Lasers* Laser

Transition

Pump

Transition

Fast decay

Fast decay

* Light Amplification by Stimulated Emission of Radiation

The Ruby Laser

1960

1965

THE LARGEST LASER IN THE WORLD

National Ignition Facility

192 beams,

4 MJ per pulse

"Experimental realization of a one-atom laser in the

regime of strong coupling," J. McKeever, A. Boca, A.

D. Boozer, J. R. Buck and H. J. Kimble, Nature 425,

268 (2003).

SINGLE ATOM LASER

NANOLASERS

Zinc oxide wires on a sapphire substrate self organized nano-wire forest

Pumped by 266 nm beamed at a slight angle laser wavelength 385 nm

The first room temperature UV nanowire lasers

P. Yang, UC Berkeley 2001

Courtesy A. Siegman

Charles Townes (and Mrs Townes) - 2006

Interaction of light with excited media

Excited media? Matter which has energy in excited energy levels

Process of excitations

Eg

Eexcited

Excitation

Absorption

De-excitation

Emission

Assumptions - quantized energy levels - electronic, vibrational rotational

Limitations – Optical processes only

Energy levels

Emission and Absorption – Basic ideas

Restrict ourselves to two level system

E1

E

2

E2 – E1 = hn = hc/l

E1

E

2

E1

E

2

E1

E

2

Three basic processes

ground state

rest state

excited state

temporary state

Absorption Spontaneous

Emission Stimulated

Emission

N2

N1

Number of atoms (or molecules) / unit volume

N = number density N = N1 + N2

N1,2 = population of levels 1 & 2

Spontaneous emission

Probability that the process occurs can be defined by

Rate of decay of the upper state population E1

E

2

N 2

N1

22 AN

dt

dN

sp

rate of spontaneous decay (units = 1/ time) Einstein A Coefficient

Asp

1 = spontaneous emission lifetime ( radiative lifetime)

Note: Rate of spontaneous decay defined for a specific transition

Absorption and Stimulated Emission

We can write the rate of change of population

2212 NW

dt

dN

st

E1

E

2

Stimulated

Emission

N2

N1

E1

E2

Absorption

N2

N1

However, now the rate of stimulated emission

is dependent on the intensity of the EM wave

FW 2121

stimulated emission

cross-section (units = area)

Photon flux

(number of photons/ unit area/unit time)

Similarly for Absorption

1121 NW

dt

dN

ab

FW 1212

absorption cross-section

Stimulated emission leads to a chain

reaction and laser emission.

Excited medium

If a medium has many excited molecules, one photon can become

many.

This is the essence of the laser. The factor by which an input beam is

amplified by a medium is called the gain and is represented by G.

Usually, additional losses in intensity occur, such as absorption, scat-

tering, and reflections. In general, the laser will lase if, in a round trip:

Gain > Loss This called achieving Threshold.

The Laser

A laser is a medium that stores energy, surrounded by two mirrors.

A partially reflecting output mirror lets some light out.

A laser will lase if the beam increases in intensity during a round trip:

that is, if 3 0I I

R = 100% R < 100%

I0 I1

I2 I3 Laser medium

with gain, G

Calculating the gain:

Einstein A and B coefficients

In 1916, Einstein considered the various transition rates between

molecular states (say, 1 and 2) involving light of irradiance, I:

Absorption rate = B N1 I

Spontaneous emission rate = A N2

Stimulated emission rate = B N2 I

2

1

Laser gain

Neglecting spontaneous emission:

2 1

2 1

dI dIc BN I - BN I

dt 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)

z L 0

I(L)

Inversion

In order to achieve G > 1, that is, stimulated emission must exceed

absorption:

B N2 I > B N1 I

Or, equivalently,

This condition is called inversion.

It does not occur naturally. It is

inherently a non-equilibrium state.

In order to achieve inversion, we must hit the laser medium very

hard in some way and choose our medium correctly.

N2 > N1

En

erg

y

Inversion

Molecules

“Negative

temperature”

Achieving inversion:

Pumping the laser medium

Now let I be the intensity of (flash lamp) light used to pump energy

into the laser medium:

R = 100% R < 100%

I0 I1

I2 I3 Laser medium

I

Will this intensity be sufficient to achieve inversion, N2 > N1?

It’ll depend on the laser medium’s energy level system.

