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Abstract
In this paper, pulsed output with pulse-widths approaching the round-trip time were generated by utilizing a cavity-less high-gain Nd:GdVO4 bounce geometry. By adopting an EOQ (electro-optics Q-switch) device, pulse-widths of 1.36 ns, 1.82 ns, and 2.39 ns were achieved at three effective cavity lengths, respectively. All these pulse-widths were close to the round-trip time of corresponding effective cavity lengths. Moreover, watt-level output power at kHz-level repetition rate was achieved, as well as the good beam quality with M2 factor less than 1.3. The output had a time-averaged continuous spectrum with 10 dB linewidth of 0.2 nm.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
3State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
4These authors contributed equally to this work
1. Introduction
Short nanosecond 1μm laser pulses are usually desirable in many industrial and medical applications [1–5]. Q-switch technique is capable of producing laser pulses with durations from sub-nanosecond to several tens of nanoseconds. By utilizing Q-switch devices, cavity losses are periodically modulated, and laser pulses are built up in the cavity and transmit through the output coupler. Generally, building up Q-switch pulses requires several to several tens of round-trips in the cavity. In order to achieve short Q-switched pulses, the cavity lengths are normally reduced, such as microchip lasers with passive Q-switch [2,3]. However, short cavity lengths will bring-small fundamental mode sizes, leading to the restriction on the output power.
Another approach to minimize the pulse-width is increasing the gain. With higher gain, not only the output power can be improved, but the pulse-widths can be narrowed since number of round-trips necessary to generate the pulse can be reduced [1,4,5]. There are several typical laser systems that can supply high gain level, such as high gain end-pumped lasers [6–9], bounce geometry lasers [10–14] and innoslab lasers [15–17]. These configurations are very successful in producing and amplifying short nanosecond pulses.
Under a given gain level, the pulse-width can also be minimized by optimizing the transmittance of the output coupler. In 1989, John J. Degnan proposed the theory of optimally coupled Q-switch laser [18]. Zayhowski et al. also investigated the optimized output coupling for minimizing pulse-widths [19,20]. It reveals that the optimized output coupling is increased as with the rising of gain level. This inspires us to explore the optimal transmittance for the output coupler under an extremely high gain level. Whether an output coupler with 100% transmittance, namely a cavity-less configuration, will satisfy the optimal condition for minimizing pulse-width under an extremely high gain is to be studied in this work.
In this paper, a cavity-less high gain bounce geometry is adopted to produce short pulses for the first time, to the best of our knowledge. With the high gain provided and the cavity-less configuration applied, experiments of three effective cavity lengths are implemented with an EOQ (electro-optics Q-switch) device. Minimum pulse-widths of 1.36 ns, 1.82 ns and 2.39 ns are achieved respectively, which are all close to the corresponding round-trip time. Moreover, the pulse-energy, beam quality and spectral characteristics are also investigated in this work.
2. Experimental setup
In 2006, G. Smith and M. J. Damzen investigated a Nd:YVO4 bounce geometry without an output coupler, and they obtained the continuous mode output of 6 W with near diffraction-limit beam quality. The cavity-less configuration we adopted here is similar to that in their studies [21,22]. As illustrated in Fig. 1, a cavity-less bounce geometry, consisted of only one reflective mirror (M0) but without another output coupling mirror was adopted in this experiment. The bounce geometry was initially proposed adopting the Nd:YVO4 crystal [10], while the configuration based on Nd:GdVO4 crystals was also demonstrated to be effective [23,24]. Here, an a-cut Nd:GdVO4 slab was adopted with the dimensions of 21 × 5 mm × 2 mm (the optical axis c-axis was parallel to the vertical direction). The doping concentration of the Nd:GdVO4 was 1.1 at. %. The end faces (5 mm × 2 mm) of the slab were 5° cut and antireflection-coated at 1064 nm. The crystal was pumped by a diode at the wavelength of 808 nm on the side surface (21 mm × 2 mm), which is anti-reflection coated at 808 nm. The pump diode had a continuous wave (CW) power up to 30 W. The pump light was focused tightly on the vertical direction by a vertical cylindrical lens (VCL0, F = 12 mm), producing the beam size of about 150 μm along the vertical direction. The polarization of pump light was parallel to c-axis of the crystal, thus corresponding to a high absorption coefficient of ~63 cm−1 [25]. The combination of the high absorption coefficient and the small pump spot can create high gain in the crystal. Therefore obvious amplified spontaneous emission (ASE) was observed from the end faces of the crystal at a high gain level. With the help of M0, ASE at some special bounce angles was collected and reflected back into the crystal. To collect more portion of ASE, a vertical cylindrical lens (VCL1) was introduced to alleviate the divergence angle and focus the ASE light. To prevent feedbacks, VCL1 was placed with an angle of ~15。 relative to the optical path. A slit was used to filter out high-order transverse modes in the horizontal direction. Hereinafter, the light source obtained from the cavity-less configuration was called cavity-less output. After exiting from the crystal, the cavity-less output was collimated by another vertical cylindrical lens (VCL2). An optical isolator (OI) was inserted before VCL2 to prevent feedbacks from other optical surfaces. The focal lengths of VCL1 and VCL2 are 60 mm and 150 mm, respectively.
