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Abstract
A special pulse Nd:YAG/Cr:YAG laser is designed. A particular output mirror consists of a polarization coupled mirror and a terbium scandium aluminum garnet (TSAG) crystal. Using the Faraday magneto-optic effect in the TSAG crystal and a high reflectance mirror, the characteristic of the pulse laser can be actively modulated by adjusting the magnetic intensity. An optimal magnetic intensity (5090 Gs) is measured for output power, pulse energy, peak power, and pulse width. This provides a modern and special reference for the design and manufacture of pulse lasers.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser diode (LD) pumped passively Q-switched all-solid-state laser has many advantages including high efficiency, small volume, light weight, compact structure, good beam quality, stable and reliable performance, and long service life. It is widely used in medical, military, industrial, information, and other fields [1,2]. Passively Q-switched technology is to set a saturable absorber into a laser resonator, and uses its saturable absorption effect to periodically control the loss of the resonator to obtain the pulse output [3,4]. The Cr:YAG crystal is the most competitive and efficient saturable absorber at the near-infrared spectra from 0.8 to 1.2 $\mu$m, which has the characteristics of stable optical performance, good thermal conductivity and high anti-damage threshold [5,6].
Compared with actively Q-switched laser, high repetition rate passively Q-switched laser has advantages like simple structure, small size, and low cost, which is suitable for complex system integration [7,8]. However, at the fixed pump power, it is more difficult to arbitrarily change parameters of the pulse laser than the actively Q-switched technology. The magneto-optical Q-switched method is a new actively Q-switched technology which has been proposed in recent years [9,10]. The sub-millimeter ferromagnetic garnet films [11] and magneto-optical crystals (terbium gallium garnet [7], gadolinium gallium garnet [12]) are usually placed into the cavity to compose a compact laser. Goto et al. observed the peak power of 30 W by utilizing the sub-millimeter ferromagnetic garnet films [11]. However, the ferromagnetic garnet films require special processing techniques, which is hard for most researchers to obtain. On the other hand, magneto-optical crystals have advantages in the performance of thermal conductivity, laser damage threshold, and so on. Hence, we focus on the pulse modulation by utilizing the normal magneto-optical crystals.
In this paper, we use a special output mirror consisted of a polarization coupled mirror, the TSAG crystal, a continuously changing magnetic field, and a high-reflectance mirror to modulate the output of the pulse laser. Combined with the magneto-optical effect, this technology can arbitrarily change the transmission of the output coupler by changing the external magnetic field. This pulse laser has the advantages of simple structure, compact cavity and narrow pulse width.
2. Properties of the TSAG crystal
Due to the Faraday effect, the polarized direction of the linear-polarized light would be deflected [13,14]. The rotation angle of the incident light vector $\alpha$ is proportional to the magnetic intensity $B$ and the length $l_{c}$ of the magneto-optical material, as in
where $V$ is the Verdet constant. It is related to the properties of magneto-optical medium and the frequency of light wave. Furthermore, the direction of the magneto-optical rotation is only related to the direction of the magnetic field, but not to the direction of light propagation. When the light passes back and forth through the magneto-optical material, the rotation angle of the beam would change to 2$\alpha$.At present, a large number of commercial magneto-optical crystals on the market are mainly TGG and RIG [15,16]. TGG crystal is suitable for the wavelength of 400 - 1100 nm (excluding 470 - 500 nm), and RIG crystal is suitable for the wavelength of 1000 - 5000 nm. With the development of optical isolator towards miniaturization and high power, other excellent magneto-optical crystal with higher Verdet constant and lower absorption (smaller thermal lens effect) is imperative [17]. TSAG is an ideal magneto-optical crystal, which is mainly used in the wavelength range of 400 - 1600 nm [18]. TSAG has the advantages of a larger Verdet constant 45.16 rad/(T$\cdot$m) at 1064 nm, about 20% higher than that of TGG), low absorption coefficient (about 30% lower than TGG), and low thermally induced birefringence, which is suitable for middle-high power lasers.
In this paper, a TSAG crystal operating at 1064 nm is selected. The length of the TSAG crystal ($l_{c}$) is 10 mm. As shown in Fig. 1, the angle variation $\alpha$ reaches 22.5 degree at the magnetic intensity of 12425 Gs (dashed blue curve). If the light at 1064 nm passes the crystal twice, the angle variation would be 45 degrees instead.
The rotation angle $\alpha$ is obtained by the photopolarimeter (Thorlabs PAX1000IR2). The transmittance T is calculated by Eq. (2) and the experimental value of T is obtained by calculating the optical power before and after incident crystal. As shown in Fig. 1, solid black curve is the theoretical transmittance and black square is for experimental data. At the magnetic intensities of 3915, 5090, 7335, 9170, 10830, and 12425 Gs, the transmittances are 6, 10, 20, 30, 40, and 50%, respectively. The experiments match the theory well.