Rate equations for a

two-level system

Rate equations for the densities of the two states:

21 2 2( )

dNBI N N AN

dt

12 1 2( )

dNBI N N AN

dt

22 2d N

BI N ANdt

Absorption Stimulated emission Spontaneous

emission

1 2N N N

1 2N N N

If the total number

of molecules is N:

2 1 2 1 22 ( ) ( )N N N N N

N N

2d N

BI N AN A Ndt

2

1

N2

N1

Laser Pump

Pump intensity

Why inversion is impossible

in a two-level system

0 2BI N AN A N

1 / sat

NN

I I

/ 2satI A B

In steady-state:

( 2 )A BI N AN

where:

N is always positive, no matter how high I is!

It’s impossible to achieve an inversion in a two-level system!

2d N

BI N AN A Ndt

/( 2 )N AN A BI

/(1 2 / )N N BI A

Isat is the saturation intensity.

2

1

N2

N1

Laser

Rate equations for a

three-level system

Assume we pump to a state 3 that

rapidly decays to level 2.

21 2

dNBIN AN

dt

11 2

dNBIN AN

dt

1 22 2d N

BIN ANdt

Absorption

Spontaneous

emission

1 2N N N

1 2N N N

The total number

of molecules is N:

22N N N

d NBIN BI N AN A N

dt

Fast decay

Laser

Transition

Pump

Transition

1

2

3

Level 3

decays

fast and

so is zero.

12N N N

Why inversion is possible

in a three-level system

1 /

1 /

sat

sat

I IN N

I I

/satI A B

In steady-state:

( ) ( )A BI N A BI N

where:

Now if I > Isat, N is negative!

( ) /( )N N A BI A BI

Isat is the saturation intensity.

d NBIN BI N AN A N

dt

0 BIN BI N AN A N

Fast decay

Laser

Transition

Pump

Transition

1

2

3

Rate equations for a

four-level system

Now assume the lower laser level 1

also rapidly decays to a ground level 0.

20 2

dNBIN AN

dt

1 0,N

22 2( )

dNBI N N AN

dt

2N N

Laser

Transition

Pump

Transition

Fast decay

Fast decay

1

2

3

0 As before:

Because 0 2N N N

The total number

of molecules is N :

0 2N N N

d NBIN BI N A N

dt

At steady state: 0 BIN BI N A N

Why inversion is easy

in a four-level system

(cont’d)

0 BIN BI N A N

/

1 /

sat

sat

I IN N

I I

/satI A Bwhere:

Isat is the saturation intensity.

Now, N is negative—always!

Laser

Transition

Pump

Transition

Fast decay

Fast decay

1

2

3

0

( / ) /(1 / )N BIN A BI A

/( )N BIN A BI

( )A BI N BIN

What about the

saturation intensity?

A is the excited-state relaxation rate: 1/

/satI A B

Laser

Transition

Pump

Transition

Fast decay

Fast decay

1

2

3

0

B is the absorption cross-section, , divided by

the energy per photon, ħw: / ħw

satIw

The saturation intensity plays a key role in laser theory.

Both and

depend on the

molecule, the

frequency, and

the various

states involved.

ħw ~10-19 J for visible/near IR light

~10-12 to 10-8 s for molecules

~10-20 to 10-16 cm2 for molecules (on

resonance)

105 to 1013 W/cm2

Two-, three-, and four-level systems

Two-level

system

Laser

Transition

Pump

Transition

At best, you get

equal populations.

No lasing.

It took laser physicists a while to realize that four-level systems are

best.

Four-level

system

Lasing is easy!

Laser

Transition

Pump

Transition

Fast decay

Fast decay

Three-level

system

If you hit it hard,

you get lasing.

Laser

Transition Pump

Transition

Fast decay

pumping

R2 R1 l gain/m = g

Round trip Gain (Loss) = egl R1 egl R2 = R1 R2 e

2gl

Threshold R1 R2 e2gl = 1

If round trip gain is > 1, then G = R1 R2 e2gl . Note this is inherently

unstable….it will gain exponentially until …... Saturation occurs…gain saturation...

