Chapter 2.................................................................................................... 19
2.4 Properties of Nd:YLF Crystal
Nd-doped yttrium lithium fluoride (Nd:YLF) is another important active medium in the field of solid-state lasers. Basic properties of the Nd:YLF crystal are illustrated in Fig. 2.4.1, which is also obtained from CASTECH [3]. Like the Nd:YVO4 crystal, the Nd:YLF crystal belongs to the tetragonal group in crystal structure. Therefore, it can emit the linearly polarized output without the thermally induced birefringence as well as the thermal depolarization loss in the high-power operation. The Nd:YLF crystal is also highly desirable for generating high-energy pulses thanks to its long upper-state lifetime [37-39], where the fluorescent lifetime is around 500 μs. For comparison, the upper-state lifetimes in the Nd:YAG and Nd:YVO4 crystals are roughly 230 and 100 μs, respectively. Note that the capability of the energy storage is directly proportional to the fluorescent time of the laser crystal. Another feature is the excellent spectral match between the emission line at 1053 nm and the gain peak of the Nd:phosphate glass, which makes the Nd:YLF crystal essentially favorable for constructing a high-energy master oscillator power amplifier [40].
Fig. 2.4.1. Basic properties of the Nd:YLF crystal.
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2.5 Continuously Pumped Passively Q-Switched a-cut Nd:YLF Laser at 1053 nm
I. Introduction
Although it is generally convenient to employ the c-cut Nd:YLF crystal as a gain medium for generating an 1053-nm laser, the isotropic property in the transverse plane typically leads the polarization state not to be linearly polarized. The a-cut Nd:YLF crystal can alternatively be employed to obtain a linearly polarized output. However, the stimulated emission cross section at 1047 nm is higher than that at 1053 nm by a factor of 1.5 for the a-cut Nd:YLF crystal [41-45]. As a result, suppressing the π-polarized emission at 1047 nm turns into an important issue in designing a linearly-polarized 1053-nm laser with the a-cut Nd:YLF crystal. Notice that the Nd:YLF crystal is an uniaxially birefringent crystal that shows distinct emission characteristics for the π- and σ-polarizations, corresponding to the emission wavelengths of 1047 and 1053 nm, respectively. Furthermore, extra losses may be enhanced by the energy-transfer upconversion (ETU) effect, which causes a reduction in the effective upper laser level lifetime and an increase in fractional thermal loading [46-49]. Therefore, it is practically important to develop an approach without introducing considerable extra losses for achieving an efficient linearly polarized Nd:YLF 1053-nm pulsed laser.
In a previous study [50], it was demonstrated that the selection of the polarization in an a-cut Nd:YVO4 laser could be attained by combining the birefringence of the laser crystal with the alignment sensitivity of the plano-plano resonator. Motivated by their work, in this section the natural birefringence of the Nd:YLF crystal is utilized to achieve a reliable TEM00-mode linearly polarized laser at 1053 nm in a compact concave-plano resonator. The efficient selection of the polarization relies on the combined effect of the difference in diffraction angles for π- and σ-polarizations of a wedged laser crystal and the alignment sensitivity of an optical resonator. We further employ a Cr4+:YAG saturable absorber to perform the PQS operation. At an incident pump power of 12 W, the maximum output power is up to 2.3 W with a pulse repetition rate of 8 kHz and a pulse width of 9 ns. The pulse energy and peak power are found to be 288 μJ and 32 kW, respectively.
II. Experimental setup
The experimental setup is schematically shown in Fig. 2.5.1. The input mirror was a concave mirror with the ROC of 500 mm. It was AR coated at 806 nm on the entrance face, and was coated for high transmission at 806 nm as well as for high reflection at 1053 nm on the second surface. The gain medium was a 0.8 at. % a-cut Nd:YLF crystal with dimensions of 3 × 3 × 20 mm3, and it was placed to be adjacent to the input mirror.
