1 Introduction

Cr\(^{3+}\):BeAl\(_2\)O\(_4\), commonly known as Alexandrite, is a vibronic laser emitting at around 720–820 nm with excellent thermo-mechanical properties (e.g. \(K_c={23}\,\hbox {Wm} {^{-1}}{\hbox{ K}}^{-1}\), \({\hbox{d}}n/{\hbox{d}}T=6 \times 10^{-6} {\hbox{ K}}^{-1}\)) [1]. As with other Cr\(^{3+}\)-doped gain media, the absorption of Alexandrite is characterised by two broad and strong peaks at the blue and red region of the visible spectrum. These properties make diode-pumped Alexandrite a highly promising efficient and compact laser operating in continuous-wave (CW) [2], Q-switched [3, 4] and mode-locked [5] regimes.

Diode-pumped Alexandrite lasers are mostly used in Q-switching applications due to its ability to directly generate mJ levels of pulse energy in the \({700}-{800}\,\hbox {nm}\) region, which cannot be obtained directly from other diode-pumped laser gain media [3].

In the CW regime, low to mid-power (\({1}{\,\hbox {mW}}-{1}\,\hbox {W}\)) and high brightness (\(M^{2}<{1.2}\)) applications are often well addressed by commercially available narrow linewidth diode lasers or Ti:Sapphire lasers with the latter also providing greater wavelength coverage. Ti:Sapphire lasers, however, are often expensive, bulky and not well suited to applications outside the laser laboratory due to its water cooling requirements. Though diode pumping is possible, the use of blue diodes has been shown to lead to parasitic issues and research on green-diode pumping is limited [6]. Other Cr-doped gain media such as Cr:LiSAF and Cr:LiCAF have reported \({2}-{3}\,\hbox {W}\) of CW laser power [7,8,9], though further power scaling is challenging due to its weaker thermo-mechanical properties.

Power scaling of diode-pumped solid-state lasers to \(>5\,\hbox {W}\) across the tuning band provides greater versatility for quantum technology applications such as Rb-cooling atom interferometry [10]. Additional applications such as single-step conversion to the UVA band and a high-brightness pump source for ultra-fast Tm-doped lasers, an area that has become a highly topical area of research [11, 12], are also of particular interest. These power levels are at the limit of commercial Ti:Sapphire lasers and frequency doubled EDFA systems have limited spectral coverage.

In our previous work, we demonstrated \(>5\,\hbox {W}\) TEM00 operation from a diode-pumped Alexandrite laser [2]. This paper builds and expands on that work with a more detailed analysis of the thermal lensing, cavity modelling as well as introducing new cavity geometries. Thermal lensing in Alexandrite is complex due to the presence of excited state absorption (ESA) which is both temperature and wavelength dependent [13]. Wavefront measurements of the lens dioptric power have also shown that the pump power dependence does not agree with the quantum defect and ESA effects, but with another contribution present. We have attributed this additional contribution as being related to the refractive index distribution of the excited ions. Altogether, this makes pump-induced lensing in Alexandrite a significant factor in power scaling. Instead of minimising the thermal lens, this work looks at using it as a focusing element to simplify the cavity design for achieving record levels of CW power across the tuning range of Alexandrite.

2 Alexandrite linear laser cavity

2.1 Plane–Plane cavity

The most straightforward and compact cavity design is a plane–plane laser cavity with the thermal lens of the laser gain medium providing the mode size control. Figure 1 shows the setup for the plane–plane cavity. The gain medium is a 0.2 at.% Cr-doped Alexandrite crystal (Crystech) with dimensions of \(4 \times 4\times {6}\,\hbox {mm}^{3}\). The crystal is mounted in a water-cooled copper heatsink. The cavity is formed of two dichroic mirrors (DM) which are highly transmissive (HT) at the pump wavelength (\({640}\,\hbox {nm}\)) and highly reflective (HR) at the laser wavelength (\({720}-{820}\,\hbox {nm}\)), and an output coupler (OC) with reflectivity \(R_{\text {OC}}\).

