One-dimensional Photonic Band Gap Structures Research Articles

Coherent emission in one-dimensional photonic band gap materials

We study the properties of super-radiant coherent emission from a two-level system of atoms embedded in a one-dimensional photonic band gap (1D-PBG) structure. A reduced system of equations is derived that enables us to explore the role of the 1D-PBG band edge in the emission characteristics of coherent pulses. The effect of the emitters' spatial location in the PBG structures is also studied in a finite 1D-PBG, where the super-radiant emission characteristics are also presented.

One-dimensional photonic bandgap structure in abalone shell

Photonic bandgap (PBG) materials are periodic com- posites of dielectric materials in which electromagnetic waves of certain frequency range cannot propagate in any or a special direction. Recently, there has been great inter- est in synthetic PBG materials due to their ability in ma- nipulation of photons. Since 500 million years ago, the natural world has been exploiting photonic structures for specific biological purposes[1]. Different types of biologi- cal PBG materials have been discovered in recent years, such as the one-dimension PBG structure in the sea mouse Aphrodita[2], and the fruits Elaeocarpus[3,4]; two-dimension PBG structure in the male peacock Pavo muticus feathers[5], Indonesian male Papilio palinurus butterfly[6], Thaumantis diores butterfly[7] and the male Ancyluris meliboeus Fabricius butterflies[8]; and three-dimension PBG structure in the weevil Pachyrhynchus argus[9].

Perturbation analysis of plane-wave transmission through a dielectric slab with Kerr-type nonlinearity

Multiple-scale analysis is employed for the analysis of plane-wave refraction at a nonlinear slab. It will be demonstrated that the perturbation method will lead to a nonuniformly valid approximation to the solution of the nonlinear wave equation. To construct a uniformly valid approximation, we will exploit multiple-scale analysis. Using this method, we will derive the zeroth-order approximation to the solution of the nonlinear wave equation analytically. This approximate solution clearly shows the effects of self-phase modulation (SPM) and cross-phase modulation (XPM) on plane-wave refraction at the nonlinear slab. As will be shown, the proposed method can be generalized to the rigorous study of nonlinear wave propagation in one-dimensional photonic band-gap structures.

Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach

An extension of the second quantization scheme based on the quasinormal-modes theory to one-dimensional photonic band gap (PBG) structures is discussed. Such structures, treated as double open optical cavities, are studied as part of a compound closed system including the electromagnetic radiative external bath. The electromagnetic field inside the photonic crystal is successfully represented by a new class of modes called quasinormal modes. Starting from this representation we introduce the Feynman's propagator to calculate the decay rate of a dipole inside a PBG structure, related to the density of modes, in the presence of the vacuum fluctuations outside the one-dimensional cavity.

Enhanced optical nonlinearity near the photonic bandgap edges of a cholesteric liquid crystal

The third-order Kerr nonlinear optical effect of a one-dimensional photonic bandgap structure of a cholesteric liquid crystal is investigated. In a femtosecond nonlinear transmission measurement, nonlinear optical changes in the bandgap edges are observed. From analysis of the dispersion relation, Kerr nonlinear coefficients of nematics, forming the cholesteric liquid crystal, are found to be enhanced by 1-2 orders of magnitude through the photonic bandgap structure.

Defect-mode dependence of two-photon-absorption enhancement in a one-dimensional photonic bandgap structure.

A one-dimensional photonic crystal containing a single CdS defect layer of various thicknesses was fabricated. The dependence of the two-photon-absorption (TPA) coefficient on the defect mode was investigated by use of a femtosecond pump-probe method. Experimental results show that the TPA coefficient of the CdS defect layer depends strongly on the defect mode in the photonic bandgap. This is consistent with the predicted dependence of light intensity within the defect layer.

Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures.

Using numerical simulations, we report the observation of a new effect--a spectral Talbot-like effect--in one-dimensional photonic bandgap structures, particularly sampled chirped fiber Bragg gratings. We derive the general conditions for which spectral Talbot-like phenomena, namely, integer and fractional spectral self-imaging, can be observed and relate them to the physical grating parameters.

Fiber-Optic Nanorefractometer Based on One-Dimensional Photonic-Bandgap Structures With Two Defects

A theoretical analysis of a fiber-optic photonic-bandgap (PBG)-based nanorefractometer is presented. Changes up to 11.2 dB in the optical output power in an index of refraction range of 1.7 with a sensitivity of 1.5/spl middot/10/sup -4/ have been demonstrated. The design is based on a one-dimensional PBG structure with two defects, which originates two defect states inside the bandgap. These states correspond to two localized modes in the defects. By selecting adequate parameters, the frequency of one of the localized modes can be fixed at the same time that its peak amplitude varies with the refractive index of the defect associated to the other localized mode. The refractive index of the defect associated to the localized mode that has been fixed in frequency remains constant. This enables a detection scheme based on a simple photodetector instead of an optical spectrum analyzer, as usual. The thickness of the defect whose refractive index varies determines the variation range of the transmitted power amplitude peak of the localized mode fixed at a concrete frequency. In addition, an analysis of the nonlinear dependence on the refractive index of the peak-transmitted power of the localized mode fixed at a concrete frequency is presented.

