Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:English for Optics Students. Английский для студентов, изучающих оптику. Учебное пособие
.pdf
velocities that could not be observed. Instead, they had a quantum state,
which was a combination of position and velocity.
In general, quantum mechanics does not predict a single definite result
for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these is. That is to say, if one made
the same measurement on a large number of similar systems, each of which
started off in the same way, one would find that the result of the measurement would be A in a certain number of cases, B in a different number, and
so on. One could predict the approximate number of times that the result
would be A or B, but one could not predict the specific result of an individual measurement. Quantum mechanics therefore introduces an unavoidable
element of unpredictability or randomness into science.
Einstein objected to this very strongly, despite the important role he had
played in the development of these ideas. Einstein was awarded the Nobel
Prize for his contribution to quantum theory. Nevertheless, Einstein never
accepted that the universe was governed by chance; his feelings were
summed up in his famous statement “God does not play dice.” Most other
scientists, however, were willing to accept quantum mechanics because
it agreed perfectly with experiment. Indeed, it has been an outstandingly
successful theory and underlies nearly all of modern science and technology. It governs the behavior of transistors and integrated circuits, which are
the essential components of electronic devices such as televisions and computers, and is also the basis of modern chemistry and biology. The only areas of physical science into which quantum mechanics has not yet been
properly incorporated are gravity and the large-scale structure of the universe.
Task 11. Match the words to their meanings.
1 perturbation
2 formal power series
3 iteratively
4 perturbation solution
5 term
6 in terms of
7 higher-order terms
8 due to
9 deviation
10 technique
11 truncating
A несколько раз, итерационно
B из-за, вследствие
C усечение
D решение методом возмущений
E на основании, исходя из …
F возмущение
G формальный степенной ряд
H отклонение
I метод, способ
J члены высшего порядка
K член уравнения; допущение
41
Task 12. Answer the questions.
A
A
A
1. Why are mathematical methods used in optics?
2. What are mathematical methods used in optics?
3. What is a perturbation series?
4. What does the term “truncation” mean?
5. Why is it not always possible to get an exact answer?
Task 13. Read the text and translate the words in italics.
Perturbation theory comprises mathematical methods for finding an
approximate solution to a problem, by starting from the exact solution of a
related, simpler problem. A critical feature of the technique is a middle step
that breaks the problem into "solvable" and "perturbation" parts. Perturbation theory is applicable if the problem at hand cannot be solved exactly,
but can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem.
Perturbation theory leads to an expression for the desired solution in
terms of a formal power series in some "small" parameter – known as a per-
turbation series – that quantifies the deviation from the exactly solvable
problem. The leading term in this power series is the solution of the exactly
solvable problem, while further terms describe the deviation in the solution,
due to the deviation from the initial problem. Formally, we have for the approximation to the full solution A, a series in the small parameter (here
called ε), like the following:
AA A A
12
01 2
In this example, A
initial problem and
would be the known solution to the exactly solvable
0
,
, ... represent the higher-order terms which
1
2
may be found iteratively by some systematic procedure. For small ε these
higher-order terms in the series become successively smaller.
An approximate "perturbation solution" is obtained by truncating the se-
ries, usually by keeping only the first two terms, the initial solution and the
"first-order" perturbation correction
AA
.
01
Task 14. Explain the words in italics from Task 13 in English.
Task 15. Ask 6 questions to the text. Write them down. Your questions
should be of different types.
42
Task 16. Complete the sentences using the following words.
gravitation, analysis, to deal with, exactly, celestial, under, interaction
Perturbation theory is closely related to methods used in numerical 1….
The earliest use of what would now be called perturbation theory was 2 …
the otherwise unsolvable mathematical problems of celestial mechanics.
One of the examples is the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing 3 … of
the Earth and the Sun.
Perturbation methods start with a simplified form of the original prob-
lem, which is simple enough to be solved 4 …. In 5 … mechanics, this is
usually a Keplerian ellipse. 6 … non-relativistic gravity, an ellipse is exactly
correct when there are only two gravitating bodies (say, the Earth and the
Moon). Though it is not quite correct when there are three or more objects
(say, the Earth, Moon, Sun, and the rest of the solar system) and not quite
correct when the gravitational 7... is stated using formulas from General
relativity.
Task 17. Read the text and make a plan to it. Write it down. Then work
in groups and compare your variant with the one of your partners.
