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Nov 16, 2013 (3 years and 8 months ago)

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Electromagnetic waves



Lecture topics



Generation of EM waves



Terminology



Wave and particle models of EM radiation



EM spectrum

Generation of EM waves



Acceleration of an electrical charge



EM
wavelength

depends on length of time that the charged
particle is accelerated



Frequency

depends on number of accelerations per second



‘Antennas’ of different sizes



Nuclear disintegrations = gamma rays



Atomic
-
scale antennas = UV, visible, IR radiation



Centimeter/Meter
-
scale antennas = radio waves



http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=35

Oscillating electric dipoles



There is no fundamental constraint on the frequency of EM radiation,
provided an oscillator with the right natural frequency and/or an energy
source with the minimum required energy is present

Water molecule

Electric dipole:
separation of
positive and negative charges
(
permanent

or
induced
)

Electromagnetic Spectrum



EM Spectrum



Continuous range of EM radiation



From very short wavelengths (<300x10
-
9
m)



High energy



To very long wavelengths (cm, m, km)



Low energy



Energy is related to wavelength (and hence
frequency)

EM wave terminology



EM waves characterized by:



Wavelength,


(m)



Amplitude,
A

(m)



Velocity,
v

or
c

(m s
-
1
)



Frequency,
f

or
ν

(s
-
1

or
Hz)


cycles per second



Sometimes period,
T

(time
for one oscillation i.e., 1/f)

Wavelength units



EM wavelength


specified using various units



cm (10
-
2
m)



mm (10
-
3
m)



micron or micrometer
,

m (10
-
6
m)



nanometer, nm (10
-
9
m)



Angstrom, Å (10
-
10
m, mostly used in astronomy)



f (or
ν
)

is waves/second, s
-
1

or Hertz (Hz)


also MHz, GHz



Wavenumber (inverse wavelength) also commonly used:
given by 1/


(sometimes also 2π/λ) e.g. cm
-
1

(symbol: )



What is the wavenumber (in cm
-
1
) equivalent to


= 1 µm?

Electromagnetic energy



EM radiation defined by wavelength (

), frequency (f) and velocity (v) where:

v = f




i.e. longer wavelengths have lower frequencies etc.



v and


can change according to medium


f is constant



Generally more useful to think in terms of


(numbers are easier)



NB. Where v = c, this relationship refers to wavelength in a vacuum.

Digression


radio waves



Why is FM radio higher quality than AM radio?

AM

FM

Digression


radio waves



Why is FM radio higher quality than AM radio?



AM = Amplitude modulation (530


1700 kHz)



FM = Frequency modulation (87.8


108 MHz)



EM wave amplitude can be affected by many things


passing
under a bridge, re
-
orienting the antenna etc.



No natural processes change the frequency



Radiation with frequency
f
will always have that frequency until it
is absorbed and converted into another form of energy

Wave phase and angular frequency



Angular frequency
ω

= 2π
f

= 2π/T



Frequency with which phase changes



Angles in
radians

(rad)



360
°

= 2


rad, so 1 rad = 360/
2


= 57.3
°



Rad to deg. (*180/

) and deg. to
rad (
*

/
180)

Light is not only a wave, but also a particle

Newton proposed wave theory of light (EMR) in 1666:
observation of light separating into spectrum


The Photoelectric Effect (H. Hertz [1887], A. Einstein
[1905])


visible light incident on sodium metal


Posed problems if light was just a wave:

The electrons were emitted immediately (no time lag)


Increasing the intensity of the light source increased
the number of electrons emitted but not their energy


Red light did not cause any electrons to be emitted, at
any intensity


Weak violet light ejected fewer electrons, but with
greater energy

Max Planck (1900) found that electron energy was proportional to the frequency of the
incident light


Wave
-
particle duality

Property of EM radiation


Consistent with
WAVE


PARTICLE


Reflection









Yes



Yes


Refraction









Yes



Yes


Interference









Yes



No


Diffraction









Yes



No


Polarization









Yes



No


Photoelectric effect







No



Yes

Photons

The energy of a single photon is:
hf

or = (
h
/2π)
ω



where
h

is Planck's constant, 6.626 x 10
-
34

Joule
-
seconds


One photon of visible light contains about 10
-
19

Joules
-

not much



Φ is the
photon flux
, or

the number of photons

per unit time in a beam.






