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

The full intensity-and-phase characterization of ultrashort laser pulses is now routine in scientific research. Techniques such as frequency-resolved optical gating (FROG) [1] have been widely applied to obtain such information, which is essential in many applications. However, what we have been able to measure so far are mostly simple laser pulses. There are many more light pulses in general, and they aren’t always emitted by lasers, and they can be extremely complicated, very weak, and quite variable from shot to shot. Many more applications involve these “ill-conditioned” pulses, and the ability to measure these pulses will be an invaluable tool to many researchers. In this report we extend the FROG technique to the measurement of ultracomplex (supercontinuum) and ultraweak (bioluminescence) light pulses. Only minor modifications to the FROG apparatus and algorithm are required for these measurements.

Measurements of Ultracomplex and Ultraweak Pulses with FROG

Summary form only given. Recently microstructure optical fibers with large air-fill fractions were demonstrated with zero group-velocity dispersion at /spl sim/770 nm. Experimentally these fibers appear to be single-mode over long propagation lengths at wavelengths ranging from 500 nm to 1550 nm. As a result of the unusual dispersion characteristics and mode properties of the microstructure fiber, a number of novel nonlinear effects at /spl sim/800 nm are now possible. Furthermore, microstructure fibers have potential applications in areas such as high bit-rate communications, dispersion compensation, and ultrashort pulse generation for wavelengths ranging from 700 nm to 1200 nm. In this paper we analyze the spatial mode properties of microstructure fibers and examine the propagation of femtosecond pulses with peak powers ranging up to 300 watts through fiber lengths ranging from 1 to 50 meters.

Pulse propagation in air-silica microstructure optical fibers

Researchers often implicitly assume in their ultrafast studies that their laser beams have separable spatial and temporal dependencies. This underlying assumption greatly simplifies the theoretical treatment of ultrashort laser pulses, but is increasingly difficult to maintain as ever shorter pulse lengths and ever greater bandwidths are routinely generated in ultrafast laboratories. With a large frequency bandwidth, any imperfect operations, such as the stretching, compression, and amplification of ultrashort laser pulses, tend to introduce spatiotemporal distortions, which can be detrimental to the application of these pulses.

Measuring Spatiotemporal Distortions with GRENOUILLE

Summary form only given. As ultrashort pulses have become broader in bandwidth, shorter in time, and more complicated, techniques for measuring them have kept pace, becoming more reliable, more sensitive, and simpler to build and use. While previously the simplest, reliable, intensity-and-phase measurement technique available was FROG (Trebino et al, 1997), the recent development of the GRENOUILLE pulse-measurement device has made pulse measurement even simpler, while building upon the same foundations that make FROG so reliable. This paper shows how a simple dithering of the lateral beam position can generate a sufficient range of angles to achieve phase-matching without measurement trade-offs. Furthermore, such a change can be made to existing GRENOUILLE setups without the need to change the existing optics.

Increased phase-matching bandwidth in GRENOUILLE measurements

In this paper we present a method for modeling ultrashort-laser-pulse compressors/stretchers using Kostenbauder matrices. In this method, a Gaussian pulse is represented by a 2×2 complex Q-matrix and an optical element is represented by a 4×4 real K-matrix. This formalism models pulse compressors and performs full spatio-temporal analysis. Additionally, this formalism allows for uncertainty and sensitivity analyses of the compressors/stretchers. While being simple to implement numerically, this method is computationally much faster than the other equivalent approaches, such as use of Wigner matrices and Wigner functions.

Rick Trebino

Papers

Measurements of Ultracomplex and Ultraweak Pulses with FROG

Pulse propagation in air-silica microstructure optical fibers

Measuring Spatiotemporal Distortions with GRENOUILLE

Increased phase-matching bandwidth in GRENOUILLE measurements

Modeling of pulse compressors using Kostenbauder matrices