1. Introduction

Yb:YCa₄O(BO₃)₃ (Yb:YCOB), along with its isomorphic compound, Yb:GdCa₄O(BO₃)₃ (Yb:GdCOB), are among the few Yb laser crystals that have been known since the early stage in the development of Yb lasers [1–4]. Although efficient continuous-wave (cw) laser action was achieved with Yb:YCOB under diode pumping in as early as 1999, generating an output power of ~0.45 W with a slope efficiency of 73% [2], since then this laser crystal had not attracted much attention. This situation lasted until 2007, when a cw output power of 2.8 W was generated with a diode pumped Yb:YCOB laser [5]. Shortly thereafter, the cw laser performance of this monoclinic crystal was evaluated thoroughly by use of samples cut along the three principal optical axes, with output power generated amounting to 7.3 W [6,7]. More importantly, complex polarization state varying behavior was observed in the laser oscillation generated with a Y-cut Yb:YCOB crystal [7]. Despite the relatively low thermal conductivity (~2 Wm⁻¹K⁻¹) of Yb:YCOB, thin-disk lasers based on this crystal have been realized in efforts of power scaling, producing an output power of ~100 W [8,9]. A wide tuning range of 997−1092 nm was also obtained with the thin-disk laser [8]. Due to its wide emission bandwidth, the Yb:YCOB crystal is very attractive in generating ultrashort laser pulses by mode-locking technique. In recent years a lot of work has been conducted on mode-locked Yb:YCOB lasers, with the pulse duration reduced from the initial 210 fs to the latest 35 fs [10–13].

In addition to possessing wide emission spectra that enable the generation of mode-locked ultrashort laser pulses, the Yb:YCOB crystal is also known to have a long fluorescence lifetime (2.2 ms [8]) and small stimulated emission cross sections (~0.3−0.4 × 10⁻²⁰ cm² at ~1030−1040 nm for E//Z [8]) which amount only to less than one fifth that of Yb:YAG (2.1 × 10⁻²⁰ cm² [14]), these features can greatly benefit Q-switching laser operation owing to the large energy storage capacity. Up to now, however, studies on the Q-switching laser performance of Yb:YCOB are still very limited, the only relevant work conducted is the demonstration of a passively Q-switched laser, with InGaAs quantum wells serving as the saturable absorber, producing an output power of 1.15 W (pulse energy of 165 μJ and duration of 100 ns) [5]. In comparison with the performance of passively Q-switched lasers based on other Yb crystals [15–18], the capacity of Yb:YCOB in generating Q-switched laser pulses has not been effectively explored. Therefore, more efforts need to be made to evaluate the real potential of this monoclinic Yb crystal in applications for making Q-switched laser devices.

In this paper we report on the passive Q-switching laser performance of Yb:YCOB crystal, demonstrated with Cr⁴⁺:YAG crystals utilized as saturable absorber. By properly selecting the initial transmission of the Cr⁴⁺:YAG crystal (T₀) and the output coupling of the resonator (T), we realized efficient Q-switched laser operation with Yb:YCOB crystal, generating laser pulses of energy as high as 476 μJ, much higher than obtained with most other Yb crystals under similar operational conditions.

