IV.B-1
IV. Light is a Photon (Quantum Optics)
IV.B. Lasers
1. Laser Amplification
A laser is a special kind of light source that is based on one or more of the types of light sources described in Section IV.A.4. The word “laser” is actually an acronym for
Light
Amplification by Stimulated Emission of Radiation.
A laser is made up of 2 key parts: an optical amplifier and an optical resonator. The amplifier increases the intensity of light each time the light passes through it, as depicted below; the resonator provides feedback to the amplifier by recirculating the light through the amplifier.
Laser Amplifier
In terms of the energy levels of an atom inside the amplifying medium, laser amplification can be understood as shown in the drawing below.
a
energy
E1 E2
E0 E3
hν = ∆E 2hν
pump level
ground level
lower laser level upper laser level fast non-radiative transition
fast non-radiative transition LASER amplification
When a photon of frequency ν is incident on an atom with two energy levels spaced by ∆E = hν, the photon either is absorbed (when the atom is in the lower-energy state with energy E1) or it stimulates the emission of another photon (when the atom is in the excited state with energy E2).
In order for stimulated emission to be more likely to occur than absorption, so that there is a net increase in the number of photons traveling through the amplifier, more atoms must be in the excited state than in the ground state. This situation is referred to as a “population inversion.”
A population inversion exists when more atoms in a laser amplifier are in the excited state than are in the ground state(s). This condition is necessary for the laser to exhibit gain , or an increase in the intensity of light traveling through the amplifier.
As the drawing above shows, a population inversion is obtained by pumping the atoms into a very high-energy pump level (E3) via optical or electrical excitation. In a good laser medium, the atoms
IV.B-2
relax very quickly from this level into the upper laser level (E2). If the rate at which atoms relax from level E2 is very slow, but the rate at which they relax from the lower laser level (E1) into the ground level (E0) is very fast, a large population inversion is produced between levels E2 and E1. 2. Laser Resonators
The second key part of a laser is an optical resonator. Typically a laser resonator consists of two parallel, nearly planar mirrors. One mirror is as close to 100% reflecting as possible, while the reflectivity of the other is slightly less than 100% so that some light can escape from the resonator to form the laser beam.
a Laser Amplifier
θ
L 100%
reflection
< 100%
reflection
Light that bounces back and forth between the mirrors multiple times interferes constructively if mλ0 =2Lcos .θ
Since only light that travels nearly perpendicular to the mirrors (θ ≅ 0˚) will remain within the resonator and thus be significantly amplified, the laser modes occur at wavelengths such that
m L L
m m
λ0 2 λ0 2
= ⇒ = .
Put another way, the cavity length L must be an integer number of half-wavelengths in order for the laser to operate at a certain wavelength, or
L= λm 0 2 .
In terms of frequency, since ν = c/λ0, then the laser mode frequencies and the separation between frequencies of successive modes are
νm m c ν
L
c
= = L
2 ; ∆ 2 .
As a result, the spectrum of light produced by a laser typically looks like a series of narrow peaks spaced by the mode spacing ∆ν.
a
“modes”
∆ν = c 2L
frequency ν intensity 〈I〉
IV.B-3
Most practical laser resonators use curved mirrors instead of true plane mirrors for two reasons:
(i) curved mirrors simplify the alignment of the laser;
(ii) curved mirrors accommodate diffraction, minimizing needless loss from the cavity.
beam waist
planar wavefront
curved wavefront (result of diffraction!)
3. How a Laser Works
The principle behind the operation of a laser is as follows. An external pump excites atoms in the amplifier creating a population inversion. These atoms spontaneously emit a few photons, which in turn produce more photons by stimulated emission. Some of these photons are returned to the cavity by the resonator, producing an avalanche of additional photons along the same direction.
Ultimately a steady-state situation is reached, in which a huge number of photons careen back-and- forth along the laser axis, with a small fraction escaping to form the laser beam.
100% < 100%
laser off
= atoms in ground state
pump on
= atoms in excited state
spontaneous emission &
rare stimulated emission
stimulated emission of light along the laser axis
steady-state laser operation
IV.B-4 4. Characteristics of Laser Light
Lasers are so useful because of the unique properties of laser beams, which can be: extremely monochromatic, extremely directional, extremely bright, and extremely coherent.
a. Monochromaticity :
Lasers produce light that is nearly a single color in contrast with non-laser sources (like thermal sources) which produce light mainly through spontaneous emission and put out polychromatic (nearly white) light.
