Enhancement of laser performance using an ... - OSA Publishing

Enhancement of laser performance using an intracavity deformable membrane mirror Walter Lubeigt, Gareth Valentine and David Burns Institute of Photonics, University of Strathclyde, 106 Rottenrow, Glasgow G4 0NW, UK [email protected]

Abstract: An intracavity deformable membrane mirror has been successfully used to optimise the brightness of solid-state lasers – a sidepumped Nd3+:YAlO laser where the oscillation of a low-order transverse mode was obtained, and a grazing incidence Nd3+:GdVO4 laser where a brightness increase by an order of magnitude with negligible drop in power was achieved. Several search algorithms were also implemented in the system and compared with respect to intracavity optimisation. ©2008 Optical Society of America OCIS codes: (140.3580) Lasers, solid-state; (140.6810) Thermal Effects; (010.1080) Adaptive Optics.

References and links 1. 2. 3. 4.

5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16.

17.

J. M. Eggleston, T. . Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, “The slab geometry laser. I. Theory,” IEEE J. Quantum Electron. QE-20, 289-301 (1984). W. Koechner, Solid-State Laser Engineering, 5th edition (Springer Series in Optical Sciences, 1999). D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, “Development of high average power picosecond laser systems,” Proc. SPIE 4629, 4629-18 (2002). W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, “Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror,” Opt. Express 10, 550-555 (2002). R.Tyson, Principles of Adaptive Optics, 2nd edition, (Academic Press, 1998). Flexible Optical B.V., PO Box 581, 2600 AN, Delft, the Netherlands, www.okotech.com. U. Wittrock, Y. Buske, and H. M. Heuck, “Adaptive aberration control in laser amplifiers and laser resonators,” Proc. SPIE 4969, 4969-122 (2003). P. N. Marsh, D. Burns, and J. M. Girkin, “Practical implementation of adaptive optics in multiphoton microscopy,” Opt. Express 11, 1123-1130 (2003). P. Welp, Y. Buske, and U. Wittrock, “Intracavity use of adaptive mirrors in Nd:YVO4 and Nd:YAG lasers,” presented at the 4th International Workshop on Adaptive Optics for Industry and Medicine, Muenster, Germany, 19-24th October 2003. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39, 8-3597 (1968). K. F. Man, Genetic Algorithms: concepts and designs, (Springer Series, 1999). S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671680 (1983). “Empirical comparison of stochastic algorithms” in Proceedings of the Second Nordic Workshop on Genetic Algorithms and their Applications, Editor: T. Jarmo, Alander, Finland (1996). DILAS Diodenlaser GmbH, Galileo Galilei-Strasse 10, D-55129 Mainz-Hechtsheim, Germany, www.dilas.de. A. Minassian, B. Thompson, and M.J. Damzen, “Ultrahigh-efficiency TEM00 diode-side-pumped Nd:YVO4 laser,” Appl. Phys. B 76, 341-343 (2003). A. J. Wright , D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 6, 36-44 (2005). N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys. 21, 1087-1092 (1953).

#94569 - $15.00 USD

(C) 2008 OSA

Received 1 Apr 2008; revised 30 Jun 2008; accepted 2 Jul 2008; published 8 Jul 2008

