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We demonstrated passive mode-locking of a Nd:YAG ceramic laser by optical interference modulation in a GaAs wafer. The combined effect of Kerr nonlinearity and optical interference in GaAs acted as an artificial saturable absorber and resulted in mode-locking. Maximum average output power of the mode-locked laser was as high as 2.84W, with a slope efficiency of 48%. The mode-locked pulse duration was as short as 4.1 ps. To our knowledge, this is the shortest pulse obtained from all Nd:YAG lasers without dispersion compensation.
©2007 Optical Society of America
1. Introduction
Passive mode-locking (ML) of diode-pumped solid-state lasers by semiconductor saturable absorber has been intensively investigated for generation of picosecond and femtosecond optical pulses [1–3]. Since GaAs has the property of high damage threshold, large optical nonlinearity, low cost and saturable absorption around 1 μm wavelength, it was used for mode-locking the Nd-doped lasers. The first mode-locking experiment by GaAs wafer was demonstrated in 1992 on a Nd:YAG single crystal laser [4]. Recently, mode-locking of other solid-state lasers by GaAs wafer has also been achieved [5–7]. As in the previous experiments the saturable absorption effect of GaAs was explored for mode-locking, the GaAs wafer was positioned as an end mirror in the lasers with all the intra-cavity laser energy passing through it. However, GaAs material has considerable two-photon-absorption (TPA) [8, 9], which severely limits the achievable pulse peak intensity and duration. In fact, once the pulse peak intensity approaches 0.2GW/cm2, TPA becomes dominant over the linear saturable absorption in GaAs [9]. Reduction of laser intensity inside the GaAs wafer is the key to eliminate the TPA limitation. On the other hand, it was observed in thick GaAs wafers that optical interference modulation could strongly influence reflectivity of a GaAs wafer [10, 11]. It provides the possibility of achieving mode-locking by controlling the optical interference condition in a GaAs wafer.
Recently, Nd:YAG ceramic lasers have attracted considerable attention. Nd:YAG ceramic material has comparable optical and thermal property with Nd:YAG single crystals, moreover, it possesses the advantages of easy fabrication, low cost, and high-doping concentration available [12]. In Nd:YAG ceramic lasers, the optical-to-optical efficiency attaining to 52.5% and a quasi-CW power as high as 236W have been achieved [13]. By Q-switching, 10 ns pulses with a repetition rate of 20 kHz were also generated [14]. Lately, mode-locking of a Nd:YAG ceramic laser using SESAM as saturable absorber has produced 8.3-ps pulses with an average output power of 1.59W [15].
In this paper, we report on mode-locking of a Nd:YAG ceramic laser based on optical interference modulation in a GaAs wafer. Different to the previous mode-locking by GaAs wafer, in our laser the GaAs wafer is positioned as an end mirror with the HR-coated surface towards the cavity. With the configuration the laser intensity transmitted into the GaAs wafer is low. Therefore, the TPA effect is reduced to a large extent. Self-started mode-locking of the laser has a new mechanism: the large third-order nonlinearity of GaAs brings significant nonlinear phase shift as a laser beam propagates through it, thus results in different reflectivity under different light intensity because of the optical interference. Under appropriate condition an artificial saturable absorption effect is generated, which leads to mode-locking of a laser. Continuous wave (CW) mode-locked pulses with pulse width as short as 4.1 ps and a maximum average output power of 2.84 W have been experimentally demonstrated.