The main reason laser light is so spectrally pure is that the gain occurs at a well-defined frequency determined by the transition frequency of the gain medium atoms. But laser light can be much narrower than even spontaneous emission from a single transition, since the resonator feedback ensures that almost all of the light is stimulated emission originating from a few, similar photons.
a
〈I〉 〈I〉 〈I〉
λ
∆λ λmax λ
∆λ λmax λ
∆λ
λmax
∆λ ~ 100’s - 1000’s nm (∆λ ~ 10–7 - 10–6 m)
∆λ ~ 0.01 - 1 Å
(∆λ ~ 10–12 - 10–10 m) ∆λ ~ 10–20 - 10–12 m ! thermal
radiation
spontaneous emission from single transition
laser light
b. Directionality :
Since almost all of the laser light is stimulated emission that originates from a few photons that travel along the laser axis, the laser beam is essentially perfectly collimated (all rays are parallel).
The beam does spread due to diffraction, since the finite sizes of the amplifier and mirrors limit the transverse size of the beam. However, as we saw in Section III.F.4.b., the beam spreads at an angle of only
θ λ~ a ,
where a is the diameter of the laser beam waist. Typically the divergence angle θ is less than 1 milliradian, or 0.05˚.
c. Brightness :
Spectral brightness is an optical property that is a measure of both the monochromaticity and the directionality of a light source. In terms of brightness, lasers are really impressive. The spectral brightness βλ is defined to be the spectral intensity per unit solid angle, or
βλ = λ
⋅ ⋅
spectral intensity
unit solid angle
power
area wavelength interval solid angle I
Ω .
IV.B-5
A solid angle is the 3-dimensional analog of an angle — just as an angle is defined to be the length of an arc on some circle divided by the radius of the circle, a solid angle is the area of a circular patch on some sphere divided by the square of the radius of the sphere. Solid angle is measured in “steradians,” in analogy to radians that measure 2-dimensional angles.
To see just how bright lasers are, let’s compare the brightness of a typical laser to the brightness of a light source you probably think is very bright: the sun!
The sun is a thermal source that emits light isotropically (uniformly in all directions). That is, it emits light over a solid angle of 4π steradians. Therefore the spectral brightness is given by
β π
π
λ λ π
λ = λ =
( )
−
I h c
h c k TB 4
2 1
1 4
2
5 exp .
The blackbody temperature of the sun can be taken to be approximately 5800 K (10,000 ˚F). At a typical visible wavelength λ ~ 0.5 µm, the spectral brightness is thus βλ ~ 7×1012 W/(m3-sterad).
Now consider a typical 1-mW Helium-Neon laser with a beam diameter of 0.5 mm. The quantities we need to calculate the spectral brightness are thus:
power Watts
area = 0.5 10 m
m
wavelength interval m
m MHz m
solid angle = = 1.22
sterad .
-3
= ×
× ×
= ×
= = =
(
×)
× × = ×
×
≅ ×
−
−
− −
−
1 10
2 2 10
633 10
3 10 1 1 3 10
7 5 10
3
2
7 2
2 9 2
8
15
2
6
π
λ λ ν
π λ
∆ ∆
Ω c
a
.
.
Putting these all together in the formula for βλ, we find that the spectral brightness of the HeNe laser is about βλ ~ 5×1023 W/(m3-sterad), which tells us that a little Helium-Neon laser is about 10,000,000,000 brighter than the sun!
d. Coherence :
Simply put, coherence is a measure of the correlation between the phases measured at different points on a wave. Even though it is a property of a propagating wave, coherence is directly related to the characteristics of the wave’s source.
For a simple picture of coherence, imagine two corks bobbing up and down in some wavy water.
Suppose the source of water waves is a single stone thrown into otherwise smooth water. Then we would find a perfect correlation between the motions of the two corks — they might not be exactly in phase (e.g., one might be up while the other is down), but the relative phase between the positions of the two corks would remain constant in time. In this case we say the source is
perfectly coherent. (Notice that a point source produces a perfectly coherent wave.)
a r
Ω = a r2
area a
IV.B-6
In contrast, suppose the waves resulted from a shower of raindrops. Since the raindrops hit the water at random times and in random locations, we would not expect the phase of the wave at one location (where the wave is the superposition of waves from many different raindrop sources) to be correlated to the phase at another location — the two corks would appear to bob up and down randomly with no apparent relationship between their motions. In this case we say the source is very incoherent.
When we describe the coherence of light waves, there are two basic kinds of coherence:
(i) temporal coherence is a measure of the correlation of a light wave’s phase at different points along the direction of propagation — it tells us how monochromatic a source is;
(ii) spatial coherence is a measure of the correlation of a light wave’s phase at different points transverse to the direction of propagation — it tells us how uniform the phase of the wavefront is.