21 July 2008 / Vol. 16, No. 15 / OPTICS EXPRESS 10943

1. Introduction Thermal induced aberrations are the main limitation in solid-state laser when scaling the power [1]. The thermally induced lens degrades the transverse mode profile of the output beam [2]. Thermally induced birefringence can be greatly reduced by careful choice of laser media and only the spherical contribution of this thermal lens can be compensated by careful laser cavity design [3]. Nevertheless, the non-spherical component cannot be compensated in the same manner leading to reduced efficiency and multi-mode oscillation as the heat load increases. Active transverse mode control and optimisation of Nd:YVO4 laser using an intracavity adaptive optics mirror was demonstrated [4]. This optimisation was achieved with a low power end-pumped Nd:YVO4 laser using a hill-climbing algorithm. The use of the latter seriously limits the search power since a hill-climbing algorithm can only ensure the local maximum to be obtained. The use of a more advanced search algorithm is, therefore, required. In this paper, we investigate the transverse mode control of a side pumped Nd:YAlO laser and of a grazing-incidence Nd:GdVO4 laser using an intracavity deformable membrane mirror (DMM) at power level of 15W with a control feedback loop featuring a genetic algorithm. The demonstration of power scaling of this simple and cost-effective system is shown in this paper. First the DMM will be described with an assessment of the feasibility of using it intracavity. Then the optimisation scheme including a description of the different algorithms used will be discussed. Finally, the results will be presented and discussed. 2. Micro-machined deformable membrane mirror Adaptive optic mirrors have been widely used in astronomical and medical imaging [5]. The mirror used is a cost-effective 15mm diameter OKOTECH [6] DMM. It comprised 37 electrostatic actuators arranged in a hexagonal pattern. The frequency response of the mirror was 1 kHz. The silicon nitride membrane was coated with a Cr/Ag layer onto which a subsequent 12 layer dielectric mirror was deposited to provide a high reflectivity at 1064nm (>99.8%). With the maximum voltage applied to all the actuators (240V), the maximum stroke was measured to be 5µm (equivalent to a curvature of ~0.18D). The actuators could be addressed individually via a personal computer using a software package. The membrane can only be ‘pulled’ by the actuators, therefore a pre-bias is required to meet the demand of some applications. The mirror was mounted behind an anti-reflection coated window to environmentally shield the fragile mirror surface and reduce the effects of air currents. Similar mirrors have been used successfully in a range of areas: master-oscillator power amplifier (MOPA) configurations [7], multiphoton microscopy [8]. 3. Assessment of the scalability of the membrane power to high intracavity powers One of the main issues with using a DMM inside a laser resonator is the stability of the membrane under conditions of high power density [9]. To assess this, a side-pumped grazing incidence Nd:GdVO4 laser shown in Fig. 1 was used and a Michelson interferometer (see Fig. 2) was configured such that one arm of the interferometer included the intracavity DMM – the interference pattern produced is then a sensitive measure of any distortions induced in the membrane by the intracavity laser field. The 1% doped, Nd:GdVO4 slab had dimensions 22mm x 5mm x 2mm – the AR-coated (1064nm @ 10o) end faces were wedged at 5.0 degrees to prevent parasitic oscillation. The slab was bonded on its two larger surfaces to a watercooled mount using 0.25mm thick indium foil to ensure good thermal contact. The pump power was delivered by two spatially coupled diode laser bars emitting at 808nm giving a total incident power of 50W. The pump beam was focussed to a 7mm x 0.25mm spot on the crystal. A x3 intracavity telescope was used to provide a 4.5mm diameter spot on the deformable mirror. In this configuration, a R=50% output coupling mirror resulted in 9W of output power.

#94569 - $15.00 USD

(C) 2008 OSA



Fig. 1. Configuration of the grazing-incidence Nd:GdVO 4 laser.

Fig. 2. Configuration of the Michelson interferometer featuring the deformable mirror.

The Michelson interferometer was used to analyse any thermally-induced distortion of the surface of the DMM. The HeNe probe beam was expanded to cover about 70% (~10.5mm) of the total aperture of the DMM, i.e. much larger than the incident intracavity laser beam. During the experiment, the protective window was removed from the DMM to ensure the distortion was solely due to the membrane surface. With an incident power of 18W, corresponding to power density of 115W/cm2 on the membrane, no significant change in the interference pattern obtained from the Michelson interferometer was observed. At this incident power level no thermally induced mirror deformation occurs. This observation was also independent of the voltages applied to the actuators of the DMM – see Figs. 3(c) and 3(d). To increase the incident intracavity power on the membrane, the reflectivity of the laser output coupler was increased to R=99%. Whilst this resulted in a reduced output power of 2W, the average intracavity power was increased considerably to 200W. For all cases, the incident intracavity beam diameter remained unchanged, and so, the resultant power density on the DMM was increased to 1.25kW/cm2 – approximately a x10 increase. Figure 4 details the interference patterns obtained at these elevated power levels for different actuator settings. It is clearly evident here that significant distortion of the membrane occurs at these intracavity power levels – examination of the fringe patterns suggest that >1μm additional deformation is being induced, which, considering the maximum stroke is only a few microns, will cause serious problems in an iterative optimisation scheme [specifically when non-deterministic search algorithms such as the genetic algorithm are deployed – see section 4]. The time constant for thermal equilibrium to be reached by the hot membrane was found to be ~10s, however, a time of >3 minutes were required for the membrane to cool and reestablish its initial shape. During these measurements the beam diameter on the DMM #94569 - $15.00 USD