Where
P

is beam power.

Particle model of radiation



EMR intimately related to atomic structure and energy



Atom: +ve charged nucleus (protons+neutrons) &
-
ve
charged electrons bound in orbits



Electron orbits are fixed at certain levels, each level
corresponding to a particular electron energy



Change of orbit either requires energy (work done), or releases
energy



Minimum energy required to move electron up a full energy level
(can’t have shift of 1/2 an energy level)



Once shifted to a higher energy state from the
ground state
, the
atom is
excited
, and possesses potential energy



Released as electron falls back to lower energy level

Particle model of radiation

Bohr quantized shell model of the atom (1913)
: electrons jump from one orbit to
another only by emitting or absorbing energy in fixed quanta (levels)

If an electron jumps one orbit closer to the nucleus, it must emit energy equal to the
difference of the energies of the two orbits. When the electron jumps to a larger orbit, it
must absorb a quantum of light equal in energy to the difference in orbits.

Particle model of radiation: atomic shells

Electron energy levels are unevenly spaced and characteristic of a
particular element. This is the basis of spectroscopy.

To be absorbed, the energy of a photon must match one of the
allowable energy levels in an atom or molecule.


Electromagnetic energy



EM radiation also considered in quantum terms, where each
photon carries an energy E (in Joules) given by:

E = hf (or

)



where h is Planck’s constant (6.626x10
-
34

J s), f = frequency

Electromagnetic energy



Combining the two relations we have:





i.e. the energy of a photon is inversely proportional to λ



Implications for sensor design, pixel size etc.

Frequency decomposition



Naturally occurring EM radiation hardly ever
consists of a single frequency or wavelength



But, any arbitrary EM fluctuation can be thought
of as a composite of a number (potentially infinite)
of different ‘pure’ periodic functions



This is known as
Fourier decomposition




So any EM wave can be regarded as a mixture
of pure sine waves with differing frequencies,
and
the propagation of each frequency component can
be tracked completely separately from the others
.



In remote sensing, the implication is that
individual frequencies can be considered
individually, then the results summed over all
relevant frequencies.


Broadband vs. Monochromatic



EM radiation composed entirely of a single frequency is termed
monochromatic

(‘one color’)



Radiation that consists of a mixture of frequencies is called
broadband
.



So transport of broadband radiation can always be understood in terms
of the transport of individual constituent frequencies (monochromatic
radiation)



Plane waves have only
one frequency, ω.

This light wave has many

frequencies. And the

frequency increases in

time (from red to blue).

Light electric field

Time

Photochemistry

Many chemical reactions that take place in the atmosphere, including
those that produce smog, are driven by sunlight.


The stratospheric ozone layer also owes its existence to
photochemical
processes

that break down oxygen molecules (O
2
).

The photon energy
E = hν
is a
crucial factor in determining which
frequencies of EM radiation
participate in these processes.

Production of tropospheric ozone (a major pollutant)

Requires λ < 0.4 µm (i.e., sunlight)

The Electromagnetic Spectrum

What wavelengths are associated with sunburn?

The EM spectrum is subdivided into a few
discrete spectral
bands
.


EM radiation spans an enormous range of
frequencies; the bands shown here are
those most often used for remote sensing.


Boundaries between bands are arbitrary
and have no physical significance, except
for the
visible band.


Note that the ‘visible’ band is subjective


some insects can see ultraviolet light!



The Ultraviolet (UV)

The UV is usually broken up into three regions, UV
-
A (320
-
400
nm), UV
-
B (290
-
320 nm), and UV
-
C (220
-
290 nm).

UV
-
C is almost completely absorbed by the atmosphere. You can
get skin cancer even from UV
-
A.

Remote sensing of ozone (O
3
) uses UV radiation.


Reaches surface;

Relatively

harmless;

Stimulates fluorescence in
some materials

Mostly absorbed by O
3

in stratosphere; small
fraction (0.31
-
0.32 µm) reaches surface and
causes sunburn (effect of ozone depletion?);
energetic enough for photochemistry

Photodissociates O
2

and O
3
; absorbed
between 30 and 60 km

Visible light

Wavelengths and frequencies
of visible light (VIS)

Atmosphere mostly transparent


optical remote
sensing techniques, surface mapping etc.



