Adaptive optics is known to
be invented as a tool for compensation of different wavefront distortions of
the light beam penetrated through some turbulent media and usually is used for
various astronomical applications . But starting from late 70th
several types of experiments showing the efficiency of the use of adaptive
systems to improve the laser beam quality were carried out . Almost
all these experiments were made on the CO2 high power lasers (up to
MWatt) and the obtained results were really promising. Here we should mention
the works of Oughuston [3,4] (theoretical calculations), and R.Freeman
et. al. [5,6,7] (mostly experiments). But then there was some sort of a
gap in the interest towards the application of active optical elements in laser
resonators. The main reason for this probably was the cost of the key elements
of any adaptive system – deformable mirrors, wavefront sensors and systems of
electronic control with the high speed computers. But later the situation
changed together with the progress in laser technology and new problems were to
be solved with the help of lasers. The interest in active laser beam control
appeared again as well as the price of the elements of adaptive systems
The main tasks that could be resolved by methods and technique of adaptive optics are:
Stabilisation and optimisation of different laser radiation parameters.
Formation and maintenance of the given intensity distribution of laser beam on the given surface.
Possible new fields of
application of adaptive systems are laser microtechnology, laser etching, laser
heating technology as well as laser ophtalmosurgery and laser dermatology.
The problem of controlling
the parameters of laser radiation has become particularly topical in view of
the widespread use of lasers in technological processes and medicine. The
comparatively high radiation power, the relatively high efficiency and the
fairly small dimensions of different types of lasers make them suitable for a
wide range of applications. The expensive optomechanical systems are employed
to achieve the required intensity distribution on the surface of a
laser-treated sample in industrial systems and high-quality (having a
homogeneous refractive index) active elements (crystals) are used to fabricate
these such lasers. Under real conditions, one of five or six industrially grown
crystals is selected as the active element of laser which raises the cost of
the whole technological system still more. Normally stable resonators are used
in CW solid state lasers having rather low gain and small active volume. Such
resonators have very poor discrimination factor between transverse modes and so
poor output beam structure. To improve beam quality in practice the hard-edged
apertures are used which, however, also produce diffraction rings in the near
field and significantly reduce output beam power. The optimum resonator for
such laser would consist in an open cavity having a lowest order modes of a
stable (for a low loss) and all the other modes for unstable type (for a good
discrimination) . The design of such type of laser was proposed in
Ref. 9 where the near-axial part of cavity is stable and other part unstable.
In contrast, it was proposed [10, 11] to use a mirror with a convex
central part and concave rim. Another way of improving laser beam quality - the
use of graded-phase mirror resonators . The technology for
fabricating such mirrors is now well developed , and many
commercial laser companies have adopted them. But one of the shortcoming of
such mirrors - their stable surface profile. This narrow the spheres of
application of such mirrors in lasers because every active element needs its own
unique graded-phase mirror.
In modern laser technology
it is often necessary to form the given intensity distribution at the surface
being treated. This has become particularly topical because of the widespread
use of component etching systems in mechanical engineering. This problem was
solved previously by using compensators, kinoforms, spatial filters, etc [14,15].
These optical elements were developed for beams having a given
structure (mostly Gaussian). When the illumination conditions vary, the efficiency
of such elements deteriorates appreciably. Another method of forming a given
intensity distribution at the laser exit involves the use of an intracavity
controlled mirror which not only can distort the profile of the laser-emitted
mode, but can also create conditions for successful generation of some and
suppression of other mode structures.
The results of some experiments with excimer, copper-vapor, CO2,
and YAG:Nd3+ industrial lasers and intracavity deformable bimorph mirrors
concerning the possibility to control and form mode structures are presented in this paper.
resonators includes optical elements with rigidly fixed surface profiles
intended for obtaining specific beam output quality. But when you need to
change some output parameters of laser beam (for example get different output
mode configuration or even change the regime of laser generation) you need to
reconstruct all laser cavity or alter the block of power supply. Such
operations are rather expensive and sometimes takes a long period of time. That
is why the use of mirrors with controllable flexible surface in laser is of
large interest. This gives the opportunity for creation of flexibly tunable
resonator of a new type.
As it was mentioned before
theoretical estimations [3, 4] showed the possibility to change the
beam structure by minor surface deformation (less than wavelength) of flexible
resonator mirror. And the possibility of intracavity compensation of the
simplest aberrations of the wavefront to increase beam quality have been
demonstrated in experiments [5,6,7].
Industrial CW CO2
laser TL-5 developed and manufactured in the NICTL RAN  is
characterized by high beam quality (divergence of less then 1 mrad at 55 mm
output beam diameter) and output power 5kW. Fig.8 shows the scheme of the
Fig.8. Scheme of CO2 - laser resonator
The unstable confocal
resonator with magnification M = 2 consists of two spherical mirrors with radii
of curvature R1 = 26 m and R2 = -13 m and 4 flat folding
mirrors between them. Resonator length was L = 6.5 m. One of the flat mirrors
was replaced by the cooled flexible mirror based on bimorph piezoelement. The
output beam of this laser had the shape of a ring with outside aperture of 55
mm and inside aperture - 25 mm. Well known parameters of this laser cavity g1
and g2, taking into a consideration deformable mirror could be
written in the following way:
where R is the radius of
curvature of flexible mirror under control voltage, L=6.5 m - the length of
laser cavity. For specified resonator parameter (with 1/R=0) we have g1
=1.5 and g2 =0.75.