The solved, but simplified problem is then “perturbed” to make the
conditions that the perturbed solution actually satisfies closer to the real
problem. In this case they include the gravitational attraction of a third body
(the Sun). The "conditions" are a formula (or several) that represent reality,
often something arising from a physical law like Newton’s second law, the
force-acceleration equation,
aFm
.
In the case of the example, the force F is calculated based on the num-
ber of gravitationally relevant bodies; the acceleration a is obtained, using
calculus, from the path of the Moon in its orbit. Both of these come in two
forms: approximate values for force and acceleration, which result from
simplifications, and hypothetical exact values for force and acceleration,
which would require the complete answer to calculate.
The slight changes that result from accommodating the perturbation,
which themselves may have been simplified yet again, are used as corrections to the approximate solution. Because of simplifications introduced
along every step of the way, the corrections are never perfect, and the conditions met by the corrected solution do not perfectly match the equation de-
43
manded by reality. However, even only one cycle of corrections often provides an excellent approximate answer to what the real solution should be.
There is no requirement to stop at only one cycle of corrections. A par-
tially corrected solution can be re-used as the new starting point for yet another cycle of perturbations and corrections. In principle, cycles of finding
increasingly better corrections could go on indefinitely. In practice, one
typically stops at one or two cycles of corrections. The usual difficulty with
the method is that the corrections progressively make the new solutions very
much more complicated, so each cycle is much more difficult to manage
than the previous cycle of corrections. Isaac Newton is reported to have
said, regarding the problem of the Moon's orbit, that "It causeth my head to
ache."
This general procedure is a widely used mathematical tool in advanced
sciences and engineering: start with a simplified problem and gradually add
corrections that make the formula that the corrected problem matches closer
and closer to the formula that represents reality. It is the natural extension to
mathematical functions of the "guess, check, and fix" method used by older
civilisations to compute certain numbers, such as square roots.
causeth (old English) - causes
Task 18. Discuss with your partner the meaning of the term “pertur-
bation” and its application.
Task 19. Work in pairs. One of you is Student A and the other is Stu-
dent B. Read the corresponding task and talk to your partner. You may
use the questions you asked in Task 15.
Student A: You are a Professor at a university. Ask a student of optics to
tell you about perturbation and ask him/her questions about it.
Student B: You are a student of optics. You are taking an exam. Get
ready to tell your Professor about perturbations and answer his questions
about perturbation.
Task 20. Discuss with your partner which theory of light you find to be
the most interesting? Why?
Task 21. Write an essay of 150 words about the theories of light.
Task 22. Use the material you have studied in the Unit Physical Optics
and make a presentation on this topic. Add any information you think
may be necessary or interesting for the class.
44
Additional texts to Unit Physical Optics
Text 1
Born approximation to the Lippmann–Schwinger equation
The Lippmann–Schwinger equation for the scattering state
momentum p and out-going (+) or in-going (−) boundary conditions is
P
with a
PP P
where
is the free particle Green's function, is a positive infinitesimal
G
quantity, and V the interaction potential.
scattering solution sometimes called incident field. The factor
()
GE i V
p
is the corresponding free
P
P
on the
right hand side is sometimes called driving field.
This equation becomes within Born approximation
PP P
()
GE i V
p
which is much easier to solve since the right hand side does not depend on
the unknown state
anymore.
P
The obtained solution is the starting point of the Born series.
The Born approximation is used in quite different physical contexts.
In neutron scattering, the first-order Born approximation is almost al-
ways adequate, except for neutron optical phenomena like internal total reflection in a neutron guide, or grazing-incidence small-angle scattering.
Distorted wave Born approximation (DWBA)
The Born approximation is simplest when the incident waves
are
P
plane waves. That is, the scatterer is treated as a perturbation to free space
or to a homogeneous medium.
In the distorted wave Born approximation (DWBA), the incident
waves are solutions
1
P
to a part
1
of the problem
V
12
VV V
that is
treated by some other method, either analytical or numerical. The interaction of interest V is treated as a perturbation
2
to some system
V
1
that can
V
be solved by some other method. For nuclear reactions, numerical optical
model waves are used. For scattering of charged particles by charged particles, analytic solutions for coulomb scattering are used. This gives the nonBorn preliminary equation
45
111
PP P
(0)
GE iV
p
and the Born approximation
11 21
PP P
(0)
GE iV
p
Other applications include bremsstrahlung and the photoelectric effect.