To implement a pulsed cavity-less output, Q-switch device should be introduced. In our previous work, an acoustic-optic Q-switch (AOQ) device was applied. However, limited to the speed and extinction ratio of AOQ device, the minimum pulse-width only reached 5.2 ns [26]. Here, a pair of RTP crystals that can compensate the natural birefringence effect were adopted. The signal generator and the driver of the Q-switch device were omitted in Fig. 1. The EOQ device had a falling edge time of ~6 ns and an extinction ratio of 23 dB for 1064 nm. Although there was no concept Q value in our cavity-less configuration, the EOQ device can still realize the storage and release of the inverted population in the crystal. When a quarter-wave voltage was applied to RTP crystals, the vertical polarization was rotated to the horizontal polarization Since ASE with horizontal polarization cannot extract the gain, the gain was stored in the laser medium, indicating there was nearly no output. Once the voltage was removed, ASE extracted the gain and experience amplification rapidly and pulses were formed.
The performances of the cavity-less output were investigated, including the output power, spatial beam quality, pulse characteristics and spectral characteristics. Divided by a beam splitter (BS), one path with most of the light power entered into the power meter. Another path of the output was used to measure the spatial beam quality and the spectral characteristics. The pulse characteristics were measured by detecting the diffused light scattered from the power meter.
3. Results and discussions
3.1. CW output power and beam quality
We firstly realized a CW mode cavity-less output with no voltage applying to the Q-switch device. Here we use the effective cavity length to represent the total optical path between M0 and the exiting surface of the crystal. The definition is chosen in this way because i) the ASE reflected from M0 obtained gain again before exiting the crystal; ii) there was unavoidable weak feedbacks from the exiting surface on Nd:GdVO4 crystal resulted from the backscattering. Three experiments under = 170 mm, 240 mm and 310 mm were conducted. At the pump power of 30 W, the output power were 4.5 W, 4.0 W and 3.6 W for three respectively, corresponding to the optical-to-optical efficiency of 15%, 13% and 12%. The output power against pump power for = 170 mm is shown in Fig. 2.
Using a beam quality analyzer (Spiricon M2-200), the M2 factor was measured. Good beam quality with Mx2 <1.3 and My2 <1.2 was realized for all three at their highest output power, as shown in Fig. 3. The inset shows the spatial profile of far-field plane.
3.2. Pulse characteristics
The pulsed cavity-less output was carried out at the same three values when the EOQ device worked. The pulse profile was measured by an InGaAs detector (bandwidth of 20 GHz) and an oscilloscope (Tektronix MSO 73304 DX, sample rate of 100 GS/s and maximum bandwidth of 33 GHz). The pulse profile and width were also measured by another detector but with a bandwidth of 1 GHz, in order to characterize the envelope of the profile from the 20 GHz detector.
Figure 4(a) illustrates the pulse width (measured by 1 GHz detector and the criteria of the full width at half maximum, FWHM) at pump power of 30 W for the repetition rate from 1 to 20 kHz for three . For all three , the pulse-widths broadened with the increase of repetition rate, because the gain decreased for higher repetition rate. For = 310 mm, the pulse-width broadened to 6.76 ns at 20 kHz (3.3 times of round-trip time), while for = 170 mm, the pulse width only broadened to 1.90 ns (1.7 times of the round-trip time). The pulse-widths broadened more rapidly for longer due to the higher diffraction loss and worse overlap efficiency. It is worth noting that the pulse-widths for mm and 310 mm at 1 kHz were 1.36 ns, 1.82 ns and 2.39 ns, respectively, reaching 1.20, 1.13 and 1.15 times the corresponding round-trip time. The corresponding pulse profiles for bandwidth of 1 GHz and 20 GHz are both presented in the Fig. 4(b) for three corresponding .
Fig. 4 Pulse characteristics of cavity-less output under three different : (a) Pulse-width against repetition rate, (b) Pulse profile at 1kHz.
