Basics of lasers · Laser wavelength 1.064 1.05-1.06 µm Laser upper lifetime σfor stimulated emission 230 28 300 3 µs 10-24 m2 Spontaneous emission linewidth Operation regime 0.45

Basics of lasers Slide: 1 - 1

Basics of lasers

Nathalie VermeulenBrussels Photonics Team (B-PHOT)

Vrije Universiteit Brussel


Some examples of laser applications

telecom

optical data storage

cutting steel cleaning and restoring art

laser projectors

laser medicine


Light

Amplification

by Stimulated

Emission

of Radiation

All special properties of laser light find their origin in this stimulated emission.

Introduction


Interaction between light and matter

Model = “thermodynamic” model of Einstein:

• atom = two-level system, energy difference ∆E (≈ eV)

• light = either a wave or a collection of photons

Interaction only possible when ∆E = h f0

Three different kinds of interaction between light and matter:

• absorption

• emission spontaneous

stimulated

f0

E2

E1

f0


General description of absorption

Each absorbing atom in energy level #1 is represented by a circular disc of area σ,

its “cross section”.

The incident light is measured by the photon flux density F.

F = number of incident photons per second and per square meter

f0

E2

E1

N2

N1

Assume we have a box with two-level atoms in it.

There are N1 atoms per m3 in lower energy level #1 and N2

atoms per m3 in upper level #2.

dzF


Absorption and transmission through matter

Lambert-Beer law for absorption

F(z) = F (0) e−σ N

1 z

F

z

dzF

dN1

dt= − F σ N1

Rate equation for absorption


Rate of change:

Spontaneous emission

E2

E1

f0

N2

N1

2 22 21 2

212 2

(1 10)

(1 11)

( ) (0) A t

dN dNN A N

dt dt

N t N e

−

−−

∝ ⇒ = −

⇒ =t

N2(0)

N2

1e

τsp=A21-10

= “life time”

Consider an atom that has been excited to level 2.

⇒ spontaneous decay to level 1 with the emission of light


Light is emitted

- in all directions

- in a broad spectral emission line

- no phase relation (= no coherence)

Example: High pressure lamp

Properties of spontaneous emission


Photon incident on excited atom:

no absorption possible, but instead the photon forces

the atom to jump to its lower level, with emission of a

new photon

⇒ stimulated emission

General description of stimulated emission

E2

E1

f0

N2

N1

The new wave has

- the same direction

- the same frequency/wavelength ⇒ the light is amplified

- the same phase (coherent)

This is the basis of laser action.

⇒ LASER = Light Amplification by Stimulated Emission of Radiation


Calculation of stimulated emission

The reasoning is completely analogous to the reasoning for absorption.

The cross section for absorption is identical to the one for stimulated emission.

⇒

Rate equation for stimulated emission

dN2

dt= − F σ N2

dz

E2

E1

f0

N2

N1


Total rate equation:

spontaneous stimulated absorption emission emission N1+N2=const ⇒ dN1= - dN2

Total rate equation and laser action

dN1

dt= A21N2 + σF(N2 − N1) (1 − 13)

In thermal equilibrium: ⇒ N2 ≈ 0 ⇒ absorption dominates

For realizing emission, the atom should be excited: N2 ≠ 0.

As long as N2 < N1, net emission is spontaneous.

Stimulated emission will be dominant only when N2 > N1 .

⇒ Amplification is only possible when this “population inversion” (N2 >>>> N1) is obtained.

N2

N1

= e−

∆E

kT ≈ 0 (1 − 14 )

E2

E1

N2

N1

(1-15)

(1-16)


Amplification of light

Lambert-Beer law for amplification

F(z) = F (0) eσ (N

2− N

1) z

(1 − 17)

F

z

dzF


Basic laser set up

Two mirrors provide feedback; they form the resonator.

One mirror (here the rear mirror at the right) is a little bit

transparent to couple part of the beam out of the resonator.

