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

4.2.1 scattering and interference _by_santana

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