The pulse-widths comparable to the round-trip time above have approached the limitation of the pulse-width in Q-switched lasers. Since in ordinary Q-switched lasers, at least several round-trips are required to build up the pulses and sweep out the gain in the crystal. The short pulses achieved here can be explained by Zayhowski’s theory. The optimized output coupling for realizing the minimum pulse-width in a Q-switched laser is [19]:
where is the output coupling loss constant, and is round-trip parasitic loss constant. represents the initial inversion density, and is the stimulated emission cross-section of the laser medium. is the round-trip intra-cavity beam path length. The relationship between the transmission of output coupler T0 and the output coupling loss constant can be written as:Equations (1) and (2) indicate that the optimal output coupling to achieve short Q-switched pulses will approach 100% if there is sufficiently high gain.In our experiment, the single-pass small signal gain was measured to be 2 × 104. Treating the term as single-pass small signal gain, should be about 0.997. It should be noted that although there was no conventional output mirror in this configuration, the backscattering from the exiting surface on the Nd:GdVO4 crystal provided weak feedbacks, helping the formation of pulses. In G. Smith and M. J. Damzen’s work [21,22], they have mentioned the backscatter reflectivity was about 2 × 10−3/sr for the optical surface tilted about 5~10°, leading to a very weak effective reflectivity about 10−8. Hence, the optimal output coupling to achieve minimum pulse-width was nearly satisfied under the weak-feedback cavity-less configuration without conventional output mirror. In this way, short pulse-widths close to round-trip time were achieved.
Figure 5 illustrates the time-delay between the high-voltage signal on the EOQ device and the measured pulse waveform at 1 kHz for = 170 mm. It can be seen that the time delay between the falling-voltage signal and the starting time of the pulse was about 4.2 ns. It is inferred that the pulse was built up in only a few round-trips, and then the gain was nearly swept out in the next one round-trip. Since there were no sufficient round-trips in the formation of the pulses, it is reasonable to deduce that the longitudinal modes in the cavity-less output cannot be sustained. It can also be found in Fig. 4(b) that the profiles for 20 GHz bandwidth detector have some random high frequency modulations. In ordinary oscillators with more than one steady longitudinal modes, the pulse profiles have certain mode beatings corresponding to the cavity lengths. Thus, the random high frequency modulations in Fig. 4(b) are induced by the mode beating of stochastic emerging longitudinal modes. The spectral characteristic will be analyzed in section 3.4.
It is well-known that cavity dumping technique is capable of producing pulse-widths approaching the round-trip time. However, the requirement for the driver of the Q-switch device is relatively high: short rising or falling time close to the round-trip time [27–29]. For = 170 mm, a Q-switch device with switching time of ~1.36 ns is needed for cavity dumping method. In our experiment, although the switching time of the EOQ driver was about 6.4 ns, pulse-width close to the round-trip time was also obtained. This indicates that a high gain cavity-less configuration can obtain short pulses with sufficient tolerance to the speed of the Q-switch device.
3.3. Pulse energy
The average output power (at the pump power of 30 W) versus repetition rate is illustrated in Fig. 6(a). With the increase of repetition rate from 1 kHz to 20 kHz, the average power increased from 1.11, 0.96 and 0.47 W to 3.15, 2.76, and 2.29 W for = 170 mm, 240 mm, and 310 mm, respectively. Compared with the corresponding CW output power, the efficiency under pulsed mode was 70%, 69%, and 63.6% at 20 kHz, accordingly. For a fixed repetition rate, the output power decreases as with the increase of due to the higher diffraction loss and the worse overlap efficiency.
Fig. 6 Pulse energy characteristics of cavity-less output under three different (a) output power against repetition rate, (b) pulse energy against repetition rate.
When a quarter-wave voltage was applied to the EOQ device on constantly, the output power cannot drop to zero, which meant the output in pulsed mode had a CW background. This output power under the high loss state is defined as the extinction power. The extinction power corresponding to 170 mm, 240 mm and 310 mm was 0.6 W, 0.4 W and 0.2 W, respectively. Subtracting the extinction power, the pulse energy was calculated by dividing the repetition rate, as illustrated in Fig. 6(b). For the shortest , the pulse energy reached 600 , thus the maximum peak power exceeded 440 kW. The average output power was above 2 W at the repetition rate of 10 kHz, while maintaining the pulse-width less than 1.5 times of the round-trip time. These results demonstrate that a high gain Nd:GdVO4 bounce geometry with cavity-less configuration is capable of obtaining wat-level output with pulse-widths close to round-trip time. As for the beam quality, it was monitored during the variation of the repetition rate and the M2 factor remained less than 1.3 in two directions.
3.4. Spectral characteristics
The spectrum of the cavity-less output operating at CW mode was monitored by an optical spectrum analyzer (Agilent 86142B, resolution of 0.06nm) at the pump power of 30 W. Since the 3 dB linewidth was very close to the resolution of 0.06 nm (16 GHz), the 10 dB spectral linewidth, which was about 0.2 nm, was adopted to characterize the spectrum, shown in Fig. 7. To get more insight to the dynamics of the cavity-less output, a scanning Fabry-Pérot (FP) interferometer was introduced to investigate the spectrum. The free spectral range (FSR) of the FP interferometer was 3 GHz.
