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

A time lens based on clock-driven phase modulators followed by linear dispersion accurately removes timing-jitter. When used prior to the receiver, the time lens greatly improves bit-error-rate performance in DWDM dispersion managed soliton transmissions.

Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions

The propagation of ultrashort (picosecond) pulses in optical fibers is a matter of considerable contemporary interest, both to communications and to pure science. The effect of the inevitable dispersion, acting alone, is always to broaden such pulses. Thus at first there would appear to be only one way to avoid pulse broadening: to tune the source to the wavelength (for low-loss silica glass fibers, typically in the neighborhood of 1.3 µm) where the (group velocity) dispersion passes through zero.

Experimental observation of picosecond pulse narrowing and solitons in optical fibers

To date erbium amplifiers have been based on fiber doped with 10 to 1000 ppm erbium oxide, providing several tens of dB gain in lengths of 100 m or less.[1–4] However, communications systems which use such high gain, "lumped" amplifiers subject the signal to large excursions in amplitude, which can cause significant interchannel interference in a wavelength division multiplexed system. Of equal importance, the amplified spontaneous emission (ASE) is significantly smaller when distributed amplification is used, and a larger signal to noise is obtained when the signal is sustained at a high level throughout the system.[5] We show here that fibers can indeed be made with the controlled, very low Er doping (10–100 ppb Er averaged over the core), required for such distributed amplification. Some of our fibers allowed for just enough gain per unit length (0.2–0.3 dB/Km) to cancel fiber loss, without at the same time introducing significant impurities or other defects.

A Distributed Erbium Doped Fiber Amplifier

Soon after the first experimental demonstration of soliton transmission in optical fibers [1], it was predicted theoretically [2,3] that solitons can be transmitted over intercontinental distances in fiber where loss is periodically compensated by Raman gain. The predicted rate-length product for such transmission is on the order of 30,000 GHz-km for a single channel, and many times that figure with wavelength multiplexing [3]. Recently, in an experiment to explore the basic principles of such long distance, repeaterless transmission, we have achieved nearly distortionless transmission of 55 ps solitons over distances in excess of 4000 km.

DEMONSTRATION OF SOLITON TRANSMISSION OVER MORE THAN 4000 km IN FIBER WITH LOSS COMPENSATED BY RAMAN GAIN

We have studied the performance of dispersion-managed (DM) soliton systems with random variations of span lengths and span path-average dispersions by numerical simulation. We show that while DM solitons still exist in systems with nonperiodic dispersion maps, those nonperiodic maps tend to degrade system performance. We investigate the performance degradation of both on-off keyed and differential phase-shift keyed DM-soliton systems with random span lengths and random span path-average dispersions. We find that the impairment caused by the span path-average dispersion variation is larger than that caused by the span length variation, and that the reduction in quality factor due to the span length and the span path-average dispersion variations is less in dense wavelength-division multiplexing (WDM) than in single-channel transmission systems. In addition, we also show that keeping the overall path-average dispersion constant within a few spans can reduce the random dispersion map-induced performance degradation.

L. F. Mollenauer

Papers

Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions

Experimental observation of picosecond pulse narrowing and solitons in optical fibers

A Distributed Erbium Doped Fiber Amplifier

DEMONSTRATION OF SOLITON TRANSMISSION OVER MORE THAN 4000 km IN FIBER WITH LOSS COMPENSATED BY RAMAN GAIN

Numerical study of random variations of span lengths and span path-average dispersions on dispersion-managed soliton system performance