2. Description of experiment

As is known, Yb:YCOB is a monoclinic biaxial crystal of very low symmetry (point group m), its spectroscopic properties and cw laser performance exhibit strong anisotropy [6,8,19]. To account for such anisotropy in evaluating the Q-switching laser performance, we prepared three crystal samples cut along the principal optical axes (X, Y, and Z) from the same crystal boule, with an identical thickness of 2.88 mm and a square aperture of 3.3 mm × 3.3 mm. The Yb ion concentration of the Yb:YCOB crystal was 8.8 × 10²⁰ cm⁻³ (20 at. %). Several Cr⁴⁺:YAG crystals were utilized as saturable absorbers for passive Q-switching action, their initial transmissions were T₀ = 97.5%, 94.4%, 93.7%, and 92.0%, respectively. These Cr⁴⁺:YAG plates were coated for antireflection at 1.06 μm on both faces. The laser resonator was formed by a plane reflector and a concave mirror of radius-of-curvature of 50 mm, which served as the output coupler. The plane reflector was coated for high reflectance (>99.9%) at 1030−1200 nm and high transmittance (>98%) at 820−990 nm. A group of output couplers were used in the optimization of the Q-switched laser operation, with output couplings ranging from T = 10% to T = 50%. To achieve efficient laser action, the uncoated Yb:YCOB crystal was held in a water-cooled copper block which was maintained at a temperature of 5 °C, and was positioned close to the plane reflector inside the resonator, while the Cr⁴⁺:YAG plate was inserted between the laser crystal and the output coupler. The physical cavity length was 28 mm. The pump source used was a fiber-coupled diode laser (fiber core diameter of 200 μm and NA of 0.22) emitting unpolarized radiation with center wavelength varying from 968 to 971 nm, which was dependent on the output power level. The emission bandwidth of this diode laser was at most 3 nm. The pump radiation was focused first by a focusing optics and then delivered through the plane reflector onto the laser crystal with a beam spot radius of approximately 100 μm. A digital oscilloscope (Infiniium DSO80304B, Agilent Co. Ltd.), with the bandwidth of 3 GHz and sampling rate up to 40 GS/s, was employed to monitor the laser pulses and measure the pulse parameters. The laser emission spectra were measured by use of a spectrometer (AvaSpec-3648, Avantes B.V.) with a resolution of 0.3 nm.

3. Results and discussion

For efficient laser action, the Yb:YCOB crystal was actively cooled with cooling water of temperature of 5 °C, in order to diminish the impact of thermally induced resonant losses inherent to a quasi-three-level laser. With the cooling water temperature rising from 5 °C to 20 °C, the laser efficiency would be reduced by about 5−10%, measured at an output power of 1.0 W when the laser was operated in cw mode. Without active cooling, significant temperature rise would occur within the pumped region inside the crystal, leading to an increase in the transition linewidth (Δω_a) as a result of the strengthened homogeneous phonon broadening, and hence reducing the stimulated emission cross section that is inversely proportional to Δω_a [20]. Such variation of stimulated emission cross section with temperature has been confirmed experimentally in a study on Yb:YAG crystal [21].

The passive Q-switching laser performance of Yb:YCOB was studied with the X-, Y-, and Z-cut crystal samples in the simple plano-concave resonator, under operational conditions of different combinations of T₀ and T. It was found experimentally that the X-cut crystal was advantageous over the Y- and Z-cut samples, in generating average output power as well as pulse energy. With the X-cut crystal efficient Q-switched laser operation could be obtained with an output coupling that varied from T = 10% to T = 50%; in the case of T < 10%, efficient laser action was also attainable, but on a risk of possible damage to the internal elements under high-power conditions. The Q-switched laser operation achieved with the Y-cut crystal proved to be less efficient, and the highest output coupling allowed to be used was limited to T ≤ 30%. With the Z-cut crystal, however, no stable Q-switching laser action could be obtained, even in the case of T₀ = 97.5%, which was the highest initial transmission of the Cr⁴⁺:YAG saturable absorber available in the current experiment. For Z-cut Yb:YCOB crystal, laser oscillation (cw) could only be realized with polarization parallel to the X axis (E//X) [6], the stimulated emission cross section for E//X proves to be even lower than for E//Z, amounting to approximately 0.25 × 10⁻²⁰ cm² [8]. This implies that a Cr⁴⁺:YAG saturable absorber of still higher T₀ might be required to generate passive Q-switching laser action.