Pump: energy input

creates the population

inversion

useful

laser beam

Amplifying medium (gas, liquid,

solid-state, semiconductor) with

population inversion


First laser: ruby laser realized by T. Maiman (1960)

Mirror

(polished crystal

facet with silver

coating)


A few examples of lasers nowadays

Solid-state laser Dye laser

Fiber laser Semiconductor laser


Modes in a laser resonator: a simple picture

Light bounces back and forth in the resonator

⇒ standing waves are created; they are called

modes.

[ ](1 22)

2

cf N

L−⇒ =

[ ][ ]( ) (1 23)300 for 0.5

2

cf MHz L m

L−∆ = ≈ =

[ ] 6(1 21)2 ( 10 ) N L Nλ −= ≈

etc etc

f

Wave picture: two distinct modes

with a different wavelength

L

λ

2

NN+1

with : optical path length

: longitudinal mode number[ ]L

N


Frequency dependence of gain: line broadening

f0f

FWHM

σ(f)

f0f

gain

Small-signal gain g0(f)Saturated gain g(f)


Lasing modes

The modes in a resonator without amplifying

medium form an infinite comb of

frequencies.

In a laser setup, i.e. a resonator with

amplifying medium, modes are only excited

if their frequencies are situated within the

gain bandwidth of the amplifying medium.

Moreover their gain should exceed the losses

of the laser.

As a result, only a limited number of

modes/frequencies will actually experience

lasing action.


Line broadening in different types of lasers

The shape and width of the gain curve (and hence the number of modes) strongly depends on

the type of amplifying medium.

Some examples

Solid-state laser (ruby):

∆f ≈ 30 GHz

⇒ ∆λ ≈ 50 pm

(many modes)

Gas laser: ∆f ≈ 1GHz Semiconductor laser: ∆f ≈ 1500 GHz

⇒ ∆λ ≈ 3 pm ⇒ ∆λ ≈ 5 nm (few modes) (many modes)


All unusual properties of laser light are a consequence of the properties of stimulated

emission.

In theory one would expect laser light to be

- monochromatic (one frequency or one wavelength)

- collimated (one direction)

- coherent (one phase)

In practice laser beams are not that perfect…

Basic properties of laser light


In theory only light rays parallel to the optical axis are amplified by stimulated emission

⇒ the laser beam should be perfectly parallel

In reality light is a wave ⇒ diffraction occurs and the laser beam diverges

Typical value: θ ≈ 10-3 rad (=1mm at a distance of 1 m)

⇒ not perfectly parallel, but better than any other light source

D

θ

laser

One direction = collimated

θ ≈ λ

D

wavelength

opening (1-32)


In theory: one frequency In reality: line broadening ⇒ multiple modes

gas laser

semiconductor laser

⇒ not perfectly monochromatic, but better than any other light source

P

λ(nm)400 800

One frequency = monochromatic


⇒ not perfectly coherent, but better than any other light source

1

cohcoh

c fτ

π= =

∆

l

One phase = coherent

In theory all waves are in phase, so laser light

should be completely coherent…

… as opposed to completely incoherent light of

other light sources.

In reality laser light is only coherent over a

limited length (coherence length lcoh) or a

limited time (coherence time τcoh)

⇒ the smaller the laser linewidth Δf,

the larger lcoh and τcoh


The total power P of a laser beam is (usually) rather small,

but the intensity I is extremely high.

Intensity = power per unit solid angle

Example (orders of magnitude)

P I

light bulb 10 W 1 W/sr

low power laser 1 mW 103 W/sr

ΩP

I =P

Ω (

W

sr)

Laser light is intense


The need for more than two energy levels

It is not possible to obtain population inversion in a

system with only two energy levels.

Reason: since σ12=σ21, the transition probability 1→2

equals the transition probability 2→1, and one obtains

at most population saturation, i.e. N1=N2 .

To obtain population inversion, one needs a 3-level or, even better, a 4-level system.