Both facets of the laser crystal were AR coated at 806 and 1053 nm. The second surface of the laser crystal was wedged at an angle θw = 3˚ with respect to the first surface, as indicated in Fig. 2.5.1. The Cr4+:YAG saturable absorber with an initial transmission of 80 % was AR coated at 1053 nm on both surfaces, and it was placed near to the output coupler. The laser crystal and saturable absorber were wrapped with the indium foil and mounted in water-cooled copper heat sinks at 20 °C. The pump source was a 15-W fiber-coupled laser diode at 806 nm with a core diameter of 400 μm and a numerical aperture of 0.2. The pump beam was reimaged into the laser crystal with a lens set that has a focal length of 25 mm and a coupling efficiency of 90 %. The flat output couplers with the transmissions of 10, 20, 30, 36, and 50 % were utilized for systematic investigation on the laser characteristics during the experiment. The cavity length was set to be 50 mm for the construction of a compact laser. With the ABCD-matrix theory, the cavity mode radii inside the laser crystal and saturable absorber were estimated to be approximately 236 and 224 μm, respectively. The pulse temporal behaviors were recorded by a LeCroy digital oscilloscope (Wavepro 7100, 10 G samples/s, 1 GHz bandwidth) with a fast Si photodiode.
47
Fig. 2.5.1. Schematic of the cavity setup for a diode-pumped PQS Nd:YLF/Cr4+:YAG laser.
0.8 % Nd:YLF
-polarization (1053 nm)
-polarization (1047 nm) b
c
t
w= 3o Laser diode
p= 806 nm, = 400 m
Input mirror R1= 500 mm
Output coupler
Cr4+:YAG T0= 80 %
Lcav= 50 mm
III. Performance of CW and PQS operations
First of all, we explore the angle tuning characteristics of the Nd:YLF laser for the σ- and π-polarizations in the CW operation, where the Cr4+:YAG saturable absorber was removed, the transmission of the output coupler was chosen to be 30 %, and the incident pump power was fixed to be 12 W to avoid the possibility of the thermal fracture in the laser crystal. As shown in Fig. 2.5.2(a), the output polarization state can be easily switched by simply tilting the orientation of the output coupler. Note that the tilting angle ϕt is defined as the included angle with respect to the orientation of the output coupler corresponding to the maximum output power at 1053 nm, as depicted in Fig.
2.5.1. The angular separation between the σ- and π-polarizations under the individual maximum output power is experimentally found to be around 1.153 mrad; that is, the angular separation between the point b and c indicated in Fig. 2.5.2(a) is approximately 1.153 mrad. On the other hand, the refractive indices for the σ- and π-polarizations in the a-cut Nd:YLF crystal are nσ = 1.448 and nπ = 1.47, respectively. With the Snell’s law under the small-angle approximation, we can theoretically derive an angular separation to be (nπ－nσ) θw～1.152 mrad between the two polarizations external to the wedged crystal, which is in a good agreement with the experimental observations. The two-dimensional spatial distributions for the σ- and π-polarizations under the individual maximum output power are recorded with a digital camera, and both are found to display a near-diffraction-limited TEM00 transverse mode, as shown in Fig. 2.5.2(b) for the case of σ-polarization.
With the optimal alignment for 1053-nm emission, we made a thorough study on the output power with respect to the output coupling at an incident pump power of 12 W.
Note that the polarization extinction ratio at 1053 nm is considerably larger than 100:1 once the cavity was aligned for the optimization at 1053 nm. The output power in the CW operation is experimentally found to decrease from 4.88 to 2.45 W by increasing the output coupling from 10 to 50 %, as revealed by the red curve in Fig. 2.5.3.
