Laser systems in practice

3C43 Lasers & Modern Optics

© D R Meacher 2003 1

3C43

LASERS & MODERN OPTICS

2 Lasers

2.2 Practical lasers

Laser systems in practice

Half the elements in the periodic table, or molecules involving them, have been used as laser gain media, but most common lasers fall into one of a small number of distinct categories, which differ in the scheme used to obtain population inversion.

• Varieties of laser:

•doped-insulator, solid-state lasers• gas lasers: atomic, molecular and ion• dye lasers• semiconductor lasers• free-electron lasers

For an exhaustive survey see:

WH pp.195-240A. E. Siegman `Lasers’ ,A E Siegman `An introduction to lasers and masers’



Doped-glass, solid-state lasers

• The Neodymium-YAG laserNeodimium impurity ions in Yttrium aluminiumgarnet host lattice. The crystal field lifts level degeneracies and makes some normally forbidden transitions allowed.

Pumping scheme:state-selective optical pumping

Energy-levelscheme:

Laser wavelength: 1064 nm (often frequency-doubled to 532 nm wavelength)

Pumping: xenon flash-lamp (pulsed)krypton flash-lamp, diode (c.w.)

( )1253 OAlY

• Laser schematic: flash-lamp pumped

typical pump pulse energy 10 kJtypical output pulse energy 1 J in 0.5 ms

• Laser schematic: diode-pumped



Atomic gas lasers

Helium-neon laser

Pumping scheme:resonant collisional energy transfer

Energy-level scheme:

Gas mixture is typically 90% He, 10% Ne

metastablelevel

metastablelevels

LS-coupling Paschen notation

• Laser schematic:

Efficiency typically 0.01 %

Rate-determining step in depopulation of lower laser level is de-excitation of the metastable excited-state by wall collisions

small active volume

At high discharge current, collisional population of lower laser state becomes important.

So, the laser is inherently a low power device (typically 1-10mW at 632nm)

diameterbore1 Power ∝

2.5 kV, 10 mA



Noble-gas ion lasers

Argon-ion laser

Pumping scheme: collisional energy transfer

In the argon-ion laser, argon atoms are ionized and then further excited through collisions with electrons.


Laser transitions351nm to 520nm

Laser schematic:

• High discharge current required (200V, 10-50 A).• Output power up to a few tens of Watts, but low efficiency (< 1%)• Line selection possible by intra-cavity prism.• Water-cooling essential to dissipate heat generated.• Axial magnetic field increases current density and reduces wall damage.• Gas recycling is necessary.



Molecular masers

The ammonia-beam maser

Pumping scheme: spatial separation of ground and excited-state molecules


Maser schematic:

Molecular gas lasers

The carbon-dioxide laser

Pumping scheme: collisional excitation of molecular vibrational states

Molecular vibrations:

Notation of vibrational states: (nmrl)

Bending mode(m quanta)

Symmetric stretch(n quanta)

Asymmetric stretch(l quanta)




• Active medium of CO2 lasers:CO2, N2, He in ratio 1:4:5

Symmetricstretch

Bendingmode

Asymmetricstretch

Example

Find the Doppler width of the carbon-dioxide laser transition at wavelength, λ=10.6 µm, assuming the laser operates at 300K.

Hence find the population inversion required to give a small-signal gain coefficient of 1 m-1 for a carbon-dioxide laser , for which the Einstein A-coefficient of the upper laser level is 200 s-1

Find the (minimum) pump power required per unit volume of the gain medium to give the above value of the gain coefficient.



