Q-Switched Mode-Locking by Cascaded Second-Order Nonlinearity in a Nd:YVO₄ Laser

Abstract

A diode-pumped Q-switched mode-locked Nd:YVO₄ laser via a positive cascaded second-order Kerr lens using periodically poled MgO:SLT at 1064 nm was reported. Q-switched mode-locking performances, including pulse duration, output power, and bandwidth, were studied under different pump conditions. Under 28 W quasi-CW (QCW) diode pump peak power, the measured mode-locked pulse train, Q-switched repetition rate, and Q-switched pulse duration were 18 ps, 300 kHz, and 50 ns, respectively. The highest peak power of a single pulse near the maximum of the Q-switched envelope was greater than 150 kW.

1. Introduction

Q-switched mode-locked (QML) lasers are the mode-locked pulses underneath a Q-switched envelope, which have higher pulse energy and peak power and are extensively utilized in laser material processing, nonlinear optics, and Raman spectroscopy [1,2]. Several schemes have been proposed and can be classified by active or passive methods. In the active method, an acousto-optic modulator (AOM) is inserted in the cavity, and the cavity round trip time is designed to match the radio frequency of the AOM [1]. In the passive method, a saturable absorber (SA), such as Cr:YAG [3], graphene [4], or molybdenum disulfide (MoS₂) [5], is implemented to modulate the cavity loss and start the Q-switching or mode-locking process. The passive scheme has the advantages of simplified cavity design and large modulation depth. However, the low damage threshold and the absorption range of SA limit the power scaling as well as the operating range of QML laser. Adopting an intracavity nonlinear second harmonic generation (SHG) process, a promising technique by which to produce a high average ML power and wide operating range has been demonstrated [6]. When the SHG process is operated under a phase-mismatched condition, the second harmonic wave (SHW) is converted back to the fundamental wave (FW) in a coherent length, and the accumulated nonlinear phase mimics the effective nonlinear index of refraction. Adopting the soft or hard aperture design in the cavity, the phase modulation generated by the cascaded process can be converted to amplitude modulation.

In the regime of low FW intensity or the large phase-mismatched regime, the $n_2^{eff}$ can be approximated by $n_2^{eff}=-{\displaystyle \frac{\mathrm{L}}{\mathsf{\Delta }k\mathrm{L}}}{\displaystyle \frac{4\pi d_{eff}^2}{n_{\omega }^2{n}_{2\mathsf{\omega }}\mathsf{\lambda }{\epsilon }_{0}C}}$ [7], where $\mathsf{\Delta }\mathrm{k}\mathrm{L}$ ($\mathsf{\Delta }\mathrm{k}\mathrm{L}=(k_{2\mathsf{\omega }}-2k_{\omega })\times L$) is the phase-mismatched term in the frequency doubling process; L is the length of nonlinear crystal; $d_{\mathrm{e}\mathrm{f}\mathrm{f}}^2$ is the square of effective nonlinear coefficient; λ is the wavelength of FW; $n_{\mathsf{\omega }}$ and $n_{2\mathsf{\omega }}$ are the refractive index of FW and SHW, respectively ; and c is velocity of light. The sign of $n_2^{eff}$ can be further manipulated by the phase-mismatched condition, ΔkL, and the magnitude of $n_2^{eff}$ is at least one order larger than the intrinsic $n_2$ (${\chi }^3$ process) [8]. To study the QML performance induced by cascaded second-order nonlinearity, we compared the CW and QCW pump schemes, where the gain-switched ML behavior was observed in the QCW pump scheme and peak power was further enhanced.

