We present the first observation, to the best of our knowledge, the spontaneous generation of picoseconds pulse trains in a diode-pumped Nd:YAP laser with gigahertz repetition rate. Spatially dependent temporal dynamics were experimentally observed. After theoretically reconstruct the experimental temporal-resolved patterns, we verify that the complicated spatially-dependent temporal dynamics were originated from simultaneous coherent locking combination of fundamental and several additional higher-order transverse modes.
© 2013 Optical Society of America
Laser possessing both the ultra-short pulses durations and high-repetition-rates inmulti-gigahertz or even more regime, have wide applications in many different fields, such as optical clocking of CPU , high-speed optical-electrical sampling , time-resolved spectroscopy , external-cavity nonlinear frequency conversion , precise measurement of group refractive indices  and frequency metrology .
Compared to other approaches for obtaining high-repetition-rate optical pulses, such as fiber laser , edge-emitting semiconductor lasers , mode-locking mechanism is entirely free of high frequency-driving electronics. Diode-pumped mode-locked high-repetition-rate solid-state lasers possess many merits, ranging from high contrast ratio, high pulse energy, low timing jitter, low cost, to miniature in scale and robustness. In the past few years, most of the diode-pumped multi-gigahertz mode-locked solid-state lasers research has concentrated on the employment of semiconductor saturable absorber mirror (SESAM) for passively mode-locking operation [9, 10]. Alternatively, SESAM-free diode-pumped self-mode-locking (SML) lasers combining Kerr-lensing together with thermal-lensing effects operating in the regime of multi-gigahertz are getting well-developed more recently [11–15]. Due to the exclusion of intracavity saturable absorbers (eg.SESAM) or active nonlinear optical modulation components, the cavity losses were significantly reduced, which in turn led to a substantial enhancement in the average output power and the optical conversion efficiency of such high-repetition-rate mode locking lasers. On the aspect of gigahertz pulse repetition rate, diode-pumped SML solid-state lasers have recently pushed the frontier by two orders of magnitude via harmonic mode locking. One to 80 GHz with the pulse duration of 616 fs by employing Nd3+ doped disorder crystal , and the other to 240 GHz with the pulse duration of 571 fs by choosing Yb3+ doped Y3Al5O12 microchip crystal . These kinds of lasers are superior to the fiber or edge-emitting semiconductor laser in terms of high Q (low-loss) and high average output power.
It is well known that the nonlinear refractive index is one of the critical parameters for reliable SML operation . The large nonlinear refractive index of YAP crystal , which is close to the magnitude of Yb:KYW ()  and making it an excellent candidate for SML operation. Additionally, the intensity dependent soft-aperture loss modulation from Kerr-lensing self-focusing in combined with thermal lensing aberration induced by the pump beam , could effectively maintain stable SML operation for Nd:YAP laser in a compact linear resonator. Nd:YAP crystal is also characterized by relatively good thermo-mechanical properties in combination with large absorption and stimulated-emission cross-sections. Besides, the strong natural birefringence of Nd:YAP crystal is advantageous for many laser applications in which polarized operation is desired, since thermally induced depolarization effects are lessened. Furthermore, the shorter lifetime of upper laser level (τ = 175 μs) compared to other Nd3+-doped crystals means it largely reduce the tendency of Q-switching mode locking state in SML Nd:YAP lasers . However, to the best of our knowledge, there is no relative reports on the SML operation of the Nd;YAP crystal until now.
In this paper, for the first time to the best of our knowledge, we experimentally investigated, the spontaneous picoseconds pulse formation in a diode-pumped Nd:YAP laser operating in gigahertz regime with the center wavelength of 1079.6 nm. Impressively, when the output beam profile displayed with some low-order multiple transverse mode (TEM00 mode and some additional high-order side-lobes); we observed a rich variety of phenomena of the spatially dependent temporal dynamics in the regime of SML. We attributed these complicated spatio-temporal dynamics to the simultaneous coherent locking of several longitudinal modes as well as some low-order multiple transverse modes.
2. Experimental design
A schematic diagram of laser resonator and pumping geometry was depicted in Fig. 1. An 808 nm fiber-coupled laser diode with a core diameter of 200 μm and a numerical aperture of 0.22 was used as pumping source. The pump beam was reimaged onto the laser crystal by a pair of plane-convex focusing lenses with about 96% coupling efficiency. For our experimental assessments, a 3 × 3 × 25 mm3, b-cut 1-at.% Nd:YAP crystal, engineered by the Fujian Institute of Research on the Structure of Matters, Chinese Academy of Sciences, was adopted.
