3.1 Output power and pumping absorbed power
The design of Yb: LuAG gain material continuous laser is shown in Fig. 1. Continuous laser output is observed when the pump absorption power is greater than Yb: LuAG gain medium laser threshold value 1.65 W. The average output power is plotted as a function of the pump absorbed power as shown in Fig. 2. It can be seen from Fig. 2 that the pump absorbed power is between 1.65 W and 8.0 W, and the increase of the laser output continuous laser power is linear with the increase of the pump absorbed power, and the central wavelength is near 1046 nm.
The peak-unstable multipulse trains observed in this experiment oscillate in fundamental transverse mode, which is consistent with the longitudinal mode oscillation of Yb3 + particle gain materials reported previously [26]. High order transverse mode is observed when the output power of Yb: LuAG CW laser is less than 50 mW, and no high order transverse mode is observed when the output power is greater than 50 mW.
3.2 Quasi-longitudinal mode and quasi double mode
The mutual conversion of Yb: LuAG ceramic laser near the central wavelength of 1046nm continuous laser output of quasi-single longitudinal mode (multiple longitudinal modes are tightly formed into a group, the distance between adjacent longitudinal modes is less than 1 nm) and quasi-double longitudinal mode (multiple longitudinal modes are tightly formed into two groups with a center distance of a few nanometers) is shown in Fig. 3 (1). In the process of passively Q-switched Yb: LuAG ceramic laser, one case is quasi-single longitudinal mode oscillation as shown in Fig. 3 (2). The other case is Q-switched quasi-double longitudinal mode oscillation. Figure 3(3) (a) shows the quasi-double longitudinal mode of the Yb: LuAG ceramic laser in the continuous optical output state. When the output power is 160 mW, the quasi-double longitudinal mode spacing is 2.42 nm. Figure 3(3) (b) shows the quasi-double longitudinal mode under the Q-adjusted state of Yb: LuAG ceramic. When the output power is 190 mW, the quasi-double longitudinal mode spacing is 2.80nm.
The conversion phenomenon shown in Fig. 3 (1) will occur in the passively Q-switched longitudinal mode, but it is different from the whole quasi-single longitudinal mode in the quasi-single longitudinal mode, which is reflected in the unstable multi-pulse train when the quasi-single longitudinal mode shown in Fig. 3 (1) occurs in the pulse coupling process, and the output pulse is a stable pulse train when the quasi-single longitudinal mode shown in Fig. 3 (2) occurs. According to the dissipative structure energy symmetry theory, the quasi-single longitudinal mode in the laser debugging process is half of the two degeneracy level is suppressed, the energy of the whole laser is missing, and the output is unstable pulse train. While the quasi-single longitudinal mode oscillation of two degeneracies in the laser energy transmission is symmetrical, which basically includes the excitation particles of the whole laser, the energy transmission is stable and symmetrical, and the output is stable pulse train. When the pumping power of the laser increases, the energy level will split [35]. However, the stable pulse is still stable, and the repetition rate increases to reach the pulse splitting. The unstable pulse is still unstable, and the increase of repetition rate is mainly achieved by the continuous occurrence of low power pulse. This is what we observed in our experiments.
3.3 Unstable pulse train of high power
Yb: LuAG Q-switched laser unstable pulse oscillation formation threshold absorption power is 1.80W. The average repetition frequency increases approximately linearly with the increase of laser pump absorption power (63 KHz-161 KHz), showing as Fig. 4. In the absorption power range of 1.80W-8.39W, the average peak power of Yb: LuAG Q-switched laser pulse increases approximately linearly with the increase of pump absorption power (1.5mW-660.3mW). The Yb: LuAG passively Q-switched laser in a light-to-light conversion efficiency is 7.80% and the slope efficiency 10.03%. In the absorption power range of 1.80W to 8.39W, the average energy of the pulse increases approximately linearly with the increase in the absorption power of the laser pump (0.28µJ-7.68µJ). In order to protect the material and film, the pumping power of the laser was not increased in this experiment.