When the cavity-less output operated at CW mode (still at the pump power of 30 W), there were several disordered peaks in the scanning output: both the amplitudes and the spacings of these peaks were stochastic. What’s more, the positions of the peaks, which mean the optical frequency, varied with time, as shown in Single Frame 1-4 of Fig. 8(a). If multiple frames were averaged (64 frames averaged in Fig. 8(a)), the scanning output become flatter. The phenomena above indicated: i) the linewidth of the cavity-less output was broader than the FSR of the interferometer; ii) no discrete and steady longitudinal modes were built up in the cavity-less configuration; iii) the stochastic and time-dependent mode hopping could be viewed as continuous spectrum in time average observation.
Fig. 8 FP scanning results of the cavity-less output (a) CW mode, (b) with output coupling mirror T = 80%; (c) pulsed mode.
To figure out how this continuous spectrum came from, a coupling mirror with transmission of 80% was inserted behind the exiting surface. From the scanning output of the FP interferometer (as shown in the Fig. 8(b)), there were 4 steady peaks with fixed interval and position, indicating that 4 discrete longitudinal modes built up in the cavity. The longitudinal mode intervals were measured to be consistent with the optical length of the oscillator.
In order to explain the spectral difference between Fig. 8(a) and Fig. 8(b), the general dynamics of the formation of the longitudinal modes in a simple FP cavity with gain medium, should be taken into account. A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces, while other wavelengths are suppressed by destructive interference. Therefore, the key ingredient for the formation of the longitudinal mode is the multiple reflections, which means enough reflectivity and enough round-trips (before the mode decays).
For the laser using output coupler with transmission of 80%, 4 longitudinal modes were formed due to the relatively high reflectivity and enough roundtrips. Imaging that the transmission of the output coupler is increased, the mode number will decrease resulting from the increased threshold. Once the transmission is very large approaching 100%, then the laser is below the threshold and no laser comes out.
While for the cavity-less output with weak feedbacks, the gain was almost extracted in one round-trip due to the large gain induced significant ASE. Although there were some longitudinal modes (originating from the initial ASE) above the threshold, the boundary condition of the cavity-less geometry could not efficiently limit the longitudinal modes. The spectral characteristic here differs from that of the ordinary ASE sources because weak feedbacks introduce time varying mode hopping. The stochastic mode hopping can also explain the high frequency modulation in the pulse profile in Fig. 4(b). When a long term observation was implemented, the spectrum was averaged to be continuous since the initial longitudinal modes here also came from the ASE. Therefore, we would like to consider the light here as an ASE source with weak feedbacks.
The spectrum of pulsed cavity-less output was also analyzed in FP interferometer. When the cavity-less output was operating at the pulsed state (100 Hz, 200 Hz and 500 Hz), the scanning output of FP interferometer had the equal repetition rate with that of the cavity-less output, as illustrated in Fig. 8(c). Furthermore, the repetition rate of the scanning output was fixed regardless of changing of the scanning voltage. The result is similar to that in the frequency-shifted feedback laser [30] and the narrow-linewidth Nd:YAG ASE source [31], both of which own a continuous spectrum.
From the results in Fig. 8(a)–(c), it can be concluded that the output of the cavity-less configuration in our experiment, whether the output was CW or pulsed, had a time-averaged continuous spectrum rather than steady longitudinal structures. This spectral characteristic might be helpful in applications such as nonlinear interactions [32,33].
4. Conclusion
In summary, a watt-level, kHz-level repetition rate output is obtained with pulse-widths close to the round-trip time. The beam quality factor is good with M2 <1.3. The spectrum is time averaged continuous and has a 10 dB linewidth of 0.2 nm. The minimum pulse-widths reach 1.36 ns, 1.82 ns, and 2.39 ns at three effective cavity lengths respectively, which are all close to the corresponding round-trip time. The short pulse-widths close to round-trip time have approached the limitation of the pulse-widths for Q-switched lasers. This is attributed to the setup combining the cavity-less configuration and the high gain Nd:GdVO4 bounce geometry. This study supplies a convenient method to produce short nanosecond pulses with watt-level power and kHz repetition rate, which is of great potential in many industrial and civilian applications.
Funding
National Key Research and Development Program of China, Ministry of Science and Technology of the People's Republic of China (2017YFB1104500); National Natural Science Foundation of China (NSFC) (61875100).
Acknowledgment
We thank Dr. Zilong Zhang and Kun Gui for their help with the measurements of Fabry-Pérot interferometer. Thank Dr. Tinghao Liu for discussing technical and logical problems during the writing process.
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