A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Science and technologies based on terahertz frequency electromagnetic radiation (100 GHz–30 THz) have developed rapidly over the last 30 years. For most of the 20th Century, terahertz radiation, then referred to as sub-millimeter wave or far-infrared radiation, was mainly utilized by astronomers and some spectroscopists. Following the development of laser based terahertz time-domain spectroscopy in the 1980s and 1990s the field of THz science and technology expanded rapidly, to the extent that it now touches many areas from fundamental science to 'real world' applications. For example THz radiation is being used to optimize materials for new solar cells, and may also be a key technology for the next generation of airport security scanners. While the field was emerging it was possible to keep track of all new developments, however now the field has grown so much that it is increasingly difficult to follow the diverse range of new discoveries and applications that are appearing. At this point in time, when the field of THz science and technology is moving from an emerging to a more established and interdisciplinary field, it is apt to present a roadmap to help identify the breadth and future directions of the field. The aim of this roadmap is to present a snapshot of the present state of THz science and technology in 2017, and provide an opinion on the challenges and opportunities that the future holds. To be able to achieve this aim, we have invited a group of international experts to write 18 sections that cover most of the key areas of THz science and technology. We hope that The 2017 Roadmap on THz science and technology will prove to be a useful resource by providing a wide ranging introduction to the capabilities of THz radiation for those outside or just entering the field as well as providing perspective and breadth for those who are well established. We also feel that this review should serve as a useful guide for government and funding agencies.

The 2016 terahertz science and technology roadmap

When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Ei…

Bose-Einstein condensation

Real-time imaging of countless femtosecond dynamics requires extreme speeds orders of magnitude beyond the limits of electronic sensors. Existing femtosecond imaging modalities either require event repetition or provide single-shot acquisition with no more than 1013 frames per second (fps) and 3 × 102 frames. Here, we report compressed ultrafast spectral photography (CUSP), which attains several new records in single-shot multi-dimensional imaging speeds. In active mode, CUSP achieves both 7 × 1013 fps and 103 frames simultaneously by synergizing spectral encoding, pulse splitting, temporal shearing, and compressed sensing—enabling unprecedented quantitative imaging of rapid nonlinear light-matter interaction. In passive mode, CUSP provides four-dimensional (4D) spectral imaging at 0.5 × 1012 fps, allowing the first single-shot spectrally resolved fluorescence lifetime imaging microscopy (SR-FLIM). As a real-time multi-dimensional imaging technology with the highest speeds and most frames, CUSP is envisioned to play instrumental roles in numerous pivotal scientific studies without the need for event repetition. Ultrafast imaging has been limited by the speed of electronic sensors. Here, the authors demonstrate single-shot compressed ultrafast spectral photography, which combines spectral encoding, pulse splitting, temporal shearing, and compressed sensing in order to achieve real-time imaging at 70 trillion frames per second.

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Single-shot ultrafast imaging attaining 70 trillion frames per second

The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrodinger equation (NLSE) including fractional one-dimensional or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too, in particular, for fast moving solitons and the results produced by the variational approximation. Moreover, dissipative solitons are briefly considered, which are governed by the fractional complex Ginzburg–Landau equation.

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Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

We construct families of fundamental, dipole, and tripole solitons in the fractional Schrodinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos 2 x and sin 2 x , respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the Levy index (LI) that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.

Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

Recent advances in generation of terahertz vortex beams and their applications

Families of coupled solitons of $\mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained $\mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $\mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.

Stable and oscillating solitons of $\mathcal{PT}$-symmetric couplers with gain and loss in fractional dimension

This work was supported partly by the National Natural Science Foundation of China (Nos. 61775142 and 61705132), the Shenzhen Basic Research Project on the subject layout (No. JCYJ20170412105812811), the Shenzhen Basic Research Projects (Nos. JCYJ20170412105812811, JCYJ20190808164007485, and JCYJ20190808115601653), and the Natural Sciences and Engineering Research Council of Canada (Nos. RGPIN-2017-05959 and RGPAS-507845-2017). There are no conflicts of interest.

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High-spatial-resolution ultrafast framing imaging at 15 trillion frames per second by optical parametric amplification

We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression (“bubbles”) can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas–Fermi and variational approximations. All these modes are stable, which is predicted by computation of eigenvalues for small perturbations and confirmed by direct numerical simulations.

Xiaowei Lu

Papers

Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

Recent advances in generation of terahertz vortex beams and their applications

Stable and oscillating solitons of $\mathcal{PT}$-symmetric couplers with gain and loss in fractional dimension

High-spatial-resolution ultrafast framing imaging at 15 trillion frames per second by optical parametric amplification

Bubbles and W-shaped solitons in Kerr media with fractional diffraction