Complex Photonic Structure Research Articles

Self-induced optical pulling in complex photonic band structure

The photonic band gap effect has been proposed to achieve a gradient-induced long-range optical pulling force, but how the properties of the photonic band gap affect the optical pulling force remains to be revealed. In this work, based on the theory of complex photonic band and Einstein–Laub formulation of force density, a concise formula is developed to investigate such unusual optical pulling force. It indicates that the optical pulling force is mainly decided by the imaginary part of the wave vector of evanescent mode in the photonic band gap and the refractive index of the object. A larger imaginary part of the wave vector and a higher refractive index of the object typically result in a larger optical pulling force, which is verified by the numerical simulation. In addition, a critical length is defined to predict the occurrence of optical pulling force. Our work gives an insight into such an optical pulling force based on the complex photonic band and offers guidance for achieving a larger optical pulling force, which is very beneficial to optical sorting and optical conveying.

Calculation of lateral optical energy flow in bound modes in organic light-emitting diodes

We investigate the lateral energy flow of light bound to an OLED (i.e., light that cannot be coupled to the substrate or air mode), with a focus on the attenuation characteristics. A methodology is developed for approximating the total bound field as a superposition of the individual guided modes constructed from multilayer eigenmodes with complex wave vectors. The field distribution and surface energy flow density obtained from our approximate expressions are found to be well matched to those calculated using the Green’s function formalism. The method presented in this study provides mode-based interpretation of the surface energy flow density versus distance characteristics, and can be used in designing OLEDs for applications where the optical energy transported by the bound field is of interest. • The complex photonic band structure of an OLED is calculated. • The bound-mode field of an OLED is constructed from eigenmodes with complex wave vectors. • The attenuation characteristics of the surface energy flow density are quantitatively described.

Coupling between plasmonic and photonic crystal modes in suspended three-dimensional meta-films.

A complementary metal oxide semiconductor (CMOS) compatible fabrication method for creating three-dimensional (3D) meta-films is presented. In contrast to metasurfaces, meta-films possess structural variation throughout the thickness of the film and can possess a sub-wavelength scale structure in all three dimensions. Here we use this approach to create 2D arrays of cubic silicon nitride unit cells with plasmonic inclusions of elliptical metallic disks in horizontal and vertical orientations with lateral array-dimensions on the order of millimeters. Fourier transform infrared (FTIR) spectroscopy is used to measure the infrared transmission of meta-films with either horizontally or vertically oriented ellipses with varying eccentricity. Shape effects due to the ellipse eccentricity, as well as localized surface plasmon resonance (LSPR) effects due to the effective plasmonic wavelength are observed in the scattering response. The structures were modeled using rigorous coupled wave analysis (RCWA), finite difference time domain (Lumerical), and frequency domain finite element (COMSOL). The silicon nitride support structure possesses a complex in-plane photonic crystal slab band structure due to the periodicity of the unit cells. We show that adjustments to the physical dimensions of the ellipses can be used to control the coupling to this band structure. The horizontally oriented ellipses show narrow, distinct plasmonic resonances while the vertically oriented ellipses possess broader resonances, with lower overall transmission amplitude for a given ellipse geometry. We attribute this difference in resonance behavior to retardation effects. The ability to couple photonic slab modes with plasmonic inclusions enables a richer space of optical functionality for design of metamaterial-inspired optical components.

Segmented Bayesian optimization of meta-gratings for sub-wavelength light focusing

Using inverse design tools to engineer functional photonic nanostructures has been a subject of great interest over the past several years. We report combining a segmented Bayesian optimization algorithm with the rigorous coupled wave analysis to design meta-gratings for sub-wavelength light focusing. Specifically, the meta-gratings comprise one-dimensional periodic arrays of supercells, each of which consists of dozens of dielectric bars. By optimizing geometry of the structure, we demonstrate two kinds of meta-gratings operating at single and double wavelengths, respectively. Both of them can focus the incoming light into periodic sub-wavelength spots with high energy density. The full width at half-maximum (FWHM) of the focusing spots for the single wavelength ( λ = 633 n m ) case can be as small as 0.36 λ , while FWHMs of the focusing spots at double wavelengths ( λ = 533 n m and 633 nm) are about 0.4 λ . This proposed approach provides an affordable method to tackle the problem of complex photonic structure design.

