Intra-cavity adaptive optics control of lasers
W. Lubeigt, G.J. Valentine and D. Burns
Institute of Photonics, University of Strathclyde, 106 Rottenrow, Glasgow G4 0NW
walter.lubeigt@strath.ac.uk
Abstract. An intra-cavity adaptive optics system has been used to optimise and control the
performance of a solid-state laser. The control program employs a mixed algorithm approach
which has been optimised for efficiency. Transient optimisation has also been investigated to
reduce the time to full brightness at laser turn-on.
1. Introduction
Thermally induced aberrations are one of the main impediments to be overcome in developing
high-power solid-state lasers [1]. These aberrations, induced by the substantial heat loading, can
severely limit the transverse mode quality in high average power laser systems [2]. Unfortunately,
there is no simple, effective means of compensating against the effects of the non-spherical component
of the induced thermal lens. The goal of this work was to investigate the potential of using intra-cavity
adaptive optics (AO) techniques as a general technique for thermal aberration correction over a wide
operating range, and so, extend the potential of high-power solid state lasers. Another potential area
for the exploitation of AO control of lasers is during the transient phase immediately following turn-on
of the laser. Here, the deformable membrane mirror (DMM) can be used to reduce the time for the
laser to reach both its maximum power level and full brightness.
A computer-controlled, self-optimisation, AO feedback system was developed to enhance the
brightness of various test-bed lasers [3]. The basic control loop deployed consisted of:
 a laser featuring an intra-cavity DMM
 a beam quality sensor to determine the laser performance, or ‘fitness value’
 a personal computer hosting the control software based around an optimisation algorithm that
searches for the optimal shape of the intra-cavity DMM
 a high voltage, multi-channel digital to analog conversion unit to interface the laser to the
optimisation scheme
In this paper, we describe the elements of the control loop necessary to exploit adaptive laser
control. In section 3, a description of the Nd:YLF laser system is given followed by a discussion of
transient control investigations.
2. The Control Loop
A computer-controlled feedback system was designed to automatically assess and optimise the
brightness of the laser. The key components of the loop were:
2.1. SHG-based brightness sensor
One of the critical elements in any optimisation scheme is the determination of the laser performance
as the control process develops. For the case considered here, - brightness enhancement -a convenient
measure of the output brightness laser is therefore required. Brightness measurements are not, in
general, straight-forward, however, for AO control schemes only a qualitative measurement is
required. In other words, an absolute measure of brightness is not required; the fitness sensor required
only needs to adequately compare two laser states. A prospective real-time brightness sensor can then
be configured based around a simple second-harmonic generation crystal and a suitable photodiode.
It can be shown that the brightness of a laser beam can be defined simply in terms of the beam
quality parameters, Mx2 and My2, and the power, P:
B
P
M M y2 2
2
x
Where P is the average power and Mx2 and My2 are the corresponding beam quality factors in the x and
y directions respectively.
It is well known that the efficiency of driving nonlinear optical effects generally improves as the
beam power and quality increase (at least for volumetric effects). A SHG crystal was therefore
configured to derive the brightness-based fitness parameter of the laser control network. For the Ndbased 1064nm laser used in these studies a KTP crystal was the most appropriate choice. The
dependence of the SHG conversion efficiency on the beam quality parameter M2 for such a
configuration was calculated and is shown in figure 1(a).
conversion efficiency in %
0.25
0.2
To power
meter
0.15
F=45mm
Laser
output
0.1
0.05
20mm KTP
Harmonic
separato
separator
r
To photodetector
0
1
6
11
16
21
26
M2
(a)
(b)
Fig. 1 (a) Influence of the beam-quality parameter on SHG conversion efficiency, (b) schematic of the
brightness sensor
The SHG conversion efficiency is strongly dependent on the M2 for values of less than about 15,
however, for higher M2 values the conversion efficiency changes at a much reduced rate. It is clear
then that SHG is a sensitive measure of laser beam quality, and becomes much more so as the laser
approaches its ultimate performance.
