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 properties³³ (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 lasers³⁷.

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 aberrations³⁸. Resonator designs have been proposed which only reduce the influence of such aberrations to a minimum³⁹. This situation has now changed considerably in view of the development of adaptive optics elements.

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 element³⁹ 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 étalon 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 software²⁰.

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 mirror.

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 element.

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)⁴¹.

Fig.17. Laser resonator with large aperture mirror: 1 - output flat mirror, 2 - active element (YAG), 3 - thermal astigmatic lens, 4 - meniscus, 5 - spherical active mirror

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 f_x=0.42 m and f_y=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 W_sp via cavity length d₂ for various radius of curvature of meniscus r.

Fig.18. Dependence of the beam radius W_sp 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 W_sp 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 W_sp when this mirror 5 was situated in the center of the stability range D~10 mm and also gives the corresponding cavity lengths d_av 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 d_av also increases by a factor of 1.7, which was not always desirable.

Dependencies of W_av and D on d₁ for f_x =0.42, f_y =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, W_av 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: f_x=0.42m, f_y=0.34m, d₁=0.3m, r=35mm, R=0.6m and W_av =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 well.

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 intracavity diaphragm.

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 intracavity-controlled mirror.

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 whole.

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 distributions (Fig. 23).

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 correctors²¹.