Study of chiroptical effects on the novel chiral photonic structure

Purpose The purpose of this paper is to demonstrate a novel chiral photonic crystal with thin thickness and small unit cells via numerical calculations. The multi-band circular dichroism is found in a wide frequency range from 400 to 600 THz by studying the transmission properties. Design/methodology/approach To investigate this chiral photonic structure, refection coefficients are analytically computed using finite element method. Numerical results are given, and physical properties are discussed, including the optical rotation, the circular dichroism and the absorption. Findings The results of this modeling and simulation under COMSOL multiphysics environment have led the authors to study the scattered parameters such as the coefficient of transmission (S21) and the coefficient of reflection (S11) for a 2D CPC nanostructure. The authors have also developed script under the Matlab environment which studies absorption and circular dichroism and ensure the existence of optical activity. According to the obtained results, the coefficient of transmission is proportional to the parameter of chirality. Originality/value The authors have designed a novel chiral photonic structure that exhibits larger circular dichroism. The CD spectrum has typically both positive and negative bands. The design principles defined in this work, which combine the concepts of the photonic crystal with the chiral structure (optical activity, circular dichroism and absorption), represent a model for simulation of the properties of a more complex chiral photonic structure. These results led to realization of novel circularly polarized devices in nanotechnologies.

Improvement of light extraction efficiency in GaN-based light-emitting diodes by addition of complex photonic crystal structure

To improve the light extraction efficiency of a GaN-based light-emitting diode (LED), a new complex periodic photonic crystal structure containing two kinds of hemispheres was designed. This complex photonic crystal structure is arrayed on the surface of the planar LED, and a finite-difference time-domain method was used to optimize the hemisphere materials (ZnO, GaN, and SiC) and the structural parameters of the complex photonic crystal (the size of the hemisphere radius and the lattice constant of complex structure). A high improvement of light extraction efficiency is achieved in complex photonic crystal LED, translated into an 8.3-fold enhancement for the case of a planar LED.

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell’s equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and μ and coupling matrices ς. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction.

COMPLEX PHOTONIC BAND STRUCTURES IN A PHOTONIC CRYSTAL CONTAINING LOSSY SEMICONDUCTOR INSB

In this work, complex photonic band structure (CPBS) in a semiconductor-dielectric photonic crystal (SDPC) operating at terahertz frequencies is theoretically investigated. The SDPC is air/(S/D) N /air where the dielectric layer D is SiO2, the semiconductor layer S is an intrinsic semiconductor InSb, and N is the number of periods. Using the experimental data for the strongly temperature- dependent plasma frequency and damping frequency for InSb, we calculate the CPBS for the inflnite SDPC at distinct operating temperatures. The CPBS is then compared with the calculated transmittance, re∞ectance, and absorptance as well in the flnite SDPC. Based on the calculated CPBS, the role played by the loss factor (damping frequency), in InSb is revealed. Additionally, from the calculated transmittance spectra, we further investigate the cutofi frequency for the SDPC. The dependences of cutofi frequency on the number of periods and the fllling factor of semiconductor layer are numerically illustrated.

Effective optical parameters of thin-film and bulk metamaterials ofmetallodielectric nanosandwiches

We report on the effective optical response of single- and multilayer periodic structures of metallodielectric nanosandwiches on the basis of rigorous, full-electrodynamic calculations by the extended layer-multiple-scattering method. It is shown that the complex photonic band structure and the reflection coefficient of the infinite and semi-infinite crystal, respectively, provide reliable bulk effective parameters, which can be used as a reference in order to resolve ambiguities and problems in the determination of these parameters for finite slabs by the S-matrix retrieval procedure. Our results show that the structures under consideration exhibit strong artificial optical magnetism and thin films consisting of a few layers already behave like the bulk metamaterial.

