中央研究院 原子與分子科學研究所

A new method for diagnosing the temporal characteristics of ultrashort electron bunches with linear energy chirp generated from a laser wakefield accelerator is described. When the ionization-injected bunch interacts with the back of the drive laser, it is deflected and stretched along the direction of the electric field of the laser. Upon exiting the plasma, if the bunch goes through a narrow slit in front of the dipole magnet that disperses the electrons in the plane of the laser polarization, it can form a series of bunchlets that have different energies but are separated by half a laser wavelength. Since only the electrons that are undeflected by the laser go through the slit, the energy spectrum of the bunch is modulated. By analyzing the modulated energy spectrum, the shots where the bunch has a linear energy chirp can be recognized. Consequently, the energy chirp and beam current profile of those bunches can be reconstructed. This method is demonstrated through particle-in-cell simulations and experiment.

The Green function method is a powerful technique for solving the initial value problem in quantum mechanics. Once the Green function is solved the whole wavefunction evolution is represented in a concise form and can be evaluated conveniently by numerical integration. We present a method for constructing the Green functions systematically which is different from the conventional methods of eigenfunction expansion or path integration. By using variable changing, function substitution, and Fourier transforms, the time dependent Schrödinger equations can be simplified and the solutions for the simplified equations can be easily derived. We then obtain the Green functions for the original equations by the reverse transforms. The method is demonstrated for the linear potential, the harmonic oscillator, the centrifugal potential, and the centripetal barrier oscillator, where the Green function for the centripetal barrier oscillator has not been solved previously by conventional methods. The method and examples illustrated in this paper can be utilised to strengthen undergraduate courses on quantum mechanics and/or partial differential equation.

Single-shot ultrashort extreme-UV(EUV) pulse waveform measurement is demonstrated by utilizing strong field ionization of H₂ gas for transmission gating. A cross-propagating intense near-IR gate pulse ionizes the EUV absorbing H₂ molecules into EUV-non-absorbing H₂⁺⁺ (two protons) and creates a time sweep of transmission encoded spatially across the EUV pulse. The temporal envelope is then retrieved from the lopsided spatial profile of the transmitted pulse. This method not only measures EUV temporal envelope for each single shot, but also determines timing jitter and envelope fluctuation statistically, thus is particularly useful for characterizing low-repetition-rate fluctuating EUV/soft x-ray sources.

A Ti:sapphire laser system has been constructed with two synchronized main beams of 110 TW and 13 TW, and a 5-TW wavelength-tunable synchronized auxiliary beam for versatile control of laser-plasma interaction. The first main beam provides 3.3-J, 30-fs, 810-nm pulses, and the second 450-mJ, 34-fs, 805-nm pulses. The auxiliary beam comes from amplified spectral windows selected from a supercontinuum of high spatial coherence and provides 38-fs pulses with tunable wavelengths (870–920 nm). The two main beams can be focused down to M² = 1.2 and 1.1, with 77 and 81% energy enclosed in the focal spots, respectively. The energy fluctuations are 1.1 and 1.8 %, and the pointing fluctuations are 4.5 and 4.8 μrad, respectively. By using a preamplifier and saturable absorber before the pulse stretcher to suppress amplified spontaneous emission, the temporal contrast of the 110-TW main beam reaches 4 ⨯10¹⁰ at the -100-ps timescale. Even though the auxiliary beam is generated from a highly nonlinear process, by confining the supercontinuum generation in a single self-trapping filament, a spatial coherence close to the main beams can be achieved. It can be focused down to M² = 1.3, with 72 % energy enclosed in the focal spot. The energy fluctuation is 2.6 %, and the pointing fluctuation is 4.7 μrad. The versatility of synchronized multiple-beams with tunable wavelengths, good energy and pointing stability, and the spatiotemporal quality of the laser system has been essential to our experiments in high-harmonic generation, extreme-UV lasers, and laser-wakefield accelerators in which precision control of laser-plasma interaction is facilitated by a concerted sequence of driving pulses.

Wepresent a theoretical and numerical study of a novel acceleration scheme by applying a combination of laser radiation pressure and shielded Coulomb repulsion in laser acceleration of protons in multi-species gaseous targets. By using a circularly polarized CO2 laser pulse with a wavelength of 10 μm—much greater than that of a Ti:Sapphire laser—the critical density is significantly reduced, and a high-pressure gaseous target can be used to achieve an overdense plasma. This gives us a larger degree of freedom in selecting the target compounds or mixtures, as well as their density and thickness profiles. By impinging such a laser beam on a carbon–hydrogen target, the gaseous target is first compressed and accelerated by radiation pressure until the electron layer disrupts, after which the protons are further accelerated by the electron-shielded carbon ion layer. An 80 MeV quasi-monoenergetic proton beam can be generated using a half-sine shaped laser beam with a peak power of 70 TW and a pulse duration of 150 wave periods.

Solvable models of the Schroedinger equation are important models of quantum systems because they are idealistic approximations of real quantum systems and much insight into real quantum systems can be gained from the exact solutions of the solvable models. In this paper we show that a universal Laplace transform scheme can be used to solve the Schroedinger equations in closed form for all known solvable models. The work demonstrates how to apply the Laplace transform to differential equations with non-constant coefficients, which is useful in many branches of physics in addition to quantum mechanics. The advantages of the Laplace transform over the power expansion method and its connection with the methods of supersymmetry shape-invariant potentials and quantum canonical transformation, which also give closed-form solutions for solvable models, are elucidated.