laser systems in practice
TRANSCRIPT
3C43 Lasers & Modern Optics
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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’
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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
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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
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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.
Energy-level scheme:
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.
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Molecular masers
The ammonia-beam maser
Pumping scheme: spatial separation of ground and excited-state molecules
Energy-level scheme:
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)
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Energy-level scheme:
• 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.
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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
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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:
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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
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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
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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
<<∆∆+=<<∆∆+=
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• 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
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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*
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• 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
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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
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• 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
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• 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.
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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
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• 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
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• 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
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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)