As the long gain medium possesses the advantages of not only enhancing the absorption efficiency, but also permitting the thermal load to be spread over a larger volume, which significantly improved the uniformity of pump and thermal dissipation. Both facets of the Nd:YAP crystal were coated for high transmission at 808 nm (T>99.6%) and anti-reflection at wavelengths in the 1000~1100 nm (R<0.1%) range. And it was wrapped with indium foil and mounted on a copper heat sink with a thermoelectric cooler module (TEC) to achieve an efficient heat removal. We explored a simple linear three elements concave-plano resonator to construct the SML operation in gigahertz regime. A high-speed photodetector (New Focus Inc. Model-1434, 25GHz) and a digital oscilloscope (LeCroy, SDA 13000 with 13 GHz electrical bandwidth) were used for monitoring the temporal dynamics of real-time pulse train.
3. Laser performance and experimental results
3.1 Performance of free running operation in Nd:YAP laser
Initially, a 200 mm radius-of-curvature concave input mirror coated with high-transmission at 808 nm (T>96%) and high-reflection (HR, R>99.9%) at the wavelengths of 1000~1100 nm incorporating a 5% plane-parallel output coupler were adopted for evaluating the free running performance of diode-pumped Nd:YAP laser. The pumping light was reimaged onto the laser crystal with 1:2 ratio, which provides a pump spot radius of around 200 μm. The optica cavity length was set around 60 mm. Figure 2(a) shows the output powers in the free running regime of Nd:YAP as functions of incident pump powers. During the free running operation, an incident pump power of 8.3 W gave rise to a maximum output power of 4.3 W at a wavelength around 1079.6 nm corresponding to a diode-to-optical conversion efficiency of 51.8% with the threshold of 1.5 W. The beam quality factor (M2) of free running state was measured to be 1.8. In the out power optimization for the free running operation, the time domain appeared to be spontaneous mode locking with small amplitude fluctuations and the CW background to some extends, which were shown in Fig. 2(b).
3.2 Fundamental transverse mode operation in self-mode-locking Nd:YAP laser
We prior to construct the fundamental transverse mode operation in the SML Nd:YAP laser through reimaging the pump spot radius of 50 µm onto the laser crystal. With the average cavity mode radius of about 150 µm, we got the mode-to-pump size ratio to be approximately 3. An intracavity adjustable aperture was set very close to the output coupler to prevent the oscillator operating in high-order transverse modes. Note that the SML operation can be obtained without using this intracavity adjustable aperture. The Nd:YAP crystal was slightly inclined for suppressing the Fabry-Perot etalon effect to obtain a stable pulse train against the CW background. The input mirror was a concave mirror with radius-of-curvature of 200 mm. A BK-7 flat-wedged output coupler with 5% transmission at 1079 nm was employed for optimizing the SML operation. The resonator could be optimized to obtain stable continuous wave mode-locking (CWML) state by finely adjusting the resonator with the help of monitoring the real-time pulse train. The maximum average output power of 550 mW was obtained under the incident pump power of 5 W. This corresponds to an optical-to-optical conversion efficiency of 11%. The average output power of the laser as functions of the incident pump power were shown in Fig. 3(a). The optical length was varied between 50 mm and 85 mm for a corresponding free spectral range of 3 to 1.76 GHz. It should be noted that once the cavity alignment was adjusted to the optimum position, the laser instantaneously stepped into the CWML state without any of the Q-switching envelope modulation. No multi-pulse split was observed from pulse to pulse separation, which proved our laser system was under the stable single pulse SML operation. This state is self-starting once the cavity has been aligned and remained stable mode-locked without deterioration for hours. It should be note that the flat-wedged output coupler is vital for sustaining a stable SML operation against CW background. Figure 3(b) showed two timescales of CWML state of Nd:YAP laser at a pulse repetition rate of ~2.5 GHz, one with time span of 5 ns for demonstrating mode-locked pulse trains, the other with time span of 5 μs demonstrating the amplitude stability.
The beam quality factor (M2) of CWML state was measured to be better than 1.2. The pulse duration in CWML operation was measured with a commercial autocorrelator at the pulse repetition rate of 2.5 GHz with the average output power of 550 mW, as shown in Fig. 4(a) .
The FWHM of the autocorrelation trace was measured to be 24.1 ps. Assuming a Gaussian-shaped temporal profile, the pulse duration was thus estimated to be 15.1 ps. Figure 4(b) shows the spectrum of the mode-locked pulses with a FWHM of 0.16 nm at the central wavelength of 1079.6 nm, measured by a Zolix Monochromator spectrograph (model Omni-λ500, resolution of the spectrum is 0.07 nm). Consequently, the time-bandwidth product of the mode-locked pulse is 0.62 which indicated the pulses to be frequency-chirped. After substituting the shorter crystals (1-at%, Φ 3 × 10 mm) for the longer one, much higher pulse repetition rate of 6 GHz could be obtained. The interval between input mirror and laser crystal was adjustable to control the amount of spatial hole-burning for a variation of pulse durations . The shortest pulse duration was achieved with shorter laser crystal of ~9 ps.
