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By theoretical calculations we search the hold-on and hold-off state of the pulse-off electro-optic (EO) Q-switch made of La3Ga5SiO14 (langasite, LGS) which exhibits both electro-optic (EO) effect and optical activity (OA), from which the proper applied voltage and orientation of LGS are determined. For the first time to our knowledge, a pulse-off EO Q-switch made of LGS is successfully designed and used in the Nd:YAG laser cavity. Q-switched pulses with energy 360 mJ and pulse width 8.3 ns are obtained, and the dynamic-static ratio is 80%.
©2005 Optical Society of America
1. Introduction
The langasite (La3Ga5SiO14, LGS) single crystal has attracted much attention recently because of its electro-optic (EO) applications [1–5]. Compared with the conventional EO Q-switch materials such as KD2PO4 (DKDP) and LiNbO3 (LN), LGS has many advantages. As is known, DKDP is water soluble and it must be carefully protected from moisture, which brings many inconveniences into the fabrication and application, while LGS is not hygroscopic in the air. Also LN has its disadvantage since its optical damage threshold is too low to be used in the medium or high power cases, and the optical damage threshold of LGS is 9 times as high as that of LN [3].
The former papers on LGS EO Q-switches have all adopted the pulse-on cavities in which quarter-wave plates (QWPs) have been used [1–5], and it was considered in [2] that LGS could not be used successfully in the pulse-off cavities in which no QWPs were used because of its optical activity (OA). But it is clear that pulse-off cavities are more compact, lossless and stable than the pulse-on ones, our work in this paper is to design the pulse-off EO Q-switch using LGS.
It is known that in the DKDP Q-switched laser cavity the X- or Y- axis of DKDP should be hold 45° with respect to the polarization direction of the light. As to the case of LGS, it is difficult to give out this angle because it exhibits both EO effect and optical activity. Here we give the Jones matrix of LGS and introduce it to the round-trip process in order to search the hold-on and hold-off state of the Q-switch, and from the calculations both the proper voltage and the orientation of LGS in the laser cavity are determined. All above are discussed in section 2, and we believe this method will be widely used into similar problems in the future.
In section 3, for the first time to our knowledge, a Pockels cell made of LGS is successfully used in the pulse-off cavity. At a repetition rate of 5 Hz, Q-switched pulses with energy 360 mJ and pulse width 8.3 ns are obtained; the dynamic-static ratio is 80%.
2. Design of pulse-off LGS EO Q-switch
Fig. 1. Diagram of the Q-switching process in the pulse-off cavity: (a) the round trip of light, in which right-hand coordinate systems are adopted and RM represents the Reflection Mirror; (b) in this figure the round trip is divided into two single pass for convenience.
It is well known that there is an appropriate orientation of the polarizer in the cavity with KDP (or DKDP) as the Q-switch; the angle between the polarization direction of the polarizer and the axes of KDP is known to be 45°. As LGS is concerned, it is difficult to tell the appropriate angle because LGS is optically active along its optic axes. Here we carry out Jones matrix analyses to determine the angle, and the diagram used is shown in Fig. 1.
First, we need to derive the Jones matrix of LGS. When electric field is applied to the X direction of LGS, the field-induced phase retardation per unit length can be obtained,
Then the matrix for LGS can be derived from literature [6] as follows:
where
and L represents the length of LGS along the optic axis. If no voltage is applied to LGS, that’s to say, ϕ′ = 0, thus r=ρ and θ=0, Eq. (2) becomes
which is the same as the Jones matrices of all common gyrotropic crystals.
We use the right-hand coordinate system in which x- and y-axis are chosen along the crystal X- and Y-axis. In Fig. 1(b), a denotes the angle between the polarization direction of the polarizer and x-axis, and the Jones matrix for the polarizer can be written as [7]
After reflected by the RM, the light will propagate in another right-hand coordinate system in which y-axis becomes its opposite direction, thus we need another matrix to describe the influence of the RM [7],
When no voltage is applied to LGS, the output amplitude after the round trip can be derived using Eqs. (4–6),
where -α represents the transform of the coordinate system, the matrix for LGS won’t change its form because y-axis becomes its opposite direction. The result of Eq. (7) can be obtained with the help of MATLAB, it is
which yields the output intensity is I 1 =|E 1x|2 + |E 1y|2 =1. It is clear that the Q-switch will keep hold-on whatever α is.