(C) 2008 OSA



maintained a constant diameter. Even though such low output coupling is inefficient and unlikely to be used in this kind of laser, the data recorded give a useful upper limit to the power handling range of these DMM devices – not limited by damage but by thermally induced membrane distortion. Actuators at 0V Laser off

a

Actuators at 0V Laser on

Actuators at 200V Laser off

b

c


d

2

Fig. 3. Interferometer patterns recorded at 115W/cm with all actuators set to 0V (a) with laser off and (b) with laser on; with all actuators set to 200V (c) with laser off and (d) with laser on.





a b c d Fig. 4. Interferometer patterns recorded at 1.25kW/cm2 with all actuators set to 0V (a) with laser off and (b) with laser on; with all actuators set to 200V (c) with laser off and (d) with laser on.

4. Control loop feedback system To facilitate distortion compensation, and so, brightness control of the laser a closed-loop feedback system was developed, the components of which will now be described. The core component of the iterative optimisation technique was a peak-location algorithm which was driven by a single, simple measurement on the operating state of the laser system. This input was derived from an assessment of the laser output fitness recorded by a sensor and the control program was then configured to maximise this value. The voltages of the actuators of the DMM, determined by the control program, were then configured via a multi-channel, high-voltage, USB addressed digital-to-analog converter (DAC). A schematic of the complete closed-loop optimisation scheme is depicted in Fig. 5. The laser beam quality sensor and the nature of the control algorithm are, of course, the essential components of the optimisation network and will now be described in more detail.

#94569 - $15.00 USD

(C) 2008 OSA



PC + optimisation algorithm + mirror driver

Beam quality sensor

Laser with intracavity AO mirror

Fig. 5. Closed-loop feedback network

4.1 Beam quality sensor An assessment of the quality of the laser output, i.e. its fitness, is an essential input to any optimisation algorithm. In this work two convenient methods were developed: firstly, a laser brightness measure based on a CMOS camera having a software aperture, and secondly, by way of second harmonic generation (SHG). The software aperture-based sensing method used a simple CMOS camera, as described in [4], where the modal output from the laser was assessed by integrating the pixel intensity within a selected region of the recorded camera image of the laser beam profile. The dimensions, location and degree of averaging within this aperture were all user settable to promote optimal performance. In addition, beam centroiding was employed such that the aperture could be automatically re-centred with respect to the laser beam image. Possible beam pointing and alignment issues were therefore eliminated in this assessment mode. An alternative beam fitness assessment method was based on SHG, as it is well known that efficient second harmonic conversion requires a bright pump beam [10]. Furthermore, the SHG efficiency follows a square-law dependence with average laser power. So clearly, the higher the brightness, the greater the SHG. This laser brightness sensor concept based on SHG is shown schematically in Fig. 6. KTP crystal SHG signal for higher M2 M

IR beam

2

Lower M IR beam

SHG signal for lower M2 M

Higher M2 IR beam Fig. 6. Comparison of SHG for two fundamental beams with same power and same size of the incident beam to the lens but different M2 and focusing size.

In practice, the output beam waist on the plane output coupling mirror was relayed onto a 20mm-long KTP crystal using a 45mm focal length lens (see Fig. 7). The infrared light was filtered out allowing the SHG signal to be recorded by a photodiode. Imaging of the beam waist at the flat output mirror ensures consistent SHG values during any laser optimisation procedure. The experimental arrangement of the SHG sensor is shown in Fig. 7 – the interface of the program featuring the user controls for these sensor systems is shown in Fig. 8. This method presented a very straightforward and low-cost way of assessing the brightness of the laser.

