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)

v

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?

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ν

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 = 2πf = 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 particleNewton 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 dualityProperty 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.

hω

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Φ= P

hv=

Pλ

hc

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 hν)

• 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.€

E =hv

λ

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).

Ligh

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ic f

ield

Time

PhotochemistryMany 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 (O2).

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 (O3) uses UV radiation.

Reaches surface;Relatively harmless;Stimulates fluorescence in some materials

Mostly absorbed by O3 in stratosphere; small fraction (0.31-0.32 µm) reaches surface and causes sunburn (effect of ozone depletion?); energetic enough for photochemistry

Photodissociates O2 and O3; 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 exploitedNote 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 microwave)

• 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, inclinedat 55 degrees to equator.

• Operates at 1.575 GHz(1.228 GHz is a referenceto compensate for atmos-pheric water effects)

• 4 signals are required;one for time, three forposition.

• 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

N2+: 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 spectraBecause 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 nmStrongly 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 AstronomyThe 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 7th 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, mec2.

hν = 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