Shown in Fig. 1 are the output characteristics of the Yb:YCOB laser operating under different Q-switching conditions (T₀ and T), measured for the X-cut crystal (a) and for the Y-cut crystal (b). The results of cw operation, which were measured in the current experiment for the case of T = 10%, under the same resonator conditions without the saturable absorber in place, are also presented for comparison. The solid straight lines plotted in this figure aim to indicate the trends of power scaling, according to which the average slope efficiencies (η) were determined. The experimental uncertainty of the measured output power was estimated to be less than 2% for all cases. The laser oscillation generated with both X- and Y-cut crystals was found to be linearly polarized, having a polarization state of E//Z which remained fixed, regardless of either the variation of T (>10%) and T₀ or the change in pump power. This is consistent with the previously reported results for the cw laser operation of the Yb:YCOB crystal [6,7]. Although the cubic Cr⁴⁺:YAG crystal was reported to exhibit some degree of anisotropy [22,23], its effect on the polarization state of the Q-switched Yb:YCOB laser was not observed in our experiment. It should also be pointed out that the polarization state of E//Z could be altered if necessary, by adding an internal polarization selecting element such as a Brewster plate, to obtain polarized oscillation with E//Y (for X-cut crystal) or with E//X (for Y-cut crystal). With the X-cut crystal, very efficient Q-switched laser operation was achieved under conditions of T = 10% and T₀ = 97.5%. Above the lasing threshold reached at an absorbed pump power (P_abs) of 1.05 W, the average output power scaled with pump power, reaching 5.02 W at P_abs = 7.8 W, giving rise to an optical-to-optical efficiency of 64%, while the slope efficiency determined for P_abs > 3.5 W was 82%. One sees from Fig. 1(a) that the Q-switched output power is very close to its cw counterpart over the entire operational range in the case of T = 10%, which is a direct indication of efficient Q-switching action. Under conditions of T = 20% and T₀ = 94.4%, the Q-switching laser action arrived at threshold at P_abs = 1.9 W, producing a maximum output power of 3.59 W at P_abs = 7.8 W, with a slope efficiency of 73%.

 

Fig. 1 Output power versus P_abs generated with the X-cut Yb:YCOB crystal (a), and with the Y-cut Yb:YCOB crystal (b).

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In general, high-energy short-duration laser pulses in passively Q-switched operation can only be obtained under conditions of high T and low T₀. According to this, the optimum combination of T and T₀, which could be used for the X-cut Yb:YCOB laser, was T = 40% and T₀ = 93.7%. In this case, the absorbed pump power required for reaching laser threshold was measured to be P_abs = 4.2 W, much higher than measured in the other two cases, due to the high overall losses. Despite the high lasing threshold, a maximum output power of 2.14 W was generated with a slope efficiency still amounting to 65%.

In our experiment, efforts were also made to operate the Q-switched X-cut Yb:YCOB laser under conditions of T > 40% and T₀ < 93.7%. However, with a coupler of T = 50%, the lasing threshold was found to be too high; while damage was easy to occur on the surface of the laser crystal or the Cr⁴⁺:YAG plate when a saturable absorber of T₀ = 92.0% was used. Due to the low stimulated emission cross section (maximum value of 0.46 × 10⁻²⁰ cm² for the laser emission band [8]), a very large energy fluence is expected to exist inside the resonator for efficient Q-switched laser action, making it very likely that damage occurs to the surface of intracavity elements. In order to prevent such damage while employing a saturable absorber of lower T₀ to produce higher pulse energy from the Yb:YCOB laser, an output coupler of larger radius-of-curvature (e.g., R₂ = 100 mm) and of suitably high transmission should be utilized to form the plano-concave resonator with longer cavity length. In this way, the oscillating mode size will become larger, whereas the resulting laser pulse duration will be longer, this will greatly reduce the internal circulating intensity while the energy fluence remains unchanged, and hence reduce the risk of intracavity element damage. Evidently, to keep mode matching with the enlarged laser mode size, the pump beam spot should also be expanded accordingly. On the other hand, more pump power is needed in this case to realize equally efficient laser operation.