For charged particle induced direct nuclear reaction, the procedure is used
twice. There are similar methods that do not use Born approximations. In
condensed-matter research, DWBA is used to analyze grazing-incidence
small-angle scattering.
Text 2
Quantum optics is a field of research that uses semi-classical and quan-
tum-mechanical physics to investigate phenomena involving light and its
interactions with matter at submicroscopic levels.
Light propagating in a vacuum has its energy and momentum quantized
according to an integer number of particles known as photons. Quantum
optics studies the nature and effects of light as quantized photons. The first
major development leading to that understanding was the correct modeling
of the blackbody radiation spectrum by Max Planck in 1899 under the hypothesis of light being emitted in discrete units of energy. The photoelectric
effect was further evidence of this quantization as explained by Einstein in a
1905 paper, a discovery for which he was to be awarded the Nobel Prize in
1921. Niels Bohr showed that the hypothesis of optical radiation being
quantized corresponded to his theory of the quantized energy levels of atoms, and the spectrum of discharge emission from hydrogen in particular.
The understanding of the interaction between light and matter following
these developments was crucial for the development of quantum mechanics
as a whole. However, the subfields of quantum mechanics dealing with matter-light interaction were principally regarded as research into matter rather
than into light; hence one rather spoke of atom physics and quantum electronics in 1960. Laser science–i.e., research into principles, design and application of these devices–became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name quantum optics became customary.
As laser science needed good theoretical foundations, and also because
research into these soon proved very fruitful, interest in quantum optics
rose. Following the work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the
46
electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light (see degree of coherence). This led to the introduction of the coherent state as a concept which
addressed variations between laser light, thermal light, exotic squeezed
states, etc. as it became understood that light cannot be fully described just
referring to the electromagnetic fields describing the waves in the classical
picture. In 1977, Kimble et al. demonstrated a single atom emitting one photon at a time, further compelling evidence that light consists of photons.
Previously unknown quantum states of light with characteristics unlike classical states, such as squeezed light were subsequently discovered.
Development of short and ultrashort laser pulses–created by Q switching and modelocking techniques–opened the way to the study of what became known as ultrafast processes. Applications for solid state research
(e.g. Raman spectroscopy) were found, and mechanical forces of light on
matter were studied. The latter led to levitating and positioning clouds of
atoms or even small biological samples in an optical trap or optical tweezers
by laser beam. This, along with Doppler cooling, was the crucial technology
needed to achieve the celebrated Bose–Einstein condensation.
Other remarkable results are the demonstration of quantum entanglement, quantum teleportation, and quantum logic gates. The latter are of
much interest in quantum information theory, a subject which partly
emerged from quantum optics, partly from theoretical computer science.
Today's fields of interest among quantum optics researchers include parametric down-conversion, parametric oscillation, even shorter (attosecond)
light pulses, use of quantum optics for quantum information, manipulation
of single atoms, Bose–Einstein condensates, their application, and how to
manipulate them (a sub-field often called atom optics), coherent perfect absorbers, and much more. Topics classified under the term of quantum optics,
especially as applied to engineering and technological innovation, often go
under the modern term photonics.
Several Nobel prizes have been awarded for work in quantum optics.
These were awarded:
in 2012, Serge Haroche and David J. Wineland "for ground-breaking
experimental methods that enable measuring & manipulation of individual
quantum systems".
in 2005, Theodor W. Hänsch, Roy J. Glauber and John L. Hall
in 2001, Wolfgang Ketterle, Eric Allin Cornell and Carl Wieman
in 1997, Steven Chu, Claude Cohen-Tannoudji and William Daniel
Phillips
47
Text 3
Concepts of quantum optics
According to quantum theory, light may be considered not only as an
electro-magnetic wave but also as a "stream" of particles called photons
which travel with c, the vacuum speed of light. These particles should not
be considered to be classical billiard balls, but as quantum mechanical particles described by a wavefunction spread over a finite region.
Each particle carries one quantum of energy, equal to hf, where h is
Planck's constant and f is the frequency of the light. That energy possessed
by a single photon corresponds exactly to the transition between discrete
energy levels in an atom (or other system) that emitted the photon; material
absorption of a photon is the reverse process. Einstein's explanation of spontaneous emission also predicted the existence of stimulated emission, the
principle upon which the laser rests. However, the actual invention of the
maser (and laser) many years later was dependent on a method to produce a
population inversion.