When the Cr4+:YAG saturable absorber was inserted into the laser cavity, the dependence of the output power in the PQS operation on the output coupling is demonstrated by the green curve in Fig. 2.5.3. Experimental results reveal that at an incident pump power of 12 W, the maximum output power of 2.3 W is achieved with the output coupling of 30 % in the PQS operation. The optical conversion efficiency
49
from 806 to 1053 nm is thus evaluated to be 18.3 %. Figure 2.5.4 illustrates the pulse repetition rate and the pulse width versus the output coupling in the PQS operation. It is experimentally found that both the pulse repetition rate and the pulse width are insensitive to the change of the output coupling; namely, when the transmission of the output coupler is varied between 10-50 %, the pulse repetition rate and the pulse width are in the ranges 8-9 kHz and 9-10 ns, respectively. According to the experimental results illustrated in Figs. 2.5.3 and 2.5.4, the pulse energy and peak power are calculated as a function of the transmission of the output coupler, as depicted in Fig.
2.5.5. For the output coupler with the transmission of 30 %, the pulse energy and the peak power as high as 288 μJ and 32 kW are achieved at an incident pump power of 12 W.
Figures 2.5.6(a) and (b) show the typical oscilloscope traces of the output pulses at 1053 nm with the time span of 2 ms and 200 ns, respectively. The temporal behaviors were recorded with the output coupling of 30 % under an incident pump power of 12 W.
The pulse-to-pulse amplitude fluctuation is found to be better than ±2 %. With a knife-edge method, the beam quality factors at 1053 nm for the orthogonal directions were measured to be Mx2 < 1.1 and My2 < 1.15, respectively.
Fig. 2.5.2. (a) The angle tuning characteristics of the 3˚-wedged a-cut Nd:YLF laser for the σ- and π-polarizations in the CW operation; (b) The two-dimensional spatial distributions for the σ-polarization under the maximum output power, indicating a near-diffraction-limited TEM00 transverse mode.
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
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Fig. 2.5.3. The maximum output powers at 1053 nm in the CW and PQS operations as a function of the output coupling.
10 20 30 40 50
1 2 3 4 5 6 7
Output power (W)
Transmission of the output coupler (%)
CW operation, Pin = 12 W
PQS operation, Pin = 12 W, T0 = 80%
Fig. 2.5.4. Dependences of the pulse repetition rate and pulse width on the output coupling.
10 20 30 40 50
4 6 8 10 12
Pin = 12 W & T0 = 80 %
pulse repetition rate pulse width
Transmission of the output coupler (%)
Pulse repetition rate (kHz)
4 6 8 10 12
Pulse width (ns)
53
Fig. 2.5.5. Dependences of the pulse energy and peak power on the output coupling.
10 20 30 40 50
100 150 200 250 300 350
pulse energy peak power
Transmission of the output coupler (%)
Puls e energy ( J)
15 20 25 30 35 40
Peak power (kW)
Pin = 12 W & T0 = 80 %
Fig. 2.5.6. Typical temporal behaviors at 1053 nm with: (a) time span of 2 ms, and (b) time span of 200 ns, which were recorded with the output coupling of 30 % under an incident pump power of 12 W.
0 200 s/div
~9 ns
0 20 ns/div
(b)
(a)
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2.6 Continuously Pumped Passively Q-Switched c-cut Nd:YLF Laser at 1053 nm
I. Introduction
If the polarization state of the output is not a critical issue, using the c-cut Nd:YLF crystal is a convenient way for generating the emission line at 1053 nm, because it can completely avoid the complexities required for the suppression of the unwanted laser transition at 1047 nm [51-53]. The fluorescent lifetime of 540 μs in the c-cut Nd:YLF crystal is also expected to be more suitable for producing high-energy pulses as compared with the 490 μs in the a-cut counterpart [54]. However, the implementation of high-pulse-energy PQS c-cut Nd:YLF lasers at 1053 nm has not been completely explored yet. The main reason is that the behavior of the thermal-lensing effect in the c-cut Nd:YLF crystal is significantly different from the ones in other popular gain media such as the Nd:YVO4 and Nd:YAG crystals. The critical difference is that the negative dependence of the refractive index on the temperature (dn/dT) over the positive contribution from the end-face bulging of the gain medium leads the c-cut Nd:YLF crystal to behave a defocusing thermal lens. Furthermore, the ETU effect reduces the effective upper-state lifetime and increases the fractional thermal loading in the laser crystal, as discussed in Refs. [46-49]. The ETU effect inevitably causes the effective focal length of the thermal lens in the PQS operation to be considerably more negative than the one in the CW operation. As a result, a reliable and efficient tactic for designing continuously pumped high-pulse-energy PQS laser at 1053 nm is highly desirable to be developed.
