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Several adaptive-optics techniques, based on the active modification of the optical properties of the laser cavity, were used to significantly reduce the time-to-full-brightness of solid-state lasers. Resonator re-configuration was achieved using a mechanical translation stage and both multi- and single-element deformable bimorph mirrors. Using these techniques the effects of thermally induced distortion in Nd:YLF and Nd:YAG lasers can be minimized and the warm-up time reduced by a factor of 3–6.
©2009 Optical Society of America
1. Introduction
At the turn-on of a solid-state laser, the build-up of heat within the laser crystal prevents the maximum brightness from being obtained until a thermal equilibrium state is reached. As the laser is typically aligned with reference to the hot state, then in the transient turn-on phase, the laser characteristics, specifically the brightness, is non-optimal. For some applications, and particularly for military use, the time taken to reach full brightness is a critical parameter and considered a major limitation in existing systems. This time, governed by the evolution of the temperature distribution within the gain medium, can vary greatly depending on parameters such as the pumping and cooling arrangement, the details of the laser cavity configuration, and, the nature of the gain medium. A characteristic time – the time-to-full-brightness (TTFB) – defined as the time taken to reach the hot equilibrium state can be in the order of a few seconds for typical Nd-based laser systems. However, for any given laser configuration the TTFB is consistent and reproducible.
The use of adaptive optics components within laser resonators has been shown to be effective in compensating for thermally-induced aberrations; however, this has largely concentrated on steady-state control of the laser. Notably, Moshe et al obtained a zero warm-up time by using a movable lens/mirror combination inside the laser cavity [1]. This system was effective, however, higher-order thermal lens correction, responsible for the reduction in efficiency and brightness, was not possible [2]. The intra-cavity use of deformable mirrors (particularly bimorph mirrors [3,4]) has the potential to control the laser output beam [5]. Here, we report the use of a new type of large-stroke deformable bimorph mirror in reducing the TTFB in a range of Nd-based lasers. These bimorph mirrors - considerably more rugged than their deformable membrane counterparts - have been developed by BAE Systems ATC [6]. Mirrors composed of an array of transducers to promote a complex mirror shape, or, a single actuator device providing only defocus correction are used here. The active aperture of these mirrors has a diameter of 18mm. A 0.3mm thick front layer of SiC is deposited on top of a 0.2mm thick PZT disk. This SiC front layer can be coated in order to achieve the high reflectivities (>99%) required for intra-cavity use.
Previously, a method to automatically enhance the brightness of a Nd:GdVO4 laser [7,8] using an intra-cavity deformable membrane mirror (DMM) from [9], a brightness sensor and a pc-based control algorithm has been developed. This system resulted in a brightness enhancement by an order of magnitude [8] and could automatically address subtle changes in operating conditions such as alignment and temperature variations. However, the iterative control scheme used resulted in an optimisation time on the order of tens of seconds, or more. Such a scheme is therefore limited to steady-state optimisation of laser performance and not relevant for fast TTFB laser control. Additionally, the stroke of the DMM (maximum ~5µm) is, in general, inadequate to fully compensate for the large thermal lens variations at the turn-on of the laser.
A simple look-up table approach, based on applying pre-determined mirror transducer voltages as time progresses, is one way to ensure that the control system efficiently compensates for the rapidly changing thermal lens. These values should reflect the nature of the laser cavity elements (their position, focal length etc) such that they can be changed during the transient phase to ensure that the size of the fundamental mode in the gain medium remains constant. In this way, the laser mode can be stabilised even though the laser rod exhibits a largely varying lens. Therefore, a thorough thermal lens study must be performed in order to calculate the adequate pre-determined values for the mirror curvature. Therefore, using a multi-element deformable mirror to reduce the warm-up time enables both the transient and steady-state optimisations to be successively performed on the same laser.
In the first instance, a test laser platform based on a 63mm long side-pumped Nd:YLF rod was configured. An analysis of the properties of the induced thermal lens throughout the transient phase was first undertaken using finite element modelling in order to calculate the look-up table values. To test the viability of the concept, a movable cavity mirror mounted on a mechanical translation stage was configured to reduce the TTFB. A similar experiment using a multi-channel deformable mirror was also performed. Finally, a single-actuator deformable mirror was used to control the TTFB of an end-pumped Nd:YAG laser.