2. Experimental setup
The experimental setup is schematically shown in Fig. 1. A 50-W fiber coupled laser diode bar was used as the pump source. The core size of the fiber is 300 μm in radius, with a numerical aperture of 0.22. The emission wavelength of the laser diode is 806 nm, which slightly deviates from the absorption peak of Nd:YAG ceramics. The pump light was focused into the Nd:YAG ceramic by two coupling lenses with a beam compression ratio of 1.8:1. The focal spot in the ceramic had a radial size of ∼ 170 μm. The Nd:YAG ceramic used has a Nd3+ -doping concentration of 0.5% and a dimension of 3 × 3 mm2 in cross section and 4 mm in length. Both sides of the ceramic were AR-coated at the laser wavelength. To efficiently remove the generated heat, the ceramic was wrapped with indium foil and mounted in a water-cooled copper holder. The temperature of the circulating water was set at 25 °C during the experiment. A Z-fold cavity was used to achieve a tightly focused spot on the GaAs wafer and simultaneously an optimum mode matching with the pump beam in the ceramic medium. With the cavity parameters shown in Fig. 1, the laser mode radius in the ceramic is ∼ 100 μm, and on the GaAs wafer is ∼ 26 μm. The high purity GaAs single crystal wafer is <100> cut and has a cross-section of 10mm × 20 mm and a thickness of about 450 μm. The GaAs wafer surface towards the cavity was coated at 1064 nm with almost linearly variable transmission from 6% to 90% along the 20-mm direction, and the other surface was AR-coated at 1064 nm (reflectivity of ∼ 0.5%).
3. Numerical simulations and analyses
The GaAs wafer in the laser operates like a nonlinear Fabry-Perot cavity. According to the multiple beam interference theory, the reflectivity R of the GaAs wafer can be written as [16]
Here R1 and R2 are the front and back surface reflectivity, respectively. α , α 0 , β are the total absorption, the linear absorption and the TPA coefficient, respectively. Φ,n 0,n 2,L are the phase shift in one round trip in the GaAs wafer, the linear and nonlinear refractive indices, and the GaAs wafer thickness, respectively. I denotes the peak intensity of pulses in GaAs wafer.
If the GaAs wafer thickness L is so selected that 2n 0 L / λ = N (N is an integer), namely the GaAs wafer operates at resonance when the laser intensity is very small (corresponding to CW operation of the Nd:YAG ceramic laser), the reflectivity of the GaAs wafer will be at the minimum value due to the optical interference effect. As GaAs has a very large nonlinear refractive index of –2700×10-13 esu[17], which is as much as ∼ 1000 times that of Ti: Sapphire, it is necessary to consider the influence of the nonlinear phase shift on the wafer’s reflectivity. Fig. 2 shows the variation of the GaAs wafer reflectivity with laser intensity under different R2. In the calculation we have considered the linear absorption and TPA of the GaAs wafer. It is to see that the reflectivity of the GaAs wafer increases with the laser intensity, which resembles an artificial saturable absorption effect. Even when R2 is as small as only 0.5%, a wafer reflectivity change of more than 1% can still be obtained, which is sufficient to start mode-locking of a laser.
Fig. 2. Reflectivity of the GaAs wafer as a function of the laser intensity under different back surface reflectivity. The front surface reflectivity R1 was set to be 90%. The other parameters were set as: n 0 =3.48; n 2 = –3.25×10-13 cm 2/W ; α 0 = 2.5cm -1 ; β = 15cm/GW ; L = 449.965μm ; λ = 1064.5nm.
In Fig. 2 the GaAs wafer reflectivity approaches 90% (the front surface reflectivity) at very large laser intensity, which can be well understood as at very large laser intensity the TPA becomes so strong that it completely absorbs the laser energy in the GaAs wafer. In practice this situation can never occur in our laser because the laser intensity in the GaAs wafer is small due to the high front surface reflectivity. The difference between the maximum and the minimum reflectivity shown in Fig. 2, which corresponds to the modulation depth of the saturable absorption, significantly changes with the R2 values. The larger the R2, the stronger is the optical interference effect, and consequently, the larger becomes the modulation depth. Through properly selecting the back surface reflectivity, one can therefore control the modulation depth of the artificial saturable absorption for optimizing the mode-locking.
In calculating Fig. 2 the GaAs wafer thickness L was set as 2n 0 L/λ = N, which means that the reflectivity R of the GaAs wafer is initially at its minimum value. It is to note that according to Eq. (1) and Eq. (3), as far as the GaAs wafer thickness meets the condition N - 1/2 ≤ 2n 0 L/λ ≤ N , the reflectivity R of the GaAs wafer can still exhibit similar artificial saturable absorption effect except that its modulation depth becomes smaller.
