The theory of quasi-phase-matched second-harmonic generation is presented in both the space domain and the wave vector mismatch domain. Departures from ideal quasi-phase matching in periodicity, wavelength, angle of propagation, and temperature are examined to determine the tuning properties and acceptance bandwidths for second-harmonic generation in periodic structures. Numerical examples are tabulated for periodically poled lithium niobate. Various types of errors in the periodicity of these structures are then analyzed to find their effects on the conversion efficiency and on the shape of the tuning curve. This analysis is useful for establishing fabrication tolerances for practical quasi-phase-matched devices. A method of designing structures having desired phase-matching tuning curve shapes is also described. The method makes use of varying domain lengths to establish a varying effective nonlinear coefficient along the interaction length. >

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Quasi-phase-matched second harmonic generation: tuning and tolerances

The ideal material for nanophotonic applications will have a large refractive index at optical frequencies, respond to both the electric and magnetic fields of light, support large optical chirality and anisotropy, confine and guide light at the nanoscale, and be able to modify the phase and amplitude of incoming radiation in a fraction of a wavelength. Artificial electromagnetic media, or metamaterials, based on metallic or polar dielectric nanostructures can provide many of these properties by coupling light to free electrons (plasmons) or phonons (phonon polaritons), respectively, but at the inevitable cost of significant energy dissipation and reduced device efficiency. Recently, however, there has been a shift in the approach to nanophotonics. Low-loss electromagnetic responses covering all four quadrants of possible permittivities and permeabilities have been achieved using completely transparent and high-refractive-index dielectric building blocks. Moreover, an emerging class of all-dielectric metamaterials consisting of anisotropic crystals has been shown to support large refractive index contrast between orthogonal polarizations of light. These advances have revived the exciting prospect of integrating exotic electromagnetic effects in practical photonic devices, to achieve, for example, ultrathin and efficient optical elements, and realize the long-standing goal of subdiffraction confinement and guiding of light without metals. In this Review, we present a broad outline of the whole range of electromagnetic effects observed using all-dielectric metamaterials: high-refractive-index nanoresonators, metasurfaces, zero-index metamaterials and anisotropic metamaterials. Finally, we discuss current challenges and future goals for the field at the intersection with quantum, thermal and silicon photonics, as well as biomimetic metasurfaces.

All-dielectric metamaterials

A design criterion that permits truly omnidirectional reflectivity for all polarizations of incident light over a wide selectable range of frequencies was used in fabricating an all-dielectric omnidirectional reflector consisting of multilayer films. The reflector was simply constructed as a stack of nine alternating micrometer-thick layers of polystyrene and tellurium and demonstrates omnidirectional reflection over the wavelength range from 10 to 15 micrometers. Because the omnidirectionality criterion is general, it can be used to design omnidirectional reflectors in many frequency ranges of interest. Potential uses depend on the geometry of the system. For example, coating of an enclosure will result in an optical cavity. A hollow tube will produce a low-loss, broadband waveguide, whereas a planar film could be used as an efficient radiative heat barrier or collector in thermoelectric devices.

https://science.sciencemag.org/content/sci/282/5394/1679.full.pdf

A Dielectric Omnidirectional Reflector

The possibility of using Bragg reflection in a cylindrical fiber to obtain lossless confined propagation in a core with a lower refractive index than that of the cladding medium is proposed and analyzed.

Theory of Bragg fiber

The propagation of electromagnetic radiation in birefringent layered media is considered. A general formulation of the plane-wave propagation in an arbitrarily birefringent layered medium is presented. The concepts of dynamical matrix and propagation matrix are introduced. A 4 × 4 transfer matrix method is used to relate the field amplitudes in different layers. Our general theory is then applied to the special case of periodic birefringent layered media, especially the Solc birefringent layered media [ I.
	 Solc
	 
	, Cesk. Casopis Fẏs.3, 366 ( 1953);Cesk. Casopis Fẏs.10, 16 ( 1960)]. The unit cell translation operator is derived. The band structures as well as the Bloch waves are obtained by diagonalizing the translation operator. Coupled mode theory is extended to the case of birefringent periodic perturbation to explain the exchange Bragg scattering. A general mode dispersion relation for guided waves is also obtained in terms of the transfer matrix elements.

Electromagnetic propagation in birefringent layered media

The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-infinite, and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. Some new phenomena with applications to integrated optics and laser technology are presented.

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Electromagnetic propagation in periodic stratified media. I. General theory

In this paper, some of our recent work in the use of holographic interference lithography and various material removal techniques to corrugate thin-film optical waveguides are reviewed. The specific applications of these periodic thin-film devices in the distributed feedback and distributed Bragg reflector semiconductor laser, and as output grating couplers, are described. Recent results in the use and fabrication of chirped and curved-line gratings are also summarized.

/pdf/holographic-interference-lithography-for-integrated-optics-4e6d79xxfm.pdf

Holographic interference lithography for integrated optics

1.3μm GaInAsP/InP buried heterostructure lasers were successfully fabricated by using a hybrid combination of liquid phase epitaxy (LPE) and metalorganic chemical vapor deposition (MO‐CVD). Definite advantages were found in the use of MO‐CVD for the overgrowth of the optical and current confining layers. Excellent optical linearity up to two times the threshold current, as well as low‐threshold current (57 mA), were obtained during cw operation at room temperature. A single longitudinal mode was observed at ∼1.11 times the threshold current.

Chi-Shain Hong

Papers

Electromagnetic propagation in periodic stratified media. I. General theory

Holographic interference lithography for integrated optics

Low‐threshold 1.3‐μm GaInAsP/InP buried heterostructure lasers by liquid phase epitaxy and metalorganic chemical vapor deposition