The passive Q-switching laser performance achieved with the Y-cut crystal, as illustrated in Fig. 1(b), turns out to be inferior to that demonstrated with the X-cut crystal. This seems to be in controversy with the previously reported results for cw laser operation, where the Y-cut crystal proved to be even slightly advantageous over the X-cut one [6]. Among other factors, the difference in optical quality between the X- and Y-cut samples used in the current experiment, which were prepared from different parts of the crystal boule, might be responsible for the less efficient operation with the Y-cut crystal. One direct evidence for this is the lasing threshold for Q-switched operation measured in the case of T = 20% and T₀ = 94.4%, which was considerably higher for the Y-cut crystal. Given the same stimulated emission cross section involved in the two cases (E//Z), a higher threshold implies greater dissipative losses arising from the Y-cut crystal. In the case of T = 10% and T₀ = 97.5%, the maximum output power measured at P_abs = 7.5 W, the highest pump power applied in this case, was 3.51 W, the corresponding optical-to-optical and slope efficiencies being 47% and 63%, respectively. The highest output power, produced in the pulsed operation achieved under conditions of T = 20% and T₀ = 94.4%, was 2.75 W, the slope efficiency being 62%.

It can also be seen from Fig. 1 that, in each case, the increase of output power with P_abs exhibited no tendency of rolling off at the highest pump power, implying that there was still more room for further power scaling. To prevent any possible crystal fracturing of the Yb:YCOB samples, we limited the highest pump power absorbed in the crystal to be 7.8 and 7.5 W, for the X- and Y-cut crystals, respectively.

In general, the transverse mode structure of a laser is determined mainly by the resonator configuration, the mode matching of pump with laser beam, and the specific laser material used; it also depends to some extent on pump power or output power level. For the Yb:YCOB laser studied in our experiment, its beam pattern was almost independent of either the output coupling or the operational fashion (cw or Q-switched). Illustrated in Fig. 2 is a typical beam profile, measured at an output power of 1.0 W for the X-cut Yb:YCOB laser operating in cw mode. The corresponding beam quality factor, M², was measured to be 2.19 and 2.27, for the horizontal and vertical directions, respectively. This indicates the presence of higher-order transverse modes in the laser oscillation. Nevertheless, the laser intensity can still be well fitted to a Gaussian distribution, in both the horizontal and vertical directions, as shown in this figure. For the resonator configuration used in this laser, the fundamental mode radius is calculated to be about 90 μm at the position of the laser crystal, in the absence of thermal lensing effect, which is somewhat smaller than the pump beam spot radius (~100 μm). With the strengthening of thermal lensing in the laser crystal, the fundamental mode radius will be reduced to some extent, facilitating the oscillation of higher-order transverse modes.

 

Fig. 2 A typical laser beam profile measured at an output power of 1.0 W for the X-cut Yb:YCOB laser operating in the cw mode.