Pumping is provided by a fibre-coupled (\(200\,\upmu \hbox {m}\)) laser diode (LD) which emits at around 640nm (\(\text {FWHM}={1.5}\,\hbox{nm}\)) with a maximum unpolarised output power of 40 W (\(\text {M}^2=100\)). Throughout this work, the fibre output is collimated with a 35nm collimator and focused to a waist \(w_p\) located at the crystal surface. The absorption coefficient is measured to be around \({6}{\,{\hbox {cm}}^{-1}} \,{\text{and}}\, {0.3}{{\hbox {cm}}^{-1}}\) along the b-axis and a-axis, respectively. Around 70% of the pump is absorbed after a single pass. The transmitted pump is retro-reflected using a curved mirror (CM) and a quarter-wave plate which on double pass rotates the transmitted pump that was primarily along the crystal a-axis to the b-axis.

Fig. 1
figure 1

Diode-pumped Alexandrite laser

The output characteristics of the three-mirror laser were measured with \(R_{\text {OC}}={98}{\%}\) and a crystal temperature of \(T_A={20}^{\circ }\text{C}\). Figure 2 shows the results with \(L_1={5}\,\hbox {mm}\), \(L_2={10}\,\hbox {mm}\) (measured from left crystal facet) and \(w_p=150\,\upmu \hbox {m}\). 12.2 W was obtained at 34.9 W absorbed pump power with a slope efficiency of 38.3%. The laser mode quality was measured to be \({\text {M}}^{2}_x={5.7}\) and \(\text {M}_y^2={6.3}\) at the maximum laser power, though it was near-diffraction limited at around 1–2 W of laser power.

Fig. 2
figure 2

Power curve for compact plane–plane cavity

Improved mode quality can be obtained with better matching of the pump and laser mode sizes. The laser mode size can be increased for better matching at higher power by increasing the cavity length. With \(L_1=15\,\hbox {mm}\), \(L_2=30\,\hbox {mm}\) and \(w_p=225\,\upmu \hbox {m}\) (where the latter has been increased to minimise damage on the mirrors), 10 W was obtained at 34.9 W absorbed pump power with a slope efficiency of 35.5%. The laser mode quality was measured to be M2 \(<{2.6}\) (in both directions) at the maximum laser power.

2.2 Convex-plane cavity

For further improvement in mode quality, a simple method to mitigate the strong thermal lens is to use a convex mirror. We recently demonstrated that using a convex-plane cavity can provide \(>5\,\hbox {W}\) with near-diffraction limited TEM00 output mode quality [2]. Here, we present further details of the cavity model, results and analysis.

Figure 3 shows a schematic of the laser cavity setup. The cavity is formed of convex DM mirror with curvature R and a plane OC. The mirror positions \(L_1\) and \(L_2\) play an important role in determining the output mode profile with a preference to slightly underfill the pump mode size at the gain medium. An understanding of the thermal lens strength is, therefore, essential to obtaining highly efficient TEM00 operation.

Fig. 3
figure 3

Convex-plane Alexandrite laser cavity

The dioptric power of the thermal lens can be directly measured using a Shack-Hartmann wavefront sensor or approximated using an analytical model [13]. Figure 4 shows the measured dioptric power as a function of the absorbed pump power for the convex-plane cavity with \(w_p={150}\,\upmu \hbox {m}\) and \(w_p={300}\,\upmu \hbox {m}\) (for further details of the experiment, see [14]). Predictions of the dioptric power for other pump sizes can be made with the help of the analytical model in combination with these measurements.

