Angular Chirp Research Articles

Spatiotemporal aberrations due to the groove density mismatching of compression gratings in ultra-intense femtosecond lasers

The groove density mismatching of compression gratings, an often-neglected key issue, can induce significant spatiotemporal aberrations especially for super-intense femtosecond lasers. We mainly investigate the angular chirp and the consequent degradation of the effective focused intensity introduced by the groove density mismatching of compression gratings in ultra-intense femtosecond lasers. The results indicate that the tolerances of grating groove density mismatching will rapidly decrease with the beam aperture or spectral bandwidth increases. For our 100PW laser under construction, the grating groove density mismatching should be as small as 0.001 gr/mm if the drop of effective focused intensity has to be controlled below 15%. More importantly, new angular chirp compensation schemes are proposed for both double-grating and four-grating compressors. This work reveals the importance of groove density matching of compression gratings, and can provide helpful guidelines for the design of ultra-intense femtosecond lasers.

Cherenkov second harmonic generation of femtosecond laser pulses in a homogeneous nonlinear crystal

In experiments on second harmonic (SH) generation (SHG), a conical structure of radiation has been observed. In the present study, a non-stationary theory of SH excitation of ultrashort laser pulses with phase modulation has been developed, which explains the properties of such a structure as Cherenkov radiation. Under phase-mismatched interactions, a maximum of the SH spectrum is observed at the Cherenkov angle, which is determined by the ratio of the SH and laser radiation phase velocities. It is shown that tightly focused laser beams are preferred to observe Cherenkov SHG. The SH spectral width depends on the group velocity mismatch and is more complicated on the excited radiation spectrum. The SH energy can be proportional to the crystal length or group delay length depending on their ratio. We also demonstrate that a complex angular distribution of spectral components (an angular chirp) appears within the SH cross-section.

Measurement and minimization of angular chirp of stretcher in chirp pulse amplification laser

Measurement and minimization of angular chirp of stretcher in chirp pulse amplification laser

Spatio-spectral couplings in optical parametric amplifiers.

Optical parametric amplification (OPA) is a powerful tool for the generation of ultrashort light pulses. However, under certain circumstances, it develops spatio-spectral couplings, color dependent aberrations that degrade the pulse properties. In this work, we present a spatio-spectral coupling generated by a non-collimated pump beam and resulting in the change of direction of the amplified signal with respect to the input seed. We experimentally characterize the effect, introduce a theoretical model to explain it as well as reproduce it through numerical simulations. It affects high-gain non-collinear OPA configurations and becomes especially relevant in sequential optical parametric synthesizers. In collinear configuration, however, beyond the direction change, also angular and spatial chirp is produced. We obtain with a synthesizer about 40% decrease in peak intensity in the experiments and local elongation of the pulse duration by more than 25% within the spatial full width at half maximum at the focus. Finally, we present strategies to correct or mitigate the coupling and demonstrate them in two different systems. Our work is important for the development of OPA-based systems as well as few-cycle sequential synthesizers.

Propagation of ultrashort laser fields with spatiotemporal couplings using Gabor's Gaussian complex decomposition.

In ultra-intense chirped pulse amplification laser systems, pulses of ultrashort duration and high energy are generated using large spectral bandwidths and large beam diameters. Hence, the spatiotemporal couplings of the laser field can become significant and affect the field structure. The propagation of such pulses is simulated in this work using a code developed in-house, based on Gabor's decomposition of the initial complex field into Fourier transform limited Gaussian pulse beam terms. Subsequently, the analysis of the temporal, spatial, and angular chirp, as well as pulse front tilt couplings for a super-Gaussian beam of 25 fs duration allows quantification of their signatures in the near field and focus.

Ray-tracing analysis of a single-grating stretcher with an arbitrary three-mirror unit-magnification telescope

This paper considers the general case of a single-grating femtosecond stretcher with an arbitrary ratio of radii of curvature of the telescope mirrors R 1 / R 2 , including the particular cases with R 1 / R 2 = − 2 and 0, known as Öffner and Martinez configurations, respectively. Analytical expressions for the general stretcher geometry, beam sizes on the elements, and linear properties are obtained with the Kostenbauder matrix formalism. Using the ray-tracing approach, the roles of both the ratio of R 1 / R 2 and the size of the telescope are analyzed in terms of the fourth-order dispersion, angular chirp, and sensitivity to misalignments.

Low-aberration single-grating femtosecond stretcher with two concave parabolic mirrors

A novel configuration of a low-aberration single diffraction grating stretcher for femtosecond chirped-pulse amplification lasers is proposed. The stretcher configuration employs two identical concave parabolic mirrors separated by a distance equal to their focal length. Using the numerical ray-tracing approach, the proposed design is compared with conventional Martinez and Offner configurations in terms of high-order dispersions, aberrations of the spectral phase, and angular chirp. Although the proposed design is not completely aberration-free, it can exhibit comparable or lower aberrations than those of the single-grating Offner configuration with similar parameters.

