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Transcript
University of Ljubljana
Faculty of Mathematics and Physics
Department of Physics
Pulsed Solid State Laser with Passive
Q-switch
Seminar
Author: Marko Kozinc
Mentor: doc. dr. Rok Petkovลกek
Ljubljana, February 2015
Abstract
In this seminar we present the structure, operating regime and use of solid state laser with passive Qswitch. We give a description and comparison of two basic concepts of optical pumping, the lamp
pumping and the diode pumping. Finally we present the Q-switch theory and more precisely passive
Q-switch theory.
Table of contents
1
Introduction ............................................................................................................................. 3
2
Solid State Laser with Passive Q-switch .................................................................................. 3
3
Pumping of SSL ........................................................................................................................ 4
3.1
Lamp-pumped SSL ............................................................................................................... 4
3.2
Diode Pumped SSL ............................................................................................................... 5
4
Q-Switch Theory ...................................................................................................................... 8
4.1
Passive Q-Switches ............................................................................................................ 10
5
Conclusion ............................................................................................................................. 12
6
Bibliography........................................................................................................................... 12
1 Introduction
Solid-state lasers (SSL) are lasers based on solid-state gain media such as crystals or glasses
doped with rare earth or transition metal ions. Beside fiber lasers they provide one of the most
versatile radiation sources in terms of output characteristics when compared to other laser systems.
A large range of output parameters, such as average and peak power, pulse width, pulse repetition
rate and wavelength, can be obtained with these systems. Today we find solid-state lasers in industry
as tools in many manufacturing processes, in hospitals and in medicine as radiation sources for
therapeutic, cosmetic, and surgical procedures, in research facilities as part of the diagnostic
instrumentation and in military systems as rangefinders, target designators, and infrared
countermeasure systems. Other types of lasers that employ solid-state gain media are
semiconductor lasers and optical fiber lasers. However, since these lasers employ very specialized
technologies and design principles, they are usually treated separately from conventional solid-state
lasers [1].
2 Solid State Laser with Passive Q-switch
Lasers can operate in continuous or pulsed regime. In some cases pulsed lasers are valuable
when peak power rather than average power is most important. One of the most applied techniques
to produce a pulsed output beam is Q-switch technique. It allows the production of light pulses with
extremely short, duration and high peak power, much higher than can be produced by the same laser
operating in continuous wave mode.
There are two main types of Q-switching - active and passive. For active Q switching the losses
are modulated with an active control element. It is an acousto-optic (AO) [2], electro-optic modulator
(EO) [3] or a single crystal photo-elastic modulator (SCPEM) [4], where the pulse is formed shortly
after an electrical trigger signal arrives. There are also mechanical Q switches such as spinning
mirrors or prism, used as end mirrors of laser resonators. In all case, the achieved pulse energy and
pulse duration depends on the energy stored in the gain medium, on the pump power and the pulse
repetition rate.
A passive Q-switch is an optical element, such as doped crystal, a cell filled with organic dye or a
passive semiconductor device. The characteristic of such material is that transmission increases when
the intensity of light exceeds some threshold. If such a material with high absorption at the laser
wavelength is placed inside the laser resonator, it will initially prevent laser oscillation. As the gain
increases during a pump pulse and exceeds the round-trip losses, the intra cavity power density
increases dramatically causing the passive Q-switch to saturate. Under this condition the losses are
low and a Q-switch pulse builds up.
Figure 1: Simple concept of a solid state laser with passive Q-switched.
Figure 1 shows the simple scheme of solid state laser with passive Q-switch. The edge of laser
resonator consists of two mirrors, output coupler (OC) and high reflected mirror (HR). Between OC
and HR lay active medium โ€“ laser crystal and passive Q-switch crystal. Important part of laser system
is also a pumping mechanism.
3 Pumping of SSL
The process by which atoms are raised from lower level to upper level is called pumping. In the
context of lasers or laser amplifiers, the goal is to achieve a population inversion in the gain medium
and thus to obtain optical amplification via stimulated emission for some range of optical
frequencies. Inversion by optical pumping becomes possible when using a three-level and a fourlevel system. Solid-state lasers are optically pumped with lamps and laser diodes.
