A. Akjouj

Localised electronic states in semiconductor superlattices

Abstract The existence and properties of localised electronic states are described in binary (two layers per period) and polytype (multiple layers per period) semiconductor superlattices. Special attention is paid to surface effects, due to the superlattice potential termination by a clad layer, and the resulting Tamm-like surface states localised at the superlattice/clad-layer interface. The effect of the Bragg confinement of electrons in coupled superlattices, particularly the formation of above-barrier bound states at the junction of superlattices or the spacer layer embedded in a superlattice, is also discussed. Based on peculiar properties of localised superlattices states, with respect to extended miniband states, their importance for both the fundamental research and various device applications is stressed out. The most frequently used Kronig–Penney-like approaches within the framework of effective-mass and envelope-function approximation, namely, the direct-matching procedure and the transfer-matrix technique, are described for bulk- and surface-electronic-structure calculations of terminated binary and polytype superlattices, as well as for coupled superlattices. Comparison of the results with experimental data and/or more advanced computations indicates that these simple models are versatile and accurate (within their domain of validity), when applied to AlGaAs-based heterostructures. Two Green-function techniques, one based on the combined factorisation and Wronskian methods, and the other on the interface-response theory, are presented for the purpose of density-of-states analysis. For terminated binary GaAs/AlGaAs superlattices, an appropriate choice of the superlattice and clad-layer parameters, as well as the surface location within the superlattice period, enables a surface state with desired energy position inside the minigap, and required extension into the superlattice bulk, to be achieved. Introduction of additional layers into the superlattice sequence, resulting in a polytype superlattice, offers a further means of influencing the energies and localisation properties of surface states, but, more importantly, creates an opportunity for surface states to occur under classical Shockley conditions, which is not possible in binary superlattices, where only Tamm-like surface states can exist. The possibility of manipulating the local density of states at the superlattice end is also indicated. For polytype superlattices, the formation of well-defined surface resonances, affecting the overall subsurface density-of-states characteristics, is pointed out. The properties of Bragg-confined states and the density of states of coupled AlGaAs-based superlattices are examined, attention being focused on the transition from interface-localised to above-barrier bound states. Finally, other electronic localisation phenomena in superlattices are briefly reviewed.

Response functions in layered dielectric media

Abstract The interface response theory was recently presented for any composite material in discrete, continuous and mixed (partly discrete — partly continuous) spaces. The aim of this report is to show how this theory can be used for solving the Maxwell equations in any composite dielectric material. General expressions for the corresponding response functions are given. These results are illustrated by a general application to layered isotropic dielectrics and in particular simple derivations of the response functions for two media separated by an interface, for one dielectric slab sandwiched between two different semi-infinite dielectrics and for dielectric superlattices.

Experimental and theoretical evidence for the existence of photonic bandgaps and selective transmissions in serial loop structures

We have investigated the electromagnetic band structure, transmission, and phase time through a one-dimensional structure made of loops pasted together with segments of finite length. In this serial loop structure, the loops and segments are constituted of dielectric monomode materials. Analytic expressions are reported for the band structure for a large number N of loops and for transmission coefficients and phase times for any value of N. Experimental and numerical results show the existence of large gaps in these structures. These gaps originate both from the periodicity of the system and the loop resonant states that create zeroes of transmission. The gap widths depend on the lengths of the finite segment and the loop diameters. Defect modes may occur in these bandgaps by introducing defective segments in the structure. The localized states appear as very narrow peaks both in the transmission spectrum and in the transmission phase time of finite serial loop structures. The localized state behavior is ...

Omnidirectional optical mirror in a cladded-superlattice structure

In recent years, it has been shown that one-dimensional photonic crystals such as superlattices can exhibit an omnidirectional reflection of light for a given frequency range. However, this property requires that the incident wave be launched from vacuum or from a low refractive index material. In this article, we show that the limitation about the choice of the substrate can be removed by adding a clad layer of low refractive index at one boundary of the superlattice. The additional layer acts like a barrier for the propagation of light. An alternative solution based on a combination of two multilayer structures is also mentioned.

Propagation and localization of acoustic waves in Fibonacci phononic circuits

A theoretical investigation is made of acoustic wave propagation in one-dimensional phononic bandgap structures made of slender tube loops pasted together with slender tubes of finite length according to a Fibonacci sequence. The band structure and transmission spectrum is studied for two particular cases. (i) Symmetric loop structures, which are shown to be equivalent to diameter-modulated slender tubes. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear in the transmission spectra inside the gaps as defect modes. The spatial localization of the modes lying in the middle of the bands and at their edges is examined by means of the local density of states. The dependence of the bandgap structure on the slender tube diameters is presented. An analysis of the transmission phase time enables us to derive the group velocity as well as the density of states in these structures. In particular, the stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the speed of sound. (ii) Asymmetric tube loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence new gaps unnoticed in the case of simple diameter-modulated slender tubes. The Fibonacci scaling property has been checked for both cases (i) and (ii), and it holds for a periodicity of three or six depending on the nature of the substrates surrounding the structure.

Transmission gaps and Fano resonances in an acoustic waveguide: analytical model

A simple acoustic device consisting of two dangling side resonators grafted at two sites on a slender tube is designed possibly to obtain transmission stop bands (where the propagation of longitudinal acoustic waves is forbidden). In contrast to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with this simple structure. This is obtained by combining appropriately the zeros of transmission of the side resonators. Sharp resonant states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for various systems of this kind within the framework of the Greens function method. The amplitude and the phase of the transmission are discussed as a function of frequency and it is shown that the width of the stop bands is very sensitive to the number of side resonators. These results should have important consequences for the suppression of low-frequency noise and for designing filters.

Nanoscale plasmon waveguide including cavity resonator

The propagation and filtering of surface plasmon polaritons in metal-insulator-metal nanosandwiches are investigated by using finite-difference time domain simulation. We study the optical transmission of a nanoscale waveguide coupled to a cavity situated either in the vicinity or in the interior of the waveguide. Depending on whether the cavity is inside or at the side of the waveguide, the transmission spectrum displays respectively peaks or dips which occur at the same frequencies. We study the dip and peak frequencies in the transmission spectrum as a function of the geometrical parameters of the cavity and the thickness of the metallic gap separating the guide from the cavity.

Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides

The photonic band structures and transmission spectra of serial loop structures (SLSs), made of loops pasted together with segments of finite length, are investigated experimentally and theoretically. These monomode structures, composed of one-dimensional dielectric materials, may exhibit large stop bands where the propagation of electromagnetic waves is forbidden. The width of these band gaps depends on the geometrical and compositional parameters of the structure and may be drastically increased in a tandem geometry made up of several successive SLSs which differ in their physical characteristics. These SLSs may have potential applications as ultrawide-band filters.

Large omnidirectional band gaps and selective transmission in one-dimensional multilayer photonic structures

It has been shown that a one-dimensional periodic structure such as a superlattice can exhibit the property of omnidirectional reflection, which means that any incident wave launched from the vacuum (or from a substrate) will undergo a total reflection at the superlattice boundary, whatever the incident angle or the polarization of light is. In this communication, we show that large omnidirectional band gaps can be obtained by associating two or several superlattices in tandem. We discuss the existence conditions for these gaps as compared to the usual case of a binary superlattice. By introducing a defect layer in the finite layered structure, one can obtain localized modes inside these omnidirectional band gaps, giving rise to the selective transmission through the structure. These modes appear as peaks in the transmission spectrum with a very high quality factor, and therefore may have useful applications in the frame of photonic band-gap materials.

Acoustic spectral gaps and discrete transmisson in slender tubes

Abstract We report the band structure and transmission spectrum for the longitudinal (acoustic) wave propagation in a system made up of N ′ dangling side branches (DSB) periodically grafted at each of the N equidistant sites on a slender tube. A periodic pattern of large stop bands is obtained for the airy DSB on a slender water tube. We emphasize the interesting result of huge gaps and the discrete transmission spectrum due only to the DSB grafted at a single site ( N =1) on the slender tube. Designing the system with open tubes allows achievement of the lowest gap below a threshold frequency and extending up to zero — thereby providing an entirely discrete band structure and transmission spectrum. This should have important consequences for the suppression of low-frequency noise and for designing filters and transducers.