Fiber-Optic Multiple-Wavelength Filter Based on One-Dimensional Photonic Bandgap Structures With Defects

In this paper, a theoretical analysis is given of an optical fiber multiple-wavelength tunable filter based on a one-dimensional (1-D) photonic bandgap (PBG) structure with four defects. To understand the positioning of the modes in the bandgap, a previous analysis of structures with one and two defects is performed. By adequate parameterization, it will be possible to control the central wavelengths of the various filters of the device. Parameters responsible for this effect are the contrast of refractive indexes of high- and low-index layers, the optical thickness of the defects, and the number of layers stacked among the defects related to those stacked at the extremes. In addition to this, the finesse of the filters can be controlled by the adequate addition of layers among defects. As a result, a simple 1-D PBG structure with defects will permit designing almost any multiple-wavelength filter, with immediate application in the treatment of wavelength-division-multiplexed (WDM) signals. The possibility of the tunability of this device can be introduced if materials are included whose refractive index changes with some parameter, such as temperature, voltage, or strain. As an example, liquid crystals change their refractive index with an applied voltage, leading to a shift of the central wavelengths of the filters.

A numerical method for one-dimensional action functionals of photonic band-gap structures

Photonic band gaps (PBG), photonic analogues of electronic semiconductor band gaps, have attracted much attention recently because of numerous potential applications in communications and computing. Aközbek and John (Phys. Rev. E, 57, 2287 (1998).) developed a variational model of such band gaps, using action functionals, where solitary waves are expanded in terms of a finite orthonormal basis. These expansions to finite order N converged to solitary waves. The nonlinear polynomial equations for the coefficients in the expansions, have nonunique solutions. Our paper, makes a study of the multiplicity of the solutions for one-dimensional photonic band-gap structures. It is found that the nonuniqueness grows dramatically with the order of the expansion N. We use homotopy, which continuously deforms the solutions of exactly solvable systems, into the solutions of the systems to be solved with new results in numeric algebraic geometry, such that all solutions are determined. We used Maple 7 to obtain the polynomial equations for the variational coefficients, extending Aközbek and John's approach. A homotopy-based package PHCpack was used to solve the systems for N ≤ 4 and a linearization-extrapolation method was developed to find real solutions for N ≥ 5. The results are compared with the exact soliton solutions and their convergence behavior is discussed. The interplay of geometrical, topological and variational methods is seen in these interesting physical band-gap structures. PACS Nos.: 42.65.Tg, 42.70.Qs, 02.30.Xx, 02.70.Wz

Soliton-like electromagnetic modes: modulation of nonlinear band edge and field distribution

We construct a modulated one-dimensional photonic band gap structures (MPBGS) and investigate the soliton-like modes induced by the nonlinear effect. It is found that due to the nonlinear modulation, the common linear gap of the MPBGS can become narrow or completely disappear, the electromagnetic eigenmodes can enter the common linear gap and develop into soliton-like modes. The field distributions for linear and soliton-like modes are also computed and discussed.

Soliton-like electromagnetic modes: modulation of nonlinear band edge and field distribution

We construct a modulated one-dimensional photonic band gap structures (MPBGS) and investigate the soliton-like modes induced by the nonlinear effect. It is found that due to the nonlinear modulation, the common linear gap of the MPBGS can become narrow or completely disappear, the electromagnetic eigenmodes can enter the common linear gap and develop into soliton-like modes. The field distributions for linear and soliton-like modes are also computed and discussed.

One-dimensional chiral photonic band gap structure analyzed by non-symmetric transmission-line method

In this paper, the formula of reflection coefficient of multi-layer chiral media is derived by non-symmetric transmission-line method. Then, it is applied to one-dimensional (1-D) chiral photonic crystal structure, which is composed of thin chiral layers sandwiched by air. The results show that it is difficult to obtain photonic band gap for general dielectric when the contrast of two media refractive indices is not large, and the reflection coefficient is small. However, for chiral photonic crystal, although the refractive index of chiral layer is small, the wave spectrum contains forbidden zones and the reflection coefficient from such a structure is found to be almost equal to 1, i.e., the wave is almost totally reflected through adjusting chiral parameter. Therefore it is easier to obtain an ideal photonic band gap.