The Yb: LuAG passively Q-switched laser has no saturation phenomenon in the range of pump power in this experiment. The average output power of unstable laser Yb: LuAG, the width of single pulse, the average peak power of pulse and the pulse repetition frequency with frequency less than 500 KHz are all in the same order of magnitude as the stable pulse under the same conditions (due to discussion the unstable pulse train is the main task in the paper, the stable pulse train is discussed in other text). In addition, if there is only one mode left when the laser oscillates in the quasi-double longitudinal mode state, it is an oscillation with nearly half of the energy transmission missing, and the pulse is also an unstable pulse. The spectrum of unstable pulse is analyzed and its excited UHF pulse is analyzed.
3.4 Low frequency and ultra high frequency pulse train
In order to compare the spectrum of stable pulse and unstable pulse, the low frequency spectrum of stable pulse train is obtained by Fourier transform in Tektronix MDO4024C Mixed Domain Oscilloscope, which is shown in Fig. 5 (1) when the absorbed power is 2.5W(output power: 260 mW). The high frequency part is not displayed due to the screen limitation. The first three frequency lines of the spectrum are calculated to be 56.82KHz, 113.61KHz and 170.45KHz respectively, and the relation is harmonic frequency (Note: the pulse train in Fig. 5(1) is a composite screen display, and the spectrum is consistent with the most obvious pulse train).
Both the low frequency (less than 500 KHz) and the ultra-high frequency (UHF) (more than 104 KHz) of the peak unstable pulse train are listed in Fig. 5 (2). The low frequency energy of the pulse train is much higher than the UHF energy. Figure 5(2)(blf) and 5(2)(dlf) are the low frequency spectra corresponding to the pulse sequences 5(2)(a)(output power 260 mW) and 5(2)(c)(output power 280 mW). The spectrum in Fig. 5(2)(blf) has at least two groups of spectrum with independent harmonic frequency relationship, one of which has slightly higher energy, and the values of the first three frequencies of its spectrum are 28.13 KHz, 56.15 KHz, and 84.28 KHz respectively. The pulse train in Fig. 5(2)(a) is assumed to be a single period (stable pulse train, as shown in Fig. 5(1)), and the estimated frequency is 56.2 KHz, with a difference of 0.74 KHz from 56.82 KHz and a difference of 0.05 KHz from 56.15 KHz. The low frequency spectrum of the unstable pulse train is of the same order of magnitude as that of the stable pulse train at the same output power. In Fig. 5(2)(blf), the corresponding frequency values of the other group of spectrum have little difference with the above frequency values, and the energy difference is small. The first three frequency values of the spectrum are respectively 27.42 KHz, 54.72 KHz and 82.25 KHz. The difference of subsequent frequency line values gradually increased, then the two spectral peaks gradually separated, and the two groups of spectral peaks could be clearly seen. The fundamental frequency values of the two groups of spectrum differ by 0.71 KHz. In Fig. 5(2)(a), the pulse train is relatively stable. The frequency spectrum and energy difference of the two pulse trains formed by quasi-double longitudinal mode are relatively small (0.71 KHz), and the total pulse train is relatively stable. Figure 5(2)(dlf) is the low-frequency portion of the pulse train spectrum in Fig. 5(2)(c). One group of frequency spectrum that can be measured the frequency value, the first three frequency values are: 60.08 KHz, 121.1 KHz, 181.2 KHz. The pulse train in Fig. 5(2)(c) is assumed to be a single period, and the estimated frequency value is 61.4 KHz, which differs 0.06 KHz from the fundamental frequency of Fig. 5(2)(dlf) of 60.08 KHz. Figure 5(2)(c) The low frequency part of the pulse train can only measure a set of spectral values. It shows that the other longitudinal modes in the quasi-double longitudinal mode have low energy and no obvious spectral peak. The spectrum of Fig. 5(2)(dlf) has many more spectrum lines behind the spectrum of stable pulse train 5(1), and the whole pulse train is unstable.
The low frequency part of the unstable pulse train is discussed above, and the corresponding ultra-high frequency part is discussed below. According to the harmonic symmetry breaking principle, the ultra-high frequency pulse is formed by the harmonic high-power pulse exciting the medium into plasma in the optical path [34]. The high-power pulse is gone, and the UHF pulse is gone.