Fig. 4
figure 4

Measured dioptric power as a function of absorbed pump power for \(w_p={150}\,\upmu \hbox {m}\) and \(w_p={300}\,\upmu \hbox {m}\) with dashed line showing non-lasing trend. Dotted black line indicates laser threshold

Figure 5 shows the laser mode size as a function of the thermal lens with \(L_1={5}\,\hbox {mm}\) and \(R=-{300}\,\hbox {mm}\). The cavity is stable at \(f\approx {300}\,\hbox {mm}\); however, laser threshold occurs when the thermal lens is slightly stronger due to mode matching. The model predicts threshold to be at a thermal lens focal length of \(f\approx {200}\,\hbox {mm}\) and increasing to \(f\approx {100}\hbox {mm}\) at around 18 W of absorbed pump power. For TEM00 operation, it is preferential to slightly under-fill the pump mode; therefore, \(L_2={50}\,\hbox {mm}\) was chosen to provide good matching to a pump size of \(w_p={225}\,\upmu \hbox {m}\) as well as good sensitivity to the change in thermal lens with increased pump power.

Fig. 5
figure 5

Theoretical laser beam width radius at crystal as a function of thermal lens focal length for convex-plane cavity

Fig. 6
figure 6

Power curve for convex-plane cavity

5.45 W was obtained at 17 W absorbed pump power with a near-diffraction limited mode quality of M2 \(<1.1\), as shown in Fig.  6. The shape of the power curve can be attributed to the variation in the thermal lens. Figure 7 shows the measured dioptric power as a function of the absorbed pump power for the convex-plane cavity (green). This was calculated from the measured laser mode size at the OC. The theoretical dioptric power under non-lasing conditions is also shown (dashed green line).

Fig. 7
figure 7

Dioptric power as a function of absorbed pump power for \(w_p={225}\,\upmu \hbox {m}\) under lasing conditions (calculated from laser mode size at OC) and under non-lasing conditions (theoretical)

At \({10}-{13}\,\hbox {W}\), the dioptric power is relatively unchanged at around \({5}{\text{m}}^{-1}\) (\(f={200}\,\hbox {mm}\)), whereas under non-lasing conditions, the dioptric power would continue to increase. This deviation from that under non-lasing conditions is attributed to a combined contribution of a thermal lens and the lens due to the distribution of the excited ions (a population lens) [13].

Above threshold, the population is fixed due to the clamped inversion. It is possible that just above threshold, only the central distribution of the inversion is clamped with the outer region still increasing. This would contribute to a negative lensing effect and give rise to a levelling out or even reduction in the total measured dioptric power until further increase in the contribution of the thermal lens. This is also evident for \(w_p={150}\,\upmu \hbox {m}\) as shown in Fig. 4.

At \({13}-{15}\,\hbox {W}\) the dioptric power increases and provides better matching to the pump mode allowing better power extraction and a higher local slope efficiency. This enables high level of output power with the under-filling of the pump size enabling excellent mode operation, as shown in Fig. 6.

At higher pump power (or stronger thermal lens), the laser power begins to plateau before either roll-over or increasing in multi-mode operation. Increasing the pump waist size alleviates the thermal lens but increases the threshold pump power. A power-scaling approach would be to increase the pump waist size and convex mirror curvature; however, at the time of this work, only the \(R={-300}\,\hbox {mm}\) mirror was available.

An alternative strategy for increasing the laser power further was to incorporate a retro-reflection system with an additional convex mirror for mitigation of the thermal lens on both sides of the crystal, as shown in Fig. 8. The second convex mirror is tilted at a small angle (\(\sim {10}^{\circ }\)) to complete a three-mirror cavity. Due to the additional complexity of the system, the mode size of the laser cavity was modelled by numerically solving the ABCD Gaussian propagation formula at a reference plane after a single round trip.

Fig. 8
figure 8

Double convex-plane cavity

Fig. 9
figure 9

Theoretical laser beam width radius at crystal as a function of thermal lens focal length for double convex-plane cavity

Fig. 10
figure 10

Power curve for double convex-plane cavity

Figure 9 shows the results of the model with \(L_1={5}\,\hbox {mm}\), \(L_{21}={35}\,\hbox {mm}\) and \(R={-300}\,\hbox {mm}\) for both mirrors. \(L_{22}={15}\,\hbox {mm}\) provides the largest stability range from around \(f={225}\,\hbox {mm}\) to \(f={75}\,\hbox {mm}\) as well as suitable under-filling of the \(w_p={225}\,\upmu \hbox {m}\) pump size.