3. Theoretical model of the Q-switched Nd:YAG laser
We modified the coupled rate equations for passively Q-switching laser, which were derived by Stein [19] and then generalized by Degnan [20]. As shown in Eq. (3) - Eq. (6).
Initially, all of the particles are in the ground state, $n_{g}$ = $n_{0}$. The initial population inversion density can be derived from Eq. (3), and is given by
When the initial population inversion density $n_{i}$ decreases to the threshold value $n_{t}$,
The relationship between $n_{i}$, $n_{t}$ and $n_{f}$ is given by Eq. (10) [20].
Thus output pulse energy and peak power can be given by the following equations [21],
The parameters for numerical simulation as listed in Table 1 come from our experiment.
Table 1. The numerical simulation parameters.
4. Experimental setup
We devise a special output mirror based on the TSAG magneto-optic crystal as shown in Fig. 2. $M_O$ is a polarization coupled mirror with high reflectance ($R_{S-wave}$ > 99.8%) for S-wave and high transmittance ($T_{P-wave}$ > 99.7%) for P-wave. $M_R$ is a high reflectance mirror at 1064 nm ($R_{1064}$ > 99.5%). The S-wave is reflected by $M_O$ and passes through the TSAG crystal with a rotation angle $\alpha$. Then, it is reflected back by $M_R$ and passes through the TSAG crystals again with a total rotation angle of 2$\alpha$. $M_O$ reflects S-wave back and lets P-wave pass through. The intra-cavity power as well as the transmission $T = P_{out}$ / $P_{in}$ is too difficult to directly measure. The transmission of the special output mirror is indirectly measured with a polarized Nd:YVO$_{4}$ laser at 1064 nm, which is demonstrated in Fig. 2. The relationship between the transmission and magnetic intensity is shown in Fig. 1. When $P_{in}$ is a fixed value, $P_{out}$ is proportional to the transmission.
Fig. 2. A special output mirror based on a TSAG magneto-optic crystal, which is used to test the relationship between the transmission and magnetic intensity.
This special output mirror is used to compose a cavity to realise a compact pulse Nd:YAG laser as shown in Fig. 3. A Nd:YAG with a size of $\phi$ 3 $\times$ 7 mm and the $Nd^{3+}$-doped concentration of 0.15% is directly pumped by an 808.1 nm c-mount LD (HGLD-808-C-GX-5W, INSPUR, Shandong, China). The spot’s diameter is 200 $\mu$m. A Cr:YAG crystal with an initial transmittance of 90.5% is inside the cavity which is constituted by three mirrors, the $M_I$, $M_O$, and $M_R$. The S-wave oscillates back and forth in the cavity and becomes larger and larger, and the P-wave part is the output part. The distances of $M_I$-$M_O$ and $M_O$-$M_R$ are 20 and 65 mm, respectively.
5. Results and discussion
The relationship between the output power and the magnetic intensity is measured and shown in Fig. 4. The pump powers are fixed at 2.5, 4.0, and 5.5 W, respectively. Figure 4(a) is for the CW output. The maximum output powers reach 810, 1450, and 2038 mW respectively at the same magnetic intensity of 5090 Gs. After the magnetic intensity is larger than 5090 Gs, the output power presents a declined trend. The pulse output with the Cr:YAG crystal inside the cavity is shown in Fig. 4(b). Similarly, the maximum output powers reach 400, 813, and 1137 mW respectively at the same magnetic intensity of 5090 Gs. This phenomenon provides a possibility to control the output power by means of the magnetic field. And the optimized magnetic intensity is about 5090 Gs. At this magnetic intensity, the threshold power for CW and pulse is about 0.5 W and 0.75 W, respectively; the corresponding maximum light-light conversion efficiency of CW and pulse is 37.1% and 20.7%; and the slope efficiency of CW and pulse is 41.2% and 24.6%, respectively. This performance is comparable to the performance measured in other reports [22].
The stability of output power is shown in Fig. 5 at the pump power of 5.5 W and the magnetic intensity of 5090 Gs. The values of maximum, minimum, and average power are 1165, 1121 and 1137 mW respectively. The power variation of the Q-switched Nd:YAG laser is less than 5% for 2.5 h, and the standard deviation is 10.98 mW. The 3D distribution of CW laser spot is shown in the insets of Fig. 5. The far-field intensity is a Gaussian distribution, but with a small energy fluctuation in the center of the spot.