Figure 5(2)(a) UHF part of Fourier spectrum transformation of the pulse train as shown in 5(2)(b). The two sets of ultra-high frequency spectrum values are 1.25*105 KHz, 2.5*105 KHz, 3.75*105 KHz and 7.773*104 KHz, 1.552*105 KHz, 2.333*105 KHz, respectively. Figure 5(2) (d) is the UHF spectrum diagram of the 5(2) (c) pulse train, and the small figure is the low frequency spectrum. The two sets of ultra-high frequency spectrum are: 2.5*105 KHz, 3.779*105 KHz and 1.555*105 KHz, 3.104*105 KHz, 4.667*105 KHz. Compare 5(2)(b), 5(2)(d), and the spectrum of peak instability pulse train is increasing with the increase of output power. The spectrum of 2.5*105 KHz and 3.779*105 KHz at 280 mW corresponds to the spectrum of 1.25*105 KHz, 2.5*105 KHz and 3.75*105 KHz at 260 mW. The spectral line does not have a distinct 1.25*105 KHz frequency line, the latter two spectral lines exist, and the spectrum is in the process of conversion to higher frequency spectral spectrum. At 280 mW, the spectral line energy of 1.555*105 KHz, 3.104*105 KHz and 4.667*105 KHz is significantly enhanced than that of 260 mW output power. The fundamental frequency of the spectrum changes from the fundamental frequency 7.773*104 KHz at 260 mW to the fundamental frequency 1.555*105 KHz at 280 mW. This group harmonic frequency is success conversion to the higher harmonic frequency spectrum, which is consistent with the frequency doubling principle generated by higher spectrum [5]. In the process of frequency spectrum conversion to higher spectrum with the increase of pump absorption power, the fundamental spectrum energy of the spectrum decreases, and the energy of the second spectral line increases obviously, and the second spectral line will become the next fundamental frequency. For easier of viewing, the first three spectral lines of the above spectrum are listed in Table 1. There are clustered pulse lines next to the 4.667*105 KHz spectral line, which is the new UHF pulse frequency line that appears later. There is also a later 1.0*105 KHz based spectral line in the spectrum, which should be the frequency oscillation of another pulse train in the laser crystal excited in the plasma.
Table 1
Frequency spectrum varying
Output power (mW)
|
Low frequency (KHz)
|
Ultra high frequency (KHz)
|
260
|
28.13
|
56.15
|
84.28
|
1.25*105
|
2.5*105
|
3.75*105
|
27.42
|
54.72
|
82.25
|
7.773*104
|
1.552*105
|
2.333*105
|
280
|
60.08
|
121.1
|
181.2
|
|
2.5*105
|
3.779*105
|
|
|
|
1.555*105
|
3.104*105
|
4.667*105
|
The UHF in Figure (6) (1) is the graph of the spectrum increasing with the pump power recorded by the oscilloscope by clicking "fft" on the oscilloscope in the pulse display state. With the increase of pump power, the base frequency of UHF pulse spectrum increases by 2n. We trace a set of harmonic frequency spectrum, and the experimental measurement shows that the fundamental frequency of 7.8W is 3.20*1011Hz. With the increase of pump power, the average power of unstable pulse train increases, and the group of frequency spectrum of UHF pulse also increases, as shown in Fig. 5(2)(b),(d). The average peak value of UHF pulse train excited by unstable high power pulse train of passive Q-switched lasers increases with the increase of pump power. High pumping power is easy to damage the material, and the pump power was not continued to increase in the experiment. In UHF pulse train obtaining the log2(frequency) as shown in Figure (6) (1), it has a linear relationship with the pump power of the laser. After high-pass filtering and Fourier transform of the pulse train in Fig. 5(2)(a), the UHF pulse train and corresponding spectrum as shown in Fig. 6 (2) are obtained, and the base frequency of the spectrum is 1.25*105 KHz. It is calculated in the experiment that the peak pulse in Fig. 5(2)(a) is 9.04 times of the average value of the peak pulse in Fig. 6(2)(a), and the low frequency pulse in 5(2)(c) is 4.2 times of the UHF peak pulse train, but the frequency spectral line after filtering is more complex than that in Fig. 6(2)(b). With the increase of laser pumping power, the average peak power of UHF pulse increases. There are also ultra-high frequency lines whose frequencies are not harmonized with each other, and it is difficult to obtain a single harmonized frequency spectrum by filtering.