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In Q-switched or cw laser operation under certain conditions of T and T₀, the oscillation wavelengths varied only slightly with pump power. Illustrated in Fig. 3 are the laser emission spectra measured at an intermediate pump power for cw or Q-switched operation achieved with the X- or Y-cut crystal under different conditions. These emission spectra were recorded for a time average of many laser pulses, depending on the response time of the spectrometer employed. One sees that the emission spectra for cw operation consist of many discrete peaks or lines which are roughly equally spaced, such modulation resulted from the effect of some etalons existing inside the resonator (e.g., formed by the uncoated crystal surface and the plane cavity mirror), with the separation between two adjacent lines corresponding to the free spectra range. In the case of passively Q-switched operation, the structure of laser emission spectrum was determined not only by such etalon effect, but also by the discrimination of longitudinal modes accompanying the passive Q-switching process [24]. Due to the presence of the latter mode selecting action, the laser emission spectrum of the passively Q-switched operation is usually narrower than its cw counterpart. In fact, under some certain circumstances only a single longitudinal mode can survive from this mode discrimination effect during the passive Q-switching process [16,25,26]. In cw laser operation for T = 10%, the oscillation wavelengths measured for the two crystal samples were very close: 1039.4−1048.0 nm (X-cut) and 1039.8−1046.6 nm (Y-cut). In Q-switched operation achieved with the X-cut crystal, the laser emission range shifted to 1033.8−1040.7 nm (T = 10%, T₀ = 97.5%), 1031.3−1033.2 nm (T = 20%, T₀ = 94.4%), and 1031.0−1032.7 nm (T = 40%, T₀ = 93.7%). Similarly, this emission range measured for the Y-cut crystal was 1035.0−1041.7 nm (T = 10%, T₀ = 97.5%) and 1026.6−1033.5 nm (T = 20%, T₀ = 94.4%), as shown in Fig. 3. The multi-longitudinal-mode oscillation obtained with the passively Q-switched Yb:YCOB laser reveals the strong mode competition, due to the very close gain seen by these individual axial modes. For the laser resonator of 28 mm in cavity length, the axial mode separation is 0.018 nm (for the oscillation at 1030 nm). Therefore, the laser emission bands, about 2−7 nm in width measured in Q-switched operation, correspond to approximately 110−390 longitudinal modes. A tendency is also clearly shown in Fig. 3 that the laser emission spectrum will shift toward short-wavelength side, as the cavity losses are increased by increasing T and/or decreasing T₀. This is a common feature for a broad-band quasi-three-level laser. As is known for such lasers, the oscillation, in the absence of an internal wavelength selector, will occur at wavelengths where the net gain reaches its maximum. Depending on the specific absorption and emission cross section spectra for a given laser crystal, the net gain is determined by the fraction of excited active ions (β), which in turn is proportional to the cavity losses. In general, the net gain maximum tends to shift to short-wavelength side with the amount of β being increased (and hence with the cavity losses increased), as calculated for the Yb:YCOB crystal [19]. This explains the behavior of oscillation wavelength shifting in connection with the change in T and/or T₀, observed with the Yb:YCOB laser in the current experiment.

 

Fig. 3 Q-switched and cw laser emission spectra measured at P_abs = 4.78 W for the X-cut crystal (a), and at P_abs = 4.71 W for the Y-cut crystal (b).

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As usual, the pulse repetition frequency (PRF) measured in passively Q-switched operation of the Yb:YCOB laser increased with pump power. Figure 4 depicts the variations of PRF with P_abs over the entire operational range, measured under different Q-switching conditions. One sees that the PRF would be greatly reduced with increasing T and decreasing T₀. For the X-cut crystal, the maximum PRF measured at P_abs = 7.8 W was 19.0 kHz (T = 10%, T₀ = 97.5%), 8.5 kHz (T = 20%, T₀ = 94.4%), and 4.5 kHz (T = 40%, T₀ = 93.7%); for the Y-cut crystal, it was 16.7 kHz (T = 10%, T₀ = 97.5%), and 6.7 kHz (T = 20%, T₀ = 94.4%), measured at P_abs = 7.5 W.

 

Fig. 4 Pulse repetition frequency as a function of P_abs, measured under different Q-switching conditions for the X-cut crystal (a) and for the Y-cut crystal (b).

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The energy contained in a single laser pulse can be determined from the measured output power and the corresponding PRF. Figure 5 illustrates the variation of pulse energy with P_abs for different Q-switching conditions. In the case of T = 10%, T₀ = 97.5%, the pulse energy generated with the X- and Y-cut crystals was 264 and 240 μJ (maximum), respectively. Under Q-switching conditions of T = 20%, T₀ = 94.4%, the pulse energy produced was 422 (X-cut) and 410 μJ (Y-cut). While in Q-switched operation achieved with the X-cut crystal under conditions of T = 40%, T₀ = 93.7%, a pulse energy as high as 476 μJ was generated.