N2

N1

level 2

level 1

level 3 N3 ≈ 0

N2

N1 ≈ 0

level 0 N0

pump

fast

laser

fast

N2

N1

level 3 N3 ≈ 0

pumpfast

laser

laserpump

Three-level scheme

Four-level scheme


CO2 laser as an example of a gas laser

CO2 laser is an electrically-pumped four-level gas laser with far-infrared laser emission

bending

symmetric stretching asymmetric stretching

Properties

Infrared radiation

Multiple vib-rot energy levels leading

to a range of emission lines

Very high power (up to multi-kW)

(001)

(100)

Wavelength (µm)


Applications of CO2 laser: material processing


Nd laser as an example of a solid-state laser

Property Nd:YAG Nd:glass units

Laser wavelength 1.064 1.05-1.06 µm

Laser upper lifetime

σ for stimulated emission

230

28

300

3

µs

10-24 m2

Spontaneous emission linewidth

Operation regime

0.45

CW+pulsed

18-28

pulsed

nm

Power levels CW: up to

several kW

Pulsed: up

to several J

up to

several J

Nd:YAG

Nd laser is an optically-pumped four-level solid-state laser with near-infrared laser emission


Applications of Nd laser: in multiple domains

1 kW CW Nd:YAG laser

pumped with flashlamp

used for material processing

50W CW diode-pumped Nd:YAG laser

used for medical applications and

for pumping other lasers


Er:glass laser as an example of a fiber laser

Er fiber laser is an optically-pumped three-level fiber laser with near-infrared laser emission


Applications of Er fiber laser: in telecom

Erbium fiber lasers and amplifiers are used in

telecom applications, e.g. EDFAs in undersea

fiber communication links.


Transients in a gas laser

time

pump

Wp

time

S

Po

wer

(a.u

.)


Transients in a solid-state laser

time

pump

Wp

time

S

S0

10 µs


Pulsed operation

Modulator

⇒ Easiest approach: simply “cut” a pulse

out of a cw laser beam using a modulator

outside the cavity

⇒ Best approach: put a modulator

inside the cavity


Pulsed operation: Q-switching

1. The laser is pumped with a closed shutter.

Hence no laser action is possible, but

population inversion does build up.

2. Suddenly the shutter opens very quickly.

3. The stored energy is immediately released

and the population inversion drops to its

steady-state value.

4. This is accompanied by the creation of a

giant laser pulse.

laser amplifier

shutter

time

shutter

time

Wp

time

N2

time

P

open

closedclosed

1

2

3

4

pumppump


Pulsed operation: modelocking (1)

Calculated time evolution of the output power of a solid-state laser with 50 modes featuring a random phase;

∆ν is the frequency difference between adjacent modes; ∆νL is the total oscillation bandwidth

• When Φl(t) is not stochastic, the total field shows a regular time pattern ⇒ mode-locking

Most lasers oscillate in many (longitudinal) modes. The total field is then

E(t) = Σ E0,l expj(ωlt+Φl(t)

• Usually Φl(t) is stochastic ⇒ all those modes behave independently from each other (they are “mutually incoherent”) ⇒ fluctuating output


Pulsed operation: modelocking (2)

∆t

∆τ

∆τ

Ppeak

Paverage

Train of pulses of a mode-locked fiber laser

16 ps


Conclusion

• Lasing action requires a laser-active medium with at least 3 energy

levels, a resonator, and pumping for establishing population inversion

in the medium.

• Only lasers generate monochromatic, coherent and highly directional

light.

• Possible danger of laser light is not in its power but in its intensity.

• Gas, solid-state, and semiconductor lasers have totally different

properties regarding lasing wavelengths, output powers, pumping

mechanisms, transient behavior, applications, …

• Pulsed operation through e.g. Q-switching or modelocking can be

obtained using an intra-cavity ‘shutter.’

Documents

Basics of lasers · Laser wavelength 1.064 1.05-1.06 µm Laser upper lifetime σfor stimulated emission 230 28 300 3 µs 10-24 m2 Spontaneous emission linewidth Operation regime 0.45