Extrusion of hollow waveguide preforms with a one-dimensional photonic bandgap structure

An extrusion technique is used to make an all-dielectric, hollow waveguide preform. The structure consists of radially alternating dielectric layers of high/low refractive index pairs. By requiring that the two dielectric materials have a high index contrast, it is possible to make a preform that will have a photonic bandgap structure when drawn into a fiber optic. The preform is made by an extrusion process in which a stack-of-plates, composed of alternating disks of chalcogenide glass and a polymer, is extruded through a die into both solid and hollow-core structures. Laminar flow during extrusion forces the periodicity from an axial to a radial orientation in the final extruded preform. For these experiments the high index material was arsenic selenide glass (As2Se3,n=2.6) and the low index material was polysulfone (PSU,n=1.55), which gives an index contrast of 1.68.

Selective Etching of GaN from AlGaN/GaN and AlN/GaN Structures

Thick GaN layers as well as AlGaN/GaN and AlN/GaN heterostructures grown by metalorganic vapor phase epitaxy have been photoelectrochemically (PEC) etched in various dilute electrolytes, and bandgap-selective etching has been demonstrated in heterostructures. This result is a significant step forward in the fabrication of group III-nitride devices and one-dimensional photonic bandgap (PBG) structures in the deep UV. Based on initial results from thick GaN layers, a method was developed to achieve self-stopping selective etching of thin GaN layers in AlGaN/GaN and AlN/GaN heterostructures. Selective PEC etching requires the use of a suitable light source with photon energies larger than the bandgap of GaN, but smaller than that of AlGaN or AlN, thus enabling selective hole generation in the GaN layers to be etched. Additionally, it is imperative to use an electrolyte that supports PEC etching of GaN without chemically etching AlGaN or AlN.

Nanotechnology of transparent metals for radio frequency electromagnetic shielding

The aim of this paper is to present an innovative one-dimensional photonic bandgap structure on plastic substrate, for electromagnetic field shielding applications in the radio frequency range. A complete study is performed, from material characterization and design, to fabrication and experimental test of a prototype sample consisting of seven alternating zinc oxide and silver (Ag) layers, on Lexan polycarbonate. The transparent metal is designed to obtain high shielding effectiveness (SE), not just as a theoretical prediction, but as experimentally measured according to the standard ASTM-D 4935/89. Actually, the shielding performance of multilayered coatings having similar values of sheet resistance but different design are strongly affected by the bonding conditions. The following properties of the structure, which contains only 66 nm of Ag, are highlighted: 1) it remains transparent in the visible range; 2) it retains the conductivity of bulk metal; 3) it has SE in the 30-kHz to 1-GHz range over 40 dB; 4) the overall thickness of the multilayer shielding coating is 312 nm; and 5) it has been realized on both glass or plastic substrate.

Numerical investigation of a self-induced transparency soliton in a nonlinear photonic bandgap structure doped uniformly with two-level atoms

We numerically study the characteristics of a nonlinear pulse that propagates through a one-dimensional photonic bandgap (PBG) structure uniformly doped with two-level atoms. The numerical model adopted is the coupled system of nonlinear coupled-mode equations and atomic Bloch equations. The simulation results show that a self-induced transparency (SIT) soliton and a gap soliton can coexist in a nonlinear PBG structure uniformly doped with resonant atoms. Although this mixed state, known as a SIT-gap soliton, near the PBG edge has been theoretically predicted, we numerically show that such a solitary wave still exists even if its central frequency is located deep inside the PBG. The propagating characteristics of the SIT-gap soliton are also discussed.

Development of an optical refractometer by analysis of one-dimensional photonic bandgap structures with defects.

A theoretical analysis of an optical fiber photonic-bandgap-based refractometer is presented. The design is based on a quarter-wave reflector with one defect. By modifying both the real and the imaginary parts of the index of refraction of the defects we begin to change either the frequency or the amplitude of the localized optical mode. So we could fabricate a specific optical fiber refractometer by combining all the variables: index of refractive index of the defects and the rest of layers, thickness of the defect, number of layers, etc. to yield a large set of design possibilities, for example, detecting wider or thinner ranges of refractive indices, or controlling the detection accuracy. Some rules for the practical implementation of the refractometer are given.

Resonance transmission modes in dual-periodical dielectric multilayer films

The resonance transmission modes with high-quality factors may generate in a one-dimensional dual-periodic photonic band-gap structure. The frequency, frequency interval, and number of these modes can be tuned as desired by adjusting its structural parameters. In this letter, we report the experimental and theoretical results on dual-periodical TiO2/SiO2 multilayer films. With perfect transmission and mode controllability, this structure opens a promising way to fabricate multiwavelength filters for future dense wavelength division application.

Finite Element Analysis of Optical Bistability in One-Dimensional Nonlinear Photonic Band Gap Structures with a Defect

We present a new approach based on the recently reported finite element scheme16 to study the optical response of a finite one-dimensional nonlinear grating. Using the transmitted wave amplitude as a numerical input parameter, we are able to find all stable and unstable solutions related to a specific incident wave which build up the complete bistability curve. The method is applied to investigate the optical bistability in a nonlinear quarter-wave reflector with a defect. With a proper choice of the incident light frequency, a very low bistability threshold is predicted for an optimized defect structure.