Lecture35 Ch13 more lasers.ppt
Transcript of Lecture35 Ch13 more lasers.ppt
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Modern opticsMore on Lasers
Chapter 13
Phys 322Lecture 35
Reminder: Please complete the online course evaluationLast lecture: Review discussion (no quiz)
The LaserThe laser is a medium that stores energy, surrounded by 2 mirrors.A partially reflecting output mirror lets some light out.
A laser will lase if the beam increases in intensity during a round trip: 3 0I I
R = 100% R < 100%
I0 I1
I2I3 Laser medium with gain, G
Necessary condition: population inversion N2 > N1
I
Laser gainNeglecting spontaneous emission:
2 1
2 1
dI dIc BN I - BN Idt dz B N - N I
2 1( ) (0)expI z I N N z
2 1expG N N L
[Stimulated emission minus absorption]
Proportionality constant is the absorption/gain cross-section,
2 1g N N
1 2N N
If N2 > N1:
If N2 < N1 :
There can be exponential gain or loss in irradiance. Normally, N2 < N1, and there is loss (absorption). But if N2 > N1, there’s gain, and we define the gain, G:
The solution is:
Laser medium
I(0)
zL0
I(L)
Two-, three-, and four-level systems
Two-level system
Laser Transition
Pump Transition
At best, you get equal populations.
No inversion.
It took laser physicists a while to realize that four-level systems are best.
Four-level system
Inversion is easy!
Laser Transition
Pump Transition
Fast decay
Fast decay
Three-level system
If you hit it hard, you get lasing.
Laser TransitionPump
Transition
Fast decay
Is inversion sufficient for lasing?
Achieving Laser ThresholdAn inversion isn’t enough. The laser output and additional losses in intensity due to absorption, scattering, and reflections, occur.
The laser will lase if the beam increases in intensity during a round trip, that is, if:
3 0 0exp( ) exp( ) exp( ) exp( )I I gL L R gL L I
R = 100% R < 100%
I0 I1
I2I3 Gain, G = exp(gL), and Absorption, A = exp(-L)
Gain > Loss
Laser medium
2( ) ln(1/ )g L R
This is called achieving Threshold. It means: I3 > I0. Here, it means:
LASER = Light Amplification by Stimulated Emission of Radiation
Laser is a device which transforms energy from other forms into (coherent and highly directional) electromagnetic radiation.
•1917 – A. Einstein postulates photons and stimulated emission•1954 – First microwave laser (MASER), Townes, Shawlow, Prokhorov•1960 – First optical laser (Maiman)•1964 – Nobel Prize in Physics: Townes, Prokhorov, Basov
•Chemical energy•Electron beam•Electric current•Electromagnetic radiation
…
Laser System1. Active (gain) medium that can amplify light that passes
through it 2. Energy pump source to create a population inversion in
the gain medium 3. Two mirrors that form a resonator cavity
Directionality
Radiation comes out of the laser in a certain direction, and spreads at a defined divergence angle ()
This angular spreading of a laser beam is generally very small compared to other sources of electromagnetic radiation, and described by a small divergence angle
Lamp: W = 100 W, 22 mW/cm1.0~
RWI
at L = 2 m
He-Ne Laser: W = 1 mW, r = 2 mm, R = r + L /2 = 2.1 mm, I = 8 mW/cm2
= 0.1 mrad
A laser beam typically has a Gaussian radial profile:
No aperture is involved.
Fraunhofer diffraction of a laser beam
2 20 0
0 0 20
( , ) exp x yE x yw
, ( , )x yE k k E x y YThe Fourier transform of a Gaussian is a Gaussian.
2 220( , ) exp
4x y
x y
k kE k k w
2w0
What will its electric field be far away?
2 2221 1
1 1 02( , ) exp4
x ykE x y wz
In terms of x1 and y1:
10 0
2z zwkw w
2 21 1
1 1 21
( , ) exp x yE x yw
or
where:
2w1
z
The beam diverges. What will its divergence angle be?
Angular divergence of a laser beam
01 /tan( ) z wwz z
2w0
The half-angle will be:
The divergence half-angle will be:
0w
z1
0
zww
w1
Recall that:
Conditions for interference1) For producing stable pattern, the two sources must have nearly
the same frequency.2) For clear pattern, the two sources must have similar amplitude.3) For producing interference pattern, coherent sources are
required.
Temporal coherence:Time interval in which the light resembles a sinusoidal wave. (~10 ns for natural light)Longitudinal coherence length: lc= ctc.Spatial coherence: longitudinal and transverseThe correlation of the phase of a light wave between different locations.
