A commentary on the article “Uniform-velocity spacetime crystals” by Zoé-Lise Deck-Léger et al. in Advanced Photonics Volume 1, Issue 5.

We present a fully automated laser system with low-intensity noise for coherent Raman scattering microscopy. The robust two-color system is pumped by a solid-state oscillator, which provides Stokes pulses fixed at 1043 nm. The tunable pump pulses of 750 to 950 nm are generated by a frequency-doubled fiber-feedback femtosecond optical parametric oscillator. The resulting pulse duration of 1.2 ps provides a viable compromise between optimal coherent Raman scattering signal and the necessary spectral resolution. Thus a spectral range of 1015 to 3695 cm ¹ with spectral resolution of <13 cm ¹ can be addressed.

Temporal contrast (TC) is one of the most important parameters of an ultrahigh intense laser pulse. The third-order autocorrelator or cross correlator has been widely used in the past decades to characterize the TC of an ultraintense laser pulse. A novel and simple single-shot fourth-order autocorrelator (FOAC) to characterize the TC with higher time resolution and better pulse contrast fidelity in comparison to third-order correlators is proposed. The single-shot fourth-order autocorrelation consists of a frequency-degenerate four-wave mixing process and a sum-frequency mixing process. The proof-of-principle experiments show that a dynamic range of ～10¹¹ compared with the noise level, a time resolution of ～160 fs, and a time window of 65 ps can successfully be obtained using the single-shot FOAC, which is to-date the highest dynamic range with simultaneously high time resolution for single-shot TC measurement. Furthermore, the TC of a laser pulse from a petawatt laser system is successfully measured in single shot with a dynamic range of about 2 × 10¹⁰ and simultaneously a time resolution of 160 fs.

We perform a comprehensive analysis of uniform-velocity bilayer spacetime crystals, combining concepts of conventional photonic crystals and special relativity. Given that a spacetime crystal consists of a sequence of spacetime discontinuities, we do this by solving the following sequence of problems: (1) the spacetime interface, (2) the double spacetime interface, or spacetime slab, (3) the unbounded crystal, and (4) the truncated crystal. For these problems, we present the following results: (1) an extension of the Stokes principle to spacetime interfaces, (2) an interference-based analysis of the interference phenomenology, (3) a quick linear approximation of the dispersion diagrams, a description of simultaneous wavenumber and frequency bandgaps, and (4) the explanation of the effects of different types of spacetime crystal truncations and the corresponding scattering coefficients. This work may constitute the foundation for a virtually unlimited number of novel canonical spacetime media and metamaterial problems.

The Abbe diffraction limit, which relates the maximum optical resolution to the numerical aperture of the lenses involved and the optical wavelength, is generally considered a practical limit that cannot be overcome with conventional imaging systems. However, it does not represent a fundamental limit to optical resolution, as demonstrated by several new imaging techniques that prove the possibility of finding the subwavelength information from the far field of an optical image. These include super-resolution fluorescence microscopy, imaging systems that use new data processing algorithms to obtain dramatically improved resolution, and the use of super-oscillating metamaterial lenses. This raises the key question of whether there is in fact a fundamental limit to the optical resolution, as opposed to practical limitations due to noise and imperfections, and if so then what it is. We derive the fundamental limit to the resolution of optical imaging and demonstrate that while a limit to the resolution of a fundamental nature does exist, contrary to the conventional wisdom it is neither exactly equal to nor necessarily close to Abbe’s estimate. Furthermore, our approach to imaging resolution, which combines the tools from the physics of wave phenomena and the methods of information theory, is general and can be extended beyond optical microscopy, e.g., to geophysical and ultrasound imaging.