Solution

Using

gives

Then using

with and

Giving, finally

Pump power required is

mTkB

Doppler 22

sλν =∆

a.u.mCO 442=

Hz .Doppler71026 ×=∆ν

cgnhBN ss

s)( )( 21

* νννκ =

)( 8

221

3*

s

Dopplers

An

Nλννκπ ∆

=

33

3

2121 8 A

νπhncB =

Dopplersg νν

∆≈ 1)(

310* 100.7 −×= cmN

)( 0321* EEANP −⋅⋅≈

( ) 3683416 106.101031063.63200 107 −−− ×÷××××⋅⋅×≈ WmP

3 .20 −≈ WmP

Varieties of CO2 laser

• Sealed-tube lasers· Reduced tube lifetime due to formation of CO· Difficult to remove heat generated (He helps)· Power limited to 100 Watts

• Gas-flow lasers· Higher power possible, 60 W/m up to few

tens of kW· Low gas pressure to enable discharge to

be struck low gain per unit length

• Transversely-excited, atmospheric (TEA) lasers· Gas at atmospheric pressure high gain· Transverse discharge to limit required

tube voltage.· In pulsed mode GW power achievable.

• Gas-dynamic lasers· N2 and CO2 compressed and heated populates excited vibrational states of N2

· Rapid expansion to low pressure N2vibrational energy rapidly transferred to (001) state of CO2

· Continuous-wave power > 100 kW achievable



Dye lasers

Liquid dyes have high density of active species (gain) and good optical homogeneity.

Pumping scheme: optical (laser-pumped)

Energy-level scheme (4-level):

electronicstates

Dye laser schematic:

Spectral range of laser dyes:



Semiconductor lasers

The simplest form of semiconductor laser is based on a heavily-doped p-n junction.

• Unbiased p-n junction

• Forward-biased p-n junction

• Diode-laser schematic

• mirror reflectivity with ns = 3.5

• Gain is high, so a higher reflectivity is not required. Threshold current density typically 10-100 A/mm2

• Well above threshold, most electron hole-pairs pumped into active region undergo stimulated recombination

high efficiency (> 0.7)

• A vast range of devices covering infra-red wavelengths 700nm-4µm and, increasingly, visible wavelengths.

mLe µ 31 −≈

2

+−

=airs

airs

nnnnR

0.3≈⇒ R



Frequency-stabilization of lasers

• Frequency of pth cavity mode

• Fluctuations in cavity length, L, cause fluctuations in frequency of the laser output

• How can the frequency of the laser be stabilized?

• Inhomogeneously-broadened laser

• Lock to the Lamb dip

Lcpp 2

=ν

When the holes burnt in the gain profile by left-and right-propagating waves coincide, there is less gain and the laser power drops. A servo circuit locks L to this dip.

Lamb dip

ννp(L0)ννp(L1)

ννp(L0) = ν0

laser outputpower

• Homogeneously-broadened laser

• Use a saturable absorber (gas) in a cell within the laser cavity. The absorber has a resonance transition at the frequency, ν0, at which it is desired to lock the laser output.

• A longitudinal mode close to frequency ν0 (to within the width of the Lamb dip) sees less absorption and so higher round-trip gain.

• Laser cavity length is adjusted for maximum output power to fix the frequency to ν0.

• Iodine vapour is often used, as it has a dense spectrum of resonances.

νν0

absorption

νν0

Laser power



Temporal modulation of lasers

• Spiking (Relaxation oscillations)

• Though, in steady-state operation, the population-inversion cannot exceed the threshold value, this is not true in a transient situation.

• Consider the case where the pumping rate, R, is suddenly switched from zero to a value above Rth.

• Analyse the situation by looking for a time-dependent solution of the rate-equations describing the level populations.

• Problem: highly non-linear equations• Solution: assume the departure from the steady-state solution is small and find a first-order correction.

