optics lasers

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,

theres 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?

Itll depend on the laser mediums 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!

Its 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

(contd)

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 negativealways!

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, w: / w

satIw

The saturation intensity plays a key role in laser theory.

Both and depend on the

molecule, the

frequency, and

the various

states involved.

w ~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