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

Measurements of two-photon fluorescence excitation (TPE) spectra are presented for 11 common molecular fluorophores in the excitation wavelength range 690 nm < λ < 1050 nm. Results of excitation by ∼100-fs pulses of a mode-locked Ti:sapphire laser are corroborated by single-mode cw Ti:sapphire excitation data in the range 710 nm < λ < 840 nm. Absolute values of the TPE cross section for Rhodamine B and Fluorescein are obtained by comparison with one-photon-excited fluorescence, assuming equal emission quantum efficiencies. TPE action cross sections for the other nine fluorophores are also determined. No differences between one-photon- and two-photon-excited fluorescence emission spectra are found. TPE emission spectra are independent of excitation wavelength. With both pulsed and cw excitation the fluorescence emission intensities are strictly proportional to the square of the excitation intensity to within ±4% for excitation intensities sufficiently below excited-state saturation.

Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm

Intracavity semiconductor saturable absorber mirrors (SESAM's) offer unique and exciting possibilities for passively pulsed solid-state laser systems, extending from Q-switched pulses in the nanosecond and picosecond regime to mode-locked pulses from 10's of picoseconds to sub-10 fs. This paper reviews the design requirements of SESAM's for stable pulse generation in both the mode-locked and Q-switched regime. The combination of device structure and material parameters for SESAM's provide sufficient design freedom to choose key parameters such as recovery time, saturation intensity, and saturation fluence, in a compact structure with low insertion loss. We have been able to demonstrate, for example, passive modelocking (with no Q-switching) using an intracavity saturable absorber in solid-state lasers with long upper state lifetimes (e.g., 1-/spl mu/m neodymium transitions), Kerr lens modelocking assisted with pulsewidths as short as 6.5 fs from a Ti:sapphire laser-the shortest pulses ever produced directly out of a laser without any external pulse compression, and passive Q-switching with pulses as short as 56 ps-the shortest pulses ever produced directly from a Q-switched solid-state laser. Diode-pumping of such lasers is leading to practical, real-world ultrafast sources, and we will review results on diode-pumped Cr:LiSAF, Nd:glass, Yb:YAG, Nd:YAG, Nd:YLF, Nd:LSB, and Nd:YVO/sub 4/.

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Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers

The evolution of the theory of mode-locking over the last three and a half decades is reviewed and some of the salient experiments are discussed in the context of the theory. The paper ends with two-cycle pulses of a mode-locked Ti:sapphire laser.

Mode-locking of lasers

This paper reports narrowing and splitting of 7-ps-duration pulses from a mode-locked color-center laser by a 700-m-long, single-mode silica-glass fiber, at a wavelength (1.55 \ensuremath{\mu}m) of loss and large but negative group-velocity dispersion. At certain critical power levels, the observed behavior is characteristic of solitons.

Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers

The soliton laser, a novel concept in ultrashort-pulse lasers, is a mode-locked laser using pulse compression and solitons in a single-mode fiber to force the laser itself to produce pulses of a well-defined shape and width. Thus the fiber is in one way or another involved in the laser’s feedback loop. Although the basic concept is a general one, we report here primarily on the first successful version[1], based on a sync-pumped, mode-locked color-center laser operating in the 1.5 pm region. To date this color-center soliton laser has directly produced pulses as short as 130 fsec, and has allowed for the production of pulses of as little as 50 fsec FWHM, by compression in a second, external fiber. Other advantages include wide tunability (limited only by power requirements for soliton production in the fiber), output pulses that are always transform limited, easy adjustment for production of ~sech2 pulse shape. and a relative simplicity of construction.

The soliton laser.

The soliton laser1 is a novel mode-locked device employing a length of single-mode fiber in its feedback loop. Its pulse width can be made to have any desired value, down to a small fraction of a picosecond, through choice of the fiber’s length. Operation is based on the ability of single-mode fibers, in the region (λ> 1.3 µm) of negative group-velocity dispersion, to support periodic soliton pulses, as well. as to narrow broader-pulses of the same energy.2,3 As the fiber is the all-important control element, pulse shape and width are largely independent of factors, such as details of gain dynamics and pump pulse width, that are normally of prime importance in mode-locked lasers.

The Soliton Laser

Performance of return-to-zero (RZ) differential phase-shift keying (DPSK) in ultralong-haul dense wavelength-division-multiplexing (WDM) dispersion managed transmission is studied experimentally and compared with conventional ON-OFF keying (OOK) in a 10-Gb/s system. We show that, while OOK out-performs phase-shift keying in a low spectral efficiency WDM system, the performance of DPSK is comparable to OOK at 10-Gb/s transmission with a spectral efficiency of 0.2. Furthermore, RZ DPSK is advantageous in a high spectral efficiency (e.g., >0.4) system and our numerical simulation results show superior performance of DPSK at 10 Gb/s with 25-GHz channel separation.

Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission

It is shown that it should be possible to send error-free signals at a 2.5-Gb rate (or higher) over distances of at least 9000 km using an amplitude shift keying (ASK) soliton modulation system. To accomplish this, the amplifiers must be kept close enough that their power gain is less than 10 dB. (It is noted that timing jitter and other noise effects measured in recent soliton transmission experiments carried out at low D and with amplifier spacing of 25 km are in close accord with predictions of this work). Frequency division multiplexing of several channels over the same fiber should also be possible, as solitons of different frequencies interact very weakly, provided the distance over which they pass through one another is large compared to the amplifier spacing. >

L. F. Mollenauer

Papers

Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers

The soliton laser.

The Soliton Laser

Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission

Effects of fiber nonlinearities and amplifier spacing on ultra-long distance transmission