High-order Photonic Band Gaps Research Articles

Control of high-order photonic band gaps in one-dimensional anodic alumina photonic crystals

Abstract One-dimensional (1D) photonic crystals based on porous anodic alumina are of high practical importance in modern materials science owing to their promising applications in the field of photonics. Although the positions of photonic band gaps can be controlled precisely by electric charge passed during the formation of repeating layers of anodic alumina, the methods for tuning the transmittance and reflectance within the photonic band gaps are limited. Here we demonstrate a simple and highly reproducible method for obtaining 1D anodic alumina photonic crystals with several reflecting layers in the unit cell. A theoretical model for the calculation of the optical properties of the prepared 1D anodic alumina photonic crystals is suggested and used for the design of an anodizing profile. The ability to tune the transmittance and reflectance within high-order photonic band gaps by controlling the position of the reflecting layers in the unit cell of the photonic crystal is demonstrated.

Laser emission at the second-order photonic band gap in an electric-field-distorted cholesteric liquid crystal

ABSTRACTWe study the optical properties of a cholesteric liquid crystal doped with a fluorescent dye in the regime of highly distorted helix without full helix unwinding. The distortion was achieved by applying a pulsed AC electric field, perpendicular to the helix axis. If the pulse is in the millisecond range, the helix is deformed but keeps its original pitch even for electric fields higher than the theoretical critical field for helix unwinding. In this field regime, very pronounced high-order photonic band gaps are observed, in agreement with our calculations. We theoretically explore the possibility of obtaining viable laser emission at the second-order photonic band gap, and experimentally find that lasing is not only possible but has a figure of merit similar to that of the usual laser at the main-gap region. Therefore, electric-field-induced high-order photonic band gaps are potentially useful for multiline laser applications.

Near-Infrared Silicon Photonic Crystals with High-Order Photonic Bandgaps for High-Sensitivity Chemical Analysis of Water-Ethanol Mixtures.

Aqueous solutions of alcohols are used in several applications, from pharmaceutics and biology, to chemical, biofuel, and food industries. Nonetheless, development of a simple, inexpensive, and portable sensing device for the quantification of water in water-ethanol mixtures remains a significant challenge. Photonic crystals (PhCs) operating at very high-order photonic bandgaps (PBGs) offer remarkable opportunities for the realization of chemical sensors with high sensitivity and low detection limit. However, high-order PhC structures have been mostly confined to mere theoretical speculations so far, their effective realization requiring microfabrication tools enabling the control of periodic refractive index modulations at the submicrometric scale with extremely high accuracy and precision. Here, we report both experimental and theoretical results on high-sensitivity chemical analysis using vertical, silicon/air 1D-PhCs with spatial period of 10 and 20 μm (namely, over 10 times the operation wavelength) featuring ultra-high-order PBGs in the near-infrared region (namely, up to 50th at 1.1 μm). Fabrication of high-order 1D-PhCs was carried out by electrochemical micromachining (ECM) of silicon, which allowed both surface roughness and deviation from vertical of etched structures to be controlled below 5 nm and 0.1%, respectively. Optical characterization of ECM-fabricated 1D-PhCs, which was performed by acquiring reflectivity spectra over the wavelength range 1-1.7 μm, highlighted the presence of ultra-high-order PBGs with minor optical losses (i.e., <1 dB in reflectivity) separated by deep reflectivity notches with high Q-factors (i.e., >6000), in good agreement with theoretical calculations. Remarkably, the use of high-order 1D-PhCs as refractometric transducers for the quantitative detection of traces of water in water-ethanol mixtures, allowed high sensitivity (namely, either 1000 nm/RIU or ∼0.4 nm/% of water), good detection limit (namely, 5 × 10-3 RIU or ∼10% water), and excellent resolution (namely, either 6 × 10-4 RIU or 1.6% of water) to be reliably achieved on a detection volume of about 168 fL.