Figure 10 shows the results for the three-mirror cavity with \(L_{22}={15}\,\hbox {mm}\). A maximum laser power of 8.6 W at 31.9 W absorbed pump power was obtained corresponding to an optical efficiency of 27%. The output mode was again excellent with M2 \(<1.1\) with a broad spectrum (\(\text {FWHM}={4}\,\hbox {nm}\)) centred at 753 nm.

This system was limited by the available pump power, though the power did plateau at the maximum pump power. Using the model, it is predicted that the dioptric power ranged from around \({10}\,{{\text{m}}^{-1}}\) at threshold to \({13}\,{{\text{m}}^{-1}}\) (\(\approx {75}\,\hbox {mm}\)) at the maximum power, therefore approaching the edge of stability. With further optimisation in waist size and mirror curvature, it is believed that 10 W can be obtained. Optimisation of the crystal doping and length would also provide further improvement in power scaling performance such as by lowering the doping level (as found in [15]) though this has not been investigated in this work.

Fig. 11
figure 11

Laser power as a function of wavelength using 1 mm thick BiFi

Fig. 12
figure 12

Spectra at dual wavelength operation for 1 mm and 4 mm thick BiFis

Wavelength tuning and dual-wavelength operation were investigated using an intra-cavity birefringent filter (BiFi), as shown in Fig. 3. Figure 11 shows the laser power as a function of wavelength using a 1 mm thick BiFi. A continuous tuning range of 735–790 nm was achieved (limited by the free spectral range) with a linewidth of \(<{0.5}\,\hbox {nm}\) and a beam quality of M2 \(<1.1\) across the entire tuning range. The output power was \(>{2.5}\) W over the entire tuning range (17 W absorbed pump power)—superior to any other diode-pumped vibronic laser in the 700–800 nm region. Figure 12 shows the laser spectrum when operating at dual wavelength operation with a peak-to-peak separation of 57 nm and an output power of 2.75 W. 4.2 W of dual wavelength operation with a 15.5 nm separation was also obtained using a 4 mm thick BiFi.

The long-term power stability of these laser cavities (and those that will be presented later) was analysed by measuring the maximum laser power over a 1-h period with a power stability of \(<{1}{\%}\) relative standard deviation. Fluctuations in the wavelength in the tunable lasers were within the resolution of the spectrometer. No self-pulsing was observed in all systems when analysing the output on the microsecond scale.

3 Alexandrite ring laser cavity

For narrow-linewidth applications, single-longitudinal-mode (SLM) operation is necessary. The large emission bandwidth of Alexandrite makes SLM microchip lasers challenging, and methods such as the twisted mode technique work only for isotropic gain media. SLM operation is preferentially obtained using a unidirectional laser cavity in a ring configuration to eliminate spatial hole burning.

The ring geometry formed of two curved optics and two planar optics (often in a bow-tie geometry) is the most typical ring laser design. This configuration provides good mode matching between a near-diffraction limited pump and a tightly focused laser mode as well as good alignment stability. Our group has developed two systems that achieved \(>{1}\,\hbox {W}\) SLM with wavelength tuning using a low-brightness diode bar [16, 17]. However, further power scaling is challenging due to the relatively low efficiency of the system and the increasing aberration contribution from the poor intensity distribution of the diode bar.

Using a fibre-coupled pump source with an increased waist size to alleviate the thermal lensing does not easily match to the mode size dynamics of the bow-tie geometry. The aim, therefore, is to use a cavity geometry that allows good mode matching for larger pump sizes and as shown previously, to use the thermal lens for mode size control.

Figure 13 shows a schematic of the experimental setup. The cavity is formed of four plane mirrors: two DMs, a HR mirror and an OC. Two methods for mode size control are considered, first, with an intra-cavity negative (diverging) lens of focal length \(f_-=-{250}\,\hbox {mm}\), and then without the negative lens.