Propagation characteristics of a spatially chirped Gaussian laser beam propagating through multiple lenses

Variation of curvature of laser beam changes characteristics of spatially chirped pulsed Gaussian (SCPG) laser beam primarily due to varying spectral divergence. Parametric dependence of different pulse parameters, e.g. angular chirp, pulse front tilt, pulse width, beam radius, radius of curvature etc., is presented for a SCPG laser beam propagating through single and pair of reflective or refractive optical system. Effect of chromatic aberration on characteristic of SCPG laser beam have also been presented under different propagation conditions. Different expressions for various parameters of pulsed Gaussian beam are extended using recursive relation for a sequence of multiple chromatic lenses generally used in large scale high energy high power laser system. Discussion is supported with few examples of lens system.

A simulation study of time-of-flight mass spectrometry with an angular chirp enhanced delay cavity

Recent developments of the time-stretch in optics have been closely related to the concept of time-of-flight in mass spectrometry. While the resolution of optical wavelength in time-stretch techniques relies on the differentiation of optical path lengths induced by either free space or dispersive media, the mass resolution in time-of-flight mass spectrometry depends on the overall length of the field-free region during a fly of ions group. In this study, we introduce the latest concept of free-space angular-chirp-enhanced delay (FACED) cavity from the field of optical time-stretch into the time-of-flight mass spectrometry. The FACED cavity in time-of-flight ion optics will be realized using a pair of angularly misaligned electrostatic ion mirrors. We study the properties of the FACED cavity in ion optics using SIMION and demonstrate how the multiple reflections in a time-of-flight mass analysis can be significantly increased.

Shaping picosecond ellipsoidal laser pulses with periodic intensity modulation for electron photoinjectors.

A method for shaping periodic intensity distributions of strongly chirped picosecond laser pulses in the infrared range by periodic phase modulation of the spectrum is proposed. The dependence of the time modulation period and depth on the parameters of periodic phase modulation of the spectrum is analyzed by analytical and numerical methods. It is demonstrated that the intensity distribution structure obtained at second- and fourth-harmonic generation can be retained by introducing an angular chirp. The electron bunch dynamics at the photoinjector test facility at DESY in Zeuthen (PITZ) was modeled numerically using ellipsoidal laser pulses with intensity modulation.

Novel method for the angular chirp compensation of passively CEP-stable few-cycle pulses.

We demonstrate a novel, energy-efficient, cost-effective simple method for seeding CEP-stable OPCPAs. We couple the CEP-stable idler of a broadband OPCPA into a hollow core Kagome fiber thus compensating for the angular chirp. We obtain either relatively narrow bandwidths with ∼36% coupling efficiency or quarter-octave spanning bandwidths with ∼2.2% coupling efficiency. We demonstrate spectral compressibility, good beam quality and CEP stability. Our source is an ideal seed for high-energy, high-average power, CEP-stable few-cycle OPCPA pulses around 2 µm, which can drive the generation of coherent soft X-ray radiation in the water window spectral region via HHG.

Real-time spectral analysis of ultrafast pulses using a free-space angular chirp-enhanced delay.

Frequency-to-time mapping is a powerful technique for observing ultrafast phenomena and nonrepetitive events in optics. However, many optical sources operate in wavelength regions, or at power levels, that are not compatible with standard frequency-to-time mapping implementations. The recently developed free-space angular chirp-enhanced delay (FACED) removes many of these limitations and offers a linear frequency-to-time mapping in any wavelength region where high-reflectivity mirrors and diffractive optics are available. In this work, we present a detailed formulation of the optical transfer function of a FACED device. Experimentally, we verify the properties of this transfer function and then present simple guidelines to guarantee the correct operation of a FACED frequency-to-time measurement. We also experimentally demonstrate the real-time spectral analysis of femtosecond and picosecond pulses using this system.

Retaining 3D shape of picosecond laser pulses during optical harmonics generation.

Collinear and noncollinear sum-frequency generation of broadband laser pulses with angular and frequency chirp is considered. The conditions of minimal distortions of 3D ellipsoidal intensity distribution of triangular chirped femtosecond pulses during generation of the second, third, and fourth harmonics of a Ti-Sa laser in LBO, BBO, and KBBF crystals are found using numerical methods. The efficiency of conversion from the fundamental to the fourth harmonic (45%) is higher than to the third harmonic (20%), and the distortions of intensity distribution are less.

Laser Requirements for High-Order Harmonic Generation by Relativistic Plasma Singularities

We discuss requirements on relativistic-irradiance (I0 > 1018 W/cm2) high-power (multi-terawatt) ultrashort (femtosecond) lasers for efficient generation of high-order harmonics in gas jet targets in a new regime discovered recently (Pirozhkov et al., 2012). Here, we present the results of several experimental campaigns performed with different irradiances, analyse the obtained results and derive the required laser parameters. In particular, we found that the root mean square (RMS) wavefront error should be smaller than ~100 nm (~λ/8). Further, the angular dispersion should be kept considerably smaller than the diffraction divergence, i.e., μrad level for 100–300-mm beam diameters. The corresponding angular chirp should not exceed 10−2 μrad/nm for a 40-nm bandwidth. We show the status of the J-KAREN-P laser (Kiriyama et al., 2015; Pirozhkov et al., 2017) and report on the progress towards satisfying these requirements.

