheless
interact differently with certain optical elements. The difference usually
manifests itself after the interaction as an inequality of the intensities
of the beams, a change in their direction of propagation, a modifica-
tion of their spectra, or a combination of these. This characteristic of
the light, to which the optical element is sensitive, is known as polariza-
tion,* and we shall be concerned in this book with defining and under-
standing it.
t The sensitivity of the eye to this characteristic has been investigated by several
workers, e.g. de Vries et al. (1950).
+
The word 'polarization' is an unfortunate choice as it does not really describe
the phenomenon involved. It would now be impossible to replace it by another in
the scientific vocabulary. The historical reason for its introduction is discussed in
Appendix I.
2
THE DESCRIPTION OF POLARIZED LIGHT
A beam of light from a source, arriving at a detecting device, must
carry information about the source, and any interactions which the
light may have suffered on its way to the observer. This information
can give us knowledge of the condition of the source or the physical
processes involved in the interaction of the light and the medium. To
extract the information it will, in general, be necessary to measure the
following:
(i) intensity as a function of frequency;
(ii) polarization as a function of frequency;
(iii) direction of propagation.
Any, or all, of these may vary with time, and measurements of these
latter variations can also convey information. It is clear that the mea-
surement of any of the above parameters must eventually involve
intensity determinations, i.e. work being done by the electromagnetic
field on the detecting device. It is not immediately obvious that, in
measuring an intensity for its own sake, polarization need be taken into
account. However, as we shall see, this is frequently necessary, as
intensity measuring instruments are sensitive to it.
In order to proceed any further, we must look more carefully into
the nature of light.
1.2. On the Nature of Light
In this section we shall be concerned with developing models to
represent light. We must first recall some of the results of classical
electromagnetic theory. In a region where there are no charges, or
current distributions other than those determined by Ohm's law, the
electric (E) and magnetic (H) fields are described by Maxwell's equa-
tions:!
da
curl Ε = — μμ . div Η = 0
0
dt
dE
curl Η = σΕ + εε . div Ε = 0
0
dt
t MKS units are used throughout.
3
POLARIZED LIGHT AND OPTICAL MEASUREMENT
where ε, μ, and a are respectively the dielectric constant, permeability
and conductivity of the medium in the region and ε and μ are,
0 0
respectively, the permittivity and permeability of free space.
These relations give rise to wave equations in the form:
2
dE
Z
\E — σμμ εεμμ = 0
0 0 0 2
dt dt
and
νΉ — ομμ εεμμ = 0
0 0 0 2
dt dt
which represent a set of six equations, one for each component of the
appropriate vector. Since the equations are linear, any combination
of solutions will also be a solution. Thus, any waveform which is
capable of Fourier analysis will be a solution, provided sinusoids are
solutions. When the most simple and special solution of a sinusoid in
a non-conducting medium is considered, the velocity of the wave in
the medium can be expressed as:
1
ν =
V εεμμ
0 0
In free space both ε and μ are unity and so the velocity under these
conditions is given by :
1
λ/ε μο
0
The ratio cjv known as the refractive index, n, of the medium, hence
9
equals y/εμ. At optical frequencies, the value of μ is very close to
unity for dielectrics and hence the refractive index is \Ιε, where ε is the
dielectric constant at the particular frequency of the wave.
An investigation of these solutions of the wave equations shows
that the wave motion is transverse to the direction of propagation and
that Ε and Η are perpendicular and in phase. In a medium of zero
conductivity, the ratio E\H = V'μμ \εε = Ζ has the dimensions of an
0 0
4
