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In side pumped laser head geometries good extraction of energy has to be weighted against diffraction effects of the amplified beam. Beam clipping at the aperture of laser rods can be avoided by using an undoped cladding around the doped core. The wings of e.g. Gaussian beams can be accommodated in the cladding. Phase distortion by the refractive index step of the rod can be compensated by a phase conjugating mirror in double pass configuration. In our proof of principle experiment the brightness of the beam from core doped amplifier rods was shown to be doubled compared to a conventional rod of the same outer diameter.
©2006 Optical Society of America
1. Introduction
The side pumped laser rod is a very suitable pump geometry to realize simple and robust table top solid state laser systems with high pulse energies and circular symmetric beams. However, the extraction of Gaussian beams from side pumped laser rods in amplifiers in master oscillator power amplifier (MOPA) configurations suffers from the trade off of energy extraction at the rod’s boundaries and beam quality deterioration by diffraction of wider intensity profiles at the rod’s aperture. Core doped ceramics laser rods have an undoped cladding so that the wings of a Gaussian profile are not clipped but accommodated in the cladding. Still, there will be a similar obstacle for the extraction of excellent beam qualities. Because of a refractive index step (Fig. 1) between core and cladding, there will be a phase distortion for a beam that propagates through such a core doped rod [1]. Since this is a phase distortion only and no intensity clipping of a hard aperture, it can be compensated by a phase conjugating mirror. Within this letter we investigate experimentally to what end an improvement in extraction efficiency can be achieved without degrading the beam quality of the extracted beam using core doped laser rods in a side pumped laser head.
An early application of a side pumped core doped rod with an undoped cladding in order to improve the beam quality is described in [2]. Here a hexagonal crystal is embedded in an undoped YAG cladding. With the upcoming of the ceramic Nd:YAG [3, 4] circular geometries became possible [5]. Kracht et al. recently demonstrated an end-pumped cw Nd:YAG oscillator with an output power of 144 W with high optical-optical efficiency of 64 %. In slab geometries composite geometries can be realized easier by bonding of doped and undoped YAG-crystals. E.g. Dascalu et al. [6] report on a side pumped microchip Yb:YAG laser with a diffusion bonded core-cladding slab. Fiber lasers inherently embody a core cladding structure which is used for index guiding the laser mode but not for accommodating the wings of the mode in the cladding (see e.g. [7]).
2. Illustration of the principle problem
To illustrate the above mentioned energy extraction trade off we set up a transversally resolved Frantz-Nodvik model [8]. The amplification is calculated in 500 parallel channels in order to include saturation effects correctly for non top hat intensity profiles.
Fig. 2 shows the calculated ratio of the extracted energy of two beams with different width as a function of different energies of ns-input-pulses. The beam propagation is calculated through a 5 mm diameter Nd:YAG rod without cladding in double pass configuration. The beam embodies a Gaussian intensity profile with an 1/e2-full width at the rod entrance face of 5 mm and 3 mm, respectively. The calculation reveals that the wider beam yields extracted energies that are up to 28 % higher compared to the narrower beam. This optimum is reached for a medium saturated amplifier of an extraction efficiency [7] of 68 % for the wider beam. In the small signal regime the extraction ratio is 1 since the gain factor is independent from the intensity. For growing pulse energies saturation becomes significant and the extraction is more efficient using the wider profile. Increasing the energy of the input pulse further leads to distinct energy losses of the wider profile compared to the stored inversion in the rod. This happens because of the truncation of the profiles at the rod’s aperture.
Fig. 2. (a) Calculated ratio of extracted pulse energies of two Gaussian beams with 2.5 mm and 1.5 mm radius from a 5 mm diameter Nd:YAG rod in double pass configuration as a function of input energy. The output energy is given in addition. The rod is pumped with 2 kW for 200 μs with an excitation efficiency of 70 %.(b) and (c) show the measured far field distributions for a probe beam with 1.5 mm and 2.5 mm radius behind the propagation through a 12 cm long 5 mm diameter laser rod without amplification.
In order to quantify the consequences of the wider beam profiles with the corresponding increase in extraction efficiency on the beam quality and on the intensity profiles in the far field a Nd:YAG probe laser was used. It emitted an almost perfect Gaussian beam with an M2 of 1.1. Its beam parameters were prepared corresponding to the above calculation and propagated through the unpumped laser rod. Increasing the beam diameter from 3 mm to 5 mm the M2 number grew from 1.1 to 1.3 and the beam profiles get distinctly modulated as shown in Fig. 2(b). This clearly illustrates the trade off of diffraction impact and optimized extraction efficiency.
