Efficient high repetition rate electro-optic Q-switched laser with an optically active langasite crystal

With an optically active langasite (LGS) crystal as the electro-optic Q-switch, we demonstrate an efficient Q-switched laser with a repetition rate of 200 kHz. Based on the theoretical analysis of the interaction between optical activity and electro-optic property, the optical activity of the crystal has no influence on the birefringence during Q-switching if the quarter wave plate used was rotated to align with the polarization direction. With a Nd:LuVO4 crystal possessing a large emission cross-section and a short fluorescence lifetime as the gain medium, a stable LGS Q-switched laser was designed with average output power of 4.39 W, corresponding to a slope efficiency of 29.4% and with a minimum pulse width of 5.1 ns. This work represents the highest repetition rate achieved so far in a LGS Q-switched laser and it can provide a practical Q-switched laser with a tunable high repetition rates for many applications, such as materials processing, laser ranging, medicine, military applications, biomacromolecule materials, remote sensing, etc.

Scientific RepoRts | 6:30517 | DOI: 10.1038/srep30517 Relying on its broadband transmission spectrum and electro-optic properties, a LGS Q-switched laser with the wavelength ranging from 1.06 μ m to 2.79 μ m was reported [21][22][23] . A LGS Q-switched laser with 30 kHz 21 repetition rate was also constructed. Since it has a small piezoelectric coefficient of 6 × 10 −12 C/N 24 , less than a quarter of that of BBO, motivation is provided to investigate LGS Q-switching in high repetition rate lasers. Based on Q-switching theory, the pulse width and peak power are dependent on the cavity length, which indicates that in LGS Q-switching based on the reversibility of optical activity would generate a larger pulse width, in spite of the design complications encountered with the laser cavity. Although LGS Q-switched lasers with a rotated quarter wave plate or polarizer have been reported, there is no analysis on the mechanism supporting the application of this technique. In this work, we theoretically analyze the coupling between optical activity and the electro-optic properties of LGS during the Q-switching process and find that the only effect of optical activity is a rotation along the propagating direction, which can be eliminated simply by rotating the quarter wave plate. Based on the theoretical analysis, we constructed a LGS Q-switched laser in experiments with a Nd:LuVO 4 crystal which has a large emission cross-section and a short fluorescence lifetime 25,26 . This work results in the operation of a laser with a 200 kHz repetition rate and a 5.1 ns pulse width, which represent the highest repetition rate and narrowest pulse width in Q-switched LGS crystal lasers.

Results
Using a two-mirror laser cavity, we studied the Q-switched laser performance. Upon removing the polarizer, LGS Q-switch and QWP, a continuous wave (cw) laser was obtained and the results were shown in Fig. 1(a). The optimized cw output power was achieved using an output coupler with a transmittance of 15%. Under an absorbed pump power of 16.56 W, the maximum output power of 7.86 W was achieved with a conversion efficiency of 47.5% and a threshold of 0.12 W. The output power linearly increases with the absorbed pump power when the slope efficiency was 50%. Using a polarizer, the output laser was identified to be π -polarized.
By inserting the polarizer, Q-switch and QWP into the cavity, a Q-switched laser is obtained by applying a driving voltage. A plot of the output power vs. the absorbed pump power with repetition rates ranging from 20 kHz to 200 kHz is presented in Fig. 1(a). From this figure, it is clear that the output power is dependent on the repetition rate and increases both as an increases of the absorbed pump power and repetition rate. With an absorbed pump power of 16.5 W, the maximum output power was measured to be 3.89 W, 4.08 W, 4.11 W, 4.46 W and 4.4 W at a repetition rate of 20 kHz, 50 kHz, 100 kHz, 150 kHz and 200 kHz, respectively. We also find that the output power is comparable at repetition rates of 150 kHz and 200 kHz, which indicates that the loss generated by the LGS switching effect for a repetition rate above 150 kHz saturates the output power. By comparison, an output coupler with a transmittance of 10% was also employed for the 200 kHz repetition rate and results are shown in Fig. 1(a) with a maximum output power of 3 W.
The pulse behavior with a transmittance of 15% was recorded with a digital oscilloscope. The variation of the pulse width with absorbed pump power is shown in Fig. 1(b). From this figure, it can be seen that the pulse width ranges from 19. 3 ns to 5.1 ns with different absorbed pump powers and repetition rates. There is no obvious relationship between the pulse width and the absorbed pump power at the same repetition rate. The 5.1 ns pulse profile achieved with an absorbed pump power of 10 W and repetition rate of 200 kHz is shown in the inset of Fig. 2. The pulse train obtained at a repetition rate of 200 kHz is shown in Fig. 2, which indicates that the pulse strength is stable with a variation of only 6.2% without any piezoelectric ringing effect. These results indicate that the LGS crystal can be used as a high repetition rate Q-switch operating at as high as 200 kHz. Using average output power and repetition rate, the pulse energy was calculated and the plots of pulse energy versus absorbed pump power at various frequency rates are shown in Fig. 1(c). The pulse energy decreases with repetition rate and linearly increases with absorbed pump power. The maximum pulse energy is 194 μ J at a repetition rate of 20 kHz and the maximum pulse energy at the repetition rate of 200 kHz is 22 μ J with an absorbed pump power of 16.5 W. With the pulse energy and pulse width, the peak power can be calculated. The maximum peak power also decreases with repetition rate and linearly increases with absorbed pump power, its plots are shown in Fig. 1(d). The maximum peak power is 16.4 kW and 1.78 kW for a repetition rate of 20 kHz and 200 kHz, respectively.