The repetition rate and pulse width in relation to the magnetic intensity are measured and shown in Fig. 6 and Fig. 7. At the magnetic intensity of 5090 Gs, the repetition rate and pulse width reaches the extreme values with the maximum repetition rate of 29.1 kHz and the narrowest pulse width of 37 ns. When the magnetic field is less than 5090 Gs, the repetition rate increases and the pulse width reduces, as the magnetic field gradually increases. However, when the magnetic field is more than 5090 Gs, the repetition rate decreases and the pulse width gets wider with the increase of the magnetic field. At the magnetic intensities of 3915, 5090, and 12425 Gs and the pump power of 5.5 W, the repetition rates are 28, 29.1, and 12.2 kHz, and the pulse widths are 45, 37, and 85 ns, respectively. It is useful to compare this pulse width modulation by magneto-optical effect with other works such as passive and active Q-switching methods. Wang et al. demonstrated the passively Q-switched Nd:YAG laser at 1064 nm, the pulse width was 129 ns [23]. Zhou et al. utilized the paramagnetic properties of rare-earth doped lasing crystals for an magneto-optical Q-switcher, the pulse width was 100 ns [24]. Due to the small linear magneto-optical response of the paramagnetic material, a large polarizer is required in the cavity, which increases the length of the cavity. Compared with those works, the pulse width obtained based on TSAG crystal is much shorter, which might be used in laser radar [25] and non-linear frequency [26].
Equation (3) –Eq. (6) are numerically solved by MATLAB with fourth-order Runge-Kutta algorithm for pump power at 2.5, 4.0, and 5.5 W. The theoretical pulse width is compared with experimental data in Fig. 7 (dash curve). When pump power is 5.5 W and the magnetic intensities of 3915, 5090, and 12425 Gs, the theoretical curve of pulse width are 38.7, 35.5, and 65.4 ns. At the magnetic field intensity is larger than 5090 Gs, the pulse width of the experimental data shows an obvious upward trend. In a strong magnetic field, the experimental data of pulse width is greater than the simulation value at the same pump power. This pulse broadening is most likely caused by the thermal lens effect of the Nd:YAG and Cr:YAG crystals [27]. The thermal lens effect will vary the focal length of the thermal lens, which leads to the increase of the diameter of the light spot on the saturated absorber and the decrease of energy density. Thus, the Cr:YAG crystal needs more time to bleach, which would subsequently lead to the broadening of pulse widths [28,29].
The dependence of pulse energy on magnetic intensity is shown in Fig. 8. At the magnetic intensity of 9170 Gs and the pump power of 2.5 W, the pulse energy reaches the maximum rate of 58.8 $\mu$J. When the magnetic field intensity is about 6250 Gs, the numerical result (dash curve) shows the optimal pulse energy. As the magnetic field intensity continues to increase, the pulse energy presents a downward trend. However, the actual measured pulse energy has no conspicuous attenuation. The difference between the numerical results and the experimental data may be caused by the thermal lens effect of the Nd:YAG crystal in the high magnetic intensity field of the real environment [30]. The thermal lens effect leads to the increase of the diameter of the light spot on the Nd:YAG crystal as well. Then, the gain region of the Nd:YAG crystal will be enlarged. Thus, the pulse energy is increased [31,32].
The experimental and theoretical peak power is shown in Fig. 9. At the magnetic intensity of 5090 Gs, the peak power reaches the maximum of 1056 W with the pump power of 5.5 W. Furthermore, the peak power can change from 475.4 to 1056 W, when the magnetic intensity declines from 12425 to 5090 Gs. When the pump power is 5.5 W and the magnetic intensity is 6250 Gs, the theoretical value of peak power reaches the optimal value of 1088 W. Compared with the actual experimental curve, the magnetic field intensity at the theoretical value of the optimal peak power is larger. In the weak magnetic field, there are some differences between the theoretical value and the simulation value. In the strong magnetic field, the theoretical value and the experimental value have the same attenuation trend.
6. Conclusion
The output coupling mirror based on the TSAG magneto-optical crystal is designed, which has a great influence on the output characteristics of the pulse laser. An optimal magnetic intensity (5090 Gs) is measured for output power, pulse energy, peak power, and pulse width respectively. When the magnetic intensity increases from 5090 to 12425 Gs at a fixed pump power of 5.5 W, the output power decreases from 1137 to 493 mW, the pulse width rises from 37 to 85 ns, and the peak power changes from 1056 to 475 W. This provides a modern and special reference for the design and manufacture of pulse lasers. Nevertheless, the conventional passive Q-switched technology could not modulate the pulse width, peak power, out power, and repetition rate at fixed pump power. However, these could be done by magneto-optical modulation which is based on the magneto-optical crystal. To a certain extent, the magneto-optical modulated methods can be used to overcome the shortcomings of passive Q-switched technology. In addition, the Verdet constant of the TSAG crystal is about 3 times larger in visible spectrum (632 nm, 755 nm) than at 1064 nm. Therefore, this work has potential application prospects on visible lasers such as Cr:BeAl$_{2}$O$_{4}$, Pr:YLF, Pr:GLF et al.
Funding
Natural Science Foundation of Fujian Province (2021I0025, 2021j011217); Science Technology Innovation of Xiamen ((3502Z20183062)); Department of Education, Fujian Province (JAT200477).
Acknowledgments
The authors gratefully acknowledge Professor Yuri Rostovtsev for fruitful discussion. Luming Song acknowledges support of Graduate Research Innovation Fellowship from Xiamen University of Technology.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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