1. Introduction

Diode-pumped solid-state passively Q-switched green laser has high power and high repetition rate pulse in nanosecond period, and various applications in micro-mechanics, measurements, film-carve, micro-operations in surgery, and so on. In recent years, Cr⁴⁺-doped crystals have attracted a great deal of attention as passive Q-switches [1–5] because they have good photochemical and thermal stabilities, large absorption cross-section, low saturable intensity and high damage threshold. Especially Cr⁴⁺-doped YAG crystal since it can be co-doped with gain medium to form self-Q-switched laser crystal. Since S. Zhou et al. [6,7] first studied the self-Q-switched laser performance of LD pumped Cr,Nd:YAG crystal, the investigations on the self-Q-switched Cr,Nd:YAG laser have been reported by several researchers [8–11]. The experimental results in these references show that the pulse temporal profile of the self-Q-switched Cr,Nd:YAG laser is usually asymmetric, with a fast rising edge and a slow falling edge. GaAs saturable absorber is another attractive passive Q-switch because of its photochemical and thermal stabilities and the large optical non-linearity. But the pulse temporal profile of the GaAs Q-switched laser is also asymmetric, with a slow rising edge and a fast falling edge [12–14]. In some applications, the symmetric pulse is more useful. For example, when such pulse is used in high power lasers, there is no need to reshape it after amplification except that the amplified pulse is heavily saturated. If we use both the self-Q-switched Cr,Nd:YAG crystal and GaAs saturable absorber in the same cavity, according to their pulse characteristics, it is possible to obtain symmetric pulses.

In this paper, using both a self-Q-switched Cr,Nd:YAG crystal and a GaAs saturable absorber, we realize a diode-pumped doubly passively Q-switched Cr,Nd:YAG/KTP green laser for the first time, to our knowledge. This laser can generate a more symmetric and shorter pulse when compared with the self-Q-switched Cr,Nd:YAG/KTP green laser. To understand the results obtained in the experiment, we introduce a rate equation model in which the spatial distributions of the intracavity photon density, the pump beam and the population-inversion density are taken into account. The numerical solutions of the rate equations are well consistent with the experimental results.

2. Experimental setup and results

 

Fig. 1. Schematic of the experimental setup.

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The experimental setup is shown in Fig. 1. The pump source is a fiber-coupled laser-diode (FAP-I system, Coherent Inc., USA) which works at the maximum absorption wavelength (808 nm) of the Nd³⁺ ions. The mirror M₁ with 150-mm curvature radius is high antireflection coated at 808 nm and high reflection coated at 1064 nm. A 1.0-at. % Nd³⁺, 4×4×5 mm³ Cr:Nd:YAG crystal with the absorption coefficient of 3.5 cm^-1 at the pumping wavelength of 808 nm is employed. Its front surface is antireflection coated at both 808 nm and 1064 nm and its rear surface is high antireflection coated at 1064 nm. It is near M₁. The output mirror M₂ is a flat one which is coated for total reflection at 1064 nm and partial transmission at 532 nm (T=85%). The distance between M₂ and M1 is 1₂ cm. The KTP crystal cut for type-II phase matching (made by Coretech Crystal Company, Shandong University, China) is 3×3×10 mm³ and both of its surfaces are antireflection coated at 1064 nm and 532 nm. It is near M₂. The distance between the 580 µm-thick GaAs wafer and M₂ is 6 cm. The temperatures of the Cr:Nd:YAG crystal and the KTP crystal are controlled at 20 °C and 22 °C by means of a temperature controller, respectively. The temporal behaviors of the green laser pulses are recorded by a TDS620B digital oscilloscope (500-MHz bandwidth, Tektronix Inc., USA) and a fast Si PIN photodiode with a rise time of about 0.8 ns. A MAX 500AD laser power meter (Coherent Inc., USA) is used to measure the generated average output power. If we take out the GaAs saturable absorber, then we obtain the experimental setup of a diode-pumped self-Q-switched Cr,Nd:YAG/KTP green laser.

 

Fig. 2. Temporal profile of single pulse: (a) double Q-switching; (b) self-Q-switching. Solid lines, oscilloscope traces; dotted lines, calculated results.