Section 2 introduces the transient optimisation strategy undertaken including an analysis of the pump-induced thermal lensing in the Nd:YLF rod. Section 3 describes the experimental work using the mechanical translation stage, and the large-stroke multi-actuator deformable mirror. Finally, section 4 will present the transient optimisation of a Nd:YAG laser using a single-actuator deformable mirror.
2. Control strategy
The non-uniform temperature distribution within the laser rod resulting from pumping leads, as a consequence of the temperature dependence of the refractive index, to the production of a thermally-induced lens [10]. This thermal lens significantly modifies the optical properties of the laser resonator and therefore, one method of reducing the TTFB of the laser is to correspondingly adapt the properties of the optical resonator during the transient turn-on period. To establish the necessary changes, a study of the thermal lens at steady-state in the gain medium must be undertaken - in this way, the look-up table correction value can be obtained.
Such a measurement can be undertaken by observing the changes made to a probe beam, however, finite element modelling can be a powerful tool in revealing both the aberrations and the time dependence of the induced lensing. In the following sub-sections a study of the thermal lens will be detailed; direct thermal lens measurement will be reported; and, the results of finite element analysis revealing the transient properties of the induced lens will be described.
2.1 Thermal lens study
The test laser system consisted of a commercially-available Nd:YLF module from CEO [11] based on a 63mm long, 3mm diameter, a-cut, 0.9% Nd-doped rod. The rod is pumped by three groups of three diode laser bars resulting in a total pump power of 180W. The rod was water-cooled on its barrel surface. Using the finite-element analysis model native to the commercial software package LASCAD [12], the pump deposition and temperature distribution within the gain medium could be obtained and are displayed in Fig. 1. The Nd:YLF parameters used in the model correspond to the case of a Nd:YLF rod cut along the a-axis emitting light polarised along the c-axis (i.e. π-polarisation) and are given in Table 1. It is immediately obvious that the pumping configuration results in an almost uniform pump deposition, with this being encouraged by retro-reflection of unabsorbed pump light back into the rod.
Table 1. The Nd:YLF parameters used in the finite-element analysis
Using the calculated temperature distribution, an approximation of the resulting focal length of the thermal lens could be obtained: the average temperature along the longitudinal axis (z in Fig. 1) of both x and y axes were used and the change in refractive index leading to the thermal lens was calculated. In this way, the focal lengths obtained from these data were -2.1m and -1m for the x and y axes respectively (N.B. these axes are parallel and perpendicular to the crystal c-axis respectively). The maximum displacement of the material along z-axis was found to be around 1.6µm, and so the bulge at the rod ends can be neglected.
Fig. 1. Temperature distribution in the rod (a), pump deposition (b) and temperature (c) distributions in the cross section located at the centre of the rod
2.2 Experimental measurement of the thermal lens
To experimentally validate the calculation described in the previous section, a 1064nm Nd:YAG probe laser was used to measure the real thermal lens in the Nd:YLF rod under steady-state pumping at the maximum pump power available. The probe beam was collimated and directed through the laser rod as shown in Fig. 2. Since Nd:YLF is a naturally birefringent crystal, the probe beam was polarised in order to obtain the focal lengths of both the π and σ polarisations.
As expected, for both polarisations, the thermal lens was found to be cylindrical. For light polarised along the c-axis of the YLF rod (i.e. the π-polarisation), the measured focal length was -0.7m perpendicular to the c-axis and -2.1m parallel to the c-axis.
For incident light polarised perpendicular to the c-axis of the rod (the σ-polarisation) the measured focal lengths were -5m and +7m perpendicular and parallel to the c-axis of the rod respectively. [In Nd:YLF, π- and σ-polarisations correspond to laser oscillation at 1047 and 1053nm respectively.] The cylindricity in the thermal lens leads to astigmatism which can be compensated through cavity design, however, this is more challenging than in the case of circularly symmetric deformations as would be the case with, say, Nd:YAG.
In further experiments the laser was configured to operate on the π-polarisation at 1047nm, this allows an evaluation of the concept of using an active element to compensate for a significant, but rapidly varying thermal lens. The focal length values of -0.7 and -2.1m were used to populate the look-up table required for transient optimisation - these measured values agree well with our modelled values from section 2.1 but more accurately reflect the real system used in the experiments.
