Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.

https://ieeexplore.ieee.org/iel5/5/31089/01447053.pdf

Nonlinear optics

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

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond optical pulses without distortion in dielectric fiber waveguides with group velocity dispersion. In the case of anomalous dispersion (∂2ω/∂k2>0) discussed here [the case of normal dispersion (∂2ω/∂k2<0) will be discussed in a succeeding letter], the stationary pulse is a ``bright'' pulse, or envelope soliton. For a typical glass fiber guide, the balancing power required to produce a stationary 1‐ps pulse is approximately 1 W. Numerical simulations show that above a certain threshold power level such pulses are stable under the influence of small perturbations, large perturbations, white noise, or absorption.

Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion

Self-Trapping of Optical Beams.

Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-\ensuremath{\mu}m-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47\ifmmode\pm\else\textpm\fi{}0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7\ifmmode\pm\else\textpm\fi{}0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (``phase time''), but not with the semiclassical time.

Measurement of the single-photon tunneling time

We report the first experimental verification of Berry's topological phase. The key element in the experiment was a single-mode, helically wound optical fiber, inside which a photon of a given helicity could be adiabatically transported around a closed path in momentum space. The experiment confirmed at the classical level that the angle of rotation of linearly polarized light in this fiber gives a direct measure of Berry's phase. The topological nature of this effect was also verified, i.e., the rotation was found to be independent of deformations of fiber path if the solid angle of the path in momentum space stayed constant.

Observation of Berry's topological phase by use of an optical fiber.

Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves

Recently, Berry recognized in quantum mechanics a topological phase factor arising from the adiabatic transport of a system around a closed circuit, which is essentially the Aharonov-Bohm effect in parameter space. Here we consider manifestations of this phase factor for a photon in a state of adiabatically invariant helicity. An interferometer is suggested to see this phase. Also, an effective optical activity for a helical optical fiber is predicted. These effects emerge on a classical level as topological features of Maxwell's theory.

Raymond Y. Chiao

Papers

Self-Trapping of Optical Beams.

Measurement of the single-photon tunneling time

Observation of Berry's topological phase by use of an optical fiber.

Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves

Manifestations of Berry's Topological Phase for the Photon