Includes wavelength of peak
emission of radiation by the Sun
(~50% of solar output in this
range)



Cloud
-
free
atmosphere mostly
transparent to VIS wavelengths
,
so most are absorbed at the
Earth’s surface



Clouds are highly reflective in
the VIS



implications for
climate?

The Infrared (IR)


Sub
-
mm wavelengths


Unimportant for atmospheric
photochemistry


why?


IR regions subdivided by wavelength
and/or source of radiation


Region just longer than visible known
as near
-
IR, NIR (0.7


4 µm)
-

partially
absorbed, mainly by water vapor


Reflective (shortwave IR, SWIR)



Emissive or thermal IR (TIR; 4


50
µm)


absorbed and emitted by water
vapor, carbon dioxide, ozone and other
trace gases; important for remote sensing
and climate


Far IR (0.05


1 mm)


absorbed by
water vapor
; not widely exploited

Note boundary (~4 µm)


separates
shortwave

and
longwave
radiation

The microwave (µ
-
wave) region


RADAR


mm to cm wavelengths


Usually specified as frequency,
not wavelength


Various bands used by RADAR
instruments


Long


so low energy, hence
require own energy source
(active
micro
wave)


Penetrates clouds, planetary
atmospheres


useful for
mapping


Weather


monitor rainfall,
tornadoes, t
-
storms etc.

The electromagnetic spectrum

Now, we’ll run through the entire electromagnetic spectrum, starting at
very low frequencies and ending with the highest
-
frequency gamma rays.

The transition wavelengths are a bit arbitrary…

60
-
Hz radiation from
power lines

This very
-
low
-
frequency current

emits 60
-
Hz electromagnetic waves.

No, it is not harmful. A flawed epide
-

miological study in 1979 claimed

otherwise, but no other study has

ever found such results.

Also, electrical power generation has increased exponentially
since 1900; cancer incidence has remained essentially constant.

Also, the 60
-
Hz electrical fields reaching the body are small;
they’re greatly reduced inside the body because it’s conducting;
and the body’s own electrical fields (nerve impulses) are much
greater.

Long
-
wavelength
EM spectrum

Arecibo radio
telescope

Radio & microwave regions (3 kHz


300 GHz)



Consists of 24 orbiting satellites in “half
-
synchronous orbits” (two
revolutions per day).




Four satellites per orbit,

equally spaced, inclined

at 55 degrees to equator.




Operates at 1.575 GHz

(1.228 GHz is a reference

to compensate for atmos
-

pheric water effects)




4 signals are required;

one for time, three for

position.




2
-
m accuracy

Global positioning system (GPS)

Microwave ovens

Microwave ovens operate at 2.45 GHz,
where water absorbs very well.

Percy LeBaron
Spencer, Inventor
of the microwave
oven

22,300 miles (36,000 km) above the earth’s surface

6 GHz uplink, 4 GHz downlink

Each satellite is actually two (one is a spare)

Geosynchronous communications satellites

Cosmic
microwave
background



Interestingly,
blackbody radiation
retains a blackbody
spectrum despite
the expansion of the
universe. It does get
colder, however.

The cosmic microwave


background is blackbody


radiation left over from


the Big Bang

Wavenumber (cm
-
1
)

Peak frequency is ~ 150 GHz

Microwave background vs. angle

IR is useful for
measuring the
temperature of
objects.

Old Faithful

Hotter and
hence brighter
in the IR

Infrared

Lie
-
detection

The military uses IR to see objects it
considers relevant

IR light penetrates fog and smoke better than visible light.

The infrared space observatory

Stars that are just
forming emit light
mainly in the IR.

Using mid
-
IR laser light
to shoot down missiles

The Tactical High Energy Laser uses a high
-
energy,
deuterium fluoride chemical laser to shoot down
short range unguided (ballistic flying) rockets.

Wavelength =
3.6 to 4.2

m

Laser welding

Near
-
IR wavelengths are
commonly used.

Laser pointer (red)

Auroras

Auroras are due to
fluorescence from
molecules excited by
these charged particles.


Different colors are from
different atoms and
molecules.