In this section, we develop a practical method to extend the power scale-up for a laser in a concave-plano cavity to be influenced by a large negative thermal lens. With the developed method, we successfully scale up the output power of a compact high-pulse-energy PQS Nd:YLF laser at 1053 nm with the Cr4+:YAG crystal as a saturable absorber. At an incident pump power of 12.6 W, the maximum output power under the optimum operation at 1053 nm reaches 2.61 W with a pulse width of 6 ns and a pulse repetition rate of 4.6 kHz. The corresponding pulse energy and peak power are estimated to be up to 570 μJ and 95 kW, respectively.
II. Numerical analysis
Previous studies have demonstrated that the mode-to-pump size ratio plays an important role for power scaling in diode-end-pumped solid-state lasers, in which the optimum mode-to-pump size ratio is practically found to be in the range 0.6-1 [36,55,56]. With the ABCD-matrix theory, here we take into account of the thermal-lensing effect to numerically calculate the mode-to-pump size ratio as a function of the thermal focal length for the cases of R1 = 50, 100, 200, and 500 mm in a concave-plano cavity, where R1 is the ROC of the input concave mirror. In the present analyses, the pump radius ωpo = 210 μm and the cavity length Lcav = 35 mm are used, and the thermally induced lens is set to be adjacent to the input concave mirror.
When the positive thermal lens is considered, we find that the mode-to-pump size ratios for all cases are well located between 0.6-1 in the large operated region, as depicted in Fig. 2.6.1(a). We also find that the magnitude of the thermal focal length |fth| should be larger than (R1Lcav)/(R1-Lcav) to satisfy the stability criterion. Because the magnitude of the thermal focal length is inversely proportional to the incident pump power, the higher incident pump power can be allowed by using the concave mirror with larger ROC when the positive thermal lens is regarded.
On the other hand, we find that the ROC of the concave mirror needs to be small enough to fulfill the optimum mode-to-pump size ratio for the case of negative thermal-lensing effect, as shown in Fig. 2.6.1(b). At the same time, the magnitude of the thermal focal length |fth| is derived to need to be larger than R1 to keep the cavity stable.
On the whole, it is numerically found that decreasing the ROC of the concave mirror is favorable for simultaneously achieving good mode-to-pump size ratio as well as power scaling in a concave-plano cavity that is affected by a negative thermal lens.
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Fig. 2.6.1. Calculated results for the mode-to-pump size ratio as a function of the thermal focal length for the cases of R1 = 50, 100, 200, and 500 mm: (a) positive thermal-lensing effect; (b) negative thermal-lensing effect.
Thermal focal length fth (mm)
-1200 -1000 -800 -600 -400 -200 0
Mode-to-pump size ratio
Thermal focal length fth (mm)
0 200 400 600 800 1000 1200
Mode-to-pump size ratio
III. Experimental setup
The experimental setup is schematically shown in Fig. 2.6.2. The input concave mirror was AR coated at 806 nm on the entrance face, and was coated for high transmission at 806 nm as well as for high reflection at 1053 nm on the second surface.
The gain medium was a 0.8 at. % c-cut Nd:YLF crystal with the diameter of 4 mm and the length of 15 mm. The Nd:YLF crystal was placed adjacent to the input concave mirror. Both facets of the laser crystal were AR coated at 806 and 1053 nm. The Cr4+:YAG saturable absorber with an initial transmission of 80 % was AR coated at 1053 nm on both surfaces, and it was placed near to the output coupler for achieving a high-quality PQS operation. The laser crystal and saturable absorber were wrapped with indium foil and mounted in water-cooled copper heat sinks at 16 °C. The pump source was a fiber-coupled laser diode at 806 nm with a core diameter of 400 μm and a numerical aperture of 0.14. The pump beam with the spot radius of 210 μm was reimaged inside the laser crystal with a lens set that has a focal length of 25 mm and a coupling efficiency of 90 %. The flat output coupler with a reflectivity of 74 % at 1053 nm was employed throughout the experiment. The cavity length was set to be 35 mm for the construction of a compact PQS laser. The pulse temporal behaviors were recorded by a LeCroy digital oscilloscope (Wavepro 7100, 10 G samples/s, 1 GHz bandwidth) with a fast InGaAs photodiode.