When a static voltage +300
V was applied to all electrodes of the flexible mirror radius of curvature of
its surface R changed from plus to minus 200 m. The value g2 was
changing correspondingly in the range of 0.69-0.82. In the dynamic regime of
mirror action the cosine voltage with frequency in the range of 1 - 10 kHz was
applied to mirror electrodes. At the mirror resonance frequency - 3.8 kHz the
deformation of mirror increased up to R= +50 m and g2 value was
changed from 0.49 to 1.0. The magnification M of unstable non-confocal
resonator could be given as:
Fig.9 shows the dependence
of resonator transmittance T = 1-1/M2 upon g2 for g1
= 1.5. One can see that when g2 changes from g2 < 0.67
(the case of stable resonator) to 1.0 the transmittance T varies from 0 and 0.93.
Fig.9. Transmittance T of laser cavity vs g2 in case g1=1.5
So, changing the curvature
of the flexible mirror surface by applying cosine voltage to the control
electrodes one could change the transmittance of the telescopic unstable
resonator with the same frequency and modulation of the laser output beam power
could be obtained. The cosine voltage of frequency up to 10 kHz and amplitude
up to 300V was applied for this purpose. Under control voltage of more than 1
kHz the period of the mirror surface oscillation could be compared with the
life-time of the CO2 laser active medium. Thus the Q-switch regime
of laser generation could be obtained.
In experiments the
dependence between output beam power and control voltage amplitude and
frequency was studied. The periodical laser generation regime with 100% power
modulation depth was obtained at near-resonance frequencies - 3.8 and 7.6 kHz.
The pulse peak power exceeded the average power threefold. The average power
drop was insignificant (<10%). Fig.10a,10b demonstrate output beam pulses
and control voltage pulses applied to deformable mirror at resonance
frequencies. Here one can see that even 120 V at 3.8 kHz and 80 V at 7.6 kHz
mirror control voltage is enough to get 100% power modulation.
Fig.9. Oscillograms of output beam power Pout and control signal Ucont at frequency
3.8 (a) and 7.6 (b) kHz
Together with the power
modulation the aperture of the output laser beam also changed from 35 to 65 mm
at the plane where the convex resonator mirror was placed. At the same time
changing the curvature of active mirror we managed to vary the beam convergence
angle of industrial laser TL-5 in the range of 2 mrad. Such change of beam
convergence by flexible mirror in resonator can be used in material processing
for dynamic focusing of laser radiation. In different technological processes
such as deep penetration welding or thick material processing the displacement
of the laser focal spot along the beam axis is needed to concentrate energy in
the developing area. This focal spot displacement usually was realized by
moving the focusing lens along the laser beam axis or using extracavity active
mirror . The technique of change the beam convergence angle using
flexible mirror within the resonator is simple and provides the focal spot
displacement in a wide range with low deformation of the mirror surface.
Thus the possibility to
obtain the pulse-periodical generation and Q-switch regime of continuous pumped
industrial laser was demonstrated. The use of the intracavity active mirrors do
not require any significant modification of the whole laser. At the same time
it broaden the possible spheres of technological lasers application and can
improve different technological processes.
2.2. Super-Gaussian laser intensity output formation by means of adaptive optics
It is usually desirable for
laser technology to have a laser device operating in a single (mostly
fundamental) mode for a good quality output beam and providing an efficient
power extraction at the same time. A gaussian beam is usually relatively narrow
and results in a poor energy extraction from the gain medium. Exponential field
distribution profile with the order more than 2 is expected to provide better
energy extraction (in comparison with the higher standard gaussian profile)
while being less affected by aperturing since it has a large beam size and a
fast decreasing of intensity near the edges.
One of such special
intensity distributions (super-gaussian) can be formed by intracavity graded reflectivity
[13,25], and graded-phase mirrors [12,26,27]. The experimental
results have shown a significant increase of the monomode laser energy output
compared with the output of a conventional semiconfocal resonator [12,27,28].
But the correctors have a serious drawback: since the mirror surface
profile is rigid, every change of laser parameters needs its own special mirror.
In this work we suggest to
overcome this problem by the use of an intracavity flexible bimorph mirror
inside laser cavity for the given intensity distribution formation.
2.2.1. Basic principles
The geometry of adaptive mirror resonator is shown in Fig.11.
Fig.11. Schematic setup of the CW CO2 laser with adaptive mirror
It consists of plane output
coupler and active mirror separated corresponds to the industrial continuos
discharge CO2 laser from the coupler at the distance L = 2m. Such
geometry ILGN-704 produced by “Istok”, Fryazino, Russia. We considered, that
the active mirror would be a bimorph water cooled one with 3 rings of
electrodes, as shown on fig. 3.2 b – all 8 electrodes of the middle and the
outer rings were connected and thus formed the rings of electrodes.
Azimutal symmetry can be
assumed which allows us to use the one-dimentional Huygens-Fresnel integral
equations29, 30 to calculate the amplitude of a mode in the empty
laser resonator, namely
where γi is the eigenvalue and Ψi(ri)
is the eigenmode of the resonator, ri are radial coordinates,
i = 1 is related to plane output mirror of the
diameter 2b, i = 2 - to the active one of the diameter 2a,
Here Jl is the Bessel function of order l (we take into account only the
lowest transverse mode with l =0), A, B, D are the constants determined
by the ABCD ray matrix of the laser resonator. We consider empty resonator, so A=1, B=L, C=0, D=1.
The algorithm of the
calculation of formation of the given fundamental mode intensity distribution
is so called “inverse propagation method” described in [12,26]. The
initial field distribution Ψ1(r,φ) is specified on the output mirror.