3.3 Multiple low-order transverse modes operation in self-mode-locking YAP laser
In the following step, a 200-mm radius-of-curvature input mirror and 5% transmission parallel-plane wedged output coupler were adopted for constructing the multiple lower-order transverse mode SML operation. Pumping light was reimaged onto the longer crystal with the spot radius of 100 μm. With the average cavity mode radius of 180 μm, the mode-to-pump ratio was approximately 1.8. The intracavity adjustable aperture was removed from the resonator. This laser system allowed the fundamental transverse mode operation to be combined with some additional higher-order sidelobes. When the incident pumping exceeded to the threshold, the temporal traces exhibited a spontaneous mode locking state. With further increase in the incident pumping power to above 2 W, the temporal traces of mode locking exhibited amplitude modulation to some extent. The maximum average output power reached 1.7 W with the incident pumping power of 7.6 W, corresponding to a diode-to-optical conversion efficiency of 22.3%.
The detailed spatially dependent temporal dynamics characterizations were measured by transversely scanning an external aperture through the output beam profile. The selected output beam profiles were sent to the high speed photodetector for measuring the transmitted temporal profiles. We attributed the amplitude envelope to the transverse modes beating (Figs. 5(b)-(c)) between fundamental transverse mode and multiple lower order transverse modes [24, 25]. The three positions were measured for real-time monitoring of the temporal dynamics. Figure 5(a) depicted the beam profile which was measured by Spiricon & Photon Laser Beam Profiler.III. The three positions were measured for real-time monitoring of the temporal dynamics. Figures 5(b)-5(d) illustrated the experimentally observed spatial dependence of the temporal traces at the three different positions of the output beam profile. The coordinates with the unit in mm for the labels 1~3 were , respectively. The horizontal and vertical directions corresponding to the x and y axes, respectively. The output laser beam propagated along the z direction with z = 0 at the output coupler. The optical length was set around 63 mm corresponding to the free spectral range of 2.38 GHz.
4. Numerical simulation and discussion
The numerical code used for the simulation of spatio-temporal dynamics of multiple lower-order transverse modes operation in self mode locking Nd:YAP laser was described as in . The longitudinal and transverse frequency spacing can be calculated to be 2.38 GHz and 451 MHz, respectively . Given that output laser consisting of a fundamental transverse mode and N longitudinal modes were totally coherent locking, the normalized electric field can be expressed as:
The normalized electric field in Eq. (1) means the fundamental transverse mode with longitudinal modes from the lowest index with equal amplitudes and phase locking. Where denotes the lowest index of the longitudinal modes. As shown in Fig. 5, the horizontal and vertical directions correspond to the and axes, respectively. The output beam propagates along the direction with at the cavity flat mirror. With this coordinates, the total mode locking of several longitudinal modes in addition to the superposition of mainly TEM00 mode central spot with additional higher-order sidelobes can be numerically expressed as:
Furthermore, we numerically fitted the coefficient of the relative amplitudes with different orders of the transverse modes through Eq. (2). The obtained proper fitting coefficients were,, and respectively. The outcomes of numerical evolution of the spatial dependent temporal trace distributions in accordance with the three positions which the same as the above experimentally observed results of the beam profile were shown in Fig. 6.It can be seen from Figs. 5 and 6 that the experimental results showed good consistency with that of numerical evolution. Therefore, we confirmed that the variety of phenomena of spatio-temporal dynamics of SML Nd:YAP laser were results of the total mode locking of several longitudinal modes in addition to the superposition of a central spot of fundamental transverse electromagnetic modes (TEM00) with additional high-order sidelobes . It should be noted that the locking of superposition of the multiple lower-order transverse modes would bring amplitude instability to mode-locked pulses. It is critical to suppress high-order transverse modes oscillation in the mode locking resonator to achieve more stable CWML against unwanted CW background and amplitude modulation.
In conclusion, we have experimentally demonstrated a diode-pumped self-mode-locking Nd:YAP laser with the centre wavelength of 1079.6 nm by using a simple three elements resonator. The relative high nonlinear refractive index n2 of Nd:YAP crystal makes it favorable in achieving the stable SML operation. With the experimentally observed and numerically simulated spatial dependence of the total mode locking in the output temporal profiles of the Nd:YAP laser, we believed the phenomenon of spatio-temporal dynamics originated from the simultaneous mode locking of several longitudinal modes in addition to the superposition of multiple lower-order transverse modes.
This work has been supported by the National Natural Science Foundation of China (No.90922035), and the Knowledge Innovation Program of the Chinese Academy of Science (Grant No.KJCX2-EW-H03). We also appreciated for the financial aid of the natural science foundation of Fujian province (2011J06023) and Fujian high Technology Research and Development Program (Grant no. 2012H0046).
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