There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Table Of Integrals Series And Products

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

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

We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of accessible solitons and establishes an important link with parametric solitons.

https://arxiv.org/pdf/physics/0308024.pdf

Route to Nonlocality and Observation of Accessible Solitons

We report on the observation and quantitative assessment of self-trapped pulsating beams in a highly nonlocal nonlinear regime. The experiments were conducted in nematic liquid crystals and allow a meaningful comparison with the prediction of a scalar theory in the perturbative limit, while addressing the need for beyond-paraxial analytical treatments.

Observation of optical spatial solitons in a highly nonlocal medium.

In certain materials, the spontaneous spreading of a laser beam (owing to diffraction) can be compensated for by the interplay of optical intensity and material nonlinearity The resulting non-diffracting beams are called ‘spatial solitons’ (refs 1–3), and they have been observed in various bulk media4,5,6 In nematic liquid crystals7,8,9, solitons can be produced at milliwatt power levels10,11,12 and have been investigated for both practical applications13 and as a means of exploring fundamental aspects of light interactions with soft matter14,15 Spatial solitons effectively operate as waveguides, and so can be considered as a means of channelling optical information along the self-sustaining filament But actual steering of these solitons within the medium has proved more problematic, being limited to tilts of just a fraction of a degree16,17,18,19,20 Here we report the results of an experimental and theoretical investigation of voltage-controlled ‘walk-off’ and steering of self-localized light in nematic liquid crystals We find not only that the propagation direction of individual spatial solitons can be tuned by several degrees, but also that an array of direction-tunable solitons can be generated by modulation instability21,22,23,24,25 Such control capabilities might find application in reconfigurable optical interconnects, optical tweezers and optical surgical techniques

Routing of anisotropic spatial solitons and modulational instability in liquid crystals

Spiral twisting offers additional opportunities for controlling the loss, dispersion, and polarization state of light in optical fibers with noncircular guiding cores. Here, we report an effect that appears in continuously twisted photonic crystal fiber. Guided by the helical lattice of hollow channels, cladding light is forced to follow a spiral path. This diverts a fraction of the axial momentum flow into the azimuthal direction, leading to the formation of discrete orbital angular momentum states at wavelengths that scale linearly with the twist rate. Core-guided light phase-matches topologically to these leaky states, causing a series of dips in the transmitted spectrum. Twisted photonic crystal fiber has potential applications in, for example, band-rejection filters and dispersion control.

http://science.sciencemag.org/content/sci/337/6093/446.full.pdf

Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber

Nonlinear optical media that are normally dispersive support a new type of localized (nondiffractive and nondispersive) wave packets that are X shaped in space and time and have slower than exponential decay. High-intensity X waves, unlike linear ones, can be formed spontaneously through a trigger mechanism of conical emission, thus playing an important role in experiments.

Claudio Conti

Papers

Route to Nonlocality and Observation of Accessible Solitons

Observation of optical spatial solitons in a highly nonlocal medium.

Routing of anisotropic spatial solitons and modulational instability in liquid crystals

Excitation of Orbital Angular Momentum Resonances in Helically Twisted Photonic Crystal Fiber

Nonlinear electromagnetic X waves.