Properties of dispersion and phase index in magnetized one dimensional ferrite photonic crystals in longitudinal configuration for TM mode

The band structure and phase index in magnetized one dimensional ferrite photonic crystals are computed for TM mode in longitudinal configuration using transfer matrix method. The parametric studies are performed to investigate the effect of filling factor, incident angle and external magnetic fields on dispersion and phase index of the considered structure. The variation of frequency and filling factor at fixed normalized parallel wave vector shows that photonic band gaps occur in the form of lobes. The variation of frequency with external magnetic fields at different normalized parallel wave vector shows that effect of the external magnetic fields have strong influence on second and higher order photonic band gaps. The phase index is also found to be sensitive function of filling factor and normalized parallel wave vector.

High-frequency light reflector via low-frequency light control

We show that the momentum of light can be reversed via the atomic coherence created by another light with one or two orders of magnitude lower frequency. Both the backward retrieval of single photons from a timed Dicke state and the reflection of continuous waves by high-order photonic band gaps are analysed. The required control field strength scales linearly with the nonlinearity order, which is explained by the dynamics of superradiance lattices. Experiments are proposed with $^{85}$Rb atoms and Be$^{2+}$ ions. This holds promise for light-controllable X-ray reflectors.

Tunable high-order photonic band gaps of ultraviolet light in cold atoms

We study a five-level $\text{quasi}\ensuremath{-}\ensuremath{\Lambda}$ system of cold atoms for achieving high-order photonic band gaps (PBGs) probed by an ultraviolet field in two cases where either an infrared or a visible control field works in the standing-wave configuration to induce one atomic grating. Transfer-matrix calculations for appropriate rubidium levels demonstrate that three fifth-order band gaps or two second-order band gaps can be generated near the probe resonance when the standing-wave control field is modulated to satisfy relevant Bragg conditions in the regime of electromagnetically induced transparency. These high-order PBGs, as characterized by homogeneous high reflectivities, can be dynamically tuned in positions and widths on demand and may be extended to develop efficient devices (like diodes and reflectors) for manipulating weak high-frequency light with strong low-frequency light.

Photonic Bandgap Inspection in 2-D Sublattices

Large photonic bandgaps (PBGs) have been obtained by sweeping linearly the parameters of complex sublattices inside the unitary cells of square- and triangular-lattice photonic crystals. An efficient frequency-domain finite-element method with periodical boundary conditions has been used for theoretical analyses. PBGs in silicon/air photonic crystals for both polarization modes have been considered for up to 21 eigenmodes and both low- and high-order PBGs have been obtained by this relatively simple systematic process.

INFLUENCE OF FLUCTUATIONS OF THE GEOMETRICAL PARAMETERS ON THE PHOTONIC BAND GAPS IN ONE-DIMENSIONAL PHOTONIC CRYSTALS

The in∞uence of random ∞uctuations in the layer thicknesses in high contrast, one-dimensional Photonic Crystals (PCs) on the transmission spectra and Photonic Band Gaps (PBGs) is investigated. The change in the PBGs depends on the magnitude of the ∞uctuations and increases with an increase in the order of the PBG. Introducing thickness non-uniformity into the PC of up to 0.004 times the value of lattice constant for difierent types of ∞uctuation distributions has a negligible efiect on either the position or the shape of the 1st and nearest PBGs. The approach suggested here allows the determination of the tolerances required in the geometrical parameters of PCs during fabrication. It also allows the optimisation of PC structures using high order PBGs.

Optical properties of high-order band gaps in one-dimensional photonic crystal

Plane wave expansion method and transfer matrix method have been used to study the optical properties of eighty ninth photonic band gaps (PBGs) in one dimensional photonic crystal (1DPCs) with a form of Si (air|Si)8. The results show that high order PBGs (HR-PBGs) in normalize dispersion curves have slower convergence speed than low order PBGs (LR-PBGs) and appear periodic detergency phenomena with the increasing of Λ/λ values (where Λ is the constant of one dimensional lattice and λ is wavelength) and their band widths and central wavelengths are more sensitive to fabrication errors than that of LR-PBG. Finally, some special forms of Si (air|Si)8 structure with input and output rib waveguides are fabricated on Silicon-on-Insulator (SOI) materials by semiconductor micromachining technology. By measuring and analyzing their insertion loss spectra, we demonstrate that the HR-PBGs of 1DPCs also have the potential application in integration optics.

