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A new scheme for efficient optical parametric chirped pulse amplification is proposed by introducing a time delay between long pump and short seed pulses. Numerical results show that high conversion efficiency from the pump to seed and high gain can be achieved simultaneously, and the amplified seed pulse is stable and not sensitive to timing jitter.
©2003 Optical Society of America
1. Introduction
Optical parametric chirped pulse amplification (OPCPA) is an attractive technique for generation of ultrashort laser pulses with high powers [1–2]. OPCPA has many advantages such as high gain without spectral narrowing and high contrast ratio. It can efficiently replace a conventional regenerative amplifier in a chirped-pulse-amplification laser system [3–5]. A power stability of 3% was achieved in an OPCPA amplifier [5]. An output power up to 3.67 TW was obtained from an OPCPA laser system, in which two optical-parametric-amplification (OPA) preamplifiers and a power OPA amplifier were involved [6]. Another feature of the OPCPA technique is its possibility to produce ultrahigh peak-power laser pulses with tabletop size and low cost. Therefore commercial Q-switched lasers are usually used as pump sources with typical pulse durations of 6–10 ns [3–5]. Temporal durations of seed pulses, however, are typically 0.5–3 ns [3–5], which are generally shorter than those of the pump pulses, generally resulting in low conversion efficiency from the pump to seed. Nevertheless, the residual energy of the pump pulse is further used to pump a conventional Ti:sapphire multipass amplifier and an overall conversion efficiency of 37 % can be obtained [7]. In addition, an extremely comprehensive numerical analysis of OPCPA systems, including factors such as spectral phase, energy extraction, pre-chirp, pulse shape, group-velocity mismatch, etc., on the system performance has been presented [8]. However, more compact, high-gain and high-efficiency single-pass OPCPA systems are still required for practical applications. In this paper, we propose a simple OPCPA scheme to increase the energy conversion efficiency from the pump to the seed by introducing a time delay between the long pump and short seed pulses so that the seed pulse interacts with all portions of the pump pulse, and the gain is guaranteed simultaneously. We present numerical results for the proposed OPCPA scheme and demonstrate that the pump energy can be efficiently transferred into the seed and idler pulses.
2. Principle of OPCPA with time delay
Fig. 1. A scheme for efficient OPCPA. p, s, and i denote the pump, seed, and idler pulses. Ts and Tp are durations of the seed and pump pulses, respectively.
Figure 1 shows the concept scheme of OPCPA with time delay. The number of OPA stages is primarily determined by the temporal duration ratio of the pump (Tp) to seed (Ts). In the example shown in Fig. 1, Tp/Ts is approximately 3. In the OPA1 stage, which can be seen as a conventional OPA scheme, the peak portion of the seed pulse (s) is temporally adjusted to match with the peak portion of the pump pulse (p). It is more favorable to first amplify the seed pulse with the central part of the pump pulse in order to avoid obvious distortions in the amplified seed pulse. The crystal thickness of the OPA1 stage is optimized so that the peak portion of the pump pulse is depleted and efficiently converted into the seed pulse. An idler pulse (i) synchronously generated transmits through a mirror in the delay line 1 and does not enter into the next stages. The seed pulse is then temporally delayed by the delay line 1 with respect to the pump pulse and interacts with the falling portion of the pump pulse. Finally, the pump pulse is inversely delayed by the delay line 2 so that the seed pulse will catch up with the rising portion of the pump pulse. Therefore, the falling and rising portions of the pump pulse can efficiently convert into the seed and idler pulses by the OPA2 and OPA3 stages, resulting in high pump-to-seed conversion efficiency and gain simultaneously. The seed pulse may first interact with the falling portion of the pump pulse in the OPA1 stage according to the durations of the pump and seed such as the case of Tp/Ts~2. The nonlinear crystals used in the OPA stages are optimized to ensure that the conversion efficiency is highest and the temporal distribution of the amplified seed pulse is nearly the same as that of the initial one simultaneously. It is possible to keep the crystal length constant by adjusting the beam size. Delay times of the delay lines are also determined by the durations of the pump and seed. In this paper, as shown in Fig. 1, the pump and seed pulses are assumed to satisfy type I (eoo) degenerate phase-matching geometry. In fact, the proposed scheme is also suitable for nondegenerate noncollinear geometry by introducing an angle between the pump and seed pulses.