Photonics with Multiwall Carbon Nanotube Arrays

We investigate the photonic properties of two-dimensional nanotube arrays for photon energies up to 40 eV and unveil the physics of two distinct applications: deep-UV photonic crystals and total visible absorbers. We find three main regimes: for small intertube spacing of 20-30 nm, we obtain strong Bragg scattering and photonic band gaps in the deep-UV range of 25 approximately 35 eV. For intermediate spacing of 40-100 nm, the photonic bands anticross with the graphite plasmon bands resulting into a complex photonic structure, and a generally reduced Bragg scattering. For large spacing >150 nm, the Bragg gap moves into the visible and decreases due to absorption. This leads to nanotube arrays behaving as total optical absorbers. Our results can guide the design of photonic applications in the visible and deep UV ranges.

Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures

Plasmonic excitations in two- and three-dimensional ordered assemblies of metal-dielectric-metal nanosandwiches are studied by means of full-electrodynamic calculations using the layer-multiple-scattering method. Plasmon hybridization results in collective electric-dipole-like and magnetic-dipole-like resonant modes, which are directly controlled by the lattice constant and the geometrical characteristics of the building units. It is shown that, in planar arrays of such composite nanoparticles on a dielectric substrate, the magnetic resonance induces a negative effective permeability, as large as $\ensuremath{-}2$, which can be tuned within the range of near-infrared and visible frequencies. However, as successive layers are stacked together to build a three-dimensional crystal, the region of negative effective permeability shrinks and disappears for relatively thick slabs. Our analysis demonstrates that the complex photonic band structure is a valuable tool in the study of three-dimensional metamaterials and their effective-medium description.

Calculating the Complex Photonic Band Structure by the Finite-Difference Time-Domain Based Method

A method to calculate the dispersion relation of light in dielectric periodic structures is proposed. The method utilizes the conventional finite-difference time-domain (FDTD) method based on the Yee's algorithm. The analytical space containing a periodic structure of a finite number of lattices is terminated by both periodic and absorbing boundaries. Complex Bloch wavenumbers of multiple electromagnetic modes that coexist in the structure are extracted from the field pattern created as a result of the multiple reflection between the surfaces of the structure. The validity of the method was checked through the photonic band calculation for the analytically soluble periodic structure. The method was found to be able to deal with evanescent modes as well as the propagating modes.

Collective plasmonic modes in ordered assemblies of metallic nanoshells

Collective plasmonic modes in two- and three-dimensional periodic assemblies ofmetallic nanoshells are studied by means of full electrodynamic calculations usingthe layer-multiple-scattering method. We consider structures made of a singletype of nanoshell as well as binary heterostructures made of two different typesof nanoshells. The complex photonic band structure of such three-dimensionalphotonic crystals is analyzed in conjunction with relevant transmission diagrams ofcorresponding finite slabs and the physical origin of the different optical modesis elucidated. Moreover, we discuss associated absorption spectra and providea consistent interpretation of the underlying physics. In the case of the binarysystems, the plasmonic modes of the two building components coexist, leading to arich structure of resonances over an extended frequency range and to broadbandabsorption.

Terahertz frequency bandpass filters

The design, measurement, and analysis of a range of artificial materials for use at terahertz frequencies are described. The chosen structures consist of arrays of cylindrical gold-plated pillars with period comparable to the wavelength of incident radiation. An ultraviolet (UV) micromachining approach to the fabrication of these high aspect-ratio pillars is described using the negative epoxy-based resin SU8. Lattice fence structures are also realized using the same method. Terahertz (THz) frequency time domain spectroscopy is performed on these structures in the range 200 GHz to 3.0 THz and the relative transmission of the structures is determined. The pass and stop bands are observed with peak transmission of up to 97%. Finite difference time domain simulations and complex photonic band structure calculations are shown to provide good descriptions of the electromagnetic properties of the structures and are used to interpret the observed transmission spectra.

Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods

A number of simple analytic theories have been proposed to define an effective plasma frequency in two-dimensional (2D) periodic systems containing metallic elements such as an array of metal rods in a simple square lattice. Such metallic structures are considered using a frequency-dependent plane-wave complex band structure approach. Detailed results are presented for the pass and stop bands for a range of rod diameters. In addition, the value of the effective plasma frequency is extracted and compared with the predictions of existing analytic models. For the structures considered the effective plasma frequency is in the THz regime.