2. Experimental Setup

Figure 1 shows a schematic of a Q-switched mode-locked Nd:YVO₄ laser by an intracavity second harmonic generation in a 1 mol.% MgO-doped, periodically poled stoichiometric lithium tantalate (MgO:PPSLT) crystal of 30 mm in length and with a Λ = 7.97 μm grating period phase-matched at 1064 nm with a temperature of 57 °C. An a-cut, 9 mm long, 0.4-at.% Nd-doped YVO₄ crystal with an aperture of 3 × 3 mm², was used as the gain medium and polished with a 1 degree wedge to prevent etalon effect. The incident surfaces of Nd:YVO₄ were coated with anti-reflection coatings (R < 0.5%) at 808 nm and 1064 nm. To dissipate the heat generation, the laser crystal was wrapped with indium foil and placed in a copper block for water cooling at 15 °C. The pump diode laser was equipped with volume Bragg grating (VBG), and the output wavelength was fixed at 808 nm. The core radius of the pump diode laser was 100 μm and refocused into the gain medium through a set of 1 to 1.4 coupling lenses. The V-folded cavity was constructed by an input coupler (IC), HR mirror, and output coupler (OC). Two intracavity lenses, f₁ (f = 250 mm) and f₂ (f = 125 mm), were used to ensure the beam radius of ~90 μm in the MgO:PPSLT crystal and ~350 μm in the gain medium when the thermal focal length of Nd:YVO₄ was estimated at ~300 mm. The distance between the gain medium and M₁ was less than 0.5 mm to utilize the spatial hole burning effect [9]. The IC and HR mirror are flat mirrors with a high-reflectance (HR) coating (R > 99.8%) at 1064 nm and a high-transmittance (HT) coating (T > 95%) at 808 and 532 nm. The OC was chosen to have a partial reflectance coating (R = 78%) at 1064 nm and an HR coating (R > 99%) at 532 nm. The HR coating at 532 nm can utilize part of a nonlinear mirror ML effect, which is helpful in stabilizing the ML pulse [10]. Therefore, the most part of green power was observed at the output of HR mirror. The distance between the MgO:PPSLT and OC was set to around 3 mm. The total optical length of one round trip was ~1.78 m, corresponding to a 168 MHz ML repetition rate. Two lenses, f₃ (f = 150 mm) and f₄ (f = 500 mm), were used to collimate and refocus the 1064 nm into the autocorrelator (APE pulseCheck), and a sech² pulse shape was assumed. The power attenuator, comprising a half-wave plate and polarization cube, was used to adjust the average power into the autocorrelator. To prevent the green background from the MgO:PPSLT, a long-pass filter was adopted to filter out the 532 nm. Enhancing the amplitude modulation via cascaded second-order nonlinearity, a hard aperture with a ~1 mm diameter was adopted near the intracavity lens f₂. The soft and hard aperture effects, combined with poor spatial overlapping between the pump and cavity beam, were beneficial to generate a self-starting ML pulse [11]. To produce the positive cascaded Kerr effect, the temperature of MgO:PPSLT was fixed at T = 41.8 °C, which generated a negative phase-mismatched $\mathsf{\Delta }\mathrm{k}\mathrm{L}~-18\mathsf{\pi }$, as shown in Figure 2. The blue line shows group velocity-mismatched (GVM) 6.7 ps/cm, multiplied by two times the coherent length at varied crystal temperatures, which is the shortest pulse duration that could be obtained through this cascaded process. For the operated temperature, 41.8 °C, the minimum pulse duration limited by GVM is approximately 2.3 ps. The reason for choosing this $\mathsf{\Delta }\mathrm{k}\mathrm{L}$ value at $~-18\mathsf{\pi }$ was to achieve a moderate cascaded Kerr effect and a short ML pulse duration. When the temperature of MgO:PPSLT was closed to phase-matched, the output power of the SHW wave increased, and the generation of stable CW ML was perturbed or ceased [8].