3. Experiments and discussion
An injection seeded Nd:YAG oscillator emitting pulse energies of up to 7 mJ with a pulse duration of 30 ns running at a repetition rate of 100 Hz was used as master for the subsequent experiments with the core doped rods. The beam quality of the oscillator was characterized resulting an M2 of 1.2. All the beam quality measurements described in this letter are conducted using an M2-200-meter by Spiricon. Three different laser rods are compared as amplifier rods in single and double pass configurations. The beam qualities and the pulse energy of the amplified pulses have been characterized. All the three rods are 120 mm long and have outer diameters of 5 mm. There are two core doped ceramic Nd:YAG rods with a core doping level of 0.8 at%. They have core diameters of 3 mm and 4 mm respectively and were purchased at Baikowski [11]. These two core doped rods are compared to a Nd:YAG crystal rod with a doping level of 0.9 at%.
Before the rods were used in the amplifier arrangement their excitation efficiencies and thermal lensing was characterized in the used laser head. The rods get side pumped by 18 diode double bars that are arranged in three 6 fold stars. The excitation efficiencies [10] were measured with a delay time analysis [12] resulting 70 % for the crystal, 56 % for the rod with 4 mm core and 42 % for the rod with the 3 mm core. The flowtube in the used laser head is designed for a 5 mm diameter laser active material. Therefore the excitation efficiency is lower for the smaller diameter cores in this specific laser head. The single pass loss factors for the rod with the 4 mm and 3 mm cores resulting from a Findlay-Clay analysis are 4 % and 3 % higher compared to the crystal rod. The measured thermally induced dioptric powers per pump power are 5.6 dpt/kW for the crystal rod, 8.4 dpt/kW for the rod with 4 mm core, and 8.3 dtp/kW for the rod with 3 mm core. The dioptric power for the 3 mm core is slightly smaller compared to the 4 mm core just because of its smaller excitation efficiency.
The input beam was prepared to embody an 1/e2-diameter of 3 mm at the position of the entrance face of the amplifier laser rod for all the carried out experiments. For the experimental comparison of the three different rods as amplifiers the input pulse energy was changed by adjusting the time delay of the Q-switch voltage with regard to the pump pulse of the oscillator. While adjusting for different pulse energies the beam parameters remained unchanged with an accuracy of better than 5 %. For all the experiments the amplifier rods were pumped with a power of 2 kW for a period of 200 μs. The setup is shown in Fig. 3. The characterization of the beam quality and pulse energy was alternatively performed after single pass or double pass, respectively. A quarter wave plate was placed between the amplifier head and the double pass mirror to partially compensate for thermally induced birefringence [13]. The depolarization loss for the double pass was in the range of 7 % to 11 %. After the insertion of the quarter wave plate it was reduced by 50 %.
Fig. 3. Oscillator power amplifier (MOPA) arrangement to investigate the potential benefits of the core doped ceramics rods.
Figure 4 depicts the extracted pulse energies from the three rods in a double pass operation using a conventional high reflecting mirror (HR-mirror) behind the amplifier. The improvement in extraction with decreasing core diameter can be clearly seen, although the excitation efficiency decreases with the decreasing active core diameter. This improvement in extraction efficiency has two major reasons. First, even with the decreased excitation efficiency in the cored doped rods the inversion density becomes higher, the smaller the core is in diameter. And second, the average intensity at the core boundaries is higher for smaller core diameters. Both correlations lead to an easier saturation of the gain in the laser rod.
The diagram also shows pulse energies calculated with our spatially resolved Frantz-Nodvik model. The calculation does not contain any fit parameter. It uses the measured pump distribution in the rod to determine the transversally varying amplification at the applied pump power level. The input beam is calculated as a Gaussian beam with the same width as in the experiment. There is good agreement between the calculated and measured pulse energies for the 5 mm diameter rod and some systematic deviation for the two core doped rods. The deviations at smaller input pulse energies might stem from a measurement error of these energies due to coarse resolution of the power meter head. Also, our Frantz-Nodvik model does not include thermal lensing. The stronger thermal lens of the core doped rods could be an additional reason for the deviation between measurement and calculation.