Additionally, as is well known, the second harmonic power, P2ω, is also quadratically dependent on
the incident fundamental power, Pω [4] via the relation:
P2   sh P22
where γsh is the SHG conversion efficiency.
Since the SHG power is quadratically dependent of the fundamental power and that the SHG
conversion efficiency is strongly dependent on the beam quality of the fundamental beam, a brightness
assessment based on SHG should be an efficient brightness sensing technique. This sensor system
does not require any electronics and so provides a significant improvement in simplicity and cost of
the system. A schematic of the SHG-based sensor is shown in figure 1(b). The limitation of reduced
sensitivity to beam quality at high M2 values is, of course, a remaining issue, however, in our studies
this was not an obvious shortcoming.
2.2. Optimisation algorithms
An optimisation algorithm was used to progress towards the optimal final shape of the DMM using the
fitness values returned from each iteration cycle. Since the membrane was controlled by 37 electrostatic actuators whose voltage value could be up to 200V, more than 1085 different combinations could
be applied. Therefore, with such a large search space and the desire for fast optimisation, the choice of
the algorithm used was fundamental.
The most straight-forward algorithm deployed in this work was a modified hill-climbing algorithm
(MHC) whose principal weakness was to only locate a local maximum. This inadequacy led to the
development and implementation of a range of more advanced non-deterministic algorithms.
2.2.1. Genetic algorithm
A stochastic algorithm called the Genetic Algorithm (GA) [5] was developed in order to ensure that
the global maximum is reached. It is an evolutionary algorithm because its procedure evolves during
its running. The GA is based on natural selection and follows the principle of the survival of the fittest.
The use of the GA ensures that the global maximum of the fitness parameter is found.
2.2.2. Simulated annealing, random search and adaptive random search
Simulated annealing employs a Monte-Carlo approach to find solutions of multi-variate/multidimensional problems [6]. As the name suggests this algorithm is analogous to the physical process of
annealing, i.e. heating followed by slow cooling to eradicate defects and dislocations to improve the
crystalline structure of solids. The algorithm progressively, but slowly, lowers the ‘temperature’ of the
system allowing the system to re-configure itself to a more optimal state. At ‘high temperatures’, the
system is allowed to change by a large extent such that the whole solution space can be searched,
whereas as the temperature lowers, only progressively smaller changes are allowed. The temperature
concept is also used to calculate the probability of acceptance of a change resulting in a lower fitness
value. This process continues until the system ‘freezes’ and no further changes occur.
Random search and adaptive random search algorithms were also used extensively. These variants
of the simulated annealing algorithm have proved to be efficient and effective in practice, however,
they do not always return the global maximum solution.
2.2.3. Algorithm tailoring
A few laser specific issues - long-term stability, noise, and modal collapse - invoke the use of
somewhat modified versions of the above algorithms. The control software was modified in order deal
with these issues along with the facility to enhance the search efficiency by employing a mixture of
algorithms, for example, an initial coarse stage (e.g. GA) followed by a refinement stage such as
MHC.
2.3. Nd:YLF laser cavity
A laser cavity was configured based on a diode-pumped Nd:YLF module from Cutting Edge
Optronics. It consisted of a 63mm long and 3mm diameter Nd:YLF rod evenly pumped by a set of
nine diode laser arrays. When installed in a basic 2-mirror laser cavity, 25W highly multimode
oscillation resulted. The natural birefringence of the Nd:YLF crystal effectively eliminates the
thermally induced birefringence from degrading the laser performance. The gross spherical thermally
induced lens was experimentally measured using a probe He-Ne laser and estimated to be f = -3m and
f = -1m for the tangential and sagittal planes respectively.