 

Fig. 5 Pulse energy versus P_abs, generated under different Q-switching conditions for the X-cut crystal (a) and for the Y-cut crystal (b).

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Unlike the pulse energy that varied to some extent with pump power, the pulse duration was found to be independent of pump power, it depended only on the T and T₀ used when the cavity length remained unchanged. Illustrated in Fig. 6 are typical profiles of the laser pulses generated under different conditions of T and T₀, measured at an intermediate pump level of P_abs = 4.78 W for the X-cut crystal (a) and P_abs = 4.71 W for the Y-cut crystal (b). In the case of T = 10%, T₀ = 97.5%, the laser pulses generated with the X- and Y-cut crystals were respectively 26.2 and 23.5 ns in duration. The laser pulse duration was reduced to 9.3 ns in the operation with the X-cut crystal under conditions of T = 40%, T₀ = 93.7%; while with the Y-cut crystal under conditions of T = 20%, T₀ = 94.4%, the pulse duration was measured to be 9.5 ns.

 

Fig. 6 Typical profiles of the laser pulses generated under different Q-switching conditions with the X-cut crystal (a) and with the Y-cut crystal (b).

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Given the pulse energy (E_p) and duration (t_p), one can estimate the peak power (P_p) of the laser pulse by P_p = E_p/t_p. The peak power reached with the X-cut crystal, under conditions of T = 40% and T₀ = 93.7%, amounted to 51.2 kW; with the Y-cut crystal, the peak power achieved was 43.2 kW under Q-switching conditions of T = 20% and T₀ = 94.4%.

In a previously reported Yb:YCOB laser passively Q-switched with InGaAs quantum wells acting as saturable absorber, the pulse energy generated was 165 μJ, while the pulse duration was 100 ns [5]. In terms of average output power, pulse energy, duration, and peak power, the passive Q-switching laser performance of Yb:YCOB demonstrated in the current experiment represents a significant improvement. It is also interesting to note that the Q-switched operation achieved with the InGaAs quantum wells occurred in a range around the center wavelength of 1086 nm [5], whereas the emission spectra measured for the present Q-switched Yb:YCOB laser fell in the range of 1025−1042 nm. Clearly, they correspond to different emission bands in the emission spectrum of the Yb:YCOB crystal [8], which originate from different transitions between Stark levels.

As most of the known Yb doped crystals, the Yb:YCOB possesses a very broad emission band, covering a wavelength range from ~950 to 1100 nm, with the strongest emission peak located at about 976 nm, which corresponds to the zero-phonon transition [8]. Given the extremely high resonant losses around this emission peak, it seems to be impractical to realize laser oscillation at this wavelength. In the passively Q-switched laser operation demonstrated in our experiment, the oscillation occurred in the wavelength range of 1025−1042 nm, since the net gain maximum was reached in this range under different Q-switching operational conditions. Without special wavelength selecting, laser oscillation at the weak emission peak of 1086 nm is achievable as long as the output coupling utilized remains sufficiently low, no matter which crystal orientation (X-, Y-, or Z-cut) is used, as indicated in a previous study on cw Yb:YCOB lasers [6]. In the passively Q-switched Yb:YCOB laser with InGaAs quantum wells as saturable absorber, specific coatings were made for 1086 nm on the crystal surface and cavity mirrors, ensuring oscillation at this wavelength [5].

Tables 1 and 2 summarize the primary parameters characterizing the passive Q-switching laser performance of the X- and Y-cut Yb:YCOB crystals demonstrated in this experiment, in which the additional symbols are defined as follows: P_avr, maximum average output power; η_opt, optical-to-optical efficiency; η_s, slope efficiency; and λ_c, center oscillation wavelength.

