1. Introduction

Q switching is a well-established technique to generate nanosecond and subnanosecond giant pulses in lasers. These pulses are useful for numerous applications such as micromachining, ranging, remote sensing, microsurgery, and nonlinear frequency conversion. Conventionally, Q-switching can be carried out by actively or passively modulating the loss inside the laser cavity using, for example, an E-O modulator, an A-O modulator, or a saturable absorber. These switches, however, inevitably result in additional expense and cost, complicate the system, and introduce extra losses. Recently, self-Q-switching has been reported in the Nd:YVO₄ microchip laser with two or three longitudinal modes.^1,2 This is described by the gain related effects between two longitudinal modes or in terms of the cross gain coupling among three modes. Self-Q-switched operation has also been observed in Nd:YVO₄,³ Nd:YAG,⁴ and ruby^4,5 lasers with an extended resonator through misalignment of the cavity mirrors. However, the mechanism for this is still unclear. In this article we report on our studies of self-pulsating phenomena in a Nd:YVO₄ laser with a plane-concave cavity. By observing the radio-frequency (RF) spectrum of mode beating, we found that a number of cavity modes were excited when the cavity length was adjusted in the neighborhood of the hemispherical resonator configuration. Adjusting the cavity length, changing the pump power, or misaligning the cavity axis with respect to the pump beam could further tune the beat frequencies of these cavity modes. Self-pulsation occurred when the cavity was aligned such that mode beating swept over the region of relaxation oscillation frequencies. In this manner, self-pulsation can be observed by using concave mirrors with different radii of curvature and at different pump powers. As a result, we can generate giant pulses of pulse width as short as 2.4-ps by using a concave mirror with 10-mm radius of curvature and obtain pulse output with the pump power as low as 300 mW.

2. Experimental setup

The experimental setup is similar to that described elsewhere,⁶ where a diode-pumped Nd:YVO₄ laser with a plane-concave cavity is used. A 1-mm-thick Nd:YVO4 laser crystal coated at the surface facing the pumping beam for less than 5% reflection at 808 nm and greater than 99.8% reflection at 1064 nm was used as the gain medium combined with a flat end-mirror (R₁=∞). The second surface of the crystal is antireflection coated at 1064 nm. The output coupler in most of our experiments is a concave mirror with radius of curvature R₂=50 mm and 90% reflection at 1064 nm. The pump beam from a 1-W continuous wave (cw) laser diode was collimated by an objective lens with numerical aperture of 0.47, beam shaped by an anamorphic prism pair, and focused onto the Nd:YVO₄ crystal by another objective lens with a focal length of 12 mm. We operated the laser diode at constant current and temperature by a current source and a temperature controller to ensure stable pumping wavelength and power.

 

Fig. 1. The laser average power measured as a function of the cavity length. The region in which giant pulses are generated is indicated by an ellipse.

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3. Results and discussion

In our experiment the output coupler was mounted on a translatable stage to offer a continuous adjustment of the cavity length L and equivalently the change of the resonator configuration. The laser resonator was aligned such that the moving direction of the translatable stage was parallel to the cavity axis. We set the cavity length range so as to cover the region of the hemispherical resonator configuration. The laser average power was measured as a function of the cavity length by an optical power meter as shown in Fig. 1. We also observed the laser output waveform by a high-speed photodetector together with a digital oscilloscope when the cavity length was changed. We found that when the cavity length was adjusted in a small region near the hemispherical resonator configuration, the laser output began to fluctuate and became unstable. Further adjusting the cavity mirrors, it turned into Qswitching-like giant pulses. The typical waveforms are shown in Fig. 2. In contrast to passive Q-switching, spontaneous generation of giant pulses frequently accompanies a train of subpulses in front of the main pulse and exhibits significant amplitude fluctuation and timing jitter. We changed the radius of curvature of the concave mirror and found that spontaneous giant pulse generation always took place when the cavity length was adjusted near the hemispherical resonator configuration. Thus the use of shorter radius of curvature of the concave mirror results in a shorter cavity length for spontaneous giant pulse operation and therefore a shorter pulse width. By using a concave mirror of 98% reflectivity and 10-mm radius of curvature, giant pulses as short as 2.4 ns with a repetition rate of approximately 10 kHz and highest peak power of 110 W are obtained at 0.8 W of pump power. This is shown in Fig. 3. The spontaneous giant pulse can also be generated at different pump powers. The lowest pump power to achieve spontaneous giant pulse generation is 300 mW corresponding to 1.2 times the threshold pump power.