DMM
63mm long and 3mm
diameter rod Nd:YLF
ROC=1m
Flat 15% output coupler
Figure 2 Nd:YLF laser cavity featuring the DMM
The output beam produced from the laser cavity was highly multi transverse mode. It was therefore
decided to minimize the M2 by modifying the laser cavity to maximise the fundamental mode size in
the gain medium. The subsequent laser cavity featuring the intra-cavity DMM shown in figure 2,
produced 11W output power with a low order transverse spatial mode.
3. Transient optimisation
The aim of this study was to investigate the potential of controlling the laser output during the
transient thermal regime at the ‘turn-on’ of the laser. The ‘turn-on’ time is defined here as the time
taken for the laser to reach a stable output where its power and/or brightness are optimal. This point is
equivalent to the time necessary for the laser to reach thermal equilibrium as described in figure 3(a).
The objective of the investigation is therefore to force the laser to evolve to its brightest state in the
minimum time, tf, using adaptive control.
Brightness
Brightness
Without AO
With AO
Time
tf
a
Δt
2Δt
3Δt
tf
Time
4Δt
b
Figure 3 (a) Evolution of the laser brightness with and without AO control, and (b) the dissection of the
thermal build-up time into several sequential Δt segments
3.1. Optimisation strategy
For transient optimisation, it was decided to segment the thermal build-up time into several sections
(or periods of Δt as shown in figure 3(b)). The number of segments can be arbitrarily chosen, however,
the width of each Δt should reflect a timescale over which thermal aberrations are minimal. The
problem can now be solved by finding the optimum shape of the DMM within each segment such that
the brightness is maximised. When the sequence of mirror shapes is known then they can be applied in
turn at the appropriate time after laser turn-on by way of a look-up table.
The first step is therefore to find the adequate mirror shape for each Δt, and the basic algorithm for
this process is described in figure 4(a). The starting mirror shape is first applied, the laser is turned on.
After a delay of Δt, a mirror shape is applied according to the optimisation algorithm used, and the
fitness is then instantly measured and recorded. The laser is then turned off and the process applied
repeatedly until the mirror shape giving the highest brightness is obtained by the search algorithm.
A similar process is then applied to obtain the best mirror shape at t=2Δt (see figure 4(b)). Here, the
starting mirror shape is applied, the laser is turned on, and after a delay of Δt, the optimum mirror
shape found earlier is applied. A process similar is then used to find the optimum mirror shape at time
2Δt. With every repetition used to find the new optimum shape at 2Δt the previously found optimal
values are applied at the appropriate time. In this way, a table of optimal values for each segment of
time is found, i.e. to find the optimal value at time t=nΔt, each previous optimal value must be known
(and applied in turn).
Apply starting
mirror shape
Laser on
at Δt, apply mirror shape
according to the algorithm
Laser off
Measure and record fitness
instantly
Apply starting
mirror shape
Laser on
at Δt, apply the adequate
mirror shape
Laser off
Measure and
record fitness
instantly
at 2Δt, apply mirror shape
according to the algorithm
a
b
Figure 4 (a) Search for the adequate membrane shape for t=Δt, and (b) search for the adequate
membrane shape for t=2 Δt
With respect to potential scenarios where transient optimisation may be relevant, two cases are
obvious:
 Case 1 – directly after the pump source to the laser is switched on
 Case 2 – after an intra-cavity blocker is removed under conditions of constant pumping
3.1.1. Measurement of the thermal build-up time
The fitness was measured using a simple power-in-a-bucket measurement, using a 100μm diameter
pinhole and photodiode to provide the laser’s operational fitness value. A chopper was inserted in the
laser cavity in order to create the necessary conditions for case 2, and the thermal build-up time was
measured to be 5ms. The fast build-up was to be expected in this case as the only contribution to the
temperature change in the laser rod was that associated with the power extracted as useful laser output.
As the output power is modest compared to the pumping power the temperature variation is small, and
so, the transient associated with re-establishing thermal equilibrium is rapid.
The thermal build-up time was also measured for the case 1. The power supply to the laser module
was modified in order to allow the intensity to change from no intensity to a maximum value in 24ms.