#94569 - $15.00 USD

(C) 2008 OSA



output coupler

f = 45mm

HR @ 1064nm

20mm KTP

photodiode

130mm laser output

60mm power meter

Fig. 7. Experimental configuration of the second harmonic generation-based beam quality sensor Optimisation progress

Video aperture control

Elite solution

DAC control parameters

‘Genetic’ parameters

‘Hillclimbing’ parameters

Fig. 8. Graphic user interface for automatic optimisation

4.2 Optimisation algorithms The DMM has 37 actuators to which voltages between 0 and 200V with 1V steps are applied. Thus, the number of possible membrane shapes is 37200, or ~1085. Optimisation to find the best possible solution of such a multi-dimensional problem is therefore rather challenging. Perhaps the simplest, and most obvious, method to deal with this problem is to employ a hillclimbing algorithm [4] – here, each actuator is considered in turn, the voltage varied, and the best value set to each actuator. This algorithm is both straightforward and fast (in practice, less than 2 minutes), however, only a local maximum solution is found, which, in general is dependent on the initial conditions of the system. Given the complexity of the search space it is unlikely that the given result would the best possible and consistent. More advanced algorithms are therefore required. In this work, the genetic algorithm (GA) and the simulated annealing (SA) algorithms were integrated within the control program. Two close variants of the simulated annealing algorithm - the adaptive random search (ARS) and random search (RS) – were also developed. 4.2.1 The genetic algorithm Non-deterministic algorithms such as the GA [11] have been developed which can efficiently find the global solution from highly complex multi-dimensional search spaces. The GA mimics evolution by way of natural selection (i.e. survival of the fittest) as an approach to effectively sample the search space and reveal the best possible solution. For the DMM #94569 - $15.00 USD

(C) 2008 OSA



optimisation, in the terminology of the genetic algorithm, each actuator is defined as a chromosome and a particular mirror shape (i.e. the combination of 37 chromosomes) as an individual. The algorithm begins by the random generation of N membrane shapes - the fitness of each shape is then assessed, and the ‘best-yet’ individual is stored. A second generation of individuals is then generated through a combination of existing individuals – this breeding process, or cross-over, is influenced by the fitness of the parents. These daughter solutions are then allowed to exhibit a (small) degree of genetic mutation to promote new solutions such that the search space can be more efficiently examined. The mutated daughter solutions then become the new parent population from which the next generation will evolve – this process is then repeated. The number of generations, the cross-over and mutation probabilities are set by the user. The full GA loop is shown schematically in Fig. 9 – note that the function which acts to stop the algorithm is included. This stopping criterion is fairly arbitrary – the one employed here stops the search if the best solution found does not change by a preset percentage (e.g. 2%) over 50 generations. We find this a practical device, especially given that system noise is present. Initial population of N DMM shapes Create new population containing 40 DMM shapes including the best solution from the previous population

Measure the fitness of each individual shape

Has the best fitness increased significantly in the last 50 generations? NO

YES

Solution found

Combine DMM shapes according to the specific fitness values allowing for an element of mutation

Fig. 9. Flowchart of the genetic algorithm.

In practice, the initial conditions and the crossover and mutation rates need to be tuned to optimise the time taken for the algorithm to converge. As is typical, the population size is chosen to be approximately the dimensionality of the search space – for the 37-element mirror, a population size of 40 was chosen. The probability of crossover occurring was set to 85% and the mutation probability used was 2% – again, these are fairly typical values [i.e. crossover – high, mutation – low] for the genetic algorithm. In a typical laser optimisation this whole process takes about 15 minutes to converge to a solution. The algorithm therefore samples only ~1200 different shapes in finding the (approximate) global maximum in such a wide space range. Although the GA is more computationally intensive than the hill-climbing algorithm, finding the global best solution is a significant advantage for this optimisation procedure. 4.2.2 The simulated annealing algorithm A simulated annealing algorithm was implemented to the laser control program. This algorithm is based on a Monte-Carlo approach [12] to find solutions of multi-dimensional problems. It is analogous to the physical process of annealing. The algorithm progressively, but slowly, lowers the ‘temperature’ allowing the system to re-configure into a more optimal state. [The concept of temperature in the algorithm is, obviously, abstract, however, it relates

