Abstract
The development of the ultrafast laser system opened up a large number of new research fields. New optical techniques have been developed to reduce the pulse duration to a few femtoseconds and/or to increase the peak power to the multi-petawatt range. The generation of ultrashort pulses implies a large bandwidth, increasing complexity of the beam propagation, and diagnostics to fully characterize the final pulse in the spatiotemporal domain. One of the spatiotemporal couplings (STCs)[1] playing a key role in a wide range of scientific areas, e.g., laser development, laser–matter interaction, is the angular dispersion (AD) of the beam. The presence of this chromatic aberration distorts the laser pulse, causing pulse front tilt (PFT)[2]. In turn, when the beam is focused, the actual pulse length in the focal spot is different from the pulse length in the near field, where it is usually measured.
The presence of PFT in the near field has been proved to have an effect on electron acceleration experiments[3], so its control and measurement are important for the development of compact laser-driven plasma accelerators and, more generally, to guarantee the best performance of high-power laser facilities.
In high-power ultrashort laser systems, slight misalignment of the compressor and/or the stretcher can generate AD[4]. Different diagnostics[5] have been proposed to characterize these aberrations, based on interferometric[6,7], spectral–temporal[8], autocorrelation[9], chromatic[10] or wave-front distortion[11] techniques. Unfortunately, these diagnostics involve complex setup[12–14], originating from complex alignment procedures, and most of them are self-referenced[15], so they need a good-quality beam, both in the spatial and the temporal domains. Moreover, they involve complex retrieval routines, sometimes leading to ambiguities in the detection of STCs[7] or providing only qualitative measurements.
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In this Letter, we propose a simple innovative single-shot method, based on an intensity mask. It is suitable for characterizing not only short pulses, as required for many available diagnostics, but also stretched pulses. The proposed instrument addresses most of the main issues of existing STC diagnostics: it is a simple retrieval routine able to retrieve different STCs without ambiguities; the simple experimental setup involves simple alignment procedures and the instrument is not a self-referenced method so it does not require a good-quality beam in the spatiotemporal domain. Above all, the main advantage of this new diagnostic is the simplicity of the setup and the ability to show, directly from the acquired image, the presence of PFT prior to the analysis in both directions. The theoretical background and the diagnostic performances are first presented together with simulations, in detail. Second, experimental results, supported by the theoretical analysis of the beam propagation, are reported, confirming the feasibility of our tool.
The basic idea of the proposed instrument is to use a diffraction element to disperse the spectral components angularly. If a transmission grating is used as the diffraction element in the horizontal direction, by focusing the diffraction order and analyzing the diffracted spot, the spectral components are diffracted at different horizontal positions while the vertical position encodes information about the AD. By using a 2D diffraction element and analyzing the diffraction orders in both directions, the AD in both directions can be retrieved. To study in detail the theory behind the instrument, let us consider a low aberrated laser beam that can be described by an electric field
In the paraxial approximation, adopting an achromatic lens of focal length
Figure 1.Simulated image of the first diffracted spot () in
The focal length of the lens has a direct implication for the resolution of the instrument: a longer focal length creates a larger deviation, encoding the information on a larger number of pixels. However, it also requires a larger camera sensor to be able to collect the first orders of diffraction. So, with the parameters of the camera (number of pixels
To validate the instrument, a software program was developed to simulate the focusing of a broad-bandwidth laser beam. The program takes an arbitrary shape of the input beam in the spectrum-space domain and simulates the focusing described by Equation (1). For each wavelength, a numerical Fourier transform is performed, obtaining the simulated focal spot images. Each image is then re-scaled to the same resolution and integration over the wavelength range is performed to obtain the final focal spot image. The program is implemented using the ArrayFire library[16] and the CUDA library and it was run on a PC with an NVIDIA M6000 graphics card. All the simulations were performed using a 2048×2048 point array with a pixel size of 5.3 μm and 64 samplings in the spectral domain. The camera had a resolution of
Starting from the image (simulated or experimental) of the focal plane (Figure 2), a background subtraction algorithm and numerical filtering were performed. The resulting image was centred and each diffracted spot was analyzed to obtain the parameters
Figure 2.Camera image comparison for a FWHM Gaussian beam with FWHM Gaussian spectrum around and AD of : (left) simulated image; (right) experimental image.
A set of images, having different amplitude of AD values as
Figure 3.Retrieved versus simulated AD for a 50 nm FWHM Gaussian spectrum and 5 mm FWHM Gaussian beam for a different AD modulus.
Beam shape | Spectral shape | ||
---|---|---|---|
Gaussian | Gaussian | 1 | 0.018 |
Gaussian | Flat-top | 1 | 0.020 |
Square flat-top | Gaussian | 0.86 | 0.020 |
Square flat-top | Flat-top | 0.85 | 0.022 |
Table 1. Influence of the beam and spectral shape.
Figure 4.Influence on calibration and retrieved error of various beam parameters: (left) beam size FWHM; (right) spectral bandwidth FWHM.
The presence of astigmatism is well tolerated if small (
Figure 5.Influence on calibration and retrieved error of various beam parameters: (left) astigmatism; (right) chromatic defocus.
Figure 6.Schematic of the experimental setup implemented in the front end of the FLAME laser system. BS, beam splitter; CCD, charge-coupled device camera; L, achromatic doublet; MK, diffractive mask.
Figure 7.AD as a function of the introduced misalignment . Experimental results (ADexp) compared with the Kostenbauder matrix formalism simulation (ADth) simulating a misaligned double-pass grating compressor.
In conclusion, AD retrieval is important for determining the performances of ultrashort high-power lasers. The proposed single-shot diagnostic, requiring a minimal number of optics and a compact layout, could be used as a real-time diagnostic, both on a high repetition rate (tens of hertz) laser system and on a low repetition rate, high-power, large laser system. Moreover, the ability to be applied also to stretched pulses will allow monitoring of AD across the entire amplification chain. The performances of the instrument were tested numerically and experimentally, proving to be robust and accurate over a wide range of parameters. Finally, thanks to the retrieval algorithm flexibility, more advanced analysis could be developed and implemented in future to perform real-time measurements of higher-order chromatic aberrations.
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