Fig. 4. Comparison of extracted pulse energies form conventional and core doped laser rods with conventional HR-mirror in double pass configuration. The full data points show measured pulse energies, the hollow points show calculated pulse energies following a spatially resolved Frantz-Nodvik model.
The beam quality for the amplified pulses from the core doped rods is deteriorated as can be seen from the measured M2-numbers given in table 1. The most likely reason for this is the phase distortion caused by the core doped rod’s refractive index step as has been discussed already within our numerical investigation in [1]. For the unpumped amplifier we measured almost the same M2 - numbers which supports the impact of the refractive index step. The deterioration increases in the double pass configuration with a conventional HR-mirror. Since the refractive index step causes a phase distortion only, it can be compensated by a phase conjugating mirror. Thus, we modified the double pass MOPA scheme by exchanging the HR-mirror for a phase conjugating mirror based on stimulated Brillouin scattering (SBS). The mirror consisted of a glass cell filled with the liquid CS2. The SBS-threshold of reflectivity for CS2 for 10 ns pulses is 0.4 mJ [14]. Since the SBS-mirror is a bulk mirror its operation requires a certain coherence length [14]. This condition was satisfied by our injection seeded oscillator.
Table 1. Measured M2-factors for 3 different MOPA-configurations. OD refers to the rod’s outer diameters and ID to the rod’s inner diameter.
Using the phase conjugating SBS-mirror the beam quality can be recovered to a satisfactory degree (see M2-numbers in Table 1). Even for a phase conjugating mirror with a perfect fidelity a perfect recovery of the beam quality is not to be expected. Since the intensity profile is wider than the gain region the intensity profile experiences a step in the amplification profile between core and cladding. There is amplification of the intensity in the core and no amplification of the intensity traveling in the cladding. This leads to an amplitude distortion which can not be compensated by a double pass utilizing a phase conjugating mirror. Also there are scattering effects at the core cladding boundary which can cause some share of radiation that either does not reach the SBS-mirror or is below SBS-threshold. However the M2-number of 1.5 for the 3 mm core doped rod still indicates a near diffraction limited beam quality for the amplified pulses.
Due to the low threshold of the SBS-mirror for input pulse energies above 8 mJ reflectivities of above 80 % are achieved. As shown in Fig. 5 the extracted pulse energies in the SBS-double pass configuration of the 4 mm core doped rod are around 80 % of the pulse energies in the configuration with the conventional mirror but still higher compared to the 5 mm diameter crystal (compare to Fig. 4). In case of the 3 mm core doped rod the extracted pulse energies are even slightly higher compared to the conventional HR-mirror double pass. This could be explained by a lower fraction of lost high divergence radiation due to the phase conjugated back reflection and compensation process in the rod. Due to a lack of purity of the specific SBS liquid CS2 being available to us we observed optical breakdown in the SBS-mirror for higher input pulse energies.
Overall the brightness related quantity pulse energy/(M2)2 of amplified pulses in this specific example was increased by a factor of two in comparison of the 5 mm diameter crystal to the rod with 3 mm doped core. To calculate this ratio we compared the extracted double pass energy from the 3 mm diameter core doped rod (68 mJ, M2 = 1.5) with the extracted pulse energy of the 5 mm diameter crystal (22 mJ, M2 = 1.2) for equal absorbed pump powers in both rods.
Fig. 5. Extracted pulse energies with and without phase conjugating SBS-mirror in double pass configuration for the rods with 4 mm doped core (top) and 3 mm doped core(bottom). The single pass extracted energies are given in addition.
In conclusion, the core doped rod design seems to be a suitable geometry in side pumped rod amplifiers to improve the extraction efficiency of the stored energy when using Gaussian beams. Applying these rods in phase conjugated double pass MOPA schemes the phase distortion resulting from the refractive index step can be compensated. Thus, improved extraction efficiency in the core doped geometry can be realized with good beam quality. The impact of the inhomogeneous amplification between core and cladding on the beam quality needs to be further investigated. In future investigations we will look at the improved mode discrimination for higher order modes utilizing core doped rods in laser oscillators.
Acknowledgements
We gratefully acknowledge Abdulrahman Scheikh-Obeid for assisting lab work in the course of the experiments. The work was partially funded by the German research foundation (DFG).
References and links
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