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Abstract
We present the design of a longitudinally diode-pumped Alexandrite laser in continuous-wave operation and resulting performance data. A laser power of 6.5 W in fundamental mode operation was measured, which is, to the best of our knowledge, the highest laser power in fundamental mode operation yet reported. The laser crystal was pumped by two diode modules emitting at 637 nm. The pump radiation was polarization-combined and spatially symmetrized. The laser operates at an output power of 6.5 W with an optical-to-optical efficiency of 26%, temporally stable output with stability of 8% on ms timescale, a beam quality of M2 = 1.1 in both spatial directions and emission of an output wavelength of 752 nm. Measurements of the thermal dioptric power at pumping intensities up to 9.5 kW/cm2 support the appropriate approach of the design. Based on our results, we estimate the potential and show our concept for future scaling of the output power.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Alexandrite has been used as a laser crystal since the late 1970s [1]. Since the availability of high-power red pumping diodes, interest in diode-pumped Alexandrite laser technology has been renewed, with groups investigating diode-pumped cw [2,3] and Q-switched operation [4,5]. Pumping Alexandrite with laser diodes with emission in the red is beneficial due to a small quantum defect and higher efficiency compared to flashlamps. Alexandrite lasers with their broad tuning range cover the resonances of several relevant atoms and ions including sodium, rubidium and ytterbium and can potentially be used for laser trapping and cooling. Recent reports about femtosecond-pulse generation [6] and SESAM-modelocking [7] underline the potential of continuously pumped Alexandrite lasers but the lasers still have been pumped with green solid-state lasers up to now. No diode-pumped modelocked Alexandrite laser has yet been reported. Their successful demonstration is especially challenging due to the long lifetime and pumping with low-brightness pumps. Using low-brightness pumps, large pump radii have to be employed, requiring large laser mode radii for effective mode size matching. The modelocking threshold increases quadratically with the laser mode radius at the laser crystal, making modelocking difficult to achieve. One solution is to raise the intracavity energy to overcome the modelocking threshold by increasing the resonator length, thus decreasing the repetition rate [6,8].
While several publications report instable temporal behavior of Alexandrite lasers including the tendency for spiking [1,9] and so-called self-Q-switching [10–14], only few report measurements or state the power stability of their continuous-wave laser’s temporal behavior [12–16]. Temporal instability has been attributed to temporal fluctuations in the gain [13] or to an interplay between a fast change in a population lens and a slow change in the thermal lens due to small perturbations [10]. Even though the underlying mechanism of temporal instability is not yet fully clear, it is of vital interest to obtain stable continuous-wave operation of Alexandrite lasers.
The highest power of a continuously-diode-pumped Alexandrite laser in multimode operation has been reported in a longitudinally pumped configuration with up to 26 W and an optical-to-optical efficiency of about 40% [2]. The highest fundamental mode power yet reported is 4.5 W from a side-pumped slab-laser configuration achieved with around 48 W absorbed pump power, resulting in about 10% optical-to-optical efficiency [10]. A double pass end-pumping scheme has been demonstrated to generate up to 1.66 W of diffraction-limited laser radiation with an efficiency of 31% [17].
Challenges for diode-pumping yet remain due to the asymmetric beam characteristics of high-power diode-laser modules commercially available. Solutions for end-pumped resonators are either complex resonator geometries (V-passes of the laser mode through the pumped area with slight angles [18]), a symmetrized pump beam (e.g. by spatial clipping of the pump beam [19] or fiber-coupling [17,20]) or spatially redistributing the pump beam [4,5]. Side-pumping has already been applied, as well [10].
2. Laser system
In our investigation we have symmetrized the pump beam by a spatial redistribution, similar to the pump setup used for our recent Q-switched system [4]. The pumping scheme comprises two commercially available diode modules, each with a cw output power of up to 45 W at a wavelength of 637 nm. The pump radiation is linearly polarized with a beam quality factor M2 of 30 and 300 in fast and slow axis, respectively. The polarization direction of the pump radiation of one module is rotated by 90° by means of a half-wave plate and afterwards the beams of both modules are combined by means of a polarizing beam combiner (Fig. 1). After polarization-combining, the pump radiation is collimated in the slow axis by a cylindrical lens with a focal length of 400 mm. The intensity profile of the pump beam is symmetrized by a step mirror. This optical element uses two consecutive mirror arrangements to split the pump beam and rotate each partial beam by 90° to redistribute the intensity profile [21]. After combining and symmetrizing we obtain a maximum pump power of 58 W with an M2 of 96 in vertical (y-) and 108 in horizontal (x-) direction, reducing the ratio of beam quality factors from 10 to 1.1. The optical setup causes a loss of about 35% to the available pump power. The symmetrized pump beam is then focused into the laser crystal by an achromatic lens with focal length fP = 150 mm. The resulting pump spot has a waist diameter of 460 and 530 µm along x- and y-axis, respectively (see inset in Fig. 1).