3.1 Lamp-pumped SSL
The pump source in lamp-pumped solid state lasers is some kind of gas discharge lamp or in rare
cases, tungsten halogen lamps, which are not gas discharge lamps but rather similar to ordinary
bulbs. Discharge lamps used for laser pumping are grouped in two categories, arc lamps and flash
lamps. Arc lamps are optimized for continuous-wave operation, whereas flash lamps produce pump
pulses for either free-running or Q-switched lasers. Both types of lamps essentially consist of a glass
tube, filled with some gas (e.g. krypton) and having a metallic electrode at each end.
Figure 2: Schematic of the flash pumped solid state laser [5].
The laser crystal of a lamp-pumped laser is usually a relatively long side-pumped rod, adapted to
the length of the lamp. In many cases, laser rod and lamp are placed within an elliptical pump
chamber with reflective walls, so that a larger percentage of the generated pump light can be
absorbed in the laser rod. Excess heat is removed by cooling water, and an additional filter glass may
be used to protect the laser rod from ultraviolet light emitted by the lamp.
The most common type of lamp-pumped laser is the ๐‘๐‘‘: ๐‘Œ๐ด๐บ laser. Krypton-filled lamps are
mostly used in this case, because the krypton emission is strong in the region between 750๐‘›๐‘š and
900๐‘›๐‘š, where ๐‘๐‘‘: ๐‘Œ๐ด๐บ has strong absorption lines. Figure 3 represents absorption spectrum of
๐‘๐‘‘: ๐‘Œ๐ด๐บ. The absorption peaks around 870 ๐‘›๐‘š are caused by a transition from the ground level
directly to the upper laser level. The absorption around 808 ๐‘›๐‘š is the result of the transition in to
the lowest pump band. The absorption around 750 ๐‘›๐‘š is the result of the manifold immediately
above the lowest pump band.
Other neodymium-doped gain media are also suitable. These have relatively broad absorption
bands and are four-level laser media, so that they can be used with moderate pump intensities and
utilize a significant part of the lamp spectrum. Less common lamp-pumped lasers are based on
alexandrite, Ti:sapphire, Cr:LiSAF, or laser dyes.
Flash lamp pump source are relatively cheap and can provide very high powers. They are fairly
robust, e.g. immune to voltage or current spikes. The lifetime of lamps is very limited, normally some
hundred or up to a few thousand hours. The wall-plug efficiency of the laser is low, typically at most
a few percent. Consequences of that are not only higher electricity consumption, but also a higher
heat load, making necessary a more powerful cooling system, and strong thermal lensing, making it
more difficult to achieve a good beam quality.
Electric power supplies for lamp-pumped lasers involve high voltages, which raise additional
safety issues. The low pump brightness, compared with that achievable with diode lasers, and the
broad emission wavelength range exclude many solid-state gain media. Lamps are relatively noisy
pump sources, leading to higher levels of laser noise.
3.2 Diode Pumped SSL
Diode pumped solid state (DPSS) lasers are solid state lasers made by pumping a solid gain media
with a laser diode. DPSS lasers have advantages in compactness and efficiency over other types of
lasers. High power DPSS lasers have replaced flashlamp pumped lasers in many industrial, medical
and scientific applications.
Figure 3: Absorption spectrum of ๐‘ต๐’…: ๐’€๐‘จ๐‘ฎ and the emission spectra of a diode laser and a flash lamp [6].
Figure 3 shows the absorption spectrum for doped ๐‘๐‘‘: ๐‘Œ๐ด๐บ and the emission spectra of a diode
laser and a flashlamp. The flashlamp emits radiation at all wavelengths while the diode laser emits
radiation at essentially a single wavelength that can be tuned to a particular absorption line. For
๐‘๐‘‘: ๐‘Œ๐ด๐บ crystal is a peak absorption value at 808 ๐‘›๐‘š, thus most of the broadband flashlamp energy
passes through the material without being absorbed. Flashlamps convert electrical energy to optical
energy more efficiently than diode laser, but, because of the inefficient absorption of pump
radiation, lamp pumped lasers typically less efficient than diode pumped lasers. Lamp pumped
system have low typically 1% electrical to optical efficiency [7], and the lamps need replacement
after approximately 200 โ„Ž๐‘œ๐‘ข๐‘Ÿ๐‘ . Diode laser pump source allow operation at about 10 โˆ’ 20%
efficiency and longer life, approximately 20 000 โ„Ž๐‘œ๐‘ข๐‘Ÿ๐‘ . Fiber lasers has a wall-plug efficiency of
> 30% [8], and has an operating lifetime in excess of 10,000 โ„Ž๐‘œ๐‘ข๐‘Ÿ๐‘ . The main disadvantage of diode
laser as pump sources is because it is much more expensive than flashlamps or arc lamps.