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Single-pulse temporal profiles for the doubly passively Q-switched and self-Q-switched green lasers with a pump power of 4.1 W are shown by the solid lines in Fig. 2. In order to compare the pulse symmetry of these two lasers, we define a pulse symmetry factor α=t_i/t_f as the ratio of the rising time t_i and falling time t_f of the pulse profile. The closer to 1 the pulse symmetry factorα, the more symmetric the pulse profile. The pulse width of the doubly passively Q-switched green laser is 28.1 ns as shown in Fig. 2(a). It is noticed that the pulse profile is rather symmetric with a pulse symmetry factorα=0.995. The pulse width of the self-Q-switched green laser is 46.8 ns as shown in Fig. 2(b), and the pulse profile is asymmetric with a pulse symmetry factorα=0.698. Figure 2 indicates that the doubly passively Q-switched green laser has a symmetric pulse temporal profile and shorter pulse width compared to the self-Q-switched green laser. This is mainly due to the nonlinear absorption of the GaAs wafer, which leads to a much faster falling edge in the pulse profile. Figure 3 shows the dependence of pulse symmetry factor on incident pump power for these two lasers. From Fig. 3, we can see that the pulse symmetry is substantially improved when the GaAs wafer is used in the diode-pumped self-Q-switched Cr:Nd:YAG/KTP green laser.

 

Fig. 3. Pulse symmetry factor versus pump power.

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Fig. 4. Pulse width versus pump power.

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The dependence of pulse width on incident pump power with the double passive Q-switching and the self-Q-switching is shown by the scattered marks in Fig. 4, from which we can see that the doubly passively Q-switched green laser can compress the pulse width, and the shortest pulse with 23.1 ns in duration is obtained at the maximum pump power of 5.72 W, corresponding to a compression of 41.4 % compared with the self-Q-switched green laser.

From Figs. 2–4, we can see that for a diode-pumped doubly passively Q-switched Cr:Nd:YAG/KTP green laser with GaAs saturable absorber, the pulse symmetry is substantially improved and the pulse width is obviously compressed when compared with the self-Q-switched Cr:Nd:YAG/KTP green laser.

The dependences of pulse repetition rate, pulse energy and peak power on incident pump power with the double passive Q-switching and the self-Q-switching are shown by the scattered marks in Figs. 5–7. Figure 5 indicates that the pulse repetition rates of these two lasers increase almost linearly with the augment of incident pump power, and the pulse repetition rate of the doubly passively Q-switched Cr:Nd:YAG/KTP green laser is higher than that of the self-Q-switched Cr:Nd:YAG/KTP green laser at the same pump power. Figures 6 and 7 show that although the pulse energy from the double passive Q-switching is much smaller than that from the self-Q-switching, the pulse peak power is not significantly reduced because of the narrower pulse width obtained in the doubly passively Q-switched Cr:Nd:YAG/KTP green laser.

As mentioned above, the output mirror M₂ is coated for partial transmission at 532 nm (T=85%), that is to say, 15% of the generated green power is reflected back into the laser cavity. This portion of the green power is mainly absorbed by GaAs saturable absorber and this makes the thermal effect of the GaAs wafer become worse, especially when the pump power is high. So the slopes of the pulse energy and peak power curves of the doubly passively Q-switched green laser are smaller than those of the self-Q-switched green laser when the pump power is higher than 4.5 W, as shown in Figs. 6 and 7.

 

Fig. 5. Pulse repetition rate versus pump power.

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Fig. 6. Single-pulse energy versus pump power.

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Fig. 7. Pulse peak power versus pump power.

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3. Theoretical analysis

According to the theory of GaAs Q-switching, the interaction between the GaAs and the 1.06 µm photons includes two mechanisms [15,16]. One is the transition from EL20 to a conduction band that absorbs photon energy and produces free electrons as well as positively charged donors EL2⁺. The other is the transition from the valence band to EL2⁺ that produces free holes in the valence band and neutral donors EL20. This kind of process is called single-photon absorption (SPA). When the pump power is sufficiently high, SPA is saturated and the absorption is dominated by two-photon absorption (TPA). By combining the SPA and TPA processes and ignoring the spontaneous radiation during the pulse formation, the coupled rate equations of a diode-pumped doubly passively Q-switched Cr,Nd:YAG/KTP green laser with GaAs saturable absorber can be written as [17,18]