#94569 - $15.00 USD

(C) 2008 OSA



to the size of the allowed perturbation, and the probability of a new state being chosen over an existing 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 system temperature is also used in calculating the probability of accepting a new state having a lower fitness value. This process continues until the system ‘freezes’ and no further changes occur. The SA, therefore, samples the search space in a completely different way (see the flowchart in Fig. 10) than the GA, and, typically returns the optimum result faster [13]. 4.2.3 Random search algorithms The RS and ARS algorithms are derivatives of the SA. Here, only positive fitness changes are accepted (see Fig. 10). The ARS involves the notion of temperature in a similar way as the SA, and this has the effect of reducing the magnitude of the search as the algorithm progresses. In the RS algorithm, the maximum perturbation is fixed and made equal to the magnitude of each axis of the search space. Therefore, the RS continues to search the full bounds of the search space for the duration of the optimisation, whereas the ARS continually narrows its focus – a property that can often lead to undesirable results. Initial DMM shape

Select actuator

Change actuator value by a random perturbation (if SA or ARS, the perturbation level varies depending on temperature – see text)

Has fitness value improved? YES Select next actuator

Accept change

NO If SA, can accept change at a probability proportional to the current temperature If RS or ARS, deny change

Has the fitness value improved significantly in the last 50 iterations? YES

NO Solution found

Fig. 10. Flowchart of the ARS, RS and SA algorithms.

4.3 Experimental laser cavity platforms To fully investigate the use of an intracavity deformable mirror to optimise the modal performance of an all-solid-state laser, several laser cavities were configured: a transversallypumped Nd:YAlO laser, shown in Fig. 11, and a side-pumped, grazing-incidence Nd:GdVO4 resonator shown in Fig. 12. It is noted that these laser cavities were simply test-beds used to elucidate the central topic to this paper, AO-based laser optimisation techniques.

#94569 - $15.00 USD

(C) 2008 OSA



4.3.1 Side-pumped Nd:YAlO laser Here, the gain medium used was a Nd:YAlO slab (15mm x 5mm x 1.5mm) with AR-coated end faces at 1079nm. It was pumped by an 8-bar DILAS [14] diode laser stack delivering up to 100W output power at 805nm. Using focussing optics, a 1.67mm x 0.3mm pumped zone on the side of the crystal was defined. Like previously, the Nd:YAlO slab was coupled to a water-cooled mount via the 15mm x 5mm faces. The absorbed pump power was measured at 35W. A x10 intracavity telescope was used to ensure a large (~12mm diameter) spot on the deformable mirror. The effect of the deformable mirror on laser cavity operation was therefore maximised as the majority of the actuators could interact with the intracavity beam. When the laser was configured with a R=80% output coupling mirror, the laser output was measured to be 6W.

Fig. 11. Configuration of the Nd:YAlO laser

4.3.2 Grazing-incidence Nd:GdVO4 laser The grazing-incidence configuration has potential for very efficient, high-power systems. TEM00 operation of 23W with an efficiency of 68% have been demonstrated in a diodepumped grazing-incidence Nd:YVO4 laser [15]. Crucial to the operation of this laser is a total internal reflection on the pump surface of the Nd:GdVO4 crystal. The bulge of this reflecting surface and high asymmetric thermal lensing produced represents a limiting factor to future power scaling of such lasers. Thus, this set-up is an excellent test-bed for laser brightness optimisation using an intracavity deformable mirror. The laser cavity, the gain medium and the pump configuration have already been described in section 3, however, the magnification of the intracavity telescope was changed. Here, a x6 intracavity telescope was chosen to promote a larger, ~8mm diameter, spot on the deformable mirror, such that, the intracavity beam better matches the transducer array dimensions. In this arrangement, a R=50% output coupler was found to optimise the laser output power at ~15W.

Fig. 12. Configuration of the grazing-incidence Nd:GdVO4 laser

#94569 - $15.00 USD

(C) 2008 OSA



5. Beam quality optimisation of solid-state lasers An optimisation routine was performed based on the genetic algorithm on the two test-bed lasers described in section 4. The software aperture technique was used as the beam quality sensor for the optimisation of the Nd:YAlO laser. Initially, the laser was optimally aligned with the DMM actuators at the middle of their voltage range (120V) and the resultant multimode output, having a power of 6W, is shown as Fig. 13(a). After optimisation, which lasted ~5 minutes, a near single transverse mode intensity profile (M2