Presentation schedule

Anderson, Aaron white light lasers 12/3/2014Carpenter, Matthew radar 12/8/2014Caudle, Bryce photoacustic medical imaging 12/5/2014Dunlap, Andrew holography 12/3/2014Govindan, Abhilash apps. laser cooling 12/10/2014Holly, Christopher display optics 12/5/2014Pensinger, Andrew photonics crystals 12/10/2014Rice, Eric free-space optical communications 12/8/2014Rubio, Matthew gravitational lenses 12/5/2014Takemoto, Yuki quantum computation 12/8/2014Tang, Shuhui nanophotonics 12/10/2014Xi, Yiming Neodymium YAG laser 12/3/2014

Modern opticsMore on Lasers

Chapter 13

Phys 322Lecture 35

Reminder: Please complete the online course evaluationLast lecture: Review discussion (no quiz)

Amplifier vs. Generator

No (or negative) feedback:

Positive feedback: generator

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

Gain spectrum can be very broad

Broadening of the gain spectrum

Laser Cavity

Laser Cavity

Longitudinal cavity modes

Longitudinal modes in Fabry-Perot cavity

Transverse modes

Challenge: How to make a laser operate in a single basic transverse mode?

Laser radiation - properties•Monochromaticity•Directionality•Coherence

Monochromaticity

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

InterferenceYoung Interference Experiment

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

Michelson Interferometer

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.

Solid state lasers

Nd ions in YAG crystal host

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).

Pumping by electric discharge

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.

Argon ion laser

High power, but low efficiency

Carbon Dioxide LaserThe CO2 laser operates analogously. N2 is pumped, transferring the energy to CO2.

CO2 Laser

Gas lasers exist in nature!

•Stellar atmospheres•Planetary atmospheres•Interstellar medium

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

Free electron lasers

Applications•Industrial applications•Medical (surgery, diagnostics)•Military (weapons, blinders, target pointers,…)•Daily (optical communications, optical storage, memory)•Research

…

Inertial confinement for nuclear fusion

Laser Fusion

D + T ==> 4He + n + 17.6 [MeV]