As an example, consider a very incoherent source: an incandescent light bulb.
many different wavelengths many spatially separated sources
with indepedent phases
We can always make an incoherent source coherent if we are willing to throw away light. Below is an example illustrating spatial filtering of an incoherent source to increase the spatial coherence, followed by spectral filtering to increase the temporal coherence.
incoherent spatially coherent
spatially &
temporally coherent
pinhole aperture
wavelength filter
essentially light from a single point source
on the filament
The exciting thing about laser light is that it is naturally very coherent!
IV.B-7
How good is the coherence of a laser? One way of quantifying temporal coherence is in terms of the coherence length Lc given by
Lc ≅ λ λ0
2
∆ ,
where ∆λ is the bandwidth of the source. The coherence length is the maximum distance that two points can be separated along the wave propagation direction at a fixed time and still have a fixed phase relationship. In terms of interference, Lc is the longest length L that will allow interference fringes to form in an interferometer like the following.
a L
laser
fringes
For example, for a He-Ne laser we might find Lc ~ 10 cm - 100 m. This should be contrasted to a typical thermal source, for which Lc ~ 1 µm = 10–6 m.
Spatial coherence is usually quantified in terms of Young’s Double Slit Experiment. The spatial
coherence width , Wc, is the maximum slit separation that still yields fringes of a certain visibility near the center of the screen. For a laser beam, the width Wc is generally on the order of the beam waist (diameter) coming out of the laser. A typical value for the spatial coherence width of a laser might be 1 mm.
5. Important Lasers and Applications
Some important types of lasers and their corresponding wavelengths are listed on the chart below.
Since lasers are often classified in terms of the state of the amplifier medium (i.e., solid, liquid, or gas), we list this property as well. There are many other lasers that have been demonstrated over the years (including the famous “Jell-O” laser), but most of these are merely laboratory curiosities.
Those listed on the chart are in widespread use today for commercial or research applications.
On the next page is a list of some of the applications for which lasers are currently used and/or are expected to be used. As is evident from this list, lasers impact a wide variety of applications.
IV.B-8
IMPORTANT LASER TYPES AND THEIR WAVELENGTHS
LASER TYPE WAVELENGTH (nm) SOLID/LIQUID/GAS Excimer Lasers ArF, KrF, XeCl, XeF 193, 248, 308, 351 gas
Helium-Cadmium 325, 442 gas
Nitrogen 337 gas
Organic Dye (in solution) 300-1000 (tunable) liquid
Krypton Ion 337-800 (mainly 647) gas
Argon Ion 351-529 (mainly 488, 514.5) gas
Helium-Neon 543, 632.8, 1150 gas
Semiconductor (GaInP family) 670-680 crystal
Ruby 694 crystal
Semiconductor (GaAlAs family) 750-900 crystal
Titanium-Sapphire 700-1100 (tunable) crystal
Neodymium-YAG / YLF 1064, 1318 / 1053 crystal
Neodymium-Glass (including fibers) 1050-1080 glass
Semiconductor (InGaAsP family) 1300-1600 crystal
Erbium-Glass (including fibers) 1480-1580 glass
Hydrogen-Fluoride Chemical 2600-3000 gas
Carbon Dioxide 9000-11000 (mainly 10600) gas
IV.B-9
HOW LASERS ARE USED Reading and Writing Information:
∗ playing audio compact discs (CD)
∗ playing video discs
∗ reading Universal Product Codes (UPC) in stores
∗ reading and writing computer data on optical discs (CD-ROM and magneto-optic)
∗ laser printers, copiers, and FAX machines
∗ optical communications sources
Microelectronics:
∗ photolithography process for producing computer CPU and RAM chips Measurement and Inspection:
∗ projecting straight lines for construction alignment and irrigation
∗ measuring the range to distant objects
∗ measuring small distances very precisely
∗ illuminating cells for biomedical measurements
∗ laser-induced fluorescence measurements
∗ probing atomic and molecular structure of matter
∗ measuring chemical and pollutant concentrations
∗ detecting flaws in rubber tires and other parts
∗ sensors in dams, bridges, and other large structures
∗ “smart materials” that automatically adjust to mechanical conditions Medicine:
∗ treatment of diabetic retinopathy to hinder blindness
∗ laser surgery
∗ bleaching of port wine stain birthmarks
∗ kidney stone ablation
∗ photodynamic therapy (laser activated drugs)
Materials Working:
∗ cutting, drilling, and welding plastics, metals, and other materials
∗ cutting cloth
∗ drilling materials from diamonds to baby-bottle nipples
∗ engraving wood
∗ marking identification codes
Military Applications:
∗ antisensor, antisatellite, and antimissile weapons
∗ battle simulation
∗ pinpointing targets for bombs and missiles
∗ simulating effects of nuclear weapons
Energy:
∗ producing nuclear fusion (U of R’s Laboratory for Laser Energetics) Visual Applications:
∗ holography
∗ laser light shows
∗ displays
∗ laser pointers