Discussions
It should be noted that there was no damage observed in any component of the laser cavity. To sum up the present results, we demonstrated Q-switched performances at different repetition rates as detailed in Table 1. The present results represent the highest repetition rate observed so far in the LGS Q-switched laser regime with a pulsed laser wavelength ranging from 1.0 μ m-3.0 μ m. The performance of the pulse laser with 200 kHz repetition rate is comparable to the BBO Q-switched laser with 200 kHz repetition rate 27 and better than the KD * P (10 kHz) 18 , LN (7 kHz) 28 and other LGS (30 kHz) 21 Q-switched lasers. Additionally, the observed pulse width of 5.1 ns is also smaller than the narrowest pulse width obtained with KD * P (20 ns) 29 , LN (12 ns) 28 and other LGS (7.8 ns) 21 Q-switch. A RTP E-O Q-switched laser with the repetition rate of 280 kHz and pulse width 18.4 ns 7 was reported, but a pair of RTP crystals should be used for compensating the natural birefringence due to the necessary of its orthogonal symmetry. Considering the achievable maximum repetition rate, the ease of crystal growth, the  natural birefringence generated by the symmetry of the electro-optic crystal, the damage threshold (950 MW/ cm 2 19 ), etc. As detailed shown in Table 2.
Compared with previous reported lasers with LGS as Q-switcher 21 , this present laser has some advantages in the repetition rates and pulse width which should be attributed to the shorter cavity length (185 mm) and lower applied electric voltage (3400 V). The shorter cavity determined the shorter roundtrip time and shorter pulse width and was constructed based on the "odd transit time" design which was proposed by the theoretical analysis on the optical active and electro-optic effects. The limitation of high repetition rates of an electro-optic Q-switched laser is the piezoelectric effect which would generate the "piezoelectric ring". The LGS crystal has a small piezoelectric coefficient of 6 × 10 −12 C/N, which indicates that the "piezoelectric ring" effect is negligible. Besides, the "piezoelectric ring" effect is also influenced by the applied electro-field. In the present experiments, we used a LGS Q-switcher with an large aspect ratio (5:1) which decreases the applied electro voltage of 3400 V lower than the previous best result in LGS Q-switched laser (3600 V) 21 . We believe that LGS crystal has great potential for application to the generation of high repetition rate laser radiation and could be used in higher power lasers. In the further, shortening the laser cavity and enlarging the aspect ratio should be helpful for the lasers with higher repetition rates and shorter pulse width which are favorable in many applications such as materials processing.
In conclusion, the interaction between optical activity and electro-optic property was theoretically analyzed and an "odd transit time" design was developed, which indicates that by rotating the quarter wave plate, the optical activity can be eliminated and the Q-switching performances can be realized when the light transits the Q-switch with odd times. Compared with the previous "even transit time" method related to the reversibility of the optical activity 30 , the present "odd transit time" design can simplify the configuration of the Q-switched laser cavity when using an optically active electro-optic crystal as the Q-switch. Using the "odd transit time" method and a Nd:LuVO 4 crystal possessing a large emission cross-section and a short fluorescence lifetime as the gain medium, a LGS electro-optic Q-switched laser was constructed with a repetition rate of 200 kHz, average output power of 4.39 W and pulse width of 5.1 ns. These results indicate that LGS can be used as a high repetition rate Q-switch and free of piezoelectric ringing effects at least at a repetition rate of 200 kHz, and that it can provide a practical Q-switched laser with a tunable high repetition rate for many applications, such as materials processing, laser ranging, remote sensing, etc.

