4.2.1 Scattering and Interference _by_Santana
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4.2.1 Scattering and Interference
ET3705301
Optoelectronic Application
Experiment
100 2
By Santana
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Outline
A Brief History
Wave Motion
Electromagnetic Theory,
Photons, and Light The Propagation of Light
Geometrical Optics
More on Geometrical Optics
The Superposition of Waves
Polarization
Interference
Diffraction
Fourier Optics Basics of Coherence
Modern Optics: Lasers and
Other Topics
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Ref.:Optics, 4th Ed., by Hercht, Eugene
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A Brief History
Prolegomenon
In the Beginning
From the Seventeenth Century
The Nineteenth Century
Twentieth-Century Optics
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Prolegomenon
In dense media, a tremendous number of close-together atoms
or molecules contribute an equally tremendous number of
scattered electromagnetic wavelets.
These wavelets overlap and interfere in a way that does not
occur in a tenuous medium. As a rule,the denser the
substance through which light advances, the less the lateral
scattering, and to understand why that's so, we must examine
the interference taking place.
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Prolegomenon
Recall that interference is the superposition of two or more
waves producing a resultant disturbance that is the sum of the
overlapping wave contributions.
Figure 2.14 shows two harmonic waves of the same frequency
traveling in the same direction. When they are precisely in-
phase (Fig. 2.14a), the resultant at every point is the sum of the
two wave-height values.
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This extreme case is calledtotal constructive interference.
When the phase difference reaches 180, the waves tend to
cancel, and we have the other extreme, calledtotal destructive
interference (Fig. 2.14d).
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The theory of Rayleigh Scattering has independent molecules
randomly arrayed in space so that the phases of the secondary
wavelets scattered off to the side have no particular
relationship to one another and there is no sustained pattern of
interference.
That situation occurs when the separation between the
molecular scatterers is roughly a wavelength or more, as it is
in a tenuous gas.
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Figure 4.3 (a) The scattering of light from a widely spaced
distribution of molecules,
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In Fig. 4.3a a parallel beam of light is incident from the left.
This so-calledprimary light field(in this instance composed of
plane waves) illuminates a group of widely spaced molecules.
A continuing progression of primary wavefronts sweep over
and successively energize and reenergize each molecule,
which, in turn, scatters light in all directions, and in particular
out to some lateral point P.
Because the lengths of their individual paths to P differ
greatly in comparison to A, some of the wavelets arriving at Pare ahead of others while some are behind, and that by
substantial fractions of a wavelength (Fig. 4.3b).
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Figure 4.3 (b) The wavelets arriving at a lateral point P have a jumble of different
phases and tend not to interfere in a sustained constructive fashion,
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In other words, the phases of the wavelets at P differ greatly.
(Remember that the molecules are also moving around, and
that changes the phases as well.)
At any moment some wavelets interfere constructively, some
destructively, and the shifting random hodgepodge of
overlapping wavelets effectively averages away the
interference.
Random, widely spaced scatterers driven by an incident
primary wave emit wavelets that are essentially independentof one another in all directions except forward.
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Laterally scattered light, unimpeded by interference, streams
out of the beam.
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Figure 4.3 (c) That can probably be appreciated most easily using phasors. Asthey arrive at P the phasors have large phase angle differences with respect to
each other. When added tip-to-tail they therefore tend to spiral around keeping
the resultant phasor quite small. Remember that we are really dealing with
millions of tiny phasors rather than four substantial ones.
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This is approximately the situation existing about 100 miles up
in the Earth's tenuous high-altitude atmosphere, where a good
deal of blue-light scattering takes place.
That the scattered irradiance should depend on 1/4 is easily
seen by returning to the concept of dipole radiation (Section
3.4.3).
Each molecule is taken as an electron oscillator driven into
vibration by the incident field. Being far apart, they are
assumed to be independent of one another and each radiates inaccord with Eq.
(3.56)
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The scattered electric fields are essentially independent, and
there is no interference laterally.
Accordingly, the net irradiance at P is the algebraic sum of the
scattered irradiances from each molecule (p. 285). For an
individual scatterer the irradiance is given by Eq.
(3.57)
and it varies with 4.
The advent of the laser has made it relatively easy to observe
Rayleigh Scattering directly in low-pressure gases, and the
results confirm the theory.
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Forward Propagation
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To see why the forward direction is special, why the wave
advances in any medium, consider Fig. 4.4. Notice that for a
forward point P all the different paths taken by the light are
about the same length; scattering alters the various path
lengths by very little. (The scattered wavelets arrive at P moreor less in-phase and essentially interfere constructively.)
A more detailed description is provided by Fig. 4.5. It depicts
a sequence in time showing two molecules A and B,
interacting with an incoming primary plane wavea solid arcrepresents wavelet is 180 out-of-phase with the incidentwave.
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(A driven oscillator is usually out-of-phase with the driver: p.
93.)
Thus A begins to radiate a trough (a negative -field) in
response to being driven by a peak (a positive -field). Part (b)
shows the spherical wavelet and the plane wave overlapping,
marching out-of-step but marching together.
The incident wavefront impinges on B, and it, in turn, begins
to reradiate a wavelet, which must also be out-of-phase by
180.
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In (c) and (d), we see the point of all of this, namely, that both
wavelets are moving forwardthey are in-phase with each
other. That condition would be true for all such wavelets
regardless of both how many molecules there were and how
they were distributed. Because of the asymmetry introduced bythe beam itself, all the scattered wavelets add constructively
with each other in the forward direction.
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From the Seventeen Century
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Wave Motion
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One-Dimensional Waves
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The Complex Representation
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Plane Waves
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Spherical Waves