Table 1. Parameters Characterizing the Passively Q-switched X-cut Yb:YCOB Laser

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Table 2. Parameters Characterizing the Passively Q-switched Y-cut Yb:YCOB Laser

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The performance of a passively Q-switched laser can be predicted theoretically on the basis of rate equations. There have been many analytical or numerical models for this purpose, most of which were developed in the past two decades [27–33]. These models turn out to be very helpful, not only in understanding the output characteristics of the passively Q-switched laser, but also in providing a useful guide to optimizing such type of lasers. In what follows, we shall carry out some theoretical calculations for the passively Q-switched Yb:YCOB laser.

We first calculate the laser pulse energy, with the help of the analytical model developed by Chen et al [30]. In this model, two parameters, α and β, are defined as follows: α = (1/γ)(σ_gs/σ)(A/A_s), and β = σ_es/σ_gs. In these definitions γ is the inversion reduction factor; σ is the stimulated emission cross section of the gain medium; σ_gs and σ_es are respectively the ground-state and excited-state absorption cross sections of the saturable absorber; A and A_s are the effective mode area in the gain medium and in the saturable absorber. For the current Yb:YCOB/Cr⁴⁺:YAG Q-switched laser, γ = 0.91; σ = 0.45 × 10⁻²⁰ cm²; σ_gs = 4.3 × 10⁻¹⁸ cm² [33]; σ_es = 0.82 × 10⁻¹⁸ cm² [33]; and A/A_s = 0.8, so we have α = 840, β = 0.19. It is worth noting that the amount of α for the Yb:YCOB laser is very much greater than that for a typical Nd laser such as Nd:YAG or Nd:YVO₄. Due to this extremely large α, the upper bound (T₀)_upper and the lower bound (R)_lower simply reduce to (T₀)_upper = 1 and (R)_lower = 0, that is, there is essentially no limit to either T₀ or R, and the second threshold condition can always be met by the Yb:YCOB laser. Thus the expression for the pulse energy, given by (26) in [30], can be written as E = (hν/σ)(A/2γ)f(α,β)ξ(R,T₀), where ξ(R,T₀) is given by ξ(R,T₀) = 2(1−β)(lnR)(lnT₀)(1−T₀^η)(L−lnR−2βlnT₀)⁻¹, the output coupler reflectivity R = 1−T, and L represents the round-trip dissipative losses. The f(α,β) and η appearing above are defined by (27) and (28) in [30]. For α = 840, β = 0.19, we get f(α,β) = 1.36. If we take L = 0.02, A = 1.77 × 10⁻⁴ cm² (effective laser beam radius of 75 μm), and hν = 1.93 × 10⁻¹⁹ J (oscillation wavelength of 1030 nm), the laser pulse energy can be simply calculated for different operational conditions. The results of calculation are listed in Table 3 .

Table 3. Analytical and Numerical Calculations of the Pulse Energy and Duration for the Yb:YCOB Laser

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Comparing the calculated laser pulse energies with the experimental results listed in Tables 1 and 2, one sees that this analytical model provides a very satisfying prediction for the pulse energy generated under conditions of T = 20%, T₀ = 94.4% or T = 40%, T₀ = 93.7%. For the case of T = 10%, T₀ = 97.5%, however, the expected pulse energy, 173 μJ, proves to be substantially lower than that measured experimentally. This discrepancy is assumed to be due to the nominal amount for T₀ (97.5%), which might be greater than its real value. As presented in Table 3, the calculated energy for T = 10%, T₀ = 96.5%, 246 μJ, agrees very well with the experimental results given in Tables 1 and 2.

Next we will calculate the laser pulse parameters by using a numerical model for passively Q-switched Yb lasers, which takes into account the resonant absorption losses inherent to a quasi-threel-level laser [33]. This model has been applied to various lasers, such as Yb:GGG, Yb:GdAB, and Yb:YGG [15,26,33].