O: 558, 630, 636 nm

N
2
+
: 391, 428 nm

H: 486, 656 nm

Solar wind particles spiral around the earth’s
magnetic field lines and collide with atmos
-
pheric molecules, electronically exciting them.

Fluorescent lights

Use phosphors (transition metal compounds that exhibit phosporescence
when exposed to UV light)


“Incandescent” lights (normal light bulbs) lack the emission lines

The eye’s response to light and color

The eye’s cones have three receptors, one for
red, another for green, and a third for blue.

The eye is poor at distinguishing spectra

Because the eye perceives intermediate colors, such as orange and
yellow, by comparing relative responses of two or more different
receptors, the eye cannot distinguish between many spectra.


The various yellow spectra below appear the same (yellow), and the
combination of red and green also looks yellow

UV from the sun

The ozone layer absorbs wavelengths less than 320 nm (UV
-
B and
UV
-
C), and clouds scatter what isn’t absorbed.

But much UV (mostly UV
-
A, but some UV
-
B) penetrates the
atmosphere anyway.

IR, Visible, and UV Light and Humans

(Sunburn)

We’re opaque in the UV and visible, but not necessarily in the IR.

Skin
surface

Flowers in the UV

Since bees see in the UV (they have a receptor peaking at 345 nm),
flowers often have UV patterns that are invisible in the visible.

Visible

UV (false color)

Arnica angustifolia
Vahl

The sun in the UV

Image taken
through a
171
-
nm filter
by NASA’s
SOHO
satellite.

The very short
-
wavelength regions

Soft x
-
rays

5 nm >

> 0.5 nm

Strongly interacts with
core

electrons

in materials

Vacuum
-
ultraviolet (VUV)

180 nm >

> 50 nm


Absorbed by <<1 mm of air

Ionizing to many materials

Extreme
-
ultraviolet (XUV or EUV)

50 nm >

> 5 nm

Ionizing radiation to
all

materials


EUV Astronomy

The solar corona is very hot (30,000,000 degrees K) and so emits
light in the EUV region.

EUV astronomy requires satellites because the earth’s atmosphere is
highly absorbing at these wavelengths.

The sun also emits x
-
rays

The sun seen in the x
-
ray region

Matter falling into a black hole emits x
-
rays

A black hole accelerates particles to very high speeds

Black hole

Nearby star

Supernovas emit x
-
rays, even afterward

A supernova
remnant in a
nearby galaxy (the
Small Magellanic
Cloud).

The false colors
show what this
supernova
remnant looks like
in the x
-
ray (blue),
visible (green) and
radio (red) regions.

X
-
rays are occasionally seen in auroras

On April 7
th

1997, a
massive solar storm
ejected a cloud of
energetic particles
toward planet Earth.

The “plasma cloud” grazed the Earth,
and its high energy particles created a
massive geomagnetic storm.

Atomic structure and x
-
rays

Ionization energy
~ .01


1 e.v.

Ionization energy
~ 100


1000 e.v.

X
-
rays penetrate tissue and do not
scatter much

Roentgen’s x
-
ray image
of his wife’s hand (and
wedding ring)

X
-
rays for photo
-
lithography

You can only focus light to
a spot size of the light
wavelength. So x
-
rays are
necessary for integrated
-
circuit applications with
structure a small fraction
of a micron.



1 keV photons from a
synchrotron:


2 micron lines over a base
of 0.5 micron lines.

Gamma rays result from matter
-
antimatter annihilation

e
-

e
+

An electron and positron self
-
annihilate, creating two gamma
rays whose energy is equal to the electron mass energy,
m
e
c
2
.

h
n

= 511 kev

More massive particles create even more energetic gamma
rays. Gamma rays are also created in nuclear decay, nuclear
reactions and explosions, pulsars, black holes, and
supernova explosions.

Gamma
-
ray bursts emit massive
amounts of gamma rays

In 10 seconds, they can emit more energy than our sun will in its
entire lifetime. Fortunately, there don’t seem to be any in our galaxy.

A new one
appears almost
every day, and
it persists for
~1 second to
~1 minute.

They’re
probably
supernovas.

The gamma
-
ray sky

Gamma Ray

The universe in
different spectral
regions…

X
-
Ray

Visible

Microwave

The universe in more spectral
regions…

IR