GAIN IN AN OPTICAL RESONATOR

Achieving Laser Threshold

An 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

I2 I3 Gain, G = exp(gL), and

Absorption, A = exp(-L)

Gain > Loss

Laser medium

2( ) ln(1/ )g L R

This called achieving Threshold (minimum pump power of a laser

required for laser emission). It means: I3 > I0. Here, it means:

21RRR where

Example:

Consider that both ends of ruby laser rod of 5 cm length are coated to have

a reflectance of R=0.9. what is the minimum fraction of excited Cr ions

achieving the threshold condition of oscillation? Assume that the

concentration of Cr ions is , the induced-emission cross-section

is , and the effective loss constant of the rod is

319101 cmN

220102 cm1011.0 cm

%5858.0101

108018.5

108018.51016036.12

101

106036.1102

032072.0/

032072.0011.0021072.0021072.0

21072.081.0

1ln52

1ln2

19

18

2

18

2

19

2

19

12

18

2012

orN

N

NN

NNN

gNN

gg

g

RLg

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 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.

Laser light properties:

Laser light has a number of very special properties:

• It is usually emitted as a laser beam which can propagate over

long lengths without much divergence and can be focused to

very small spots.

• It can have a very narrow bandwidth, while e.g. most lamps emit

light with a very broad spectrum.

• It may be emitted continuously, or alternatively in the form of

short or ultrashort pulses, with durations from microseconds

down to a few femtoseconds.

The Ruby Laser

Invented 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.

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. http://en.wikipedia.org/wiki/Helium-neon_laser

Carbon Dioxide Laser

The CO2 laser operates analogously. N2 is pumped, transferring

the energy to CO2.

The Helium Cadmium Laser

The population inversion scheme in HeCd is similar to

that in HeNe’s except that the active medium is

Cd+ ions.

The laser transitions occur in the blue and the

ultraviolet at 442 nm, 354 nm and 325 nm.

The UV lines are useful for applications that require

short wavelength lasers, such as high precision

printing on photosensitive materials. Examples include

lithography of electronic circuitry and making

master copies of compact disks.

The Argon

Ion Laser

Argon lines:

Wavelength Relative Power Absolute Power

454.6 nm .03 .8 W

457.9 nm .06 1.5 W

465.8 nm .03 .8 W

472.7 nm .05 1.3 W

476.5 nm .12 3.0 W

488.0 nm .32 8.0 W

496.5 nm .12 3.0 W

501.7 nm .07 1.8 W

514.5 nm .40 10.0 W

528.7 nm .07 1.8 W

The Krypton Ion Laser

Krypton lines

Wavelength Power

406.7 nm .9 W

413.1 nm 1.8 W

415.4 nm .28 W

468.0 nm .5 W

476.2 nm .4 W

482.5 nm .4 W

520.8 nm .7 W

530.9 nm 1.5 W

568.2 nm 1.1 W

647.1 nm 3.5 W

676.4 nm 1.2 W

Dye lasers

Dye lasers are an ideal four-level system, and a given dye will lase

over a range of ~100 nm.

A dye’s energy levels

The lower laser level can be almost any level in the S0 manifold.

S0: Ground

electronic state

manifold

S1: 1st excited

electronic state

manifold

Laser Transitions

Dyes are so ideal that it’s often difficult to stop them from lasing in all

directions!

Pump Transition

Dyes cover the visible, near-IR, and

near-UV ranges.

Titanium: Sapphire (Ti:Sapphire)

oxygen

aluminum Al2O3 lattice

Absorption and emission

spectra of Ti:Sapphire

Upper level lifetime:

3.2 msec

Ti:Sapphire lases from

~700 nm to ~1000 nm.

Diode Lasers

Some everyday applications of diode

lasers

A CD burner Laser Printer

Laser Safety Classifications

Class I - These lasers are not hazardous.

Class IA - A special designation that applies only to lasers that are

"not intended for viewing," such as a supermarket laser scanner. The

upper power limit of Class IA is 4 mW.

Class II - Low-power visible lasers that emit above Class I levels but at

a radiant power not above 1 mW. The concept is that the human

aversion reaction to bright light will protect a person.

Class IIIA - Intermediate-power lasers (cw: 1-5 mW), which are

hazardous only for intrabeam viewing. Most pen-like pointing lasers

are in this class.

Class IIIB - Moderate-power lasers (~ tens of mW).

Class IV - High-power lasers (cw: 500 mW, pulsed: 10 J/cm2 or the

diffuse reflection limit), which are hazardous to view under any

condition (directly or diffusely scattered), and are a potential fire

hazard and a skin hazard. Significant controls are required of Class IV

laser facilities.