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

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrodinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

Optical rogue waves

We review the field of femtosecond pulse shaping, in which Fourier synthesis methods are used to generate nearly arbitrarily shaped ultrafast optical wave forms according to user specification. An emphasis is placed on programmable pulse shaping methods based on the use of spatial light modulators. After outlining the fundamental principles of pulse shaping, we then present a detailed discussion of pulse shaping using several different types of spatial light modulators. Finally, new research directions in pulse shaping, and applications of pulse shaping to optical communications, biomedical optical imaging, high power laser amplifiers, quantum control, and laser-electron beam interactions are reviewed.

Femtosecond pulse shaping using spatial light modulators

Recent advances in ultrafast extreme ultraviolet (EUV) and x-ray light sources provide direct access to fundamental time and length scales for biology, chemistry, and materials physics. However, such light pulses are challenging to measure due to the need for femtosecond time resolution at difficult-to-detect wavelengths. Also, single-shot measurements are needed because severe pulse-to-pulse fluctuations are common. Here we demonstrate single-shot, complete field measurements by applying a novel version of frequency resolved optical gating. An EUV free electron laser beam creates a transient grating containing the pulse’s electric field information, which is read out with a 400 nm probe pulse. By varying the time delay between two copies of the EUV pump, rather than between the pump and the probe, we separate the needed coherent wave mixing from the slow incoherent response. Because this approach uses photoionization, it should be applicable from the vacuum ultraviolet to hard x rays.

All-optical single-shot complete electric field measurement of extreme ultraviolet free electron laser pulses

Using SEA TADPOLE, we directly measure the spatio-temporal field of diffracting ultrashort pulses with fs-temporal and µm-spatial resolutions. Using a circular aperture and an opaque disk, we observe boundary wave pulses including their superluminal speeds.

Measuring the spatio-temporal field of diffracting ultrashort pulses

We demonstrate a novel algorithmic approach for the second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) ultrashort-pulse-measurement technique that always converges and, for complex pulses, is also much faster. It takes advantage of the Paley-Wiener Theorem to retrieve the precise pulse spectrum (half the desired information) directly from the measured trace. It also uses a multi-grid approach, permitting the algorithm to operate on smaller arrays for early iterations and on the complete array for only the final few iterations. We tested this approach on more than 25,000 randomly generated complex pulses, yielding SHG FROG traces to which noise was added, and have achieved convergence to the correct pulse in all cases. Moreover, convergence occurs in less than half the time for extremely large traces corresponding to extremely complex pulses with time-bandwidth products up to 100.

100% Reliable Algorithm for Second-Harmonic-Generation Frequency-Resolved Optical Gating

Disclosed are an apparatus and methods for determining electric field characteristics of pulses. In one example, a method is provided in which an unknown pulse is propagated through a first optical fiber. A reference pulse is propagated through a second optical fiber. The unknown pulse and the reference pulse are directed out of the first and second optical fibers into a spectrometer. The unknown pulse and the reference pulse propagated along a pair of crossing trajectories through the spectrometer to form an interferogram. The electric field of the unknown pulse is determined by processing this interferogram.

Use of crossed-beam spectral interferometry to characterize optical pulses

We further improve and then demonstrate the reliability of the previously introduced RANA approach for the second-harmonic-generation frequency-resolved optical gating (SHG FROG) phase-retrieval algorithm in the presence of significant noise in the traces. We provide a set of relevant parameters for this approach according to the noise level and trace size. Using it, we achieve 100% convergence for thousands of even extremely complex sample pulses, even when contaminated with the introduced significant noise.

Rick Trebino

Papers

All-optical single-shot complete electric field measurement of extreme ultraviolet free electron laser pulses

Measuring the spatio-temporal field of diffracting ultrashort pulses

100% Reliable Algorithm for Second-Harmonic-Generation Frequency-Resolved Optical Gating

Use of crossed-beam spectral interferometry to characterize optical pulses

Extremely Robust Pulse Retrieval From Even Noisy Second-Harmonic-Generation Frequency-Resolved Optical Gating Traces