Coherence review
The coherence time is the reciprocal of the bandwidth (related to monochromaticity).
The coherence time is given by:
where is the light bandwidth (the width of the spectrum).
Sunlight is temporally very incoherent because its bandwidth isvery large (the entire visible spectrum).
Lasers can have coherence times as long as about a second,which is amazing; that's >1014 cycles!
1/c v
The Temporal Coherence Time and the Spatial Coherence LengthThe temporal coherence time is the time the wave-fronts remain equally spaced. That is, the field remains sinusoidal with one wavelength:
The transverse spatial coherence length is the distance over which the beam wave-fronts remain flat:
Since there are two transverse dimensions, we can define a coherence area.
Temporal Coherence
Time, c
Transverse Spatial Coherence Length
Spatial and Temporal Coherence
Beams can be coherent or
only partially coherent (indeed, even incoherent)
in both space and time.
Spatial andTemporal
Coherence:
TemporalCoherence;
Spatial Incoherence
Spatial Coherence;
TemporalIncoherence
Spatial andTemporal
Incoherence
Coherence (chapter 12)Completely incoherent waves: no interference fringesCompletely coherent waves: interference fringes best pronounced
Laser
Add glass plate
Laser
temporal coherence
LampAdd glass plateLamp
Laser Types
Lasers can be divided into groups according to different criteria:
1. The state of matter of the active medium: solid, liquid, gas, or plasma. 2. The spectral range of the laser wavelength: visible, Infra-Red (IR), etc. 3. The excitation (pumping) method of the active medium: Optical
pumping, electric pumping, etc. 4. The characteristics of the radiation emitted from the laser. 5. The number of energy levels which participate in the lasing process.
Classification by active medium• Gas lasers (atoms, ions, molecules)• Solid-state lasers• Semiconductor lasers
– Diode lasers– Unipolar (quantum cascade) lasers
• Dye lasers (liquid)• X-ray lasers• Free electron lasers
Types of Lasers• Solid-state lasers have lasing material distributed in a solid matrix
(such as ruby or neodymium:yttrium-aluminum garnet "YAG"). Flash lamps are the most common power source. The Nd:YAG laser emits infrared light at 1.064 nm.
• Semiconductor lasers, sometimes called diode lasers, are pn junctions. Current is the pump source. Applications: laser printers or CD/DVD/BlueRay players.
• Dye lasers use complex organic dyes, such as rhodamine 6G, in liquid solution or suspension as lasing media. They are tunable over a broad range of wavelengths.
• Gas lasers are pumped by current. Helium-Neon lases in the visible and IR. Argon lases in the visible and UV. CO2 lasers emit light in the far-infrared (10.6 mm), and are used for cutting hard materials.
• Excimer lasers (from the terms excited and dimers) use reactive gases, such as chlorine and fluorine, mixed with inert gases such as argon, krypton, or xenon. When electrically stimulated, a pseudo
molecule (dimer) is produced. Excimers lase in the UV.
The Ruby LaserInvented in 1960 by Ted Maiman at Hughes Research Labs, it was the first laser.
Ruby is a three-level system, so you have to hit it hard.
Gas LasersThe laser active medium is a gas at a low pressure (A few milli-torr).
The main reasons for using low pressure are:•To enable an electric discharge in a long path, while the electrodes
are at both ends of a long tube. •To obtain narrow spectral width not expanded by collisions between
atoms.
The first gas laser was operated by T. H. Maiman in 1961, one year after the first laser (Ruby) was demonstrated.
The first gas laser was a Helium-Neon laser, operating at a wavelength of 1152.27 [nm] (Near Infra-Red).
The Helium-Neon Laser
Energetic electrons in a glow discharge collide with and excite He atoms, which then collide with and transfer the excitation to Ne atoms, an ideal 4-level system.
Carbon Dioxide LaserThe CO2 laser operates analogously. N2 is pumped, transferring the energy to CO2.
CO2 laser in the Martian
atmosphere
Detuning from line center (MHz)
The atmosphere is thin and the sun is dim, but the gain per molecule is high, and the pathlength is long.
Semiconductor lasers
material
CB
VB
diodelaser:
layer thickness
CB
QC-laser:
Conventional semiconductor laser
Quantum cascade laser: unipolar semiconductor laser using intersubband transitions
Applications•Industrial applications•Medical (surgery, diagnostics)•Military (weapons, blinders, target pointers,…)•Daily (optical communications, optical storage, memory)•Research
…