2.3 Transient thermal lens
Since the object of this study was to determine a technique to reduce the TTFB of the laser, it is important to assess the temperature build-up within the gain medium leading to the establishment of the steady-state thermal lens. Using the FEA-based software (Comsol Multiphysics [13]), the time dependence of the temperature at the centre of the rod was calculated and is shown in Fig. 3. The model used a 2.5 second duration square-shaped input pump having a power of 180W.
The maximum temperature increase obtained of just over 10K evaluated from the model was consistent with that measured previously using the LASCAD software. From this time dependent model, it can clearly be seen that the majority (>90%) of the temperature rise occurs within the first 500ms, the temperature reaching the steady-state within approximately 1.2s. The transient optimisation scheme must then track the thermal lens changes over this timescale – further evidence that iterative optimisation methods are inappropriate in this situation. Furthermore, ~1.5 second after the pump pulse is turned off, the temperature within the laser rod cools to the background level. This timescale for rod cooling was therefore much faster than the time between consecutive pump pulses, and so, it was assured that the rod had fully recovered between pump pulses.
3. Transient optimisation system
The test laser platform was configured around the Nd:YLF laser unit described in the previous section. It was ensured that laser oscillations always occurred on the π-polarisation (i.e. at 1047nm). With the values for the focal length (-0.7m perpendicular to the c-axis and -2.1m parallel to the c-axis) and the duration (>1s) of the thermal lens occurring in the gain medium, the challenge is to track the variation using an intra-cavity adaptive optic element. By actively re-configuring the optical resonator, the size of the fundamental mode within the gain medium can be maintained during the turn-on of the laser. To facilitate this, three different elements were used: a mechanical translation stage, a large-stroke multi-element deformable mirror, and, a large-stroke single-element deformable mirror. In all cases, a look-up table was calculated with reference to the previously measured final value of the thermal lens. A description of these investigations is given in the following sections – 3.1, 3.2 and 4.
3.1 Transient optimisation using a mechanical translation stage
A basic 2-mirror Nd:YLF laser was constructed where the output coupler was mounted on a mechanical translation stage – see schematic shown in Fig. 4. To assess the feasibility of transient optimisation, a simple technique based on the compensation of the first order component of the thermal lens was used and the laser cavity designed accordingly. Here the distance, d, between the output coupler and the laser crystal is varied such that the fundamental mode size within the laser rod remains constant over time. The initial (cold) and final (hot) values of d were calculated using the ray-matrix software Winlase [14] and chosen to avoid any beam ellipticity induced by the astigmatic nature of the thermal lens. In this analysis, attention was given in maintaining high brightness operation of the laser, and to this end, the fundamental mode within the gain medium was made relatively large (~550µm with d=380mm). In practice, to ensure single transverse mode oscillation, the incorporation of an aperture was required. The resulting laser output was then single transverse mode at a power of ~6.5W. For the cold cavity, a plot of the fundamental transverse mode was calculated and is shown as Fig. 5(a).
A similar plot, taking into account the full thermal lens and an increased distance d, is shown in Fig. 5(b). From these data, at d=353mm, the fundamental mode radius was 562µm for the cold cavity, while, at d=386mm, mode radius is 540µm in the π-plane and 546µm in the σ-plane when the thermal lens is included. It is therefore apparent that a 33mm translation of the output coupler will ensure that both laser configurations have effectively the same beam parameters within the rod at the extremes of the thermal lens. The 3% difference in the calculated beam sizes lies within the accuracy of the thermal lens measurement (+/- 10%). Table 2 shows the variation of the mode size as function of d and the focal length of the thermal lens. From Table 2 and Fig. 5, it is clear that the beam size differs in both planes due to the cylindricity of the thermal lens induced in the Nd:YLF rod. This changes in the beam size also becomes more significant as the thermal lens increases.
Fig. 4. Test-bed laser cavity. The π plane is in the plane of the figure whereas the σ plane is perpendicular to the plane of the figure.
Fig. 5. Fundamental mode radius along the laser cavity (a) for the cold cavity (d=353mm) and (b) with the maximum thermal lens (d=386mm).