4. Experimental results and discussions
The output characteristics of the laser under CW and ML operations are presented in Fig. 3. For CW operation the GaAs wafer was replaced by a 6%-transmission coupler. A maximum CW output power of 2.88 W was obtained under 6.9 W pump, with a slope efficiency of 45%. Under even stronger pump, the laser cavity became unstable due to thermal lens effect in the ceramic, which would break the stable mode-locking. When the GaAs wafer was used, continuous wave mode-locking was obtained with pump power beyond 3 W. A typical CW mode-locked pulse train is shown in Fig. 4, in either the nanosecond time scale (Fig. 4 (a)) or the millisecond time scale (Fig. 4 (b)) to illustrate its repetition rate and stability. As the traces were recorded with a 400 MHz bandwidth digital oscilloscope, the pulse profile is limited by the detection system bandwidth. Nevertheless, Fig. 4 (a) clearly shows that the pulse period is 7.76 ns, which corresponds to a repetition rate of 129 MHz. The pulse-to-pulse intensity fluctuation is estimated to be less than 5%. Although even in the millisecond scale the pulse train exhibited good stability, the long-term stability of the pulses was not as good as those obtained with the SESAM mode-locking technique [1, 3], which is determined by the interference nature of the mode-locking.
Fig. 4. Oscilloscope traces of the mode-locked pulse trains. (a) under nanosecond scale; (b) under millisecond scale.
A typical autocorrelation trace of the mode-locked pulses is shown in Fig. 5. The FWHM of the autocorrelation trace is about 6.3 ps. If a Sech2 pulse shape is assumed, the pulse duration of the mode-locked pulses is 4.1 ps. The spectrum of the pulse is shown in the inset of Fig. 5. It has a 3dB width of about 0.32 nm. Therefore, the time-bandwidth product of the pulses is 0.35, close to the value of a transform-limited Sech2-shape pulse. Under ML operation the maximum average output power achieved was 2.84 W, and the slope efficiency was as high as 48%, which was even higher than that of the CW operation. The high slope efficiency is attributed to the optimized GaAs wafer transmission selection, achieved by translating the GaAs wafer along its 20 mm side direction. On the other hand, as under the ML operation the mode-locked pulse duration is less than the round trip time of the GaAs wafer (∼10 ps), in fact after stable ML operation is established, optical interference in GaAs wafer no longer occur. Thus the GaAs wafer reflectivity is determined by the front surface reflectivity of the wafer, which in our laser can be continuously changed.
The 4.1 ps pulse was generated at a measured GaAs output coupling of 7.2%. Experimentally we found that under the pump strength of 4.64 W stable CW mode-locking could always be obtained as far as the GaAs output coupling was below 10%. When the GaAs coupling strength was shifted to larger values, then the Q-switched mode locking was observed. Furthermore, altering the GaAs coupling did not cause measurable pulse duration changes, indicating again that the function of the optical interference is to initiate the mode-locking.
Fig. 5. Measured autocorrelation trace of the mode-locked pulses. Assuming a Sech2 pulse shape, the pulse duration is about 4.1 ps. Inset: spectrum of the mode-locked pulses.
5. Conclusions
In conclusion, we have demonstrated passive mode-locking of a Nd:YAG ceramic laser by a GaAs wafer, and shown that the mode-locking mechanism is the nonlinear interference modulation on the wafer’s reflectivity. A maximum average output power of 2.84 W with a slope efficiency as high as 48% was obtained. The mode-locked pulse duration was as short as 4.1 ps. The mode-locking technique by optical interference modulation has a number of advantages, such as suppressing TPA in GaAs, achieving high slop efficiency and generating short mode-locked pulses.
Acknowledgments
Dingyuan Tang acknowledges the financial support from the State Key Laboratory for Advanced Photonic Materials and Devices, Fudan University.
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