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

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

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

Microcavity physics and design will be reviewed. Following an overview of applications in quantum optics, communications and biosensing, recent advances in ultra-high-Q research will be presented.

Optical microcavities

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

A laser cavity formed from a single defect in a two-dimensional photonic crystal is demonstrated. The optical microcavity consists of a half wavelength–thick waveguide for vertical confinement and a two-dimensional photonic crystal mirror for lateral localization. A defect in the photonic crystal is introduced to trap photons inside a volume of 2.5 cubic half-wavelengths, approximately 0.03 cubic micrometers. The laser is fabricated in the indium gallium arsenic phosphide material system, and optical gain is provided by strained quantum wells designed for a peak emission wavelength of 1.55 micrometers at room temperature. Pulsed lasing action has been observed at a wavelength of 1.5 micrometers from optically pumped devices with a substrate temperature of 143 kelvin.

https://science.sciencemag.org/content/sci/284/5421/1819.full.pdf

Two-Dimensional Photonic Band-Gap Defect Mode Laser

We propose a new type of optical waveguide that consists of a sequence of coupled high- Q resonators. Unlike other types of optical waveguide, waveguiding in the coupled-resonator optical waveguide (CROW) is achieved through weak coupling between otherwise localized high- Q optical cavities. Employing a formalism similar to the tight-binding method in solid-state physics, we obtain the relations for the dispersion and the group velocity of the photonic band of the CROW's and find that they are solely characterized by coupling factor k 1 . We also demonstrate the possibility of highly efficient nonlinear optical frequency conversion and perfect transmission through bends in CROW's.

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Coupled-resonator optical waveguide:?a proposal and analysis

We combine fiber Bragg grating (FBG) technology with a wet chemical etch-erosion procedure and demonstrate two types of refractive index sensors using single-mode optical fibers. The first index sensor device is an etch-eroded single FBG with a radius of 3 μm, which is used to measure the indices of four different liquids. The second index sensor device is an etch-eroded fiber Fabry-Perot interferometer (FFPI) with a radius of ~1.5 μm and is used to measure the refractive indices of isopropyl alcohol solutions of different concentrations. Due to its narrower resonance spectral feature, the FFPI sensor has a higher sensitivity than the FBG sensor and can detect an index variation of 1.4 X 10(-5). Since we can measure the reflection signal, these two types of sensors can be fabricated at the end of a fiber and used as point sensors.

/pdf/highly-sensitive-fiber-bragg-grating-refractive-index-4wf3wo8jri.pdf

Highly sensitive fiber Bragg grating refractive index sensors

Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We give the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant frequency. Based on these results, the recently proposed concept of "critical coupling" is discussed. Using a matrix formalism based on the scattering analysis, we find the dispersion relation of indirectly coupled resonator optical waveguides. The coupling between waveguides and multiple cavities is investigated and the reflection and transmission coefficients are derived.

Scattering-theory analysis of waveguide-resonator coupling

We form a new type of optical microcavity using 2D photonic crystals embedded in a half wavelength thick waveguide Modes localized to a single defect in the photonic crystal can be theoretically shown to have small mode volumes The flexibility in design of the photonic crystal enables one to tailor the device for vertical emission or for coupling into an in-plane waveguide The added versatility in being able to etch the laser cavity may also help develop low threshold laser sources in material systems in which high index contrast epitaxial mirrors do not exist

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Reginald K. Lee

Papers

Two-Dimensional Photonic Band-Gap Defect Mode Laser

Coupled-resonator optical waveguide:?a proposal and analysis

Highly sensitive fiber Bragg grating refractive index sensors

Scattering-theory analysis of waveguide-resonator coupling

Two-dimensional photonic bandgap defect laser