Methods
Theoretical analysis. Optical activity can be considered to be the birefringence of right-handed and lefthanded circularly polarized light with refractive indices of n R and n L 31 , respectively, where n R and n L can be expressed as: where n includes n x and n y , the refractive indices along the X-and Y-directions as light propagates in an optically active crystal along the Z-direction. The polarization state of right-handed and left-handed circularly polarized light can be expressed as 32 : where ∧ x and ∧ y represent unit vectors along the X-and Y-axes, respectively. Therefore, for light with a polarization direction at an angle of 45° with the X-axis, the polarization state of the light is given as: when the above light propagates in an optically active crystal along the Z-direction with length L and refractive index n x and n y along the X-and Y-directions, respectively, the polarization state can be expressed as:   , and g is the gyration tensor component of the optically active crystal. To highlight the influence of optical activity on the birefringence, the polarization state can be simplified to: x y 1 From eq. (5), we see that optical activity for propagation along the Z-axis involves only the polarization rotation direction with angle θ between left and right handed direction, based on Euler's rotation theorem 33 . This result corresponds to a polarization rotation defined in an optically active process 34 or the rotation of frames along the Z-axis with a rotation of θ from the right to the left-handed direction. This rotation would be eliminated when the light propagates along the -Z direction by taking advantage of the reversibility of optical activity 35 . For a uniaxial optically active crystal, such as LGS, n x = n y = n o , where n o is the refractive index of O-light. However, for LGS which has optically activity and electro-optic properties, when we apply an electric field E along the X-direction, the refractive indices along the X-and Y-axes are given by: x o y o 3 11 3 11 where: the birefringence is γ ∆ = n E 1 2 3 11 and the electro-optic coefficient is γ 11 . If E [used same symbol for electric field earlier] is the quarter-wave voltage, the rotation also indicates that a quarter wave plate should be rotated by an angle of θ in coincidence with the frame rotation. When the light is back-reflected, the frame rotation is eliminated and the polarization direction becomes parallel to that of the incident light, which means that the other components in the laser cavity are not influenced by the optical activity. Therefore, we conclude that the optical activity only induces frame rotation in the electro-optic crystal and the quarter wave plate rather than generating additional birefringence. By rotating the quarter wave plate, the electro-optic crystal with optical activity can generate electro-optic modulation similar to those crystals with no optical activity, such as KD * P 29 and BBO 36 . Compared with the "even transit time" 30 design, which is described as follows: the light propagates in the LGS crystal along the Z direction and then along the -Z direction in order to eliminate the effect of optical activity in the laser cavity 30 , the present analyzed "odd transit time" design requires only the rotation of a quarter wave plate thus simplifying the laser cavity configuration.
Experiments of Q-switched laser. Based on the above theoretical analysis, a straight cavity of "odd transit time" design as the following experiments were performed. A two-mirror straight cavity with a length of about 185 mm is employed and the configuration is shown in Fig. 3. The LGS electro-optic crystal was cut along the Z-axis with dimensions of 5 mm × 5 mm × 25 mm (X × Y × Z). The transmission surfaces were polished and AR coated at 1066 nm and the YZ surfaces were unpolished and coated with Au. The quarter wave voltage was calculated to be 3400 V based on a 5:1 aspect ratio. The crystal was rotated around the Z-axis, with the light polarization direction making an angle of 45° with the X-axis. The polarization direction is rotated to 27.5° after propagation through the LGS crystal and determined the rotation of the quarter wave plate (QWP) at 1066 nm at an angle of 27.5°. In other words, the optical activity has no influence on the polarization direction of the light with the rotated quarter wave plate as the light propagated through the Q-switch. The voltage was supplied with a homemade electro-driver with a maximum repetition rate of 200 kHz and a rise time of 8 ns. The pump source was a fiber-coupled laser diode with a central wavelength of 808 nm. The fiber diameter is 200 μ m with a numerical aperture of 0.22. The pump light is focused onto the laser crystal by an imaging unit with a beam compression ratio of 1:1. The input mirror M 1 is plane, antireflection (AR) coated for the pump wavelength and high-reflective (HR) coated for the laser wavelength at 1066 nm. The output coupler M 2 is a plano-concave mirror with a radius of curvature of 200 mm and an output coupler (OC) transmission at 1066 nm of 15% or 10%. A Nd:LuVO 4 crystal cut along the a-axis with a doping concentration of 0.4 at% was chosen as the laser crystal, since it has a large emission cross-section (14.6 × 10 −19 cm 2 ) 25 , short fluorescence lifetime (82 μ s) 25 and high conductivity (9.94 W/ mK) 26 , all of which are beneficial for obtaining high repetition rate laser output with short pulse width and high peak power. The dimensions of the Nd:LuVO 4 sample were 3 mm × 3 mm × 8 mm and the two 3 mm × 3 mm surfaces were polished and AR coated at 808 nm and 1066 nm. The polarizer was a quartz plate oriented along the Brewster angle. The average output power was measured by a power meter (1916-R, Newport, Inc.) and the temporal pulse behavior of the LGS Q-switched laser was recorded by a MSO3054 digital oscilloscope (500 MHz bandwidth and 2.5 GS/s sample rate, Tektronix, Inc.).