Fig. 1. Pumping configuration with two diode modules. After passing through half-wave plates (HWP), the radiation is combined by a polarization combining cube (PC). Afterwards the fast- and slow-axis are symmetrized by a step mirror (SM). An achromatic lens (AC) (fP = 150 mm) is used to focus the radiation into the crystal. Inset shows pump beam profile at focus position. The crystal is longitudinally pumped from both sides, with the pump beam entering the crystal through its aperture close to DM1, then the residual beam passes through DM2. The beam is afterwards collimated by a lens with the same focal length as AC and reduced in size by a telescope. For double pass end-pumping, the polarization of the pump radiation is rotated 90° by passing a quarter wave plate (QWP) twice and being reflected by an HR mirror (RM) between the passes.
The Alexandrite crystal has a quadratic aperture of 2.4 × 2.4 mm2 (parallel to a- and b-axis of the crystal) and a length of 7 mm. The crystal is cut along the c-axis and has a dopant concentration of 0.2 at%. The crystal is oriented such that the b-axis corresponds to the horizontal axis of the pump radiation. The temperature of the crystal is controlled by means of a thermo-electric element to 30°C. The facets are coated with an antireflective coating for pump and laser radiation.
Due to the anisotropic nature of Alexandrite only the radiation polarized in parallel to the b-axis of the crystal is well absorbed (91%). The radiation polarized in parallel to the a-axis is less absorbed (24%) and therefore to a large proportion transmitted through the crystal. This transmission corresponds to absorption coefficients of 0.34 mm−1 and 0.04 mm−1 for pump radiation polarized in parallel to the b-axis and a-axis, respectively. This is slightly lower than described by the literature for crystals of similar dopant concentration [2]. To improve the overall pump absorption we use a pump retroreflection scheme with polarization flipping, similar to the ones described in the literature [4,17]. The unabsorbed portion of the pumping radiation is transmitted through a dichroic mirror, collimated and its diameter reduced by a telescope (left side of Fig. 1). By passing through a quarter-wave plate, being reflected by a high-reflective mirror and passing the quarter-wave plate again, the polarization direction of this part of the radiation is rotated by 90°. The radiation is then polarized in parallel to the b-axis and refocused into the laser crystal. The optics cause a single pass transmission loss of about 6%, so the overall loss of the polarization-flipped radiation is about 12%.
The amount of absorbed pump radiation is not accessible to a direct measurement. Therefore we estimate the absorbed pump power with the single-pass absorption coefficients we measured and taking the loss factor from the double-pass end-pumping configuration and the crystal coatings into account. Considering these factors we estimate that about 89% of the overall pump power is absorbed in the laser crystal.
To design the resonator, we have the following three criteria in mind: It shall be adaptable for different beam radii, dynamically stable for a range of thermal dioptric powers and able to store energy within the resonator for future experiments toward modelocking. For the first goal we choose an asymmetric resonator with focusing elements on both sides of the laser crystal and an additional focusing element. Mirrors with different radii of curvature at one position can be used to manipulate the beam size at one end of the resonator easily without changing the mode size in the crystal. For the dynamical stability we choose a compromise between mode matching of laser and pump beam and the stability to include the unpumped case on one hand and up to several diopters on the other hand. To store energy within the resonator we elongate it to increase the resonator round trip time.
A resonator configuration that is in agreement with the design criteria is displayed in Fig. 2(a). The linear cavity with a length of 1.2 m comprises two plane end mirrors, a high-reflective mirror (EM) at one end and an outcoupling mirror (OC) with 97% reflectivity for the laser radiation at the other end. Three curved concave mirrors (CM1, CM2 and CM3 with radius of curvature of 250 mm, 150 mm and 250 mm, respectively) form the laser mode. These radii were selected to form a stable resonator eigenmode with a beam radius of around 190 µm within the laser crystal. Two dichroic mirrors (DM1 and DM2, HR750 AR636) and additional plane high reflective mirrors (FM1, FM2) are used to fold the laser cavity for a reduced footprint. Pumping the crystal generates a thermal gradient and therefore a thermal lens inside. The resonator configuration is stable in the fundamental mode for thermal dioptric powers of the laser crystal of up to 27 ${\textrm{m}^{ - 1}}$. Modeling the resonator with ABCD-matrices (e.g. [22]) identifies an unstable region of thermal dioptric power for either the x- or y-axis between 12.6 - 12.8 ${\textrm{m}^{ - 1}}$ and 14.1 - 14.6 ${\textrm{m}^{ - 1}}$, respectively (Fig. 2(b)).