3. Results

When the diode pump was operated in the CW mode and reached the cavity threshold (around 4 W), the output power of 1064 nm increased monotonically. Figure 3 shows that the self-starting continuous-wave ML (CWML) pulses at the pump power ranged between 8.9 W and 9.6 W, and the maximum CWML output power reaches 1.39 W. When the pump power was further increased to 9.8~10.4 W, the QML output power reached 1.91 W and turned into the unstable QML (UQML) under higher pump power. The cavity was run into thermal instability when the pump power was higher than 12 W. The filled and open markers represent the measured output power of 1064 and 532 nm, respectively. The maximum 532 nm output power reached 153 mW at the beginning of the CWML regime and decreased to 74 mW at the end of CWML/QML regime. When the pump power was further increased and ran into the QML regime, the green power jumped down to 37 mW. The pulse temporal characteristic was monitored by an oscilloscope (1 GHz bandwidth) with a fast photodiode (70 ps rise time). Figure 4a,b show a typical time span of 20 μs and a 20 ns oscilloscope signal, which represent a pure CWML without QML background. In the QML regime, the Q-switched pulse repetition rate and pulse duration were measured to be ~140 kHz and 140 ns, respectively. The passive Q-switched mechanism reveals the timing and power instability, as shown in Figure 4c. Without an active control, the timing jitter of the Q-switched pulse was larger than 30%. Figure 4d shows the full modulation of the QML pulse, which shows the contribution of the large cascaded Kerr effect. A scanning monochromator with 0.1 nm resolution was adopted to characterize the output spectrum and the ML bandwidths were to be 0.91 nm and 0.67 nm for CWML and QML, respectively. The CW Nd:YVO₄ laser spectrum labeled by a filled square was measured as a reference to calibrate the monochromator, as depicted in Figure 5. In the CWML regime, the measured autocorrelator pulse durations were kept at ~6 ps, leapt to ~12 ps, and further increased to ~16 ps at the edge of QML/UQML regime, as shown in the inset. The suddenly increased pulse durations could be explained by the round-trip time of the ML pulse, which was limited by the ~140 ns Q-switched pulse. Therefore, the ML pulse in the QML regime was broadened, and the reduced bandwidth was also observed in Figure 5. Due to the large instability in UQML regime, we did not record the temporal and spectral behaviors. Based on the previous measurements, the reduced tendency of green power in the range of the CWML and QML regimes can be explained by the ML pulse broadening and the intensity diminishing at 1064 nm. However, the ML pulse duration in the CWML regime was maintained at ~6 ps. To explain the green power behavior in CWML regime, we speculated that the cavity beam size in the MgO:PPSLT was increased under a strong, cascaded Kerr effect, where the conversion efficiency of SHG was decreased.

To extensively study the QML performances, we modulated the pump laser by controlling the current driver into QCW mode. Figure 6 shows the 1064 nm and 532 nm output behaviors under three QCW pump modes. The repetition rate was kept at 1 kHz, and three kinds of open interval time—950 μs, 550 μs, and 350 μs—were used for comparison, as shown in the inset of Figure 6. The peak power of QML pump thresholds were measured to be 9.8 W, 16.9 W, and 26.7 W for 950 μs, 550 μs, and 350 μs pump modes, respectively. Accounting the duty cycle of open interval time, the averaged powers of three QML pump thresholds were 9.31 W, 9.3 W, and 9.35 W. Comparing with the CW pump mode, the similar QML threshold (9.8 W) reveals that the soft aperture mechanism dominates the ML process, where the combination of thermal lensing and a cascaded second-order effect in the laser gain medium has to match the pump beam size. Although the similar average pump power of the three QCW pump modes, the higher pump peak power has larger output power. Comparing the performances between the 950 μs and 350 μs pump modes, the 1064 nm and 532 nm maximum output power of the 350 μs mode reached 2.3 W and 0.129 W, respectively, resulting in a 28% (1064 nm) and 93% (532 nm) enhancement of the 950 μs mode. Since the green output was generated via a phase-mismatched SHG process, the conversion efficiency was proportional to the pump intensity. Therefore, the enhancement of the green output between two pump modes, i.e., 350 μs and 950 μs, was enlarged. To further study the temporal behaviors, we measured the repetition rate and the deduced the pulse energy of Q-switched pulses, as shown in Figure 7. The repetition rate was measured to be ~130 kHz at the 950 μs pump mode and increased to ~300 kHz at the 350 μs pump mode. Considering the total pulse numbers in one second, the effective repetition rate, f_eff, can be calculated as f_eff = f $\times$ t_open, where f and t_open are the measured repetition rate and open interval time, respectively. The effective repetition rates were found in the range of 100 kHz to 120 kHz for three QCW pump modes. The pulse energy was then deduced from the average power and effective repetition rate. At the 350 μs pump mode, the pulse energy was reached 22.3 μJ, which was a 56% enhancement over the 950 μs pump mode, where the short open interval provides high pump pulse energy and improves the pulse generation. The pulse duration was also observed to narrow under the high-pump-power mode, which also satisfied the characteristics of the gain switching scheme [12], as shown in Figure 8. The pulse durations were measured to be in the range of 120 ns to 140 ns under CW or the 950 μs pump mode and then decreased to ~50 ns at the 350 μs pump mode. More than 50% pulse duration narrowing was observed when we shrank the pump open interval and increased the pump power. Due to the limitation of 30 W maximum pump power, the pulse duration of the Q-switched pulse was restrained, and this can be further reduced with a higher pump source. The QML pulse duration was also monitored by the autocorrelator and found in the range of 15 ps to 18 ps, which has the same tendency of the inset of Figure 5. Adopting the above experimental results, the highest peak power of a single pulse near the maximum of the Q-switched ML envelope was greater than 150 kW in the 350 μs pump mode.