Table 2. Fundamental mode radius as a function of cavity length and focal length of the thermal lens
The output coupler stage [15] was addressed by a PC-based control program. The temperature dependence within the laser rod shown in Fig. 3, was used in conjunction with the optimal values of d to control the speed of the stage during the turn-on of the laser. The stage velocity profile should then mirror the time dependence of the thermal lens. However, in practice, due to the rapid turn-on of the laser, varying the stage speed to exactly match optimum profile was not possible, and so, the translation stage was set to its maximum velocity (~10cm/s) to provide appropriate optimisation.
Figure 6 shows the transverse intensity distribution of the laser output during the laser turn-on when (a) the mirror is fixed at d=353mm and (b) at d=386mm and (c) when the output coupler is moved from d=353mm to d=386mm. In the case of d=353mm, the output beam profiles quickly builds up to a single mode before degrading after about 0.3s into multi-transverse mode oscillation. This degradation is due to the decrease of the laser fundamental mode size within the gain medium as a consequence of the induced thermal lens. In the case of d=386mm, single transverse mode is maintained throughout, however, the full beam beam power is only obtained after ~0.4s at which the fundamental mode size reduces to the optimum value. For the case of the translating output coupler, a much better compromise results: the rapid high brightness state (typified by d=353mm) appears instantly and this is maintained over the whole transient turn-on period. The TTFB was then reduced from ~0.5s to below 0.1s. Some degree of astigmatism is evident, specifically around t~0.25s, due to the cylindricity of the thermal lens. Using an isotropic crystal such as Nd:YAG would, of course, eliminate this effect.
Fig. 6. Instantaneous transverse intensity distributions as a function of time after laser turn-on for (a) d=353mm, (b) d=386mm and (c) the output coupler moving at maximum speed from d=353mm to d=386mm.
Another variation of the laser cavity was configured as shown in Fig. 7. Using this folded cavity allowed the speed of the mirror translation to be effectively doubled and the required translation reduced to Δd~15mm. To represent output brightness, the intensity distribution of the output laser beam was apertured through a pinhole before being recorded by a photodiode. This measure of on-axis power gives a reasonable estimate of the output beam quality as it effectively discriminates between the fundamental laser mode and higher-order modes having a larger fraction of off-axis power. Again, the resulting profiles at the laser turn-on for the 3 different cases (fixed mirror optimised for (a) the cold cavity, (b) the full extent of the thermal lens, and (c) the moving compensating mirror) are shown in Fig. 8. The intensity recorded by the photodiode in Fig. 8(a), initially peaks, then reduces by about 20% before settling to a steady state after ~800ms. This is in contrast to the laser turn-on brightness profile of Fig. 8(b) which is characterised by a steady increase until at ~200ms when an equilibrium state is obtained. Finally, for the case of the translating mirror, the intensity remains essentially consistent throughout the full laser turn-on period. There is however, a slight discontinuity around t=200ms due to the rapid deceleration as the moving mirror comes to rest – this may possibly be eliminated by appropriate damping of the mirror/translation stage assembly.
Fig. 7. Folded laser cavity [N.B. the tangential plane is now along the σ-axis while the sagittal plane is along the π-axis]
Fig. 8. On-axis output power measured by a pinhole/photodiode arrangement for (a).d=170mm, (b) d=185mm and, (c) moving mirror laser
In conclusion, the moving method successfully reduced the TTFB of a Nd:YLF laser by approximately a factor of 5. Significant limitations were due, in this case, to the inability to compensate the astigmatism induced by the difference in thermal lens strength between the sagittal and tangential planes. Additionally, the precise velocity profile of the mechanical translation stage was found to be difficult to implement using the current apparatus. Using a variable speed during the optimisation (i.e. fast in the initial phase and slower for the final part) should increase the quality of the optimisation, however, even in the simple case used here, significant improvement was observed
3.2 Transient optimisation using a large stroke multi-element deformable mirror
With the transient optimisation strategy based on maintaining a constant mode radius within the gain medium in the presence of a varying thermal lens proving successful, the moving mirror was replaced by an intracavity deformable mirror to further optimise the concept. The deformable mirror used was an 18mm diameter bimorph device, shown in Fig. 9(a), developed by BAE Systems ATC and featured 31 actuators and a 20µm maximum stroke – equivalent to a convex mirror of -1.67m radius of curvature (ROC). The mirror could also produce a concave curvature of ~10m. To ensure a high reflectivity the mirror was coated with chrome-gold – the reflectivity will, of course, be improved by applying a high reflectivity multi-layer dielectric stack.