Approaching the diffraction-limited, bandwidth-limited Petawatt.

J-KAREN-P is a high-power laser facility aiming at the highest beam quality and irradiance for performing state-of-the art experiments at the frontier of modern science. Here we approached the physical limits of the beam quality: diffraction limit of the focal spot and bandwidth limit of the pulse shape, removing the chromatic aberration, angular chirp, wavefront and spectral phase distortions. We performed accurate measurements of the spot and peak fluence after an f/1.3 off-axis parabolic mirror under the full amplification at the power of 0.3 PW attenuated with ten high-quality wedges, resulting in the irradiance of ~1022 W/cm2 and the Strehl ratio of ~0.5.

High-Power, Few-Cycle, Angular Dispersion Compensated Mid-Infrared Pulses From a Noncollinear Optical Parametric Amplifier

We demonstrate a scheme for correcting the angular dispersion of the 3.1- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX"> $\mu$</tex-math></inline-formula> m idler beam from a high repetition rate, KTiOAsO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_4$</tex-math></inline-formula> (KTA) based noncollinear optical parametric amplifier pumped at 1.03 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m and seeded by broadband signal pulses at 1.55 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m. Following angular dispersion correction, successful temporal chirp compensation was possible, and a close to transform-limited pulse duration of 70 fs and a pulse energy of 30 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX"> $\mu$</tex-math></inline-formula> J at a repetition rate of 100 kHz were obtained. The angular chirp compensated KTA-based scheme is scalable to higher pulse energies and average powers and has various advantages compared to periodically poled and angle-tuned LiNbO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_3$</tex-math></inline-formula> -based amplifiers, which exhibit low resistance to photorefractive damage.

High-order-harmonic generation driven by pulses with angular spatial chirp

We present and analyze a technique to drive high-order harmonics by laser pulses with an angular spatial chirp. Results of our numerical simulations show that each harmonic is emitted with an angular chirp which scales inversely with the harmonic order and leads to additional control of the spatial and temporal resolution of the spectrum. In particular, the use of angular chirp leads to separation of the harmonics in two dimensions where (i) high spectral resolution can be achieved and (ii) the temporal periodicity of the harmonic pulse trains can be controlled. We show that this technique does not require carrier-envelope-phase stabilization when using few-cycle laser pulses.

Broadband interferometric characterization of divergence and spatial chirp.

We demonstrate a spectral interferometric method to characterize lateral and angular spatial chirp to optimize intensity localization in spatio-temporally focused ultrafast beams. Interference between two spatially sheared beams in an interferometer will lead to straight fringes if the wavefronts are curved. To produce reference fringes, we delay one arm relative to another in order to measure fringe rotation in the spatially resolved spectral interferogram. With Fourier analysis, we can obtain frequency-resolved divergence. In another arrangement, we spatially flip one beam relative to the other, which allows the frequency-dependent beamlet direction (angular spatial chirp) to be measured. Blocking one beam shows the spatial variation of the beamlet position with frequency (i.e., the lateral spatial chirp).

Role of misalignment-induced angular chirp in the electro-optic detection of THz waves.

A general description of electro-optic detection including non-collinear phase matching and finite transverse beam profiles is presented. It is shown theoretically and experimentally that non-collinear phase matching in ZnTe (and similar materials) produces an angular chirp in the χ(2)-generated optical signal. Due to this, in non-collinear THz and probe arrangements such as single-shot THz measurements or through accidental misalignment, measurement of an undistorted THz signal is critically dependent on having sufficient angular acceptance in the optical probe path. The associated spatial walk-off can also preclude the phase retardation approximation used in THz-TDS. The rate of misalignment-induced chirping in commonly used ZnTe and GaP schemes is tabulated, allowing ready analysis of a detection system.

High precision elimination of angular chirp in CPA laser systems with large stretching factors or high bandwidth

We present a novel and highly sensitive method to determine the residual angular dispersion of high-power laser pulses after stretching, amplification, and re-compression of the pulses in a chirped-pulse amplification laser system. This method is based on the intentional deflection of a part of the the spectrum within the compressor and aligning the centers of gravity of the two resulting and separated foci with largest possible spectral separation in the far field. Using this technique, we were able to reduce the residual angular dispersion on pulses to less than 0.05 μrad/nm in the vertical plane and less than 0.03 μrad/nm in the horizontal plane, respectively. With this method, it is possible to minimize the deviation of the actual peak intensity for the focused laser pulses to less than 2 % of its theoretical limit.