In addition to σ_gs, σ_es, σ, γ, A/A_s, and L, whose values were given above, the other parameters needed in the numerical calculation include (using the same symbols as in [33]):ω_L = 70 μm, ω_p = 100 μm, l = 2.88 mm, n₀ = 8.8 × 10²⁰ cm⁻³, n_a0 = f_an₀ = 0.36 × 10²⁰ cm⁻³, and t_r = 0.20 ns. The results obtained from this numerical calculation for the pulse energy and duration are also listed in Table 3. By a comparison with the measured results given in Tables 1 and 2, one sees that the numerical calculation gives a fairly close expectation for the pulse energy and duration, except that the calculated energy for the case of T = 10%, T₀ = 97.5% is again much lower than the measured result. The possible reason for this is just as mentioned in the analytical calculation.

It is instructive to make a direct comparison of Yb:YCOB with other Yb crystals in passive Q-switching laser performance. Table 4 summarizes the pulse energy, duration, and peak power, obtained in Cr⁴⁺:YAG passively Q-switched laser operations with various Yb crystals, which were achieved with similar plano-concave resonators under similar pumping conditions. In these studies, the cavity lengths in different experiments were in a range of 22−40 mm, while the laser crystals utilized were 2−4 mm in thickness. The Q-switching operational conditions (T and T₀) are also listed for each crystal. These data are cited from the following references: Yb:YAB [34], Yb:GdAB [15], Yb:CYB [35], Yb:KLuW [36], Yb:NaGdW [16], Yb:NaYW [17], Yb:CNGG and Yb:CLNGG [18], Yb:LuGG [25], and Yb:YGG [26]. In addition to laser parameters, the stimulated emission cross section (σ_em), fluorescence lifetime (τ_f), and thermal conductivity (κ_c), all of which are important for passive Q-switching laser operation, are also listed in Table 4 for each crystal if available, the values presented here are for room-temperature. One can clearly see that the laser pulse energy produced with Yb:YCOB is considerably higher than generated with others except for Yb:GdCOB, an isomorphic crystal belonging to the same oxyborates family. In fact, the two Yb:oxyborates are very similar in spectroscopic properties [8,19,37]. Possessing a still longer fluorescence lifetime (2.5 ms [37]), the Yb:GdCOB seems to be slightly more advantageous in generating Q-switched laser pulses. However, Yb:YCOB is of greater capability to accommodate more Yb ions while maintaining high crystal quality, which is due to the closer ionic radii of Yb and Y. According to our experimental results, the maximum output power, generated under the same Q-switching operational conditions of T = 20%, T₀ = 94.4% with a 2 mm thick Y-cut Yb:GdCOB crystal, amounted only to 1.05 W, despite the very close pulse energy obtained.

Table 4. Comparison of Passive Q-switching Laser Performance Achieved with Various Yb crystals

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4. Conclusion

In summary, the passive Q-switching laser performance of the Yb:YCOB has been studied with crystal samples cut along the principal optical axes, employing different Cr⁴⁺:YAG saturable absorbers. Highly efficient Q-switched laser operation was realized by use of the X-cut crystal, with a Cr⁴⁺:YAG saturable absorber of T₀ = 97.5% and an output coupler of T = 10%, generating an output power of 5.02 W at a pulse repetition rate of 19.0 kHz, with optical-to-optical and slope efficiencies determined to be 82% and 64%, respectively. While in the pulsed operation achieved with the X-cut crystal under conditions of T = 40% and T₀ = 93.7%, the output power reached 2.14 W at a pulse repetition rate of 4.5 kHz, with a slope efficiency of 65%, the resulting laser pulse was 9.3 ns in duration, with energy as high as 476 μJ and peak power amounting to 51.2 kW. It turns out that the passive Q-switching laser performance of Yb:YCOB is much superior to most of other Yb crystals which are available at present, revealing its great potential in developing high-energy compact, miniature, or microchip pulsed laser devices.