The thermal build-up as measured at about 15s.
The large thermal build-up time for case 1 can be explained by the large temperature change
between the lasing (i.e. pump on) and non-lasing (pump off) state. It is noted that the transient
response of the laser output associated with the thermalisation within the laser rod could vary
significantly (from 4s to 15s) according to the specific pumping and alignment conditions.
The response of the control program i.e. the time taken for a full iteration was reduced to 12ms. It
was therefore decided to concentrate on case 1 as this represents a more real-world requirement for
high power/energy laser systems.
3.1.2. Results and observation
The initial attempts for the transient optimisation were performed on the laser cavity shown in figure 3
which had a 15s thermal build-up time. The value for Δt was 3s. The frequency of the laser operation
was kept at 25mHz to ensure the steady state temperature to be reached. Several optimisations were
undertaken, however, only marginal improvement in the brightness value were recorded after Δt=3s.
In this system the thermal lens varies from a negligible value (i.e. the laser is unpumped) to a state
where the thermally induced lens has tangential and sagittal focal lengths of f=-3m and f=-1m
respectively. This then leads to a considerable reconfiguration of the laser cavity, as evidenced by an
ABCD matrix analysis (see later). This analysis also makes clear that the DMM used here does not
possess sufficient stroke to compensate for the induced aberrations. So, in the presence of the large
thermal lens changes, associated with laser turn-on, another technique is required to maintain mode
control and stability.
Flat mirror
Lens
Translation
63mm long Nd:YLF rod
ROC=1m
Flat 15% output coupler
Figure 5 Nd:YLF laser cavity featuring intra-cavity active optics
The ABCD matrix-based approach was used to predict the size of the fundamental mode of the
cavity shown in figure 5. This laser cavity is identical to that used previously apart from the inclusion
of an intra-cavity lens. In this configuration, it was observed that a translation of the end-mirror could
be used to compensate for the first-order thermal lensing associated with the turn-on of our Nd:YLF
laser. With no pumping, the beam radius within the middle of the laser rod is 731μm in both sagittal
and tangential planes. Using the measured values for the thermally induced lensing, it was found that a
4mm translation of the intra-cavity lens resulted in a beam radius of 703μm and 755μm for the
tangential and sagittal planes respectively. The mode volume for the cold and hot cavities can
therefore be made approximately equal by the lens motion. It is clear that by controlling the position
of, in this example, an intra-cavity lens, that the thermal transients associated with laser turn-on should
be controllable. Higher-order distortion control would then be implemented via the DMM as
demonstrated in our steady-state studies. Further investigations are currently underway to assess this
technique.
4. Conclusion
The work described in this report was concerned with the automatic control of a solid-state laser using
an intra-cavity DMM. A closed-loop control system was developed to compensate for the thermallyinduced lens responsible for degradation of the beam quality and efficiency of the laser output.
Investigations on the potential for transient optimisation were also undertaken on a Nd:YLF laser.
Here, the DMM was found to lack sufficient stroke to fully compensate for the variation in the thermal
lensing relating to laser turn-on. It was found, however, that the use of an active optics technique
should allow full temporal thermal distortion compensation.
5. References
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[2] W. Koechner, Solid-State Laser Engineering, 5th edition (Springer Series in Optical Sciences,
1999)
[3] W. Lubeigt, G. Valentine, and D. Burns, Proceedings of the 5th International Workshop on
Adaptive Optics for Industry and Medicine (Springer Proceedings in Physics, New York,
2006).
[4] W. J. Kozlovsky, C. D. Nabors and R. L. Byer, “Efficient second harmonic generation of a
diode-laser-pumped CW Nd:YAG laser using monolithic MgO:LiNbO3 external resonant
cavities,” IEEE J. Q. Electron. 24 (6), pp. 913-919, 1988
[5]
[6]
K.F. Man, Genetic Algorithm: Concept and Designs, Springer Series, 1999
S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, “Optimization by simulated annealing,” Science
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