The use of statistical mechanics is fundamental to the concepts of quantum optics: Light is described in terms of field operators for creation and
annihilation of photons–i.e. in the language of quantum electrodynamics.
A frequently encountered state of the light field is the coherent state, as
introduced by Roy J. Glauber in 1963. This state, which can be used to approximately describe the output of a single-frequency laser well above the
laser threshold, exhibits Poissonian photon number statistics. Via certain
nonlinear interactions, a coherent state can be transformed into a squeezed
coherent state,by applying a squeezing operator which can exhibit super- or
sub-Poissonian photon statistics. Such light is called squeezed light. Other
important quantum aspects are related to correlations of photon statistics
between different beams. For example, spontaneous parametric downconversion can generate so-called 'twin beams', where (ideally) each photon
of one beam is associated with a photon in the other beam.
Atoms are considered as quantum mechanical oscillators with a discrete
energy spectrum, with the transitions between the energy eigenstates being
driven by the absorption or emission of light according to Einstein's theory.
For solid state matter, one uses the energy band models of solid state
physics. This is important for understanding how light is detected by a
solid-state devices, commonly used in experiments.
48
Text 4
Quantum electronics
Quantum electronics is a term that was used mainly between the 1950s
and 1970s to denote the area of physics dealing with the effects of quantum
mechanics on the behavior of electrons in matter, together with their interactions with photons. Today, it is rarely considered a sub-field in its own right,
and it has been absorbed by other fields. Solid state physics regularly takes
quantum mechanics into account, and is usually concerned with electrons.
Specific applications of quantum mechanics in electronics is researched
within semiconductor physics. The term also encompassed the basic processes of laser operation, which is today studied as a topic in quantum optics. Usage of the term overlapped early work on the quantum Hall effect
and quantum cellular automata.
Text 5
Optical physics is a subfield of atomic, molecular, and optical physics.
It is the study of the generation of electromagnetic radiation, the properties
of that radiation, and the interaction of that radiation with matter, especially
its manipulation and control. It differs from general optics and optical engineering in that it is focused on the discovery and application of new phenomena. There is no strong distinction, however, between optical physics,
applied optics, and optical engineering, since the devices of optical engineering and the applications of applied optics are necessary for basic research in optical physics, and that research leads to the development of new
devices and applications. Often the same people are involved in both the
basic research and the applied technology development, for example the
experimental demonstration of electromagnetically induced transparency by
S. E. Harris and of slow light by Harris and Lene Vestergaard Hau.
Researchers in optical physics use and develop light sources that span
the electromagnetic spectrum from microwaves to X-rays. The field includes
the generation and detection of light, linear and nonlinear optical processes,
and spectroscopy. Lasers and laser spectroscopy have transformed optical
science. Major study in optical physics is also devoted to quantum optics and
coherence, and to femtosecond optics. In optical physics, research is also
encouraged in areas such as the nonlinear response of isolated atoms to intense, ultra-short electromagnetic fields, the atom-cavity interaction at high
fields, and quantum properties of the electromagnetic field. Other important
areas of research include the development of novel optical techniques for
nano-optical measurements, diffractive optics, low-coherence interferometry,
optical coherence tomography, and near-field microscopy. Research in optical
physics places an emphasis on ultrafast optical science and technology.
The applications of optical physics create advancements in communications,
medicine, manufacturing, and even entertainment.
49
p
UNIT SUPERPOSITION AND INTERFERENCE
Terminology
amplitude
constructive interference
correlate
crest
destructive interference
displacement
magnitude
odd multiple
plane wave
pointwise sum
superposition
trough
Task 1. Match the words 1 – 11 to their translations A - K. Use the dictionary if necessary.
1 constructive interference
2 correlate
3 crest
4 destructive interference
5 displacement
6 magnitude
7 odd multiple
8 pointwise sum
9 superposition
10 trough
11 refer to
12
lane wave
A ослабляющая интерференция
B впадина волны
C точечная сумма
D усиливающая интерференция
E нечетное кратное
F смещение
G вершина волны, импульса
H величина
I соотносить(ся)
J объяснять чем-то, относиться к
K планарная, плоская волна
L наложение
Task 2. Answer the questions.
1. What optical phenomena do you know?
2. What happens when two waves overlap?
3. What do waves in different media have in common?
4. How can wave amplitude be increased/decreased?
5. How is the frequency of a wave connected with its characteristics?
50
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]