Theory of quarter-wave-stack dielectric mirrors used in a thin fabry-perot filter

I present a new derivation of the analytic form for the phase shift near resonance and the optical penetration length upon reflection from a distributed dielectric mirror consisting of a quarter-wave stack. The requirement of proper termination to achieve high reflectivity is suspended to investigate large optical penetration depths. Separate equations, derived for N and N + 1/2 layer pairs, are convenient for the design of tunable Fabry-Perot filters with a specified tuning range. The analysis is also applicable to distributed Bragg reflectors, vertical-cavity surface-emitting lasers, and resonant photodiodes. I show that the penetration length can sharply reduce the overly broad free spectral range of an ultrathin Fabry-Perot filter that might be useful in applications such as tunable wavelength filters for wavelength division multiplexing applications. The results also demonstrate regimes of zero dispersion and of superluminal reflection in the dielectric mirrors, which are of particular interest in photonic bandgap structures.     

Grating coupler dispersion compensation with a surface-relief reflection grating

Experimental results are presented that show that diffraction off a surface-relief reflection grating can be used to extend the FWHM input coupling efficiency versus the coupled-light wavelength of a grating coupler from 0.7 to 17 nm. Use of a surface-relief reflection grating allows high diffraction efficiency over a wide wavelength range. Dispersion-matching calculations are included that illustrate that for certain output coupling applications the FWHM can be extended to 33 am. Analysis shows that for inputcoupling applications the lateral beam shift resulting from angular dispersion may be the limiting factor for wavelength compensation.     

Inside Front Cover: Experimental Evidence for Superprism Effects in Three‐Dimensional Polymer Photonic Crystals (Adv. Mater. 2/2006)

The inside cover illustrates the highly dispersive propagation of light in a three‐dimensional polymer photonic crystal. White light is coupled into a woodpile structure and split into its wavelength components due to the frequency‐dependent dispersion properties of the structure. This superprism effect is orders of magnitudes higher than in a conventional glass prism and is caused by the strong anisotropy of the dispersion surface at frequencies slightly above the photonic bandgap. In work reported on p. 221, Serbin and Gu fabricated these woodpile structures operating in the near‐infrared wavelength range by means of two‐photon polymerization and give theoretical and experimental evidence for the superprism effect in these low‐index photonic‐crystal structures.     

Periodic defects in 2D-PBG materials: full-wave analysis and design

In this paper, an accurate and efficient characterization of two-dimensional photonic bandgap structures with periodic defects is performed, which exploits a full-wave diffraction theory developed for one-dimensional gratings. The high convergence rate of the proposed technique is demonstrated. Results are presented for both TE and TM polarizations, showing the efficiencies as a function of wavelength, incidence angle, geometrical and physical parameters. A comparison with other theoretical results reported in the literature is shown with a good agreement. The transmission properties of photonic crystals with periodic defects are studied, investigating the effects of the variation of geometrical and physical parameters; design efficiency maps and formulas are given; moreover, the application of the analyzed structures as filters is discussed.     

Characterization of chromatic dispersion and polarizationsensitivity in fiber gratings

Fiber gratings have already become key passive components in fiber optic communication systems. We have characterized gratings used in reflection for dispersion compensation and long period gratings used in transmission for gain flattening using a low-loss, low-noise experimental setup having a picometer optical wavelength resolution. Our measurements include reflection or transmission response, group delay and polarization dependent loss. We have scanned the spectrum of our devices using a very narrow linewidth tunable laser. A network analyzer is used for the chromatic dispersion measurements. Time delays corresponding to the design values have been measured within the useful bandwidth of the gratings for dispersion compensation and the devices have been found to have reasonably small ripples that increase in magnitude toward the shorter wavelength range. The long period gratings for gain flattening have very small group delays. Polarization dependent loss has been measured for the first time in these devices. A polarization analyzer was used and Jones matrix analysis was applied to obtain the measurements. The gratings for dispersion compensation have small a polarization dependent loss within their useful bandwidth, while the long period gratings exhibit higher values and a stronger wavelength dependency in the polarization dependent loss     

Advanced design and optimization of single mode photonic crystal fibers

This paper proposes a combination of differential evolution (DE) and estimation of distribution algorithm (EDA) to design photonic crystal fiber structures with desired properties over the C communication band. In order to determine the properties of PCFs such as dispersion, dispersion slope and loss, an artificial intelligence method, the Nero-Fuzzy system, is applied. In addition, a special cost function which simultaneously includes the confinement loss, dispersion and its slope is used in the proposed design approach. The results revealed that the proposed method is a powerful tool for solving this optimization problem. The optimized PCF exhibits an ultra low confinement loss and low dispersion at 1.55 µm wavelength with a nearly zero dispersion slope over the C communication band.     

Multilayer thin-film structures with high spatial dispersion

We demonstrate how to design thin-film multilayer structures that separate multiple wavelength channels with a single stack by spatial dispersion, thus allowing compact manufacturable wavelength multiplexers and demultiplexers and possibly beam-steering or dispersion-control devices. We discuss four types of structure--periodic one-dimensional photonic crystal superprism structures, double-chirped structures exploiting wavelength-dependent penetration depth, coupled-cavity structures with dispersion that is due to stored energy, and numerically optimized nonperiodic structures utilizing a mixture of the other dispersion effects. We experimentally test the spatial dispersion of a 200-layer periodic structure and a 66-layer nonperiodic structure. Probably because of its greater design freedom, the nonperiodic structure can give both a linear shift with wavelength and a larger usable shift than the thicker periodic structure gives.     

Tilted bilayer membranes as simple transmission quarter-wave retardation plates

A tilted bilayer membrane, which consists of two thin films of transparent optically isotropic materials of different refractive indices, can function as a transmission quarter-wave retarder (QWR) at a high angle of incidence. A specific design using a cryolite-Si membrane in the infrared is presented, and its tolerances to small shifts of wavelength, incidence angle, and film thickness errors are discussed. Some designs provide a dual QWR in transmission and reflection. Such devices provide simple linear-to-circular (and circular-to-linear) polarization transformers. Bilayer eighth-wave retarders without diattenuation are also introduced.     

纳米尺度HfO_2薄膜的光谱椭偏模型建立

为了建立厚度为1 nm左右HfO_2超薄膜的光谱椭偏测量方法,采用掠入射X射线反射技术进行国家/地区实验室间比对认证,其膜厚准确量值作为参比值,建立了HfO_2超薄膜的光谱椭偏结构拟合模型。研究了HfO_2超薄膜的光谱椭偏色散模型和拟合参数,最后确定了拟合色散模型为Tauc-Lorentz 3,拟合光谱范围为3.45~4.35 eV,表面污染层孔隙比例为60:40。     

Bandgap-assisted surface-plasmon sensing

Surface-plasmon resonance (SPR) is a sensing technique widely used for its label-free feature. However, its sensitivity is contingent on the divergence angle of the excitation beam. The problem becomes pronounced for compact systems when a low-cost LED is used as the light source. When the Kretschmann configuration with a periodically modulated surface is used, a bandgap appears in the surface plasmon dispersion relation. We recognize that the high density of modes on the edge of the surface-plasmon bandgap permits the coupling of a wider range of incidence angles of excitation photons to surface-plasmon polaritons than what is possible in the traditional Kretschmann configuration. Here, the numerical simulation illustrates that the sensitivity, detection limit, and reflectivity minimum of an amplitude-based SPR bandgap-assisted surface-plasmon sensor are almost independent of the divergence angle. Two different bandgap structures are compared with the Kretschmann configuration using the rigorous coupled-wave analysis technique. The results indicate that the bandgap-assisted sensing outperforms traditional SPR sensing when the angular standard deviation of the excitation beam is above 1 degree.     

Visor-display design based on planar holographic optics

A method for designing and recording visor displays based on planar holographic optics is presented. This method can deal with the problem of recording-readout wavelength shift. The display system is composed of two holographic optical elements that are recorded on the same substrate. One element collimates the waves from each data point in the display into a plane wave that is trapped inside the substrate by total internal reflection. The other diffracts the plane waves into the eye of an observer. Because the chromatic dispersion of the first element can be corrected by the dispersion of the second, this configuration is relatively insensitive to source wavelength shifts. The method is illustrated by the design, recording, and testing of a compact holographic doublet visor display. The recording was at a wavelength of 458 nm, and readout was at 633 nm. The results indicate that diffraction-limited performance and relatively low chromatic dispersion over a wide field of view can be obtained.     

Mathematical formulation for zero reflection from multilayer metamaterial structures and their notable applications

The behaviour of bilayer structures composed of common materials and metamaterials (MTMs) under oblique incidence of plane waves is investigated by exact analytical methods. The TE, TM and elliptical polarisations are analysed. There are several combinations of double positive (DPS), double negative (DNG), epsilon negative (ENG) and mu negative (MNG) media for the bilayer structures, but only DPS?DPS, DPS?DNG and ENG?MNG bilayers with TE, TM and circular polarisations are analysed in detail. For homogeneous and isotropic MTM media, exact mathematical relations are derived for the design of reflectionless bilayer structures as a function of their geometry (thickness) and electric and magnetic parameters. Frequency dispersion is included in the formulations. It is shown that bilayers composed of common materials are not effective for the construction of zero reflection bilayer surfaces, whereas the application of MTMs is required to realise reflectionless phenomena. For the design of zero reflection bilayer structures, their thicknesses and values of ε and μ are determined. Finally, the performance of forward and backward notch filters observed by MTM bilayer structures are studied in detail and their designs and applications are investigated. The bandwidth of lossy MTMs increases considerably.     

Numerical study of antireflection coatings in waveguide structures with silicon nanoparticles interlayer

In this paper, the reflection properties of a multilayer structure containing silicon nanoparticles (Si-NPs), silicon nitride (Si₃N₄), and silicon (Si) is investigated theoretically and numerically. The structure is arranged and its main parameters are defined. The required equations for the propagation of electromagnetic plane waves are derived in detail to obtain the reflection coefficients in a closed form. The reflected power of the structure is determined using these coefficients. In the numerical results, the mentioned power is computed and illustrated as a function of wavelength of the incident radiation, angle of incidence, and Si-NPs parameters. Optimal Si-NPs parameters (particle’s diameter, space between particles, and layer thickness) for low reflection are proposed. These theoretical parameters could effectively be used to design new solar cells.     

Optical properties of dielectric thin films including quantum dots

Depending on the minimum size of their micro/nanostructure, thin films can exhibit very different behaviors and optical properties. From optical waveguides down to artificial anisotropy, through diffractive optics and photonic crystals, the application changes when decreasing the minimum feature size. Rigorous electromagnetic theory can be used to model most of the components, but, when the size is a few nanometers, quantum theory also has to be used. The materials, including quantum structures, are of particular interest for many applications, in particular for solar cells because of their luminescent and electronic properties. We show that the properties of electrons in periodic and nonperiodic multiple quantum well structures can be easily modeled with a formalism similar to that used for multilayer waveguides. The effects of different parameters, in particular the coupling between wells and well thickness dispersion, on possible discrete energy levels or the energy band of electrons and on electron wave functions are given. When such quantum confinement appears, the spectral absorption and extinction coefficient dispersion with wavelength are modified. The dispersion of the real part of the refractive index can be deduced from the Kramers-Kronig relations. Associated with homogenization theory, this approach gives a new model of the refractive index for thin films including quantum dots. The bandgap of ZnO quantum dots in solution obtained from the absorption spectrum is in good agreement with our calculation.     

Gravity wave interaction with porous structures in two-layer fluid

Oblique wave interaction with rectangular porous structures of various configurations in two-layer fluid are analyzed in finite water depth. Wave characteristics within the porous structure are analyzed based on plane wave approximation. Oblique wave scattering by a porous structure of finite width and wave trapping by a porous structure near a wall are studied under small amplitude wave theory. The effectiveness of three types of porous structures—a semi-infinite porous structure, a finite porous structure backed by a rigid wall, and a porous structure with perforated front and rigid back walls—in reflecting and dissipating wave energy are analyzed. The reflection and transmission coefficients for waves in surface and internal modes and the hydrodynamic forces on porous structures of the aforementioned configurations are computed for various physical parameters in two-layer fluid. The eigenfunction expansion method is used to deal with waves past the porous structure in two-layer fluid assuming the associated eigenvalues are distinct. An alternate procedure based on the Green’s function technique is highlighted to deal with cases where the roots of the dispersion relation in the porous medium coalesce. Long wave equations are derived and the dispersion relation is compared with that derived based on small amplitude wave theory. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy.     

Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice

The photonic crystal structure with parallelogram lattice, capable of bending a self-collimated wave with free angles and partial bandgap reflection, is presented. The equifrequency contours show that the direction of the collimation wave can be turned by tuning the angle between the two basic vectors of the lattice. Acute, right, and obtuse angles of collimating waveguide bends have been realized by arc lattices of parallelogram photonic crystals. Moreover, partial bandgap reflection of the parallelogram lattice photonic crystals is validated from the equifrequency contours and the projected band structures. A waveguide taper based on this partial bandgap reflection is also designed and proved to have above 85% transmittance over a very wide operating bandwidth of 180 nm.     

Omnidirectional reflection from Solc-type anisotropic periodic dielectric structures

Recently it was shown theoretically [Opt. Commun. 174, 43 (2000)] that a Solc folded-type anisotropic dielectric structure under certain conditions exhibits omnidirectional reflection at any polarization over a wide spectral range. Here, omnidirectional reflection from Solc folded-type dielectric periodic structures is further analyzed. Transfer-matrix methodology is applied. Simple expressions are obtained for transfer matrices at interfaces and the unit cell translation matrix. Dispersion relations are determined. Numerical examples are shown comparatively for isotropic and Solc-type anisotropic periodic structures. The Solc-type structure has a wider band of omnidirectional reflection. The results demonstrate that anisotropic materials should be useful in photonic bandgap structures.     

Multiband wavelength-division demultiplexing with a cascaded substrate-mode grating structure

A multiband wavelength-division-demultiplexing (WDDM) structure, which incorporates cascaded substrate-mode holograms, is presented. The method can be used to design a WDDM device that consists of two or more layers of fundamental units (i.e., substrate-mode holograms). The fundamental unit is based on a diffracted grating and a substrate that include angular dispersion, wavelength bandwidth, and total internal reflection, which can be used to separate optical signals of different wavelengths. We have designed and built a multiband WDDM device, incorporating cascaded substrate-mode holograms in dichromated gelatin.     

Analytical expressions for group-delay dispersion and third-order dispersion of a reflection grism-pair compressor

We provide a detailed analytical expression of group-delay dispersion (GDD) and third-order dispersion (TOD) for a reflection grism-pair compressor without the first-order approximation of grating diffraction. The analytical expressions can be used to design a grism-pair compressor for compensating the dispersive material without ray tracing. Furthermore, the dispersion performance of the grism pair compressor, depending on compressor parameters, is comprehensively analyzed. Results are shown that we can adjust several parameters to obtain a certain GDD and TOD, such as the incidence angle of the beam, refractive index of the prism, grating constant, and the separation of the grism pair.     

Optical dispersion in synthetic opal matrices filled with europium-oxide-doped silica sols

We have studied typical features in reflection spectra of the (111) surface of opal photonic crystals based on synthetic opals filled with Eu₂O₃-doped silica sols. The reflection spectrum of the composite of opal and europium-doped silica sols is found to contain a resonance at a wavelength of 617.5 nm. A theory has been developed for describing the optical dispersion of resonant photonic crystals. We have calculated the dispersion curves and reflectivity of undoped and Eu₂O₃-doped opal crystals and compared the calculated reflection spectra to experimental data. Nanocomposites of opal and europium-doped silica sols can be used in laser cavities.