Surface wave photonic device based on porous silicon multilayers

Porous silicon is widely studied in the field of photonics due to its interesting optical properties. In this work, we present theoretical and first experimental studies of a new kind of porous silicon photonic device based on optical surface wave. A theoretical analysis of the device is presented using plane-wave approximation. The porous silicon multilayered structures are realized using electrochemical etching of p⁺-type silicon. Morphological and optical characterizations of the realized structures are reported.     

Photoreflectance study at the micrometer scale

Photoreflectance (PR) spectroscopy has proven to be a very efficient non-destructive tool to get information on various semiconducting epitaxial structures as it is very sensitive to every direct optical transitions in semiconducting quantum structures and allows as well to optically measure internal electric fields in space charge layers, through Franz-Keldysh oscillation (FKO) analysis. We have developed an experimental setup to get micro-PR spectra on epitaxial structures or devices on a few micrometer size spots. Due to very low signal intensity, experimental conditions have to be very carefully controlled: the signal/noise ratio strongly depends on the pump-probe power ratio.We give experimental micro-PR results recorded on antimonide-based heterojunction bipolar transistors (HBTs), which give the local electric field at the emitter-base junction under different biasing conditions. A second part of the paper is devoted to micro-PR analysis performed on tuneable vertical cavity surface emitting layers (VCSELs) with InP/air Bragg mirrors. In such VCSELs, both the cavity Fabry-Perot peak and the active region quantum well ground state are giving transitions in the micro-PR spectrum. This is very useful in the case of a tuneable structure. Feasibility of micro-PR analysis at the device scale is demonstrated.     

Diffraction effects in guided photonic band gap structure

The concept of the photonic band gap (PBG) structures stems from ideas of Yablonovitch. The idea is to design components so that they affect the properties of photons, in much the same way that ordinary semiconductor crystals affect the properties of electrons. In fact, the PBG structures forbid propagation of photons for a particular range of energy. They can be used to realise optical filters with large stop band and sharp transmission resonance. In the guided PBG structures, the existence of diffractive effects in the vertical dimension could limit the quality factor of such filters. In this paper, we have investigated the origin of diffraction losses in one-dimensional guided PGB structures using 2D and 3D numerical tools. We propose an analytical approach based on Bragg diffraction relation to explain these losses phenomenon. From this approach, the influence of some design parameters on the electromagnetic behaviour and the spectral response of PBG resonators will be explained.     

Curious congruences related to the Bell polynomials

In this paper we give some congruences on the r-derangement polynomials (defined below), Lah polynomials and some versions of Bell numbers and polynomials.     

Slow Bloch surface wave devices on porous silicon for sensing applications

A new type of biosensor using slow Bloch surface waves in photonic devices based on porous silicon is presented. After optimization of the devices, a theoretical performance study is performed and demonstrates an increase in sensitivity by a factor 10 compared to surface wave sensors based on porous-silicon multilayers. First results of the experimental realization of the sensor are also shown.     

General Decay for a Viscoelastic Equation of Variable Coefficients in the Presence of Past History with Delay Term in the Boundary Feedback and Acoustic Boundary Conditions

In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function \(g\). Our result extends the decay result obtained for problems with finite history to those with infinite history.     

Evidence of Bloch wave propagation within photonic crystal waveguides

We report in this paper results obtained from characterizations of photonic band gap waveguide, using near field optical microscopy. We will show evidence of a Bloch wave propagating within our W1 photonic crystal waveguides (PCWs) structure, using a 2D Fourier transform approach. The processed image will then be compared to simulations obtained from plane wave method. This comparison exhibits that near-field measurements, using tapered optical fibers as probes, are mainly sensitive to the electric field propagating within the structure. PACS 42.25.-p; 42.30.Va; 42.770.-Qs; 42.82.-Et     

Complete identification of the Ti-related levels in GaP

A complete understanding of the electrical and optical properties of all the Ti-related levels is deduced from a number of different characterization techniques performed on several types of Ti-doped GaP materials (n-type, p-type and semi-insulating) grown by LEC. The Ti³⁺ /Ti⁴⁺ donor level and the Ti²⁺ /Ti³⁺ acceptor level are found at E_v + 0.92 and about E_c - 0.56 eV, respectively. Likewise, a comprehensive scheme of the two internal transitions ³T₂→³A₂ of the Ti²⁺ charge state and ²T₂→²E of the Ti³⁺ charge state is given.     

Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions

A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.     

Global solvability and decay estimates for a type III thermo-viscoelastic coupled system with infinite memory and boundary interaction feedback

A type III thermo-viscoelastic coupled system with infinite memory and distributed delay is considered. The interaction feedback between the nonlinear damping and the acoustic conditions are reacted on portion of the boundary. We obtain the well posedness and regularity of the system by using semigroup theory which is combined with Schauder's fixed point theorem. Moreover, the general decay estimates are established under a much larger class of relaxation functions. Our results are obtained without the boundedness condition of initial data assumed in many earlier papers in the literature. This work generalizes the composite stability between infinite memory and nonlinear damping.