1. Introduction

In average power lasers, the repetition-rate Pockels cell is usually used as isolators and Q-switch to obtain high output power. In the conventional Pockels cell, a longitudinal electric field is applied to the electro-optical crystal through external ring electrodes. To achieve a reasonably uniform field distribution in the crystal, the crystal-aspect ratio (length/diameter) must be greater than 1:1. That results in excessive optical absorption which deposits in the crystal as heat. It induced depolarized loss and wave-front distortion. Kurtev [1] carried out some experiments to observe thermally induced depolarization loss of Q-switch and its effects on the output energy of a laser oscillator. In the experiment, a Pockels cell based on the longitudinal electro-optical effect in crystal of DKDP was used and its size was Φ10mm×25mm. The Nd:YAG laser repetition rate was from 10 to 100 pulses/s. Under these experimental conditions, the depolarization in the Pockels cell began to take place at output power of 5W. With a further increase in output power, the depolarization increased considerably.

To reduce thermo-optic depolarization, a direct way is to use the thin crystal with small absorption and large heat-transfer coefficient. For the transversal Pockels cell, the electric field uniformity is independent on the crystal length, but there is natural birefringence. For high average power application, it is necessary to use two pieces of identical crystal to compensate the thermal depolarization loss induced by natural birefringence. The compensated switch with an aperture of 3.25cm×6cm developed by LLNL can be used for average power of 300W. Because the half-wave voltage is proportional to the aspect ratio of the crystal, it limits the aperture of Pockels cell. Plasma Pockels cell [2,3] can be used longitudinally in large aperture with thin crystal, thus it reduces the thermal effects. It is an ideal choice for medium-scale and large-aperture average power optical switches.

2. Key problems of PPC for repetition-rate application

Since the PPC conception was put forward, two operating modes have been developed. To generate conventional plasma PPC, there are two steps. Firstly, highly conductive plasma forms at either side of the electro-optical crystal through gas discharge. Secondly, the switch voltage is applied to the crystal utilizing plasma electrodes. The other operating mode is one-pulse process. [4–6] The high-voltage pulse can be directly applied between the gas cells without prior ionization of the gas. In this way, the supply source would be simpler and the discharge time decreases from tens of milliseconds to hundreds of nanoseconds, so the life of the switch is longer because of less sputter of the discharge electrode material.

The present PPC operating modes are insufficient for the repetition rate application. One-pulse driven PPC need higher pulse voltage to breakdown the neutral gas filled in the cell. The switching voltage is used not only as the switching pulse but also as the gas discharging pulse. So this PPC generally use KDP as its electro-optic crystal, because of its high half-wave voltage. But KDP is unsuitable for average power application because of large absorption coefficient (~5.5%cm ^-1). In the conventional PPC, DKDP can be used as the electro-optic crystal. But the gas discharging time maintains tens of milliseconds. Because the discharge electrodes heat the crystal, it will induce thermo-distortion of the incident laser [7]. In one word, to apply the PPC switch for repetition rate, first, thermal effects induced by the high-average laser power load should be analyzed. On the other hand, the problem that one-pulse driven PPC working with lower switching voltage should be solved, so that it can use DKDP as electro-optic crystal.

3. Thermo-optic effects in repetition-rate PPC

The key thermal effects in the repetition rate PPC is thermo-induced depolarization because of crystal absorption. If the electro-optic crystal coefficient is α, the thermo-power density is

Here, I_(x,y) is the power density of the laser beam and z is the transmission direction of the beam. For thin DKDP, because the absorption coefficient is small, Eq. (1) becomes

For the longitudinal PPC, we individually analyze the thermo-effects in 10mm and 5mm thick DKDP by the finite-element method. The aperture of the crystal is 80mm×80mm. The thermal source is loaded on the model as volume heat productivity. The incident laser power is 1kW (100J, 10Hz), wavelength is 1.064um, and the beam dimension is 60mm×60mm. The initial temperature in the crystal is 18°C. The simulation results show that the temperature distribution in 5mm thick and 10mm thick crystal are similar.

 

Fig. 1. The thermo-induced depolarization loss distribution when the incident laser power is 1kW. (a) Incident laser power of 1kW for 10s. (b) Incident laser power of 1kW for 90s

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Employing thermo-elasticity modeling, the thermo-stress distribution is numerically calculated. Because of the elastic-optical effect, the refractive index of the crystal changes and it will induce depolarization. When the beam passes through the PPC, which is placed between the polarizer and the analyzer, its intensity become

Here Φ is the angle from the polarizer direction to the principal axis of crystal, and δ is the phase retardation between two principal polarized waves, given by

 

Fig. 2. The change of the total depolarized loss at the transmission aperture when the incident beam power is 1kW.

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Figure 1 shows the depolarization loss distribution after the beam passes through the PPC switch. Figure 2 shows the change of the total depolarized loss with time when the incident laser power is 1kW. From Fig. 2, we can see: the depolarized loss in 5mm thick DKDP crystal is much smaller than that in 10mm thick DKDP crystal; when 1kW beam heats the 5mm thick DKDP for 10s and 30s, the depolarization loss is 0.85% and 4% respectively, but for 10mm thick DKDP the depolarization loss is 4.4% and 37.3% respectively.

4. One-pulse driven plasma Pockels cell with DKDP crystal

To realize uniform and stable gas discharge in the case of low voltages (the half wave voltage of the DKDP is about one-half of the KDP), it is necessary to optimize the PPC and choose the inert gas with low breakdown voltages. According to Paschen’s curve, neon has lower breakdown voltage than helium gas. The stainless steel discharge electrode is replaced with a material which work function of 2.42eV in terms of auto-electronic performance; and the discharge electrodes are processed into a pyramidal structure. For the PPC construction, the thin discharge cavity has an optimized thickness of 8mm to increase the gas discharge plasma density. The experiment results show that the stable breakdown voltage in optimized one-pulse driven PPC decreases to 11kV. Compared to the conventional operating mode, the discharge voltage largely decreases, but it is still higher than the half-wave voltage of the DKDP crystal.

The experiment results above indicate that it is insufficient to drive the PPC with the DKDP crystal using one pulse by optimizing the conventional PPC only. We propose a new idea. That is,during the gas discharging process, a higher pulse voltage is applied to ensure the gas discharging stability. But, the voltage on the crystal is equal to the DKDP half-wave voltage. By theoretical calculation and experimental research, we design a capacity-dividing method for one-pulse driven plasma Pockel’s cell with the DKDP crystal. Figure 3 shows the schematic diagram, and its equivalent circuit diagram is given in Fig. 4. In Fig. 4, the PPC is simplified as a variation capacity C_PC. C₀ is a high voltage capacity, Z is the resistance of the transmission line, and the end matching resistance R is equal to the resistance of the transmission line. The voltage on the PPC V_pc is

Before the gas breakdowns, the equivalent capacity of the 80mm×80mm aperture PPC is small, i.e. about 11pF, so nearly all the output voltage of the switch pulse generator is applied on the PPC. The gas discharges and breakdowns to form plasma electrodes. At the same time, the equivalent capacity of the PPC (C_PC) increases to 240pF and the voltage applied on the PPC decreases because a part of the output voltage of the switch pulse generator is applied on C₀. By adjusting C₀ and the output voltage of the switch pulse generator, the two goals, higher breakdown voltage of PPC and lower half wave voltage of the DKDP crystal can be both satisfied.

 

Fig. 3. The schematic diagram of one-pulse driven plasma Pockel’s cell with DKDP crystal

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Fig. 4. The equivalent circuit diagram of one-pulse driven plasma Pockel’s cell with DKDP crystal.

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A one-pulse driving PPC with DKDP crystal, manufactured at the Research Center of Laser Fusion of China Academy of Engineering Physics, is shown in Fig. 5. And its driving voltage pulse waveform is measured by the oscillograph and high voltage probe, shown in Fig. 6. The red curve in CH3 is the voltage pulse applied on the PPC, and the green curve in CH4 is the output voltage of the switch pulse generator. When the switch pulse voltage reaches about 11kV, neon in the gaseous cell begin to breakdown. After about 150ns, the pulse voltage on the PPC is steadied at 8.2kV, which is the half-voltage at 1.064um of the one-pulse driven PPC switch with DKDP crystal of the deuterium is 98%. We also took photo of the neon plasma by CCD camera, which shows the plasma formed by gas discharge filled in the whole 80mm aperture of PPC. The switch efficiency of PPC is measured, which in whole aperture is better than 99%.

 

Fig. 5. A photo of one-pulse driving PPC with DKDP crystal.

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Fig. 6. The oscillograme of driving voltage pulse of PPC. The red curve is the voltage pulse applied on the PPC, and the green curve is the output voltage of the switch pulse generator.

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5. Conclusion

Using thermo-elasticity mode, we simulated thermo-optical effects of the electro-optical crystal in the PPC. The result shows the PPC with a 5mm DKDP crystal can work at 1.064um above 1kW, without significant depolarization. By reformative PPC structure and employing a capacity to share the gas discharge voltage, the uniform plasma electrodes are acquired at the half-wave voltage of DKDP. A one-pulse driving PPC with DKDP crystal is manufactured, which can work at 10Hz with excellent switching performance.