Fig. 2. Resonator layout comprising the crystal with thermal dioptric power, dichroic mirrors (DM1, DM2), curved mirrors (CM1, CM2, CM3), end (EM) and outcoupling mirror (OC) and folding mirrors (FM1, FM2). Pump beam input (orange arrows) and laser mode (red line) is drawn for orientation (a). Rayleigh length beyond OC and fundamental laser mode radius at the crystal’s position as a function of the thermal dioptric power inside the laser crystal for x-axis (blue, grey) and y-axis (orange, green), calculated with ABCD matrices. The x-axis corresponds to crystal’s b-axis. (b).
This resonator configuration can flexibly be adapted for variations in the pump setup and requirements of the laser mode. As an example, in order to being able to employ greater thermal dioptric powers, increasing the radius of curvature of CM2 can be used without a large impact on the mode size matching, shifting the stable region to larger dioptric powers. The resonator length can also be adapted, because of the collimated beam beyond CM3 the distance of this arm to the end mirror EM can be varied without a large impact on the mode size in the crystal and on the overall stability range. A summary of the influence of a change of resonator elements on the resonator mode is given in Table 1.
Table 1. Influence of resonator elements on the resonator mode
3. Results and discussion
The laser threshold is about 8 W of absorbed pump power. Increasing the absorbed pump power leads to an increase in thermal dioptric power of the laser crystal’s thermal lens and a changing resonator Eigenmode, resulting in a discontinuous input-output curve (Fig. 3(a)). At the highest absorbed pump power of 25 W a laser output power of 6.5 W is measured. The output beam has a beam quality factor M2 of 1.1 in both spatial directions (Fig. 3(b)) with a Gaussian spatial intensity profile (inset in Fig. 3(b)). Without additional beam shaping, the beam profile is round with ellipticity of 0.11 and shows only little astigmatism with focal positions of both axes separated by less than a Rayleigh length. Increasing the absorbed pump power above 25 W stops the laser operation within seconds. The optical-to-optical efficiency with respect to the absorbed pump power is 26%. The laser wavelength shifts with increasing pump power from 746 nm to 752 nm. The spectrum consists of several wavelengths emitted within a narrow wavelength region of less than 1 nm (Fig. 3(c)), measured with an Echelle spectrometer with a maximum resolution of 0.3 pm and an absolute accuracy of ± 5 pm by calibration to an Hg lamp.
Fig. 3. Output power of the Alexandrite laser with respect to absorbed pump power. Filled symbols indicate fundamental mode output, hollow symbols aberrated output. Dark squares are the working points used for evaluating the thermal dioptric power of the laser crystal (a). Beam caustic at 6.5 W output power with M2 = 1.1 in both axes, inset shows transverse intensity profile at the focus (b). Spectrum of the output radiation at maximum laser power (c). Temporally resolved measurement at maximum output power, dashed lines indicating the standard deviation of the average signal strength (d).
As summarized in the introduction, the temporal stability of cw operation of Alexandrite lasers is a challenge. Therefore we measured the output with a photodiode (150 MHz bandwidth). At maximum output power, the output is temporally stable with a standard deviation of about 8% of the average signal and no spiking is observed (Fig. 3(d)). At intermediate output powers the emission can have significantly instable characteristics with large power fluctuations both on a thermopile sensor and photodiode, including regular self-Q-switching with repetition rates in the range of 10-30 kHz and random spiking, as was earlier observed in Alexandrite lasers [12,14].
In order to better understand the power curve we evaluated the thermal dioptric power inside the laser crystal. To obtain the thermal dioptric power, we use the Rayleigh length of the output beam in an approach similar to the literature [23]. We measure the Rayleigh length ${z_{\textrm{R}({\textrm{x},\textrm{y}} )}}$ of the output beam with respect to the absorbed pump power. Using the resonator’s ABCD matrix we calculate the dioptric power of the pumped crystal that results in ${z_{\textrm{R}({\textrm{x},\textrm{y}} )}}$. The unstable regions in the stability diagram (Fig. 2(b)) are identified at the steep drop of output power at an absorbed pump power of 18 W and 22 W. The discontinuous power curve implies a discontinuous heating efficiency. Therefore we assume a constant heating efficiency only where the slope of the output power is close to the maximum slope efficiency ${\eta _\textrm{S}}$ (squares in Fig. 3(a)).