There are many advantages of using diode lasers to pump a solid state laser, instead of using the
diode laser output directly. The output of the solid state lasers can produce higher peak power, have
higher radiance and is more coherent than the diode laser pump source. Solid state laser store the
pump power from a diode laser and this stored energy can be released in 10 ๐‘›๐‘  pulses by Qswitching, which leads to a peak output power 104 times greater than the diode laser [6].
The most common DPSS laser in use is the 532 ๐‘›๐‘š wavelengths green laser pointer. A powerful
808 ๐‘›๐‘š wavelength infrared GaAlAs laser diode pumps a ๐‘๐‘‘: ๐‘Œ๐ด๐บ or a ๐‘๐‘‘: ๐‘Œ๐‘‰๐‘‚4 crystal which
produce 1064 ๐‘›๐‘š wavelength light. This light is then frequency doubled using a nonlinear optical
process in a KTP crystal (๐พ๐‘‡๐‘–๐‘‚๐‘ƒ๐‘‚4 ), so we get a 532 ๐‘›๐‘š green light. Such DPSS lasers are usually
around 20% efficient or even up to 35% [7]. For example, a green DPSS laser using 2,5 ๐‘Š pump
diode would be expected to output around 500 โˆ’ 900 ๐‘š๐‘Š of green light. In optimal conditions,
๐‘๐‘‘: ๐‘Œ๐‘‰๐‘‚4 has a conversion efficiency of 60%, while KTP has a conversion efficiency of 80% [7]. A
green DPSS laser can theoretically have an overall efficiency of 48%. But high power output can
cause damage on the KTP crystal. Thus, high power DPSS lasers generally have a larger beam
diameter, as the beam is expended before it reaches the KTP crystal, reducing the irradiance from
the infrared light. In order to obtain high conversion efficiency with KTP crystal, the phase vectors of
input beams and generated beams have to be matched. The phase matching occurs when a constant
phase relationship is maintained between the generated and propagating waves.
The output power ๐‘ƒ๐‘œ๐‘ข๐‘ก of laser as a function of the pump power ๐‘ƒ๐‘ can be determined from the
relationship [9]
๐‘ƒ๐‘œ๐‘ข๐‘ก = ๐œ‚๐‘  (๐‘ƒ๐‘ โˆ’ ๐‘ƒ๐‘กโ„Ž ),
(1)
where ฮทs is the slope efficiency of generation and ๐‘ƒ๐‘กโ„Ž is the threshold power. The parameters ๐‘ƒ๐‘กโ„Ž
and ฮทs are determined with properties of active medium and its excitation efficiency
๐‘ƒ๐‘กโ„Ž โˆ ๐ด๐‘š
๐ผ๐‘ 
๐œ–,
๐œ‚๐‘’๐‘ฅ๐‘
(2)
๐œ†๐‘ ๐‘‡
,
๐œ†๐‘” ๐œ–
(3)
๐œ‚๐‘  โˆ ๐œ‚๐‘’๐‘ฅ๐‘
where ๐ผ๐‘  = โ„Ž๐œˆ๐‘” โ„๐œŽ๐‘’ ๐œ๐‘“ is the saturation power, ๐œ– are total resonator losses, ๐‘‡ is the mirror
transmission, ๐ด๐‘š is the averaged medium area, ๐œŽ๐‘’ is the stimulated emission cross section, ๐œ๐‘“ is the
lifetime on upper laser level. Laser output power is determined by material parameters ๐œŽ๐‘’ and ๐œ๐‘“ ,
resonator losses ๐œ– and ๐‘‡, average pump wavelengths and generation wavelength ๐œ†๐‘ โ„๐œ†๐‘” and
efficiency of excitation energy transfer from pump to active material dopant ๐œ‚๐‘’๐‘ฅ๐‘ . Excitation
efficiency includes all losses occurring during pumping process and it is expressed as
๐œ‚๐‘’๐‘ฅ๐‘ = ๐œ‚๐‘Ÿ ๐œ‚๐‘๐‘Ÿ๐‘œ ๐œ‚๐‘Ž๐‘๐‘  ๐œ‚๐‘ž ๐œ‚๐‘’๐‘ฅ๐‘ก ,
(4)
where ๐œ‚๐‘Ÿ is the radiation efficiency determining part of electrical energy delivered to pump changing
into radiant energy, ๐œ‚๐‘๐‘Ÿ๐‘œ is the projection efficiency determining a part of energy radiated by a pump
that reaches laser active material, ๐œ‚๐‘Ž๐‘๐‘  is the absorption efficiency determining value of energy
absorbed by active ions of laser medium, ๐œ‚๐‘ž is the quantum efficiency determining a part of excide
ions reaching higher laser level, ๐œ‚๐‘’๐‘ฅ๐‘ก is the efficiency of energy excitation determining a part of
energy accumulated in excited ions that is emitted as a laser radiation.