Investigation of optical properties of Tamm states in higher bands of multilayer stacks including right and left handed materials

We study the electromagnetic surface wave localizing, the so-called surface Tamm states, at an interface separating a left-handed metamaterial (LHM) and a semi-infinite one-dimensional photonic crystal made of alternative left-handed metamaterial and right-handed materials. We show that the existence of metamaterial causes the Tamm states with backward energy flow and allows flexible control of dispersion properties of the surface modes. We study the effect of the physical parameters of the photonic crystal on the dispersion properties and the group velocity of the Tamm states. We also study dispersion properties of the Tamm states in higher order photonic band gaps of the photonic crystal and compare our results with the case when the LHM medium is replaced by a right-handed material (RHM).

Formation of Infrared Regions of Transparency in One-Dimensional Silicon Photonic Crystals

The optical properties of three-component one-dimensional photonic crystal (1-D PC) structures were investigated by modeling them as two-component PCs with an additional regular <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -layer, using the gap map approach and the transfer matrix method. Numerical results demonstrate that the introduction of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -layer affects the properties of the high-order photonic band gaps, replacing them with transmission bands and creating regions of transparency over certain wavelength ranges. For the first time, a map of the transmission bands for a three-component 1-D PC was generated. This map constitutes a unique design tool for infrared optical filters for silicon-based photonic integrated circuits.

Versatility and multifunctionality of highly reflecting Bragg mirrors based on nanoparticle multilayers

The use of both supported and flexible self-standing nanoparticle-based one dimensional photonic crystal films as effective frequency selective filters in the UV-vis-NIR is herein evaluated. The requirements to achieve a flat spectral response at the desired frequency range are analyzed and a synthetic route to realize materials with such properties presented. Strict control over the structural parameters yields multilayers in which the opening or closing of higher order photonic band gaps can be devised, thus leading to films capable of blocking the UV and NIR ranges simultaneously. Furthermore, the physico-chemical properties of the mirror can be modified to yield either moisture-repelling or, on the contrary, environmentally responsive optical filters. These materials present a great potential to be used as versatile and multifunctional optical elements.

Optical transmission in triple-film hetero-opals

Angle-resolved transmission of s-polarized light in triple-film hetero-opals has been investigated in the spectral range including high-order photonic band gaps, and compared to the transmission of its constituent single-film opals. The interfaces do not destroy the predominantly ballistic light propagation over the studied frequency and angular ranges, but heterostructuring leads to a smoothed angular distribution of intensity of the transmitted light and to the reconstruction of the transmission minima dispersion. The interface transmission function has been extracted by comparing the transmission of the hetero-opal and its components in order to demonstrate the difference. This deviation from the superposition principle was provisionally assigned to light refraction and reflection at the photonic crystal interfaces and to the mismatch between mode group velocities in hetero-opal components.

Optical and Crystallographic Properties of Inverse Opal Photonic Crystals Grown by Atomic Layer Deposition

ABSTRACTWe report a technique for the formation of infiltrated and inverse opal structures that produces high quality, low porosity conformal material structures. ZnS:Mn and TiO2 were deposited within the void space of an opal lattice by atomic layer deposition. The resulting structures were etched with HF to remove the silica opal template. Infiltrated and inverse opals were characterized by SEM, XRD, and transmission/reflection spectroscopy. The reflectance spectra exhibited features corresponding to strong low and high order photonic band gaps in the (111) direction (γ-L). In addition, deliberate partial infiltrations and multi-layered inverse opals have been formed. The effectiveness of a post-deposition heat treatment for converting TiO2 films to rutile was also studied.