The total thermal dioptric power rises from 4 ${\textrm{m}^{ - 1}}$ at the laser threshold to 20 ${\textrm{m}^{ - 1}}$ at maximum pump power (corresponding to an intensity of 9.5 kW/cm2) with relative uncertainties between 6% and 23% (Fig. 4), derived from the measurement of the Rayleigh length. Fitting the experimental data yields slopes of ${d_{\textrm{th}}}\textrm{/}{P_{\textrm{abs}}}$ of (0.66 ± 0.05) ${\textrm{m}^{ - 1}}$/W for x- and (0.61 ± 0.02) ${\textrm{m}^{ - 1}}$/W for y-axis (Fig. 4) with respect to absorbed pump power. The instable region at absorbed pump power in the range of 12 W to 15 W cannot be attributed to the resonator’s stability. In this case, the calculated dioptric power would be the same (within 5%) for 16 W and 21 W of pump power. Therefore, the origin of this instability cannot be fully explained. While this happens at the region in the stability diagram where the resonator mode is smallest, the mode might become instable because of parasitic effects due to the low overlap between laser and pump mode. Other detrimental effects like self-Q-switching or excited state absorption could also play a role. The early extinguishing of the laser radiation at 20 ${\textrm{m}^{ - 1}}$ can be attributed to the resonator branch for high dioptric powers being the one with higher alignment sensitivity (zone II according to Magni [22]). Small fluctuations at high pumping powers can lead to decreasing output power and thereby increasing lensing due to thermal load by excited state absorption [24] or a population lens [25], leading to a runaway effect and ultimately shifting the resonator out of the stable regime.
Fig. 4. Thermal dioptric power with respect to absorbed pump power; rectangles represent data from laser operation (squares in Fig. 3(a)). Lines represent linear fits to the data.
We expect the thermal dioptric power ${d_{\textrm{th}}}$ to follow the function [26]
Comparing the experimentally obtained slopes to the theoretical prediction, we estimate a fraction of 33% absorbed optical pump power to be transformed into heat in our setup. For comparison we calculated the heating efficiency using the model in [24], including Stokes-shift and heating due to excited state absorption of laser and pump photons, to 27%. Both values are in the same order of magnitude.
In our experiment, the resonator stability limited the maximum output power while about half of the available pump power was used. This is because the resonator was initially designed to be stable for the pump power of only one pump module. We calculated with the resonator model that by changing the curved mirrors of the cavity without changing the resonator lengths, the resonator stability can be extended to the necessary thermal dioptric powers. Increasing the radius of curvature of CM2 from 150 mm to 180 mm, the stability can be scaled to 30 - 45 ${\textrm{m}^{ - 1}}$ without deteriorating the mode matching of laser and pump mode. Using such adapted resonator all of the available pump power can be used and the output power scaled. Considering the emission of 6.5 W at an incident pump power of 29 W, the generation of more than 10 W of laser radiation is close at hand.
Further power scaling requires both work on the pump setup and adapting the resonator. Currently we work on concepts for a diode pump setup to provide a pump power of up to 200 W with a beam quality factor M2 of 370 with the possibility to expand it to 400 W with M2 of ∼460. Such pump setup can be achieved by polarization-coupling and geometrical stacking of several diode bars, symmetrizing the laser radiation by means of a tailored step mirror and subsequent fiber-coupling into a multimode fiber with a large core in order to further homogenize the output beam [32]. An improvement of optical-to-optical efficiency by using a fiber-coupled pump has already been demonstrated in case of a Q-switched Alexandrite laser, where it was increased by 30% compared to the same system pumped without using the fiber [33]. In our case this enables us to increase the output power at the same thermal load.
When scaling the available pump power, the pump beam radius can be deliberately increased to maintain a constant pump power density and thermal dioptric power. To achieve a good mode size matching, the resonator has to be redesigned for an increased laser mode size. As known from resonator theory (e.g. [22]), the resonator becomes less dynamically stable to thermal lensing and has to be designed for a rather specific thermal dioptric power. Additional measures such as inserting a negative lens into the cavity or polishing the laser crystal’s facets to be concave are further well established measures to deal with higher thermal lensing (e.g. [26]). Our results from this paper regarding the strength of thermal lensing are an important stepping stone toward the design of such high-power laser. Once this pump power is available it should allow further scaling of the laser power to the multi-ten Watt class.
4. Conclusion
In conclusion we developed a longitudinally diode-pumped Alexandrite laser with a laser power of up to 6.5 W in temporally stable fundamental mode operation and an optical-to-optical efficiency of 26%. The maximum output power is temporally stable with power fluctuations of 8% with no spiking observed. For pumping we use a spatially symmetrized diode pump source. We have elaborated on our roadmap towards a more powerful diode pump setup which should allow to scale the laser power even further.
Disclosures
The authors declare no conflicts of interest.
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