The same strategy used in the previous section to reduce the TTFB of the 1.5W Nd:YLF laser shown Fig. 10 was employed. The laser was built around the Nd:YLF crystal analysed previously in section 2. An intra-cavity aperture was used to ensure the laser oscillation was single transverse mode. Since the same gain medium and pump configuration were used, a look-up table was directly calculated: to ensure that the size of the fundamental transverse mode in the gain medium remained constant at 340µm during the laser turn-on, the deformable mirror required a ROC of -1.8m at the start and have a final curvature of -3m and -5.5m for the tangential and sagittal planes respectively. Given the cylindricity of the thermal lens, an additional investigation was required to obtain the appropriate voltage distribution for the actuators. The distribution was obtained by assessing the resulting ROC as a function of the voltage applied to the actuators. It was found that by applying 100V and 160V to all actuators resulted in a ROC of -5.5m and -3m respectively while 230V were required to ensured a ROC of -1.8m. Therefore, the mirror was divided into 4 groups as shown in Fig. 9(b): 160V was applied to the actuators in the green regions while 100V was applied to the actuators in the red regions. The central actuator voltage was driven with an average of both voltages, i.e. 130V. This calculation was only an approximation, however, the use of a Shack-Hartmann sensor to accurately measure the curvatures would ensure the perfect cylindricity required for the final mirror shape. In order to efficiently track the thermal lens build-up shown previously in Fig. 3, the ROC variation was divided into a sequence of 5 parts corresponding to the implementation of 3 intermediate mirror shapes in addition to the initial and final optimum shapes. The first 3 mirrors shapes were applied at intervals of 100ms whereas the final two shapes were implemented at a slower rate (300ms/change). The results obtained from this procedure are shown in Fig. 11.
Fig. 9. (a) View of the bimorph mirror, and (b) the corresponding actuator pattern where the actuator division is shown (160V and 100V were respectively applied to the actuators in green and in red)
Without correction, the free-running laser reached its optimum brightness in ~600ms. When the optimization scheme, as described above, was deployed, the resultant output displayed negligible astigmatism and the TTFB was reduced to ~200ms. The large stroke bimorph mirror therefore efficiently reduces the laser turn-on time, eliminates any astigmatic effects, and does not introduce any high-speed intensity modulation. As the bimorph mirror has a frequency response of ~6kHz, tracking between the extreme states of the laser can be achieved much more efficiently than possible with translating optics. This opens up the possibility of implementing this scheme in a wide range of lasers and temporal domains. The ability for the deformable mirror to track astigmatic cavity changes is a unique feature in this type of optimization scheme.
Fig. 11. Transverse intensity distribution at the turn-on time without (a) and with (b) transient correction of the bimorph mirror.
Finally, as has previously been demonstrated, such a large-stroke bimorph mirror can be employed to optimize the laser brightness in the steady-state regime [8]. Therefore, the prospect of combining transient and steady-state optimization with a single correcting element is a distinct possibility. The maximum stroke afforded by this type of mirror (>20µm) in combination with careful cavity design and mirror position should make this technique valid for a wide range of high-power laser systems.
4. Transient optimization of a side-pumped Nd:YAG laser using a single-actuator deformable mirror
In this section, a single-element deformable mirror was used to reduce the TTFB of a Nd:YAG laser. The use of a single-element deformable mirror is motivated by the fact that the transient optimization is largely based on the compensation of the first order component of the thermal lens. The use of such a simple deformable mirror would obviously be inappropriate in laser cavities operating at higher powers and/or those having anisotropic gain media and featuring astigmatic optical elements. In these, more general cases, a multi-element deformable mirror should be used to define the initial and final mirror shapes, as described previously in section 3.2.
The deformable mirror, having a single actuator, could access a variable ROC in the range -1m to +10m. The surface of the mirror was coated with a quarter-wave dielectric stack having a reflectivity in excess of 99%. As the mirror only employs one transducer, then a much simpler control system is required.