59
Fig. 2.6.2. Configuration of the cavity setup for a diode-pumped PQS Nd:YLF/Cr4+:YAG laser.
Lcav= 35 mm Laser diode
p= 806 nm, = 400 m
0.8 % Nd:YLF Cr4+:YAG, T0= 80 % Output coupler ROC= 74 % @ 1053 nm Input mirror
IV. Performance of CW and PQS operations
First of all, the CW operation without the saturable absorber was studied. Figure 2.6.3(a) shows the output powers at 1053 nm as a function of the incident pump power at 806 nm for the cases of R1 = 50, 100, 200, and 500 mm. It is obvious that although the pump thresholds for all cases are almost identical, the slope efficiency obtained with R1 = 500 mm is remarkably lower than those obtained with other three cases. This observation is a result of the poorer mode-to-pump size ratio, as can be referred to Fig.
2.6.1(b) for R1 = 500 mm case.
When the Cr4+:YAG saturable absorber was inserted into the resonator, the degradations in the output power together with the roll-over phenomena for R1 = 200 and 500 mm in the PQS operation further highlight the crucial importance of using small ROC of the concave mirror for power scale-up, as depicted in Fig. 2.6.3(b).
During the early researches on the Nd:YLF crystal, many investigations indicated that power scaling in the Nd:YLF laser is practically hindered by the ETU effect [46-49].
The combined effect of the ETU effect and its subsequent multiphonon relaxation brings in the considerable enhancement of the thermal-lensing effect in the Nd:YLF laser. As a consequence, the increased thermal-lensing effect in the present PQS operation is believed to cause the deterioration in the output powers for R1 = 200 and 500 mm. From the analysis of the coupled rate equation, the criterion for good PQS operation is given by Eq. (2.1). Since the σgsa value of the Cr4+:YAG crystal (~(20 ± 5)
× 10-19 cm2) is remarkably larger than the σ value of the Nd:YLF crystal (1.2 × 10-19 cm2), the criterion for good PQS operation is generally satisfied in the Nd:YLF/Cr4+:YAG laser despite the ratio of the mode area A/As varies with the incident pump power and the ROC of the concave mirror. In other words, the influence of the changing mode area in the saturable absorber on the PQS performance can be neglected undoubtedly.
To further investigate the influence of the negative thermal lens on the Nd:YLF laser, we evaluate the effective focal length of the thermal lens with the help of Eqs.
(2.6) and (2.7). With the following parameters: Kc = 6.3 W/m K, α = 0.18 mm-1, λp = 806 nm, lcry = 15 mm, dn/dT = -2 × 10-6 K-1, n = 1.448, αT = 8.3 × 10-6 K-1, M2 = 115, ωpo = 210 μm, and z0 = 3.8 mm, the thermal focal length with respect to the incident pump power is plotted in Fig. 2.6.4. Numerical calculation for the CW case with =
61
0.24 is found to be consistent with the previously published data, where the fractional thermal loading is derived from the quantum defect value. According to the previous studies, the fractional thermal loading influenced by the ETU effect is usually magnified by a factor of ~3 as compared with the value in the CW operation. Therefore, we use
= 0.7 to calculate the PQS case, as revealed in Fig. 2.6.4. Numerical calculation for the PQS case is found to be in good agreement with the estimated results deduced from the
= 0.7 to calculate the PQS case, as revealed in Fig. 2.6.4. Numerical calculation for the PQS case is found to be in good agreement with the estimated results deduced from the