For lamp pumping the main sources of losses are connected with non-effective transfer of
excitation energy from a lamp to active medium and lack of matching between emission spectrum of
a lamp pump and absorption bands of active medium. Projection and absorption efficiencies of diode
pump can be as high as 95 โˆ’ 98%. The total efficiency ๐œ‚ = ๐‘ƒ๐‘œ๐‘ข๐‘ก โ„๐‘ƒ๐‘ of lamp-pumped ๐‘๐‘‘: ๐‘Œ๐ด๐บ lasers
usually is of 1 โˆ’ 3%. Diode pumping efficiency is up to 8 โˆ’ 30%, in dependence on medium
geometry, method of its excitation, regime of operation and generated power.
Table 1: All parameters determining efficiency of diode pumped and lamp pumped system for ๐‘ต๐’…: ๐’€๐‘จ๐‘ฎ medium [9].
Pump source
Radiation efficiency
Projection efficiency
Absorption efficiency
Quantum efficiency
Excitation efficiency
Lamp
50%
35%
50%
40%
3,5%
Diode laser
40%
95%
98%
76%
28,3%
There are two types of diode pumping geometry, longitudinal or end pumping and transverse or
side pumping. End pumping is much more complicated from technological point of view because it
requires adequate shape of pumping beam and adequate layers should be deposited on the endsurfaces of active materials what ensures high transmission of pumping radiation and simultaneously
low resonator losses. The lasers with an end pump configuration are more efficient when side
pumped system are used in high power lasers. The set of high power pumping diodes have relatively
large dimensions. Transformation of radiation from such large surfaces into small pumping volume
for end pumping becomes difficult problem.
Figure 4: Basic schemes of diode pumping: a) end-pumping and b) side pumping [9].
Diode-pumped active laser materials undergo rapid thermal changes. Such changes especially
affect the media being in form of rods with circular cross-section, particularly end pumped ones.
They are heated near their axes from pump radiation and generation, but cooled through their sides.
As a result of this effect is thermally deformed laser rod, in result of changes in its geometry and
thermal dispersion of refractive index, starts to act as a lens and resonator can be out of its stability
range for extreme case. Thermal deformation also generates stresses inside medium that cause
changes in polarisation of transmitted radiation [7, 9].
4 Q-Switch Theory
With Q-switch technique pulsed operation of laser is achieved by variable Q factor of the optical
resonator. The quality factor Q is defined as the ratio of the energy stored in the resonator cavity to
the energy loss per cycle. The Q-switched pulse duration is so short that we can neglect both
spontaneous emission and optical pumping. Rate of change of the photon density within the laser
resonator is then [1]
๐œ•๐œ™
๐‘™ ๐œ–
= ๐œ™ (๐‘๐œŽ๐‘’ ๐‘› โˆ’ )
๐œ•๐‘ก
๐ฟ ๐‘ก๐‘Ÿ
(5)
๐œ•๐‘›
= โˆ’๐›พ๐‘›๐œ™๐œŽ๐‘’ ๐‘,
๐œ•๐‘ก
(6)
and inversion population density
where ๐‘ is speed, ๐œŽ๐‘’ cross section for stimulated emission, ๐‘™ length of laser rod, ๐ฟ length of
resonator, ๐œ– losses in resonator cavity, t r =
๐›พ =1+
๐‘”2
๐‘”1
2L
c
the round-trip time of a photon in the resonator,
and ๐‘”๐‘– states density. The losses in a cavity can be represented by
๐œ– = โˆ’๐‘™๐‘›๐‘… + ๐›ฟ + ๐œ(๐‘ก, ๐œ™),
(7)
where the first term represents the output coupling losses determined by mirror reflectivity ๐‘…,
second term contains all the incidental losses such as scattering, diffraction and absorption, and last
term represent the cavity loss introduced by the Q-switch. Q-switching is accomplished by making ๐œ–
an explicit function of time (e. g. rotating mirror or Pockels cell) or a function of the photon density
(e. g. saturable absorber).