Fig. 13
figure 13

Alexandrite ring laser setup with intra-cavity lens of focal length \(f_{-}\)

The mode size of the laser cavity can be modelled by numerically solving the ABCD Gaussian propagation formula at a reference plane after a single round trip with two thermal lenses f at either side of the crystal. Figure 14 shows the laser beam width radius at the crystal (left-hand side) as a function of the thermal lens focal length with \(f_-=-{250}\,\hbox {mm}\) and \(L_x={25}\,\hbox {mm}\). Cavity stability is reached at \(f< {500}\,\hbox {mm}\) when the combined thermal lens is strong enough to overcome the defocusing of the intra-cavity negative lens. Similar to that shown with the convex-plane cavity, the laser mode size increases with cavity length but the stability range shortens.

Fig. 14
figure 14

Theoretical laser beam width radius at crystal as a function of thermal lens focal length for ring laser

\(L_y={25}\,\hbox {mm}\) and \(L_y={50}\,\hbox {mm}\) were tested with an optimum result of 4 W of total laser power (sum of bidirectional outputs) at 27.1 W of absorbed pump power with a near-diffraction limited beam quality of M2 \(<1.1.\) Both systems had a high threshold of 15 W and displayed a power roll-over at the 3-4 W level due to the cavity approaching instability, as shown in Fig. 15.

Fig. 15
figure 15

Power curve for ring cavity with \(f=-{250}\,\hbox {mm}\) lens

Figure 14 also shows the beam width for the ring cavity with \(L_x=L_y={25}\,\hbox {mm}\) without any intra-cavity lens. The benefit of this setup is that the initial dioptric power of the thermal lens is significantly lower due to the lower threshold. The cavity length is simply adjusted to provide the best matching to the pump size. For SLM operation, an intra-cavity unidirectional device would also need to be included. Due to the relatively low emission cross-section of Alexandrite, losses from intra-cavity components have a significant effect on the overall efficiency (AR coatings need to be ideally \(<{0.2}{\%}\)). Therefore, it is of additional advantage to minimise the number of components such as lenses in addition to the unidirectional device. Furthermore, removal of the internal lens provides a lower laser threshold and, therefore, a weaker population lens at the onset of lasing. This should lessen the likelihood of roll-over at the 3-4 W level.

Fig. 16
figure 16

Power curve for lens-free ring cavity

Figure 16 shows the laser power as a function of the absorbed pump power for the ring cavity without any intra-cavity lens. 7.5 W was obtained at 27.1 W of absorbed pump power corresponding to an optical efficiency of 28% and a slope efficiency of 35% with no indication of roll-over. The beam quality at the maximum power was \(\text {M}^2_x={1.85}\), \(\text {M}^2_y={1.60}\). Better beam quality was obtained at lower power with \(\text {M}^2<{1.1}\) measured at a laser power of 5.1 W. To the best of our knowledge, these power levels are the highest obtained for an Alexandrite ring laser and show potential for a multi-watt SLM Alexandrite laser which is currently in progress.

4 Conclusion

In this work, we have presented several cavity designs for achieving multi-watt levels of output power from a diode-pumped Alexandrite in near-diffraction limited mode (M2 \(<1.1\)). This paper has shown that using the thermal lens together with convex mirror, high brightness and high power can be achieved with a maximum output power of 8.6 W with M2 \(<1.1\) demonstrated. A detailed description of the cavity setup and modelling has also been provided and we believe it could be of use to other researchers examining power scaling of rod-type gain media. 7.5 W with 27% optical efficiency was also demonstrated using a four-mirror ring laser.

We believe that a plane-mirror ring laser to be the most suitable for diode-pumped Alexandrite SLM lasers owing to the low-loss requirements. The main challenge for this work will be obtaining low-loss (\(<{0.1}{\%}\)) intra-cavity isolator devices and packaging of all optical components into a small footprint.

Altogether, these results demonstrate the power capabilities of diode-pumped Alexandrite lasers across the 720–820 nm range—superior to any other diode-pumped vibronic laser. Its low cost, compactness and ruggedness make it an ideal laser source for growing applications in the near-infrared and ultra-violet ranges.