3. Numerical results
We carried out numerical calculations for the proposed OPCPA scheme with the following coupled differential equations for difference frequency generation [4, 9],
where Es, Ei, and Ep are the amplitudes of the electric field of the seed, idler, and pump pulses, respectively, nj(j=s, i, p) is the refractive index, deff is the effective nonlinearity, Δk is the phase-mismatching factor, and Ij is the intensity with respect to Ej. Spatially flat-topped laser beams are assumed for the incident pulses and initially temporal shapes of the incident pulses are assumed as Gaussain. A fourth-order Runge-Kutta algorithm is applied to numerically solve Eq. (1), and to evaluate the pump-to-seed energy conversion efficiency, gain, and tempo-spatial profiles of the interacting pulses. The pulse energy is calculated by tempo-spatially integrating the intensity of the pulse. The parameters of the pump and seed pulses are listed in Table 1 [3–5]. Nonlinear crystals of three stages are assumed to be β-barium borate (BBO) crystal with a same phase-matching angle of 22.8 degree.
Table 1. Parameters of seed and pump laser pulses
Figure 2 shows the pump-to-seed energy conversion efficiency and gain as functions of the crystal thickness. The feature of the conversion process from the pump to seed can be considered as three different regions: conversion, depletion, and back-conversion regions. In the conversion region, the seed pulse increases with the crystal thickness, and the corresponding temporal evolution is almost the same as that of the initial Gaussian distribution. The pump pulse will be depleted in the depletion region and the temporal distortion in the seed pulse occurs. In the back-conversion region, the seed pulse begins to convert to the pulse. The conversion efficiency is gradually decreased with the crystal thickness and the corresponding temporal evolution is further distorted. Therefore, it is necessary to evaluate both energy conversion efficiency and pulse distribution in order to optimize the crystal thickness. In the calculation, the thickness of the nonlinear crystal is corresponding to the maximum value of the product between the energy and peak-intensity conversion efficiencies. In the front of the OPA1 stage, the peak of the seed pulse is temporally adjusted to be overlapped onto that of the pump pulse. The highest pump-to-seed conversion efficiency is 23 % at the crystal thickness of 16 mm. Behind the OPA1 stage, the seed pulse is delayed by the half of the pump duration of 5 ns and interacts with the falling portion of the pump pulse in the OPA2 stage. The falling portion is then depleted and the seed pulse is further amplified. The net pump-to-seed conversion efficiency of the OPA2 stage, which is defined as the ratio of the net energy increased in the seed pulse to that of the residual energy of the pump pulse, is 21% with respect to the thickness of 5 mm. In the front of the OPA3 stage, the pump pulse is delayed by the pump duration of 10 ns and the seed pulse interacts with the rising portion of the pump pulse. The optimized thickness of the OPA3 is 4.4 mm with the corresponding net pump-to-seed conversion efficiency of 35 %. The gains of the OPA1, OPA2, and OPA3 stages are respectively 400, 1.5, and 1.3. The overall energy conversion efficiency from the pump to seed is 45.7% through OPA1, OPA2, and OPA3 stages, and the overall gain is approximately 784. This conversion efficiency, which is near the theoretical limit of 50% pump-to-seed conversion efficiency, is comparable with most efficient Ti:sapphire chirped-pulse amplifiers [10]. The residual energy of the pump pulse unconverted to the seed and idler is only 9.5 % of the input one. Figure 3 shows the temporal evolutions of the pump and seed pulses under the same conditions used in Fig. 1. The peak portion of the seed pulse is slightly saturated due to the OPA processes but other obvious distortions in the pulse cannot be found out.
In practical OPCPA systems, timing jitter and pump variation cannot be avoided and should be investigated in the numerical calculation. For pump intensities of 300±30 MW/cm2, the variation in the overall gain is correspondingly less than 7.2 %, while the overall pump-to-seed energy conversion varies within 1.5 %, which are respectively calculated from the ratios of standard deviations to average values of the gain and conversion efficiency under the same conditions of Fig. 1 except for the initial pump intensity. Thus the pump-pulse fluctuations are almost not imprinted on the seed pulse [6]. In addition, for initial timing jitters of ±1 ns between the pump and seed pulses, the pump-to-seed energy conversion efficiency and gain are both less than 0.25%. The weak sensitivity observed in the numerical simulations is resulted from the saturation of the parametric amplification [11]. The demerit of the temporal mismatch between the pump and seed pulse durations in the conventional OPCPA scheme becomes a merit in the proposed scheme, which is suitable for the purpose of the high stable amplification.
Fig. 3. Temporal profiles of the seed and pump pulses behind the OPA3 stage on both linear (a) and logarithmic (b) scales.
4. Conclusion
An OPCPA scheme is proposed by introducing a time delay to long pump and short seed pulses with degenerate phase-matching BBO crystals. Numerical calculations show that the OPA conversion process, which has simultaneously high pump-to-seed energy conversion efficiency and high gain, is quite stable both in the energy conversion efficiency and gain. Also the scheme can be applied to a nondegenerate geometry. The idea of OPCPA with time delay can be realized to construct low-cost, compact high-peak power laser systems that only require commercially-available Q-switched Nd:YAG lasers.
References and links
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