In many instances Q-switches are so fast that ๐œ can be approximated by step function. In this case
we assume that at ๐‘ก = 0 the laser has an initial population inversion ๐‘›๐‘– , and the radiation in the
cavity as some small but finite photon density ๐œ™๐‘– , laser is being pumped and the cavity losses are
๐œ–๐‘š๐‘Ž๐‘ฅ = โˆ’ln ๐‘… + ๐›ฟ + ๐œ๐‘š๐‘Ž๐‘ฅ as illustrated in Figure 5. The losses are suddenly reduced to ๐œ–๐‘š๐‘–๐‘› =
โˆ’ln ๐‘… + ๐›ฟ . The photon density rises from ๐œ™๐‘– , reaches a peak ๐œ™๐‘š๐‘Ž๐‘ฅ many orders of magnitude higher
than ๐œ™๐‘– , and then declines to zero. The population inversion is a monotone decreasing function of
time starting at the initial inversion ๐‘›๐‘– and ending at the final inversion ๐‘›๐‘“ . At ๐‘›๐‘ก the photon flux is
maximum and the rate of change of the inversion
๐‘‘๐‘›
๐‘‘๐‘ก
is still large and negative, and ๐‘› falls below the
threshold value ๐‘›๐‘ก and finally reaches the value ๐‘›๐‘“ . If ๐‘›๐‘– is not too far above ๐‘›๐‘ก , that is, the initial gain
is close to threshold, then the final inversion ๐‘›๐‘“ is about the same amount below threshold as ๐‘›๐‘– is
above and the output pulse is symmetric.
Figure 5: Development of a Q-switched laser pulse. The resonator loss a), population inversion b), and photon flux c) as a
function of time are shown [1].
On the other hand, if the active material is pumped considerably above threshold, the gain drops
quickly in a few cavity transit times ๐‘ก๐‘Ÿ to where it equalizes the losses. After the maximum peak
power is reached at ๐‘›๐‘ก , there are enough photons left inside the laser cavity to erase the remaining
population excess and drive it quickly to zero. In this case the major portion of the decay proceeds
with a characteristic time constant ๐œ๐‘ , which is the cavity time constant.
The output energy of the Q-switched laser is [1]
๐ธ๐‘œ๐‘ข๐‘ก =
โ„Ž๐œˆ๐ด
1
๐‘›๐‘–
ln ( ) ln ( ) ,
2๐œŽ๐‘’ ๐›พ
๐‘…
๐‘›๐‘“
(8)
where โ„Ž๐œˆ is the laser photon energy and ๐ด is the effective beam cross-section area. The initial and
final population inversion densities, ๐‘›๐‘– and ๐‘›๐‘“ are related by transcendental equation
๐‘›๐‘– โˆ’ ๐‘›๐‘“ = ๐‘›๐‘ก ๐‘™๐‘› (
๐‘›๐‘–
),
๐‘›๐‘“
where ๐‘›๐‘ก is the population inversion density at threshold, that is
(9)
๐‘›๐‘ก =
1
1
(๐‘™๐‘› + ๐›ฟ).
2๐œŽ๐‘’ ๐‘™
๐‘…
(10)
The pulse width of the Q-switch pulse can also be expressed as a function of the inversion levels ๐‘›๐‘– ,
๐‘›๐‘“ and ๐‘›๐‘ก
๐‘ก๐‘ = ๐‘ก๐‘Ÿ
๐‘›๐‘– โˆ’ ๐‘›๐‘“
.