The back-propagation of the laser beam through all resonator’s elements to
active corrector is calculated using Huygens-Fresnel integral Eqs. (3.1, 3.2).
In the plane of the active corrector the wavefront is calculated and served to
determine the appropriate mirror phase profile φmirror:
φmirror= - φbeam.
Such phase profile of laser
beam could be completely reconstructed by ideal corrector (graded-phase mirror)
[12,26]. In our case bimorph mirror can approximate the necessary phase
profile with some error. Such minimal RMS error was calculated using the
experimentally measured response functions of the mirror. In other words:
where Z(r) is the profile
to be reconstructed, Fi(r) are response functions of adaptive mirror
electrodes, Ui are weight coefficients corresponding to the voltages
applied to each electrode.
Left side of the Eq.(3.4) has a minimum when it’s first derivative equals to 0:
From the Eq.(3.5) the
applied voltages to approximate the necessary shape of laser beam were determined.
Described above procedure gives us reconstructed mirror surface
φmirror(r) which was substituted into
Eq.(3.3). To solve integral equations (3.1), (3.2) we used the Fox and Li
iterative method of successive approximations [29, 30], to take into
account edge diffraction and non-ideal reproduction of the necessary phase profile
of the laser beam by adaptive mirror.
2.2.2. Main results
Main parameters of the
laser resonator (Fig.11) are: Fresnel numbers N1 = b2/(Bλ),
N2= a2/(Bλ) and
geometrical factor is G = (1-L/R2) where λ = 10.6 μm is wavelength,
R2 = 4m
is the radius of curvature of active mirror and L = 2m is the length of the
resonator cavity. The initial field distribution on the plane coupler is chosen
as Ψ(r)=Exp(-(r / w))², where n determines
the order of super-gaussian function and w is the beam waist. The particular
beam waist was calculated according to the methods of moments of laser beam :
M² is the beam quality factor
, defined for a super-gaussian beam
of the order of n in 31 as:
Γ(x) is the Gamma function.
18.104.22.168. Formation of a super-gaussian beam of the 4-th order (n=4)
The super-gaussian beam
waist was calculated from Eqs.(3.6, 3.7): w=3.1 mm. Fig.12(a) represents the
phase distribution of super-gaussian beam (curve 1 (thin)) propagated through
resonator at the distance L=2m from the output plane coupler to adaptive
mirror. Curve 2 (thick-dotted) (Fig.12(a)) illustrates the phase profile of
the active mirror reproducing with RMS error = 0.3% the phase shape of laser
beam. Fig.12(b) shows intensity distributions of laser beam on the plane
Fig.12. Formation of a super-gaussian beam of the 4-th order, N1=1,
a) the phase profile on the active mirror;
(b) normalized intensity distributions on plane coupler
Curve 1 corresponds to the
fundamental gaussian mode of the same resonator but with pure spherical mirror.
Curve 2 (thin-solid) shows the given super-gaussian relative intensity profile,
curve 3 (thick-dotted) – profile produced with ideal corrector (graded-phase
mirror), approximating completely the necessary phase profile of the laser
beam, and the curve 4 (thick) corresponds to the intensity distribution in the
resonator with adaptive mirror.
One may see from Fig.12(b)
that applying the active corrector (curve 4) the mode volume of the output
intensity distribution increases in 1.5 times in comparison with the pure
gaussian beam (curve 1) while diffraction losses per transit decrease in 1.7 times.
Users of lasers often
dislike top-hat intensity distributions for their side lobes in far field
patterns. Such side lobes contain about 14% of the total energy26.
However, a super-gaussian function is an apodized top-hat distribution; the
distinction is important since the smoother edge implies a reduction of higher
spatial frequencies. Hence the far field pattern with reasonable n (n < 10)
should show an important reduction of the side lobes. Moreover, the formed
super-gaussian distribution is not exactly the super-gaussian function: it’s
form has been changed by edge diffraction and by limited possibility of active
mirror to form the necessary phase profile. That is why the side lobes of the
beam formed by active mirror contain only 2% of the total energy (dashed curve
3 on Fig.13) that makes this intensity profile very attractive for industrial
applications. For a comparison curve 2 in Fig.13(a),(b) represents the far
field pattern for the super-gaussian beam formed by an ideal (graded-phase)
Fig.13. Formation of a super-gaussian beam profile of the 4-th order.
(a) Intensity distributions in far-field zone:
1 - gaussian beam, 2 - beam formed by ideal corrector (graded-phase mirror),
3(thin curve) - beam formed by active mirror; (b) fragment of the same
22.214.171.124. Formation of a super-gaussian beam of the 6-th order (n=6)
The beam waist of the given
initial distribution is 3.3 mm. Fig.14(a) represents the exact phase
distribution of the given super-gaussian beam and the phase profile of active
mirror (RMS error of the approximation is about 0.1%). Fig.14(b) shows how the
active mirror can form intensity distributions on the plane coupler. The
far-field results are very close to the case of formation of the 4-th order of
the super-gaussian beam represented in Fig.13(a)(b).
Fig.14. Formation of a super-gaussian beam profile of the 6-th order.
N1=1, N2=14.1, G=0.5.