• Consider, for simplicity a simple two-level laser, without degeneracies:

Population-inversion and photon density evolve according to

writingand

)(1 )(

)( 2))(1(1))(1(

*

**

2

**

tntn(t)NKdtdn

tn(t)NKtNtNRdt

dN

cτ

τ

−=

−+−−=

2

21

2*

212*

12

dtdN

dtdN

NNNNNNN

=⇒

−=−=⇒

+=

00

00*

),()( ),()(

nntnntnNNtNNtN

<<∆∆+=<<∆∆+=



• The steady-state solution is:

• To first order in ∆, the evolution equations are,

where

)( 2)()1(11

)( 2)()1(11

*0

*

222

*

22

*

(t)NKndt

nd

tntNrr

tntNrRdt

Nd

c

c

∆=∆

∆−∆

−++−=

∆−∆

−++−=

∆

ττττ

τττ

22

220

*0

1111

12

1 12

1

1

τττ

τ

τττ

τ

≈

−+

⋅≡

−⋅≈

−⋅

+=

==

c

cth

thth

c

cth

KKR

RR

KRR

KKn

KNN

,thR

Rr ≡

• Using a trial solution and assuming

we find the secular equation:

whence

sttnsttN

exp)(exp)(

∝∆∝∆

0)1(

21

22

2

2 =−−

+

sr

rsc

τ

ττ

22

2

22

414 ,2

i-

τωτγ

ωγ

rττ

)(r-r

s

c

−=≡

±=

exponential decay oscillations

12<<τ

τ c



e.g. Nd:YAG has

giving

25.1 ,500 ,10 28 === − rsτsτc µ

kHzfmsτ 502

, 51≈=≈=

πω

γ

Q-switching

• Q-switching allows short, high intensity pulses to be obtained from flash-lamp pumped doped-glass lasers and suppresses relaxation oscillations.

• Achieved by spoiling the cavity quality-factor, Q (i.e. increasing losses) until maximum population-inversion is achieved.

• Pumping rate must be much faster than rate of spontaneous decay from upper laser level

threshold N*



• Temporal variation of population-inversion and output power from a Q-switched laser:

The laser output energy is compressed into a pulse of duration 10-4 of that of non-Q-switched laser.

• Q-switching in practice

• Rotating mirror method (practically obsolete)

• Passive Q-switching using a saturable absorber

• Q-switch using a Pockels cell electro-optic modulator

Estimate of the maximum power in a Q-switched laser pulse

3532414 10 ,10 ,1 ,105 mVmNnsHz pulse−− =≈≈×≈ τν

J 1.8 ≈E GW 1.8 ≈P



Mode locking• Mode-locking allows the production of high-power pulses at high repetition-rate from a low average power, multi-mode laser.

• Time-dependence of the amplitude in the output of a multi-longitudinal mode laser:

With

so that the intensity

∑ +=n

nnn tiata,modes

)(exp)( ϕω

ωωω ∆+= nn 0

∑ +∆⋅=n

nn tniatita,modes

0 )(exp exp)( ϕωω

[ ]∑ −+∆−=

∝

mnmnmn tmniaa

tatI

,,modes

*

2

)()(exp

)()(

ϕϕω

[ ]∑

∑

>

−+∆−⋅

+=

mnmnmn

nn

tmnaa

a

,modes

*

,modes

2

)()(cos 2 ϕϕω

Mean-value

Fluctuations

• But if we can force for all oscillating modes, n

Now, when for integer p, all the cosine terms equal 1 and the output intensity has a sharp maximum.

Pulses repeat at time intervals , the cavity round-trip time.

Approximate temporal width of output peak: Fastest-varying cosine term is approximately

where N is the number of oscillating modes. So the peak full-width is approximately

ϕϕ =n

[ ]∑∑>

∆−⋅+=mn

mnn

n tmnaaatI ,modes

*

,modes

2 )(cos 2 )( ω

πω pt 2 =∆

[ ]ttN 2cos ω∆

NNcavτ

ωπτ =∆

=2

ωπτ

∆=

2 cav



• Slightly more sophisticated analysis

Setting the phase and writing for the sum of the geometric progression:

So

0=ϕ

2 sin

2 sin

exp)( 0 t

tNtita ω

ωω

∆

∆⋅∝

2

2

2 sin

2 sin

)()( t

tNtatI ω

ω

∆

∆≈∝

∑=

=

+∆⋅=Nn

nn tniatita

0 ,modes0 )(exp exp)( ϕωω

τcav

τcav/N

N=10

• Mode-locking in practice

• Mode-locking techniques rely on temporal modulation of the cavity loss to lock the mode phases.

