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

We summarize the problem of measuring an ultrashort laser pulse and describe in detail a technique that completely characterizes a pulse in time: frequency-resolved optical gating. Emphasis is placed on the choice of experimental beam geometry and the implementation of the iterative phase-retrieval algorithm that together yield an accurate measurement of the pulse time-dependent intensity and phase over a wide range of circumstances. We compare several commonly used beam geometries, displaying sample traces for each and showing where each is appropriate, and we give a detailed description of the pulse-retrieval algorithm for each of these cases.

Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating

Authors and Contributors. Read Me! (Preface). 1. The Dilemma. 2. Ultrashort Laser Pulses. 3. Nonlinear Optics. 4. The Autocorrelation, the Spectrum and Phase Retrieval. 5. FROG. 6. FROG Beam Geometries. 7. Geometrical Issues: Single-shot FROG. 8. The FROG Algorithm. 9. Noise: Its Effects and Suppression. 10. Practical Issues, Marginals, Error Checks, and Error Correction. 11. Improvisation in FROG. 12. Very Simple FROG Apparatus: GRENOUILLE. 13. Ultraviolet and High-Power Pulse Measurement. 14. FROG in the Single-Cycle Regime. 15. FROG Characterization of Pulses with Complex Intensity and Phase. 16. XFROG - Cross-correlation frequency-resolved optical gating. 17. Measuring extremely complex pulses. 18. Non-instantaneous Nonlinearities. 19. Fiber-FROG. 20. Measuring Two Pulses Simultaneously: Blind FROG. 21. Principal Component Generalized Projections FROG Algorithm. 22. Measuring Ultraweak Pulses: TADPOLE. 23. Measuring Ultrafast Polarization Dynamics: POLLIWOG. 24. Multi-pulse Interferometric FROG. 25. The Future of Pulse Measurement: New Dilemmas. Index.

Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses

The frequency-resolved optical gating (FROG) technique for characterizing and displaying arbitrary femtosecond pulses is presented. The method is simple, general, broadband, and does not require a reference pulse. Using virtually any instantaneous nonlinear-optical effect, FROG involves measuring the spectrum of the signal pulse as a function of the delay between two input pulses. The resulting trace of intensity versus frequency and delay is related to the pulse's spectrogram a visually intuitive transform containing time and frequency information. It is proven using phase retrieval concepts that the FROG trace yields the full intensity I(t) and phase phi (t) of an arbitrary ultrashort pulse with no physically significant ambiguities. FROG appears to have temporal resolution limited only by the response of the nonlinear medium. The method is demonstrated by using self-diffraction through the electronic Kerr effect in BK-7 glass and 620-nm, linearly chirped, approximately 200-fs pulses of a few microjoules. >

Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating

We recently introduced a new technique, frequency-resolved optical gating (FROG), for directly determining the full intensity I(t) and phase φ(t) of a single femtosecond pulse. By using almost any instantaneous nonlinear-optical interaction of two replicas of the ultrashort pulse to be measured, FROG involves measuring the spectrum of the signal pulse as a function of the delay between the replicas. The resulting trace of intensity versus frequency and delay yields an intuitive display of the pulse that is similar to the pulse spectrogram, except that the gate is a function of the pulse to be measured. The problem of inverting the FROG trace to obtain the pulse intensity and phase can also be considered a complex two-dimensional phase-retrieval problem. As a result, the FROG trace yields, in principle, an essentially unique pulse intensity and phase. We show that this is also the case in practice. We present an iterative-Fourier-transform algorithm for inverting the FROG trace. The algorithm is unusual in its use of a novel constraint: the mathematical form of the signal field. Without the use of a support constraint, the algorithm performs quite well in practice, even for pulses with serious phase distortions and for experimental data with noise, although it occasionally stagnates when pulses with large intensity fluctuations are used.

Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating

We introduce a new technique, frequency-resolved optical gating, for measuring the intensity I(t) and the phase ϕ(t) of an individual arbitrary ultrashort pulse. Using an instantaneous nonlinear-optical interaction of two variably delayed replicas of the pulse, frequency-resolved optical gating involves measuring the spectrum of the signal pulse versus relative delay. The resulting trace, a spectrogram, yields an intuitive full-information display of the pulse. Inversion of this trace to obtain the pulse intensity and phase is equivalent to the well-known two-dimensional phase-retrieval problem and thus yields essentially unambiguous results for I(t) and ϕ(t).

Rick Trebino

Papers

Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating

Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses

Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating

Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating

Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating