Single-mode propagation of light in one-dimensional all-dielectric light-guiding systems

Numerical results are presented for single-mode guidance, which is based on photonic band gap (PBG) effect, in one-dimensional planar all-dielectric light-guiding systems. In such systems there may be two kinds of light-speed point (the intersection of a mode-dispersion curve and the light line of guiding region ambient medium): one is the intrinsic light-speed point that is independent of the guiding region width, and the other is the movable light-speed point that varies with the guiding region width. It is found that the intrinsic light-speed point plays an important role to form the single-mode regime by destroying the coexistence of the lowest guided TM and TE modes that are born with a degeneration point. A sufficient and necessary condition for intrinsic light-speed points is given. The transverse resonance condition is derived in the Maxwell optics frame, and it is shown that there is a significant revision to the traditional one in the ray optics model. A mode-lost phenomenon is exposed and this phenomenon suggests a way of how to identify PBG-guided fundamental modes. Quasi-cutoff-free index-guided modes in the PBG guiding structures, which appear when the higher-index layers are adjacent to the guiding region and the guiding region width is small, are exposed and analyzed as well.Comment: 13 pages, 8 figures, 32 reference

Properties and numerical solutions of dispersion curves in general isotropic waveguides

In this paper, some properties of dispersion curves in general isotropic piecewise homogeneous waveguides are rigorously derived. These properties are leveraged in a numerical implementation capable of determining the dispersion curves of such waveguides with cross-section materials that can be highly conductive (such as copper). In a numerical example, the influence of a lossy shielding conductor on the complex modes of a shielded dielectric image guide is investigated for the first time

Towards all-dielectric metamaterials and nanophotonics

We review a new, rapidly developing field of all-dielectric nanophotonics which allows to control both magnetic and electric response of structured matter by engineering the Mie resonances in high-index dielectric nanoparticles. We discuss optical properties of such dielectric nanoparticles, methods of their fabrication, and also recent advances in all-dielectric metadevices including couple-resonator dielectric waveguides, nanoantennas, and metasurfaces

Analytical approach to dielectric optical bent slab waveguides

A rigorous classical analytic frequency domain model of con?ned optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties

Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap

We present the design of mid-infrared and THz quantum cascade laser cavities formed from planar photonic crystals with a complete in-plane photonic bandgap. The design is based on a honeycomb lattice, and achieves a full in-plane photonic gap for transverse-magnetic polarized light while preserving a connected pattern for efficient electrical injection. Candidate defects modes for lasing are identified. This lattice is then used as a model system to demonstrate a novel effect: under certain conditions - that are typically satisfied in the THz range - a complete photonic gap can be obtained by the sole patterning of the top metal contact. This possibility greatly reduces the required fabrication complexity and avoids potential damage of the semiconductor active region.Comment: 14 pages, 14 figure

Dielectric multilayer waveguides for TE and TM mode matching

We analyse theoretically for the first time to our knowledge the perfect phase matching of guided TE and TM modes with a multilayer waveguide composed of linear isotropic dielectric materials. Alongside strict investigation into dispersion relations for multilayer systems, we give an explicit qualitative explanation for the phenomenon of mode matching on the basis of the standard one-dimensional homogenization technique, and discuss the minimum number of layers and the refractive index profile for the proposed device scheme. Direct applications of the scheme include polarization-insensitive, intermodal dispersion-free planar propagation, efficient fibre-to-planar waveguide coupling and, potentially, mode filtering. As a self-sufficient result, we present compact analytical expressions for the mode dispersion in a finite, N-period, three-layer dielectric superlattice.Comment: 13 pages with figure

Modal Analysis and Coupling in Metal-Insulator-Metal Waveguides

This paper shows how to analyze plasmonic metal-insulator-metal waveguides using the full modal structure of these guides. The analysis applies to all frequencies, particularly including the near infrared and visible spectrum, and to a wide range of sizes, including nanometallic structures. We use the approach here specifically to analyze waveguide junctions. We show that the full modal structure of the metal-insulator-metal (MIM) waveguides--which consists of real and complex discrete eigenvalue spectra, as well as the continuous spectrum--forms a complete basis set. We provide the derivation of these modes using the techniques developed for Sturm-Liouville and generalized eigenvalue equations. We demonstrate the need to include all parts of the spectrum to have a complete set of basis vectors to describe scattering within MIM waveguides with the mode-matching technique. We numerically compare the mode-matching formulation with finite-difference frequency-domain analysis and find very good agreement between the two for modal scattering at symmetric MIM waveguide junctions. We touch upon the similarities between the underlying mathematical structure of the MIM waveguide and the PT symmetric quantum mechanical pseudo-Hermitian Hamiltonians. The rich set of modes that the MIM waveguide supports forms a canonical example against which other more complicated geometries can be compared. Our work here encompasses the microwave results, but extends also to waveguides with real metals even at infrared and optical frequencies.Comment: 17 pages, 13 figures, 2 tables, references expanded, typos fixed, figures slightly modifie

Chains of coupled square dielectric optical microcavities

Chains of coupled square dielectric cavities are investigated in a 2-D setting, by means of a quasi-analytical eigenmode expansion method. Resonant transfer of optical power can be achieved along quite arbitrary, moderately long rectangular paths (up to 9 coupled cavities are considered), even with individual standing-wave resonators of limited quality. We introduce an ab-initio coupled mode model, based on a simple superposition of slab mode profiles as a template for the field of individual cavities. Although no loss mechanisms are built in, the model can still help to interprete the results of the former numerical experiments

Axially open nonradiative structures: an example of single-mode resonator based on the sample holder

The concept of nonradiative dielectric resonator is generalized in order to include axially open configurations having rotational invariance. The resulting additional nonradiative conditions are established for the different resonance modes on the basis of their azimuthal modal index. An approximate chart of the allowed dielectric and geometrical parameters for the TE011 mode is given. A practical realization of the proposed device based on commercial fused quartz tubes is demonstrated at millimeter wavelengths, together with simple excitation and tuning mechanisms. The observed resonances are characterized in their basic parameters, as well as in the field distribution by means of a finite element method. The predictions of the theoretical analysis are well confirmed, both in the general behaviour and in the expected quality factors. The resulting device, in which the sample holder acts itself as single-mode resonating element, combines an extreme ease of realization with state-of-the-art performances. The general benefits of the proposed open single-mode resonators are finally discussed.Comment: 18 pages, 10 figure