๐‘›
๐‘›๐‘– โˆ’ ๐‘›๐‘ก [1 + ๐‘™๐‘›( ๐‘–โ„๐‘›๐‘ก )]
(11)
4.1 Passive Q-Switches
The passive Q-switch is switched by the laser radiation itself and it does not require high voltage,
fast electro-optic driver, or RF generator as an active methods. The passive Q-switch offers the
advantage of an exceptional simple design, which leads to very small, robust, and low-cost systems.
The major drawbacks of a passive Q-switch are the lack of a precision external trigger capability and a
lower output compared to electro-optic or acousto-optic Q-switched lasers.
Figure 6: Energy levels of a saturable absorber with excited-state. ๐ˆ๐’ˆ๐’” is the ground-state absorption cross section and
๐ˆ๐’†๐’” is the excited-state absorption cross sections. ๐‰ is the upper state lifetime Napaka! Vira sklicevanja ni bilo mogoฤe
najti.[10].
A simple energy-level scheme of saturable absorber is shown in Figure 6. Absorption at the
wavelength of interest occurs at the 1โ€“3 transition. We assume that the 3โ€“2 transition is fast. The
ground-state absorption cross section has to be large and, simultaneously, the upper state lifetime,
the life time of level 2, has to be long enough to enable considerable depletion of the ground state by
the laser radiation. When the absorber is inserted into the laser cavity, it will look opaque to the laser
radiation until the photon flux is large enough to depopulate the ground level. If the upper state is
sufficiently populated the absorber becomes transparent to the laser radiation, a situation that is
similar to a three-level laser material pumped to a zero inversion level.
A passive Q-switch requires a material which exhibits saturation of the ground-state absorption.
However, most materials also exhibit absorption from an excited state. This is illustrated in Figure 6
by the transition from the upper state, level 2 to some higher level 4 which has an energy level
corresponding to the laser transition. As the ground state is depleted, absorption takes place
increasingly between levels 2 and 4. Excited-state absorption results in a residual loss in the
resonator when the ground-state absorption has been saturated. The 2โ€“4 transition does not
saturate because of the fast relaxation of level 4. A saturable absorber is useful for Q-switching only
as long as ๐œŽ๐‘”๐‘  > ๐œŽ๐‘’๐‘  , where ๐œŽ๐‘’๐‘  is the cross section for excited-state absorption [10].
Solutions of the rate equation lead to an absorption coefficient which is intensity dependent
ฮฑ0 (๐ธ) =
ฮฑ0
,
๐ธ
1 + ๐‘–โ„๐ธ
๐‘ 
(12)
where ๐›ผ0 is the small-signal absorption coefficient and ๐ธ๐‘  is a saturation fluence
๐ธ๐‘  =
โ„Ž๐œˆ
,
๐œŽ๐‘”๐‘ 
(13)
where ๐œŽ๐‘”๐‘  is the absorption cross section for the 1-3 transition.
Important characteristics of a saturable absorber are the initial transmission ๐‘‡0 , the fluence ๐ธ๐‘  at
which saturation becomes appreciable, and the residual absorption which results in a ๐‘‡๐‘š๐‘Ž๐‘ฅ of the
fully bleached absorber. The small signal transmission of the absorber is
๐‘‡0 = exp(โˆ’ฮฑ0 ๐‘™๐‘  ) = exp(โˆ’๐‘›๐‘” ๐œŽ๐‘”๐‘  ๐‘™๐‘  )
(14)
where ๐‘™๐‘  is the thickness of the bleachable crystal and ๐‘›๐‘” is the ground state density. In order to
calculate the transmission as a function of fluence, the photon flux and population density must be
considered as a function of position within the absorbing medium. The energy transmission ๐‘‡๐‘– of an
ideal saturable absorber as a function of input fluence ๐ธ๐‘– is given by
๐‘‡๐‘– =
๐ธ๐‘–
๐ธ๐‘ 
โ„
ln [1 + (๐‘’ ๐ธ๐‘  โˆ’ 1) ๐‘‡0 ].
๐ธ๐‘–
(15)
A saturable absorber with excited-state absorption can be described by a four-level model. In this
case, maximum transmission ๐‘‡๐‘š๐‘Ž๐‘ฅ is given by
๐‘‡๐‘š๐‘Ž๐‘ฅ = exp(โˆ’๐‘›๐‘” ๐œŽ๐‘’๐‘  ๐‘™๐‘  ).