• Passive-mode locking using a saturable absorber. Periodic bleaching of the absorber allows a localized `packet of photons’ to oscillate in the cavity.

Advantage: simplicityDisadvantage: no control over output pulses



• Active mode-locking using an intra-cavity acousto-optic device

A transducer (rather like a speaker) bonded to one surface sets up r.f. acoustic standing-waves in a transparent crystal.

At times when the acoustic standing-wave has a maximum intensity, the light is diffracted out of the cavity. When the standing-wave has a temporal node, light passes through without scattering.

Acoustic standing-wave frequency is half of the inter-mode frequency.

Example

A Neodimium:YAG laser has a gain bandwidth of 1011 Hz. The laser cavity is 15 cm long and the YAG rod, which has a refractive index of 2 is 10cm long.

Find the pulse duration and repetition rateObtained when the laser is mode-locked.



Solution

Optical path length in cavity,

Cavity-round-trip time (= 1/pulse repetition rate) ,

Number of modes oscillation,

So pulse duration,

cmcmcmL 251025 =×+=

HznscL

cavcav

cav81067.121

×=∆⇒==∆

= νν

τ

1700106101

8

11

=××

≈N

psnspulse 1

17007.1

==τ

Properties of laser light

The geometric characteristics of laser beams derive from the fact that they closely approximate Gaussian beams. (see part 3). These characteristics include:

• DirectionalityFundamental limit to directionality is set

by the beam divergence due to diffraction.

• FocusabilityA laser beam can be focused to a minimum spot size of the order of the optical wavelength

• Brightness-defined as the power emitted per unit area of the source per unit solid angle.(We shall see in part 3 that the brightness of even a low-power laser can exceed that of the sun!)

λ≈minw



• Narrow spectral linewidth

The spectral linewidth of individual laser

cavity modes can be extremely narrow

(though the laser output will only be

spectrally narrow if steps are taken to

ensure single-mode operation).

• Tunability (sometimes)e.g. dye lasers

diode lasers nm50≈∆λnm5≈∆λ

• Longitudinal coherence

(also known as temporal coherence)

Related to the phase correlation between the oscillating electric field at the same point in space but different points in time (or equivalently at the same time but at two points with a spatial separation in the beam propagation direction).

The coherence length, Lc is related to the coherence time tc through

Good temporalcoherence

Limited temporalcoherence.

Coherence length Lc

ν∆=⋅=

ctcL cc



• Transverse coherence

Related to the phase correlation between different points across a wave-front of the output beam

A striking manifestation of the

transverse coherence of lasers is

provided by the speckle that is seen

whenever a laser beam strikes a

reflecting surface.

Applications of lasers

• As a directed source of energy

( medical, industrial,motion/distance sensing,laser fusion,guide stars,checkout readers, CD read/write, printers)

• As a spectroscopic tool(atomic clocks, sensing of rare species/pollutants, motion sensing, fundamental science)

• Interferometric applications

(holography, quantum physics … )

• For more details, see the review inPedrotti & Pedrotti



Laser applications

Type of laser used

Dire

ctio

nalit

y

Nar

row

line

wid

th

Coh

eren

ce

Tigh

t-foc

ussi

ng

Hig

h-br

ight

ness

Tuna

bilit

y

CO2, Nd:YAG

CO2, Er:YAG

Nd:YAG

He:Ne

Telecommunications link diode

diode

diode

Ar+

Nd:glass

chemical

diode

diode

Cu vapour

Ar+

Range-finding (e.g. of the moon)

Bar-code reader

Laser printer

Lecture pointer

Laser guide-star

Holography

CD player

Club laser-show

Laser fusion experiment

Satellite-based anti-ICBM system

Surgical (cutting/ablation)

Caesium atomic clock

Important propertiesApplication

Drilling (sheet metal, plastics)

Documents

Laser systems in practice