(a) solid - the phase profile of laser beam to
be reconstructed and dotted - phase profile of active mirror; (b) normalized
intensity distributions: 1 (thick) - the given initial super-gaussian beam, 2
(thin-dotted) - intensity formed by active corrector
The mode volume of output
intensity distribution increases for this case by a factor of 1.3 in comparison
with pure gaussian beam while diffraction losses per transit decrease in 1.5
The diffraction analysis
presented in this paper has confirmed the possibility to form a wide class of
interesting for technology intensity distributions of the fundamental mode in
the near-field zone by flexible mirror. Such diffraction analysis contains an inverse-propagation
calculation, the approximation of laser beam phase with experimentally measured
response functions of the sample of the semipassive bimorph flexible mirror
with three ring controlling electrodes and numerical Fox and Li simulations. It
has been shown that in all cases mode volume of formed intensity distributions
increased in 1.3-1.6 times while diffraction losses per transit decreased in
1.5-1.7 times in comparison with pure gaussian mode of the resonator with the
same parameters but with spherical mirror. Sure, in case of formation of the
super-gaussian modes we loose in beam quality in comparison with the gaussian
beam profile: for example, in our case for the 4-th order of super-gaussian
beam M2=1.1. But the output radiance defined as
will also increase in 1.07 - 1.25 times (depending on the type of the order of the super-gaussian laser beam).
These results may be
improved by making some optimisation procedure – varying the parameters of a
resonator or the radii of the electrodes r1 and r2 of the
bimorph corrector. The obtained far field patterns of formed modes are also
very suited for technological applications.
The experiments carried out
in NICTL proved the correctness of these calculations and were in good
agreement with the theoretical results. As it was shown in the experiments we
were able to increase the output power of TEM00 mode about 1.1
times, and increase the peak intensity in far field (in the focus of lens) in
1.7 times .
3. CW technological rod YAG:Nd3+ laser with the intracavity active bimorph mirror
3.1. Correction of an active element thermal lens by a deformable mirror
In our work an active system for controlling intensity distribution of CW
flash lamp pumped YAG:Nd3+ laser has been proposed. It is well known
that thermal stresses in active elements of solid-state lasers causes the
change of their birefringence properties  (this effect is discussed
in details in Chapter 1 of this book) as well as the dependence of the
refractive index of their matrices on the spatial coordinates. The first
approximation of this dependence is similar to a simple focusing lens which is
called as the thermal lens [34,35]. And of course it is very important
to take thermal lens into account when designing resonators for solid-state
lasers. It is essential to remember that the parameters of thermal lens are not
constant, but depend on the pumping conditions and the cooling method, which
determine the temperature profile of the active element [35,36]. These
fluctuations are one source of instability of the power and emission spectrum
of lasers .
When optimizing the emission parameters of solid-state lasers one must take
into account the role of astigmatism and other optical aberrations introduced
by a thermal lens. Interference methods were employed to determine these
aberrations . Resonator designs have been proposed which only
reduce the influence of such aberrations to a minimum . This
situation has now changed considerably in view of the development of adaptive
We made a detailed investigation of the optical distortions caused by a
thermal lens in a rod YAG crystal, employing a Fizeau interferometer and considering
the possibilities of compensating distortions in a laser resonator by an
adaptive mirror. Because astigmatism induced in the thermal lens of active
element  is the main aberration that distorts an "ideal"
lens, in order to correct this aberration one should use a type of deformable
mirrors that can efficiently reproduce this kind of aberration. One of the most
suitable types of active mirrors are a modal bimorph corrector [16,40].
The experimental setup for testing and correcting distortions of a rod YAG
laser is presented in Fig.15.
Fig.15. Experimental setup for testing thermal lens of rod YAG active element:
1 - He-Ne laser; 2- micro
objective lens; 3 - beam splitter; 4 - lens; 5 - reference plate; 6 - thermal
lens; 7 - 8 - telescopic system; 9 - active mirror; 10 - block of manual
control; 11 - TV camera; 12 - TV monitor; 13 - IBM computer
Radiation from a stabilized single-frequency helium-neon laser 1 with wavelength
0.63 m was beam-expanded by means of lenses 2 and 4 and directed to
semitransparent Ètalon plate 5. A light beam then passed through a laser active
element 6. Because the diameter of the beam that emerged from this element was
quite small (6 mm), it was expanded by lenses 7 and 8 to a 40 mm diameter - the
aperture of a 13 electrode flexible bimorph mirror 9. After reflection from
this mirror, controlled by the unit 10, the radiation of helium-neon laser
transverse the entire path in the opposite direction. The fringe pattern formed
by the waves reflected from the standard plate and the flexible mirror was
projected on the TV camera 11 by a beam splitting cube 3. The beam-expanding
system consisting of lenses 7 and 8 also performed the function of compensating
the overall curvature of the thermal lens. The fringe pattern was transferred
to computer 13 and then processed with the help of a special software .
This setup was realized for investigating and compensating the thermal lens
by a double pass of radiation through an active element having plane-parallel
ends in almost the same way as in the real resonators of working solid state
lasers. Experimental investigations of the thermal lens showed a considerable
reduction of its focal length and an increase in its astigmatism when the pump
power was raised (Fig. 16a, b). By changing the shape of the deformable mirror
it was possible to compensate the distortions caused by the double pass of the
radiation through the active element (Fig.16c).
Fig.16. Map level of thermal lens aberrations:
a - without pump; b - pump power
2.8 kW and no correction; c - with correction
As an example, Table 5 shows the coefficients for the first five aberrations
presenting the wavefront distortions before and after compensation (pump 2.8
kW). It can be seen from table 5 that we were able to reduce the coefficients
of the majority of the aberrations by a factor of 5. This demonstrates the possibility
of performing effective correction of low order aberrations with a bimorph
Table 5.A1 and A2 presents astigmatism, C1 and C2 presents coma, and SA is spherical
aberration (coefficients are given in microns)
At the same time it must be mentioned that such a way of enlarging the
diameter of the beam on an active mirror with the help of lenses 7 and 8 (Fig.