An end-pumped Nd:YAG laser, shown in Fig. 12, was constructed using a x1.6 telescope to ensure a large spot size (1mm) on the deformable mirror, and so, maximize the effects of the variable ROC. The pump was delivered by a fibre-coupled diode laser emitting at 808nm and delivering up to 9W. Using a spherical lens, the pump spot was focused into the crystal to a radius of 250µm. The gain medium was a 10×3×2mm Nd:YAG ceramic rod with 808/1064nm AR-coated faces. Using the method described in section 2.1, the focal length of the steady-state thermal lens was measured to be 0.5m – the build-up time of the thermal lens was calculated as ~800ms. Again, using a ray-matrix analysis, an optimization look-up table of optimal ROC values versus time was determined. Here, the deformable mirror had an initial flat shape and a final ROC of -5m. The range of ROC was divided into 14 equal steps: the first 7 steps with an equal time delay (~10ms) between applications and the next 7 steps had a time delay of ~100ms.
The resulting laser optimization is shown in Fig. 13. In the case of the laser turn-on without mirror correction, the TTFB was measured to be ~630ms. With transient optimization, this value is reduced to ~90ms. Therefore, the single-element deformable mirror successfully reduced the TTFB by a factor of 6, and as expected, negligible astigmatism was observed. The very simple nature of the single-element mirror and its corresponding ease of control make this system potentially widely applicable in a variety of laser configurations, such as the rapid thermal lens compensation demonstrated here, but also in schemes to maintain resonator fidelity as components undergo significant axial motion. Furthermore, in contrast to the look-up table approach described here, a fast closed-loop scheme could be developed using a simple brightness or power sensor.
Fig. 13. Transverse intensity distribution at the turn-on time without (a) and with (b) transient correction of the bimorph mirror.
5. Conclusion
A range of methods for reducing the time-to-full-brightness (TTFB) at the turn-on of a laser have been successfully demonstrated. All three schemes were based on the active modification of the optical parameters of the laser resonator such that the fundamental mode-size within the laser rod remained constant during the turn-on phase. The build-up of the thermal lens within the gain medium of each laser platform was measured to be on the order of ~1s thus using of a closed-loop optimisation system is impractical. In the procedures discussed here, the optimisations of the TTFB were based on a look-up table approach based on knowledge of the thermal lens – the temporal dependence and measurement of the initial and final values.
The first system was based on physical translation of one of the intra-cavity mirrors (i.e. the output coupler). The test-laser platform was based on a 63mm long Nd:YLF rod and produced a single transverse mode power of 6.5W. During the translation, the TTFB was reduced to a value of ~50ms, and the optimal brightness was maintained over the full pump pulse. The limitations of this technique relate to the astigmatism of the thermal lens, the difficulty in adapting the mirror velocity profile to accurately track the thermal lens build-up, and also the high translation velocity required.
The second optimisation system was based on a large-stroke, 31-element, deformable bimorph mirror to optimise a laser cavity based on the same Nd:YLF rod. The laser output was 1.5W, and the TTFB was reduced by a factor of 3. Here, the effects of thermal lens astigmatism were significantly reduced as the mirror shape could be controlled and varied accordingly over time. Such mirrors pave the way for combined transient and steady-state aberration correction as it can be integrated into the automatic control loop schemes previously demonstrated [7,8].
Finally, the last optimization system featured a simple single-element deformable bimorph mirror to reduce the TTFB of an end-pumped Nd:YAG laser providing an output of 1.5W. Here, the warm-up time was reduced by approximately a factor of 6. This technique is elegant in its simplicity and does provide near-instant and progressive compensation, however, such a device is only appropriate for non-astigmatic transient control.
In conclusion, we have demonstrated the efficacy of rapid thermal lens control based on maintaining the mode dimensions in the gain medium using resonator re-configuration using new large-stroke bimorph mirrors. It is clear that the characteristics of these devices make them suitable for rapid thermal lens control schemes where variations over tens of milliseconds can be effectively tracked. Furthermore, the large-stroke (20µm) allows for ROC at the dioptre level to be accommodated – an order of magnitude greater than their deformable membrane counterparts.
Acknowledgements
This work was funded by the UK Department of Trade and Industry under the INCAO project.
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