where ϕ(r, t)=ϕ(0, t)exp(-2r ²/$w_l^{\mathit{2}}$ ) is the average intracavity photon density, in which ϕ(0, t) is the photon density in the laser axis and w_l is the average radius of the TEM₀₀ mode. ϕ_g(r, t), ϕ_s(r, t), and ϕ_k(r, t) (ϕ_i (r, t)=($w_l^2$/$w_i^2$)ϕ(0, t)exp(-2r ²/$w_{\mathrm{i}}^2$) i=g, s, k [17]) are the photon densities at the positions of Cr,Nd:YAG crystal, GaAs wafer, and KTP crystal, where w_g, w_s , and w_k are the radii of the TEM₀₀ mode at the above-mentioned three positions, respectively, which can be obtained by the means of Ref. [17], w_g, w_s, w_k , and w_l as functions of incident pump power are shown in Fig. 8. n(r, t) is the spatial distribution of the population-inversion density. n_s1 (r,t) and n _s0 are the ground-state and total population densities of Cr⁴⁺:YAG saturable absorber, respectively. σ and l are the stimulated-emission cross section and length of the gain medium, respectively. σ_g and σ_e are the ground-state and excited-state absorption cross sections of Cr⁴⁺:YAG saturable absorber, respectively. n ₀ is the total population density of the EL2 defect level (including EL20 and EL2⁺) of GaAs saturable absorber. n ⁺(r, t) is the population density of positively charged EL2⁺. σ ⁰ and σ ⁺ are the absorption cross sections of EL2⁰ and EL2⁺, respectively. l_s is the thickness of GaAs wafer. t_r is the round-trip time of light in the resonator {t_r =[2n ₁ l+2n ₂ l s+2n ₃ l_k +2(L_e -l-l_s -l_k )]/c}, in which n ₁, n ₂, and n ₃ are the refractive indices of Cr,Nd:YAG crystal, GaAs saturable absorber, and KTP crystal, respectively, L_e is the cavity length, l_k is the length of KTP crystal, c is the velocity of light in vacuum. B=6βhγc(w_g/w_s )² is the coupling coefficient of TPA in GaAs [13], where β is the absorption coefficient of TPA, hγ is the single photon energy of the fundamental wave. L is the intrinsic loss. τ is the stimulated-radiation lifetime of the gain medium. τ_s is the excited-state lifetime of Cr⁴⁺:YAG saturable absorber. R_in(r)=P_inexp(-2r ²/$w_p^2$)[1-exp(-αl)]/hγ_p${\pi w}_p^{\mathit{2}}$l is the pump rate, where P_in is the pump power, hγ_p is the single-photon energy of the pump light, w_p is the average radius of the pump beam, α is the absorption coefficient of the gain medium. The coefficient δ_k which is related to the second harmonic conversion can be expressed as [18]

where ω is the angle frequency of the fundamental wave. d_eff is the effective nonlinear coefficient. ε₀ is the dielectric permeability of vacuum. $n_e^{\mathit{2}\omega }$ is the refractive index of second-harmonic wave. $n_{\mathit{0}}^{\omega }$ and $n_e^{\omega }$ are fundamental-wave refractive indices of o and e light, respectively.

 

Fig. 8. Beam size versus pump power.

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Table 1. The parameters of the theoretical calculation.

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According to the corresponding parameters shown in Table 1, by numerically solving Eqs. (1)–(4), we obtain the theoretical pulse profiles for the doubly passively Q-switched and self-Q-switched green lasers with a pump power of 4.1 W as shown by the dotted lines in Fig. 2(a) and 2(b). The pulse widths of these two lasers are 28.5 ns and 47.4 ns, respectively. The theoretical results indicate that the doubly passively Q-switched green laser has a symmetric pulse temporal profile and shorter pulse width compared to the self-Q-switched green laser. The theoretical calculation curves for pulse width, pulse repetition rate, pulse energy and peak power versus pump power with these two lasers are shown by the solid lines in Figs. 4–7, respectively.

From Fig. 2 and Figs. 4–7, we can see that the theoretical calculations are in good agreement with the experimental results.

4. Conclusions

We have successfully realized a diode-pumped doubly passively Q-switched Cr,Nd:YAG/KTP green laser with GaAs saturable absorber for the first time, to our knowledge. This laser can generate a more symmetric and shorter pulse when compared with the self-Q-switched Cr,Nd:YAG/KTP green laser. A rate equation model is introduced to theoretically analyze the results obtained in the experiment, in which the spatial distributions of the intracavity photon density, the pump beam and the population-inversion density are taken into account. The numerical solutions of the rate equations agree with the experimental results well.