12) is not optimal from the point of view of obtaining the maximal laser output
power. The losses on the these lenses prevent one from realizing a high
efficiency of such a device. However, this problem can be solved by employing a
concave spherical active mirror and making a negative lens on one end of active
3.2. Laser cavity with large-aperture flexible mirror
All active mirrors have rather large-aperture - their diameter is 20 mm and
more. It is difficult to use such deformable mirrors in cavities of industrial
CW solid-state lasers because of relatively small apertures of the beams in
stable resonators. We suggested an expansion of the beam inside laser cavity up
to the diameter of the adaptive mirror by using a meniscus on the one end of
active element (Fig.17) .
Fig.17. Laser resonator with large aperture mirror:
1 - output flat mirror, 2 -
active element (YAG), 3 - thermal astigmatic lens, 4 - meniscus, 5 - spherical
At the same, time active mirror had a concave spherical profile. Such laser
resonator permitting the use of wide aperture mirrors without any supplementary
optical elements and therefore without undesirable loss, has been calculated
and constructed. The aim of the design was to select parameters of the
spherical mirror, the meniscus radius and relative position of cavity elements
for which the resonator was stable and insensitive to the position of the
mirrors and variation of active element thermal lens. The size of the laser
beam at spherical active mirror should be 20 - 30 mm and the optical length of
the cavity about 1 - 1.5 m (for convenience). We note that the thermal lens of
active element was astigmatic, having two focal lengths fx=0.42 m
and fy=0.34 m (experimental result for pump power 3.8 kW).
It is fairly difficult to satisfy all these requirements simultaneously. For
example, Fig. 18 gives dependencies of the beam radius at the spherical mirror
Wsp via cavity length d2 for various radius of curvature
of meniscus r.
Fig.18. Dependence of the beam
radius Wsp vs cavity length d2 for different r
The radius of curvature of the mirror 5 (Fig.17) was 0.5 m and the distance
between the center of the crystal and output flat mirror was d1 =0.2
m. It can be seen that an increase in the beam radius Wsp with
decreasing r was accompanied by a narrowing of the permissible range of displacement
of the spherical mirror D for which the cavity was remained stable. This would
cause some difficulties in aligning the laser resonator and reduce the output
power stability. It should be added that additional difficulties would be
involved in fabricating a shorter-focus meniscus of the desired optical quality
and this would raise the cost of the crystal.
An increase of the beam radius at the spherical mirror 5 may also be
achieved by enlargement the radius of curvature R of this mirror. Table 6 gives
the calculated values of the beam radius reaching the spherical mirror Wsp
when this mirror 5 was situated in the center of the stability range D~10 mm
and also gives the corresponding cavity lengths dav for R=0.5 and 1
m when r=30 mm and d1=200 mm. It can be seen that doubling the
radius of curvature R was accompanied by approximate doubling of the beam
radius at the spherical mirror. However, the cavity length dav also
increases by a factor of 1.7, which was not always desirable.
Dependencies of Wav and D on d1 for fx
=0.42, fy =0.34 m, r=35 mm and R=0.5 m are presented in Table 7. It
can be readily seen that d1 should be as small as possible to increase
the range of stability. In this case, however, Wav was reduced and
had values clearly inadequate for the efficient operation of an active mirror.
In addition, the integral filling of the active element for small d1
was several times less than that for large d1. This is illustrated
in Table 8, where the coefficient q characterizes the filling of the active
element (the other parameters are the same as in table 7).
From an analysis of the results of these calculations, we selected a cavity
configuration satisfying the requirements specified above. The cavity
parameters were: fx=0.42m, fy=0.34m, d1=0.3m,
r=35mm, R=0.6m and Wav =6mm.
It should be noted that these calculations apply to a single mode lasing
regime in terms of transverse indexes. When selecting the cavity parameters, it
must be remembered that the optimal features for the single-mode and the
multimode lasing regimes may differ. For example, in the multimode regime the
beam radius at the mirrors is seven or eight times greater than that for the
single-mode regime39. It is known that in a laser with a symmetric
linear cavity, the filling of the active element and thus the radiation power
in the single mode regime increase with increasing d1, where d1
may increase to values not exceeding 2.0f. When d1 is reduced within
certain limits in the multimode regime, it is easier to generate a large number
of transverse modes. In this case, in spite of the reduction in the filling of
the crystal by the dominant TEM00 mode, the whole crystal volume
involved into lasing is increased and so the output power is also raised. This
effect is observed in a laser having a cavity containing an active mirror as
One of the unique characteristics of our resonator is a nonsymmetrical
dependence of the laser crystal filling q through d2 (Fig.19).