4. Discussion

Comparing with the SA-based QML [3,4,5], the advantages of the cascaded Kerr lens are the large modulation depth (100% in this report), the wide operation range (visible to mid-IR) [13], and the dual-color output. To comprehend the ML output performance, the plane wave coupled wave equations were used to calculate the nonlinear phase and deduce the cascaded Kerr focal length [14]. Average pump intensity, $I_{ave}=P_{peak}/\left(\pi {\omega }^2\right)$, and effective nonlinear coefficient of MgO:PPSLT, $d_{eff}=9\mathrm{p}\mathrm{m}/\mathrm{V}$, were used in the calculation. Adopting the measured average FW power, pulse repetition, and pulse durations at a fixed phase-mismatched condition, $\mathsf{\Delta }\mathrm{k}\mathrm{L}=-18\mathsf{\pi }$, the single-pass nonlinear phase shift, ${\varphi }_{nl}$, was calculated via the Runge–Kutta method [15]. The cascaded Kerr coefficient, $n_2^{eff}$, was then deduced from $n_2^{eff}={\displaystyle \frac{\lambda {\varphi }_{nl}}{2\pi I_{ave}L}}$ [11] and found in the scale of $1.9\times {10}^{-17}{\mathrm{m}}^2/\mathrm{W}$, which was about one order larger than the Kerr coefficient of Nd:YVO₄ (n₂ = $1\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$) [16]. Therefore, the cascaded Kerr effect dominated the ML process of this report. Using an aberrationless approximation model and the ABCD beam propagation method [17], a Kerr lens with an effective focal lengths of ~50 mm was achieved in the CWML scheme, and the calculated beam radius at the gain medium versus the thermal focal length is shown in Figure 9. When the thermal focal length was fixed at 300 mm, the inset shows that the cavity was run into the unstable regime under a strong cascaded Kerr effect, which could explain why the CWML scheme (Figure 3) only existed in a varied pump power range under 1 W. Although the cavity stability was sensitive to the cascaded Kerr effect, the large amplitude modulation caused by the soft aperture was beneficial for the generation of QML [18].

5. Conclusions

In conclusion, we have investigated the performance of a Q-switched mode-locked Nd:YVO₄ laser at 1064 nm induced by a cascaded second-order Kerr effect. Combining a phase-mismatched MgO:PPSLT crystal in an intracavity second-harmonic process and soft aperture configuration, QML pulses with 100% modulation depth were achieved at the average pump power of ~9.3 W, which was related to the thermal focal length of the Nd:YVO₄ crystal and cavity design. Moreover, in a QCW-pumped scheme, the Q-switched behaviors were related to the gain-switching mechanism and favored in a high-pump-power scheme. Under 28 W pump peak power, the measured mode-locked pulse train, the Q-switched repetition rate, and the Q-switched pulse duration were 18 ps, 300 kHz, and 50 ns, respectively. The highest peak power of a single pulse near the maximum of the Q-switched envelope was greater than 150 kW. No optical damage issue was observed during the measurement, and this can be extended to the other wavelength regime. This report provides an alternative and simple method by which to construct a passive QML laser with large modulation depth. Further manipulations of Q-switched pulses can be achieved by varying the pump laser.