For a nonideal absorber the transmission ๐‘‡๐‘› can be approximated by
๐‘‡๐‘› = ๐‘‡0 +
๐‘‡๐‘– โˆ’ ๐‘‡0
(๐‘‡
โˆ’ ๐‘‡0 ),
1 โˆ’ ๐‘‡0 ๐‘š๐‘Ž๐‘ฅ
(16)
(17)
where ๐‘‡๐‘– is the transmission of an ideal absorber, ๐‘‡0 and ๐‘‡๐‘š๐‘Ž๐‘ฅ are the lower and upper limits of the
transmission.
The most common passive Q-switch material is ๐ถ๐‘Ÿ 4+ : ๐‘Œ๐ด๐บ crystal. The ๐ถ๐‘Ÿ 4+ ions provide the
high absorption cross section of the laser wavelength and the ๐‘Œ๐ด๐บ provides suitable chemical,
thermal and mechanical properties. The crystal ๐ถ๐‘Ÿ 4+ : ๐‘Œ๐ด๐บ has broad absorption bands centred at
410 ๐‘›๐‘š, 480 ๐‘›๐‘š, 640 ๐‘›๐‘š and 1050 ๐‘›๐‘š. The typical values of cross sections are ๐œŽ๐‘”๐‘  = 7 ×
10โˆ’18 ๐‘๐‘š2 for ground-state absorption and ๐œŽ๐‘’๐‘  = 2 × 10โˆ’18 ๐‘๐‘š2 for excited-state absorption at the
๐‘๐‘‘: ๐‘Œ๐ด๐บ wavelength. The excited-state lifetime (level 2) is 4,1 ๐œ‡๐‘  and the lifetime of the higher
excited state (level 4) is 0.5 ๐‘›๐‘ . With โ„Ž๐œˆ = 1.87 × 10โˆ’19 ๐ฝ at 1.06 ๐œ‡๐‘š and the above value for ๐œŽ๐‘”๐‘ 
one obtains a saturation fluence of ๐ธ๐‘  = 27 ๐‘š๐ฝโ„๐‘๐‘š2 for ๐ถ๐‘Ÿ 4+ : ๐‘Œ๐ด๐บ [10].
Commercially available ๐ถ๐‘Ÿ 4+ : ๐‘Œ๐ด๐บ passive Q-switches are specified by the low-power
transmission at the laser wavelength. Typical transmission values range from 30 โˆ’ 50%, and the
crystal thickness is usually between 1 โˆ’ 5 ๐‘š๐‘š. Values of the small signal absorption coefficient ๐›ผ0
vary from 3 โˆ’ 6 ๐‘๐‘šโˆ’1. For example, for ๐›ผ0 = 4๐‘๐‘šโˆ’1 and ๐‘™๐‘  = 2๐‘š๐‘š the low-power transmission is
๐‘‡0 = 45%. The pulse repetition rate can only indirectly be controlled, e.g. by varying the laser's
pump power and the amount of saturable absorber in the cavity. Direct control of the repetition rate
can be achieved by using a pulsed pump source as well as passive Q-switching.
5 Conclusion
A passively Q-switched laser contains a saturable absorber instead of the modulator. For
continuous pumping, a regular pulse train is obtained, where the timing of the pulses usually cannot
be precisely controlled with external means, and the pulse repetition rate increases with increasing
pump power. In the medical fields solid-state Q-switch lasers have found applications in
ophthalmology for vision correction and photocoagulation, skin resurfacing, and as replacements for
scalpels in certain surgical procedures. In medicine we need pulsed lasers with low repetition rate
and high energy. A low energy and high repetition laser system was developed for applications in
industry for material processing. This is easier to achieve by active Q-switching techniques.
Particularly for low pulse repetition rates, lamp pumping can be an economically favourable
option, since discharge lamps are much cheaper than laser diodes for a given peak power. For
average powers, however, diode pumping becomes more attractive, also because thermal effects in
the laser crystal are strongly reduced. With a wide range of wavelengths, short pulse durations, high
average powers and high pulse energies, compact and cost-effective DPSS lasers have a promising
future in medical device manufacturing. One reason limiting their implementation is high price of
pumping diodes. However, market analysis shows that their price decrease and the main obstacle in
development and expansion of DPSS lasers in medicine and industry will disappear.
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