Fig.19. Filling of active element q
with the main TEM00 mode versus d2
The minimum of this curve is shifted to the right-hand border of the
stability region. This can allow the resonator to work near the left-hand part
of the border, where filling q is rather high and at the same time depends
rather slowly on d2. As was shown in experiments, the left-hand
region of Fig. 19 is optimal for extracting mode TEM00 with an
3.3. Control of the parameters of a CW solid-state laser radiation using methods of
Experimental setup shown schematically in Fig. 20 was used to study the
feasibility of controlling the mode structure and improving beam quality of
radiation from CW industrial low power YAG laser by using an
Fig.20. Experimental setup of active intracavity correction:
1 - active element, 2 - lens on
the end of active element, 3 - concave active bimorph mirror, 4 - flat
resonator mirror, 5, 6 - lenses, 7, 19 - infrared visualizer, 8 - block of
control, 9, 18 - beam splitters, 10, 17 - mirrors, 11 - diaphragm, 12 - LFD-2A
avalanche photodiode, 13 - S4-45 spectrum analyzer, 14 - pin-hole, 15 -
photodiode, 16 - automatic plotter
The rod active element with diameter 5 mm and 100 mm length was inserted in
the laser head of Russian K-301 system with 5-kW flashlamp. The radiation
coupled out of the resonator was passed to a system of lenses. One lens 5
focused the radiation and the other 6 was used to obtain a magnified image of
the focal spot on a visualizer 7 and photo diode 15. A control unit 8 was used
to apply various constant control voltages between -300 V and +300 V to
different electrodes of the adaptive mirror (see Chapter 3.2.2). The size of a
pin-hole 14 was much smaller than the diameter of laser beam in its vicinity. A
photo diode 15, and a pin-hole 14 were placed on a mechanism which moved it
perpendicular to the direction of propagation of the beam; we used this to
study the change of the size of focal spot when controlled by a flexible
mirror. In this way, the cross section of the beam intensity in the focal plane
of the lens 5 could be recorded by an automatic plotter. Visualizer 19 with a
beam splitter 9 were used to measure the size of the beam just before lens 5.
It is known that radiation of TEM00 dominant transverse mode has
the highest beam quality. However, generation of this radiation always involves
introduction fairly high losses in the resonator when diaphragms are inserted, the
resonator is misaligned, etc. This sometimes reduce more then fivefold laser
output power. Expensive laser crystals are used to obtain higher power
radiation in the TEM00 mode. However, in many modern applications in
laser technology the highest beam quality is not required. It is sufficient
merely to increase the beam quality severalfold without altering the laser
output power appreciably.
Our experiments showed that by changing the shape of the surface of an
intracavity bimorph 8-electrode mirror the divergence of multimode radiation
from a solid state laser can be reduced by a factor of 2 - 2.5 while the almost
constant initial beam size. Measured beam parameter product38
BP=1/4(Waist diameter•full far field
angle) without active correction was about 7mm•
mrad and with correction - 3mm•mrad
(for TEM00 mode BP=0.4 mm•
mrad). The control voltages applied to the mirror electrodes were selected to
minimize the half-width of the beam at the visualizer 7. Fig. 21 shows traces
of the signal from the photo diode 15 obtained on the automatic plotter.
Fig.21. Intensity distribution at the focus of lens 5:
1 - before correction, 2 - after correction
Curve 1 shows the intensity distribution of the initial multimode laser
beam. In this case, the integrated radiation power was 30 W. Curve 2 gives the
intensity profile when the adaptive mirror was controlled and the divergence of
the laser radiation was reduced. The lasing power was then reduced by 40%
compared with its initial value. Such power reduction thanks to decreasing of a
pump power or using a corresponding pin-hole didn't lead to such detectable
changing of starting divergence. This result can be explained as follows. Deformation
of active mirror results in change of the resonator configuration and thus
establishes conditions for the more efficient generation of some modes and
suppression of others. Thus, by selecting the voltage applied to the mirror
electrodes, we can isolate modes having small transverse indexes, m and n, thus
reduce the divergence of the laser radiation.
We studied the feasibility of controlling the transverse intensity
distribution of a laser beam using an intracavity flexible mirror. We analyzed
both the single-mode and multimode regimes of generation. The intermode beat
spectrum was used to monitor the single-mode regime (for this purpose we used a
spectrum analyzer). The spectrum was recorded in the range up to 100 MHz. For
our selected laser configuration the minimal spacing between two transverse
modes was 45 MHz and the spacing between two longitudinal modes was 210 MHz.
Thus, when, in addition to the fundamental mode, additional transverse lasing
modes appeared we observed a signal corresponding to the intermode beat of the
transverse modes in the 0-100 MHz range.
For the single-mode regime (when the laser output was W=5 watts), which was
achieved by inserting a pin-hole in the resonator, the output spot could be
made “triangular” or “rectangular” (Fig. 22c, 22b) by selecting the voltages
applied to the mirror electrodes and controlling the tilt of the mirror as a
Fig.22. Output field distribution in the single mode regime:
a - initial beam structure
without active mirror beam control; b-e - with active beam control
When the diameter of the pin-hole was increased, the laser spectrum of the
transverse modes became multimode in terms of transverse modes and this was
accompanied by a rise in radiation power. By control of the adaptive mirror, it
was possible to select specific modes and obtain various intensity
Fig.23. Mode structure in far field zone in multymode regime
The stable lifetime of all these mode structures was at least a few seconds,
and a distinct mode configuration could be observed on the visualizer
throughout this time period. Then, as a result of fluctuations of the pump
power and flexibility of the resonator structure, this structure became blurred
for fractions for a second and then restored.
When the pinhole was not used, a change in the surface shape of adaptive
mirror merely resulted in deformation of the laser beam. In this case the
output power of laser beam slightly increased due to the more accurate
alignment of the resonator and some compensation of the thermal lens
aberrations. The radiation power increased from 25 W (without control of the
active mirror) to 30 W (with control); the flashlamp power was 3.4 kW.