A plane-wave-based approach for complex photonic band structure and its applications to semi-infinite and finite system

A plane-wave-based approach for complex photonic band structure is developed and applied to analyse the behaviour of electromagnetic (EM) waves at the surface of semi-infinite and finite photonic crystals (PCs). The complex photonic band structures of two-dimensional and three-dimensional PCs have been calculated by the present approach and verified by conventional plane wave expansion method and plane-wave-based transfer matrix method. Based on the eigen modes of present approach, equations in matrix form are given to describe the boundary conditions of PCs, and consequently the behaviour of EM waves at the surface of semi-infinite and finite PCs is discussed. These results have also verified the validity and efficiency of the current approach.

Self-guiding in two-dimensional photonic crystals

Dielectric periodic media can possess a complex photonic band structure with allowed bands displaying strong dispersion and anisotropy. We show that for some frequencies the form of iso-frequency contours mimics the form of the first Brillouin zone of the crystal. A wide angular range of flat dispersion exists for such frequencies. The regions of iso-frequency contours with near-zero curvature cancel out diffraction of the light beam, leading to a self-guided beam.

Strong discontinuities in the complex photonic band structure of transmission metallic gratings

Complex photonic band structures (CPBS) of transmission metallic gratings with rectangular slits are shown to exhibit strong discontinuities that are not evidenced in the usual energetic band structures. These discontinuities are located on Wood's anomalies and reveal unambiguously two different types of resonances, which are identified as horizontal and vertical surface-plasmon resonances. Spectral position and width of peaks in the transmission spectrum can be directly extracted from CPBS for both kinds of resonances.

Two-dimensional vector-coupled-mode theory for textured planar waveguides

We develop a model to treat coupling between guided modes in planar dielectric waveguides that have been textured in two dimensions with a thin surface grating. The formulation is based on a general Green's-function technique that self-consistently determines the field in the surface grating due to the polarization there. With simplifying approximations, this formalism is cast into a two-dimensional (2D) vector-coupled-mode theory that is more computationally efficient, and that gives considerable insight into the nature of mode coupling in 2D textured structures. These models are applied, by way of example, to illustrate some interesting properties of leaky and bound modes that are coupled together by 2D periodic texture. In particular we discuss the complex photonic band structure describing the dispersion, lifetimes, and polarization properties of the resonant states associated with the textured waveguide. In our analysis we emphasize the fundamental differences between coupling in 2D textured waveguides and infinite 2D photonic crystals. We also show that the vector-coupled-mode theory agrees well with the self-consistent formulation.

Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components

We study the distribution of the electromagnetic field of the eigenmodes and corresponding group velocities associated with the photonic band structures of two-dimensional periodic systems consisting of an array of infinitely long parallel metallic rods whose intersections with a perpendicular plane form a simple square lattice. We consider both nondissipative and lossy metallic components characterized by a complex frequency-dependent dielectric function. Our analysis is based on the calculation of the complex photonic band structure obtained by using a modified plane-wave method that transforms the problem of solving Maxwell's equations into the problem of diagonalizing an equivalent non-Hermitian matrix. In order to investigate the nature and the symmetry properties of the eigenvectors, which significantly affect the optical properties of the photonic lattices, we evaluate the associated field distribution at the high symmetry points and along high symmetry directions in the two-dimensional first Brillouin zone of the periodic system. By considering both lossless and lossy metallic rods we study the effect of damping on the spatial distribution of the eigenvectors. Then we use the Hellmann-Feynman theorem and the eigenvectors and eigenfrequencies obtained from a photonic band-structure calculation based on a standard plane-wave approach applied to the nondissipative system to calculate the components of the group velocities associated with individual bands as functions of the wave vector in the first Brillouin zone. From the group velocity of each eigenmode the flow of energy is examined. The results obtained indicate a strong directional dependence of the group velocity, and confirm the experimental observation that a photonic crystal is a potentially efficient tool in controlling photon propagation.