When an electric field is applied, the output amplitude after the round trip can be derived with the help of Eqs. (2, 5, and 6),
we can obtain the output intensity
However, the result of Eq. (10) from MATLAB program contains 48 terms, which makes it too complicated to simplify. Numerical analysis is used to deal with this problem, instead.
The LGS crystal used in our experiment has the size of 8.0×8.0×32.5 mm3, the rotatory power that is ρ 0=1.1 °/mm at λ=1064 nm can be obtained from reference [8]. Then the rotatory angle after LGS is 0.624 rad. The following figure can be obtained from MATLAB.
Fig. 2. The output intensity vs. α and ϕL/2 obtained from Eq. (10), which is just one of the periods, and α varies from 0 to π/2, ϕL/2 from 0 toπ. The red arrow shows the selected hold-off position of the Q-switch.
From Fig. 2 we can find in one period there are two hold-off positions, and we select the position where the voltage is lower as the red arrow shows. We can obtain the most appropriate value of α and ϕL/2, the results are 0.38 and 0.85, respectively. Till now, we have obtained the orientation angle of the polarizer that is 21.7°; With ϕL/2 equaling 0.85, the applied voltage can be derived from Eq. (1) as follows
Substituting no=1.88 at λ=1064 nm [8] and other parameters into Eq. (11) yields V=4.85 kV that is a little higher than V λ/4. This is very different from the case of DKDP and LN.
3. Q-switched laser
With the above knowledge we design a EO Q-switch of LGS, and it performs wonderfully in the Nd:YAG cavity in the pulse-off case. The experiment setup is shown in Fig. 3.
Fig. 3. Scheme of Nd:YAG laser Q-switched by LGS in the pulse-off cavity (A) rear mirror; (B) LGS; (C) Brewster window; (D) Xe-lamp; (E) Nd:YAG rod; (F) output coupler.
In our experiment, the electric field is applied to the X direction of LGS and the voltage is turned to about 4.85 k V. When LGS or the Brewster window is rotated about 22°, the Q-switch can reach hold-off state and it can work properly to produce giant pulses. If the longitudinal-transverse ratio (l/d) of LGS is larger, we can get a lower voltage.
The input energy is adjusted to 30 J, and we measured the following output results. When LGS is inserted into the cavity and the Q-switch driver is off, we measured the output energy E 1=450 mJ; when the Q-switch driver turns to DC high voltage, it is the hold-off state and the energy measured is about E 2=2.8 mJ; when the Q-switch works and the repetition is 5 Hz, we get E 3=360 mJ. From our experiment data, the dynamic-static ratio E 3/E 1 is 80%; and the contrast ratio E 3/E 2 is about 160:1. The pulse shape is shown in Fig. 4, from which we can obtain the pulse width about 8.3 ns.
4. Conclusion
We have carried out matrix calculations to search the hold-on and hold-off state of LGS which exhibits both EO effect and OA simultaneously, from which we have obtained the applied voltage and orientation of the LGS Q-switch. This method is very useful to similar problems. At last, for the first time to our best knowledge, an LGS EO Q-switch working in the pulse-off case is successfully used in the Nd:YAG laser cavity. At a repetition of 5 Hz, Q-switched pulses with energy 360 mJ and pulse width 8.3 ns have been obtained, and the dynamic-static ratio is 80%.
Acknowledgments
The work is supported by National Natural Science Foundation of China (Grant 69978009) and Natural Science Foundation of Shandong Province of China (Grant Y2002G06) and Research Fund for the Doctoral Program of Higher Education of China (Grant 2002022048). We are indebted to Mr. Shaojun Zhang of Institute of Crystal Materials of Shandong University for his help with the LGS crystal. One of the authors Zhaojun Liu is grateful to Prof. Fuquan Wu and Mr. Hengjing Tang of Qufu Normal University and Mr. Yunchu Li in our Lab for their helpful suggestions in the experiment.
References
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