These investigations have shown that it is efficient to use a flexible
intracavity mirror to control the divergence of solid-state laser radiation and
to form a mode structure, and this may have widespread application in various
industrial processes. Of course, the use of active intracavity mirrors do not
allow to correct induced birefringence in rod YAG element. The application of
active bimorph mirrors in more powerful lasers requires the use of water cooled
Copper vapor lasers are
used increasingly in microtechnology and medicine. Investigations of their
characteristics are reported in, for example, [42,43]. In practical
applications of these lasers there are special requirements in respect of the
distribution of the intensity of the output beam and in rapid changes of its
In the view of high gain of
the laser, it is quite easy to construct an unstable telescopic resonator with
a high value of the gain. In our experiments we used ILGI-101 laser, produced
in Russia. This laser emitted pulses of 40 ns duration at repetition frequency
of 10 kHz. The experimental setup is shown in Fig.24.
Fig.24. Copper vapor laser with intracavity active mirror:
1 – active bimorph corrector; 2 – resonator
mirror; 3 – active media; 4 – telescope; 5 - semireflecting plate; 6 – focusing
lens; 7 – plate with calibrating scale; 8 – imaging lens; 9 – screen
Active 13-electrode bimorph
mirror  1, and a nontransmitting spherical mirror 2 with a radius
of curvature 50 mm formed an unstable telescopic resonator with a magnification
of about 100 and of 2 m length. The aperture of the laser active element (tube)
was 15 mm. So, a telescopic expander 4, with a threefold magnification,
consisted of two lenses was used to expand the beam incident on the mirror 1.
Misalignment of this telescopic expander could be used to vary the
magnification in a certain range. The radiation was coupled out of the
resonator using a plan-parallel glass plate 5. A thin plate 7 with a reading
scale (calibrated in scale of 0.1 mm) was placed in the focal plane of a lens 6
(focal length 250 mm). The images of the focal spot and the reading scale were
projected by a lens onto screen 9.
The divergence of the
output radiation was 0.25 mrad for the optimal tuning of the resonator, but
variation of the shape of the adaptive mirror surface made it possible to
relimit the divergence to 0,08 mrad. The diffraction limit of the divergence
was 0.04 mrad. The output radiation divergence was measured near the lasing
Placing of the adaptive
mirror inside the laser cavity made it possible to correct the phase
distortions caused by change in the refractive index of the active medium and
by aberrations of the optical components . Changes in the phase of
the output beam resulted in a redistribution of the radiation intensity in the
far field zone. We determined the distribution of the intensity in the focal
plane of the lens when the minimum divergence was reached (Fig.25b).
Fig.25. Different intensity distributions in the focal plane
When the mirror sag was 4 μ the divergence increased by a factor of 10 (Fig.25c).
induced astigmatic aberration converted the focal spot to a rectangular segment
of 0.6x0.02 mm dimensions (Fig. 25c). Application of various combinations of
the control voltage to the adaptive mirror electrodes produced different
distributions of the radiation intensity in the focal plane.
5. Control of the output beam of the excimer laser
The parameters of an excimer laser beam depend largely on various distortions inside the resonator.
In most cases these distortions are manifested in the pure phase form such as
fluctuations of the refractive index of the active medium, thermal deformations
of the cavity mirrors, etc. This in turn may result in an uneven distribution
of the intensity of the radiation over the beam cross section and increase the
divergence. If an electrically controlled mirror is placed inside the
resonator, it is possible to reduce these undesirable effects, influence the
geometry of the output modes, stabilise the output energy, and suppress
fluctuations of the output radiation power.
A typical amplitude w
of deformation of the surface of an active mirror usually does not exceed 5–7
μ, which represents ~0.5λ for infrared CO2 lasers and ~20λ
for excimer lasers. Such strong modulation of the phase in the
ultraviolet part of the spectrum makes it possible to influence significantly
the parameters of the output radiation even when the beam is controlled outside
the resonator. In the case of the intracavity control of the radiation inside
the resonator with a plane mirrors, when the pulses are short, so that the mode
structure does not form in available time, the range of correction wc
can be estimated from the following relationship
where N=t c/L, t - is the pulse duration, L is the length
of the resonator, c - is the velocity of light. The factor N determined the
number of passes of the radiation across the resonator during one pulse. In the
case of our excimer laser (L=1 m, t =30 ns) N is equal to 10, and
consequently, the depth of modulation of the phase was wc~170λ.
This estimation demonstrates the exceptionally great opportunities
for intracavity control of excimer laser radiation by active corrector.
An excimer laser (model
ELI-91, made in USSR) utilizing a mixture of HCl:Xe:Ne=1:10:1000 composition at
a total pressure of 4 atm generated 308 nm pulses of 30 ns duration at
midamplitude with an energy 80 mJ (in the absence of an intracavity telescopic
expander). The laser resonator was formed by a plane-parallel quartz plate and
a nontransmitting 13-electrode controlled bimorph mirror with the aluminum
reflecting coating (Fig.26).
The maximum filling of the
adaptive mirror surface with the radiation due to the discharge in the XeCl
laser was ensured by a quartz telescopic expander (with a magnification 3x).
The distribution of the intensity over the beam cross section was photographed
at a distance of 1 m from exit window of the laser and in the focal plane of a
lens (f=15 cm).
The results of our experiments are presented in Fig.27.
Fig.27. Distribution of the intensity of the radiation across a beam at
the exit from XeCl laser (a, c) and in the far-field zone, obtained for
different control voltages applied to an intracavity adaptive mirror (b, d, e, f)
The structure of the
radiation at the resonator exit and in the far-field zone (i.e., in the focal
plane of the lens), obtained in the absence of control voltages on the mirror
electrodes, is shown on Figs.24a,b . The capabilities of
intracavity control are illustrated by photographs in Figs.27c,d. The
constant voltages applied to the electrodes were selected to form a rectangular
spot on the resonator exit. Deformation of the surface of this controlled
mirror had the strongest influence on the phase of the output radiation. On the
other hand, the experimental results presented on Figs.27c,d demonstrate
that intracavity phase correction could have a direct influence on the
distribution of the intensity of the output radiation obtained from an excimer.