 

Fig. 2. Typical oscilloscope traces of spontaneous giant pulse generation from the Nd:YVO₄ laser; trace (a) exhibits a time-expanded scale (10 µs) to show three pulses in a screen and trace (b) displays the waveform with the same time scale as (a) but its voltage scale (20 mV) is magnified by 10 times to observe subpulses

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Fig. 3. Oscilloscope traces of the giant pulse output from the Nd:YVO₄ with 10-mm radius of curvature of concave mirror; trace (a) is the pulse train and trace (b) exhibits a time-expanded single pulse showing a 2.4-ns width (FWHM).

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To reveal the mechanism for giant pulse output in our experiment, we examine the cavity-length-dependent mode beating and relaxation oscillation with two RF spectrum analyzers. Generally, the ratio of longitudinal mode spacing Δν_l to the transverse mode spacing Δν_t is a function of the resonator configuration and can be expressed as $\frac{\Delta {\mathit{\nu }}_l}{\Delta {\nu }_t}=\frac{{\cos }^{-1}\sqrt{g_1{g}_2}}{\pi }$ where g1 and g2 are cavity parameters and equal 1 and 1-L/R, respectively, for a plano-concave cavity with cavity length L and radius of curvature of concave mirror R. When the cavity length is tuned to a region near the radius of curvature of the concave mirror we find that a number of mode beats appear as shown in Fig. 4. The beat frequencies come into view near half of the longitudinal mode spacing indicating that they are cavity modes taking place where the cavity length is near the hemispherical resonator configuration (g₁=1, g₂=0). These cavity modes have been characterized as off-axis beams.6 Different beat frequencies confirm that they are not the higher-order transverse mode but are comprised of independent cavity modes. In addition, we find that there are low frequency components resulting from near-degenerate mode beating. In the low frequency region, we may also see the relaxation oscillation noise spectrum. The small-signal relaxation oscillation frequency fRO is given by $2\pi f_{RO}=\sqrt{\left(r-1\right){\gamma }_2{\gamma }_c}$, 7 where r is the population inversion ratio above threshold, γ2 is the atomic decay rate, and γC is the cavity decay rate. Generally, changing the pump power, misaligning the cavity axis or adjusting the cavity length, may result in the change of the relaxation oscillation frequency and/or the beat frequency between cavity modes (as shown in Fig. 5). We find that self-pulsation occurs when the cavity is aligned such that beats among near-degenerate modes sweep over the region of relaxation oscillation frequencies.

 

Fig. 4. Mode beats as a function of the cavity length. The inset shows the power spectrum observed at the cavity length where the giant pulse can be excited.

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Pulsed output from a laser modulated by pump power, output coupling, or cavity frequency have been demonstrated when the modulation frequency was adjusted at or near the relaxation oscillation frequency.^8-10 It was also obtained from a cw diode-pumped Nd:YVO₄ laser without the use of intracavity elements and achieved by tuning a stable amplitude modulation owing to polarization beating onto the natural relaxation-oscillation frequency of the laser cavity.¹¹ In our work, the amplitude modulation is carried out by beating among near-degenerate cavity modes. When the modulation frequency is tuned to sweep over the region of relaxation-oscillation frequencies of laser modes, one of the laser modes is resonantly enhanced to generate the giant pulse. Note that frequency degeneracy occurs for every cavity with the fractionally degenerate resonator configuration.¹² However, we have never found the generation of giant pulses with resonator configurations other than the hemispherical cavity, for example, g₁g₂=1/4, 1/2, and 3/4. The unique feature of the hemispherical cavity is that it is near the border of the stability region and is subject to significant diffraction loss (see Fig.1) while the other frequency degenerate resonator configurations are not. High diffraction loss and instantaneous resonant enhancement of a laser mode are therefore two key factors in generating giant pulses in our situation.

 

Fig. 5. (a) Power spectrum of the diode-pumped Nd: YVO₄ laser, showing the relaxation oscillation (RO) and near-degenerate mode beating (3.6 MHz). (b) A power spectrum when the laser beat frequency (2 MHz) was adjusted so that it approached the relaxation-oscillation frequency (~800 kHz).

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4. Conclusion

In conclusion, we have generated giant pulses from a free-running Nd:YVO₄ laser end-pumped by a cw diode laser without the use of any intracavity components except the gain medium inside a plane-concave resonator. This is achieved by operating the laser cavity near the hemispherical resonator configuration where multiple cavity modes are readily excited. Giant pulses are obtained by fine adjustment of the cavity length, changing the pump power, and misaligning the cavity axis such that the beat frequency between near-degenerate cavity modes overlaps with the relaxation oscillation frequency of laser modes. In this way, we can generate giant pulses by using concave mirrors with different radii of curvature and at different pump powers. By using a concave mirror of 98% reflectivity and 10-mm radius of curvature, giant pulses as short as 2.4 ns with a repetition rate of approximately 10 kHz and highest peak power of 110 W are obtained at 0.8 W of pump power. The lowest pump power to achieve the spontaneous giant pulse generation is 300 mW corresponding to 1.2 times the threshold pump power.