The patterns shown on Figs.27e,f provide a clear demonstration of the feasibility of control of
the spatial structure of the radiation in the focal plane of the lens when
various voltages were applied to the mirror electrodes. The energy of the
pulses was then 30-50 mJ.
demonstrated that the use of an intracavity adaptive optical components in
excimer lasers provides an effective means for controlling the characteristics
of the output radiation and compensating for the aberrations of a laser cavity
as well as laser active media.
The results of our study to
improve the output parameters of various types of lasers by intracavity bimorph
active corrector showed that this way of laser beam correction is rather
efficient and allows to achieve rather promising experimental results. We hope
that this should lead in the near future to the development of laser systems
with basically new capabilities suitable for tackling a number of research,
industrial, and practical tasks.
A.V.Kudryashov, G.A.Kosheleva, S.I.Nazarkin, Yu.F.Suslov, and
V.I.Shmalgauzen, “Adaptive cooled mirror for the resonator of an
industrial laser”, Sov. J. of Quantum Electron. 15, p.888, 1985.
V.S.Golubev, F.V.Lebedev, Engineering
bases of industrial lasers design, Vishaja shkola, Moscow, 1988 (in
A.V.Kudryashov, V.V.Samarkin, “Control of
high power CO2 laser beam by adaptive optical elements”, Opt. Comm.
118, pp.317-322, 1995
H.Haferkamp, H.Schmidt, D.Seebaum,
A.Homburg, “Beam delivery using adaptive optics for material processing
applications with high power CO lasers”, Paper presented at the Int.
Symp. “Optical Tools for Manufacturing and Advanced Automation” Sept,
pp.14-22, 1993, Boston, MA.
S.De Silvestri, V.Magni, O.Svelto, and
G.Valentini, “Lasers with super-gaussian mirrors,” IEEE J.Quantum
Electron. 26, pp.1500-1509, 1990.
C. Pare, P.A. Belanger, “Custom laser resonators using
graded-phase mirrors: circular geometry,” IEEE J.Quantum Electron. 30, pp.1141-1148, 1994.
C.Pare, P.A.Belanger, “Optical resonators with graded
phase mirrors,”(Invited paper), in Laser Resonators, Alexis
Kudryashov, Pierre Galarneau, Editors, Proceedings of SPIE 3267, pp.226-234, 1998.
S. De Silvestri, P.Laporta, V.Magni,
G.Valentini and G.Cerullo, “Comparative analysis of Nd YAG unstable
resonators with super-gaussian variable reflectance mirrors”, Opt.Comm. 77, pp.179-184, 1990.
A.G.Fox, T.Li, “Resonant modes in a maser
interferometer,” The Bell Syst.Tech.J. 40(3), pp.453-488, 1961.
T.Li, “Diffraction loss and selection of
modes in maser resonators with circular mirrors,” The Bell Syst.
Tech.J. 44(5), pp.917-932, 1965.
P.A.Belanger and C.Pare, “Optical resonators using graded phase
mirrors,” Opt.Lett. 16, pp.1057-1059, 1991.
N.Kugler; S.Dong; Q.Lu; H.Weber, “Investigation
of the misalignment sensitivity of a birefringence-compensated two-rod
Nd:YAG laser system”, Appl.Opt. 36(36), pp.9359-9366, 1997.
W.Koechner, Solid-State Laser
Engineering, Springer-Verlag, New York, 1976.
H.P.Kortz, R.Ifflander and H.Weber, “Stability
and beam divergence of multimode lasers with internal variable lenses”, Appl.
Opt. 20, pp.4124-4134, 1981.
W.Koechner, “Absorbed pump power. termal
profile and stresses in a CW pump Nd:YAG crystals”, Appl.Opt. 9, pp.1429-1434, 1970.
K.N.Evtyukhov, B.Zborzhil and L.N.Kaptsov,
“Influence of thermal extraction in active element on the frequency
stability of CW YAG laser radiation”, Izv. Vyssh. Uchebn. Zaved. ser.
Priborostroenie 26(11), pp.91-95, 1983 (in Russian).
U.Wittrock, “High power rod, slab and tube
lasers”, in Solid State Lasers, NATO ASI Series B: Physics, 317, pp.45-66,
Plenum, New York, 1993.
G.M.Zverev and Yu.D.Golyaev, Lasers
on crystals and their application (in Russian), Radio i Svyaz',
D.W.Coutts, D.J.W.Brown, “Formation of
output in copper vapor lasers”, Appl.Opt.34, pp.1502-1512, 1995.
S.A.Gnedoi, A.V.Kudryashov, V.V.Samarkin,
V.P.Yakunin, “The use of an intracavity adaptive mirror in control of the
radiation emmitted from a copper-vapor laser”, Sov.J. of Quantum
Electr. 19, pp.1182-1183, 1989.
A.V.Kudryashov, V.Ya.Panchenko, V.K.Popov, A.Yu.Poroikov,
V.I.Shmal’gauzen, “Control of spatial characteristics of excimer laser
radiation by an intracavity controllyed mirror”, Sov.J. of Quantum. Electr. 18(8), pp.955-956, 1988.