The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

CeO2 nanocubes (and nanorods) enclosed by six {200} planes with controlled sizes have been prepared through a facile one-pot method. The nanocubes have a strong tendency to assemble into 2D and 3D arrays with regular patterns on a substrate, which is probably driven by the dipole−dipole interaction of polar {200} planes. The possible formation mechanism of the nanocubes has been put forward as the oriented aggregation mediated precursor growth. It is possible to use the synthesized nanocubes as building blocks to achieve {200}-perfect-oriented monolayers or thickness-controlled films and to apply the preparative method in the incorporation of heterogeneous atoms or nanoparticles for semiconductor doping or heterogeneous nanostructures.

Controlled synthesis and self-assembly of CeO2 nanocubes.

We investigate the electronic properties of nanocrystalline cerium oxide $({\mathrm{CeO}}_{x})$ films, grown by various techniques, and we establish universal relations between them and the film structure, composition, and morphology The nanocrystalline ${\mathrm{CeO}}_{x}$ films mainly consist of ${\mathrm{CeO}}_{2}$ grains, while a considerable concentration of trivalent ${\mathrm{Ce}}^{3+}$ is distributed at the ${\mathrm{CeO}}_{2}$ grain boundaries forming amorphous ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ A small portion of ${\mathrm{Ce}}^{3+}$ is also located around O-vacancy sites The optical properties of the ${\mathrm{CeO}}_{x}$ films are considered, taking into account the reported band-structure calculations The fundamental gap ${E}_{g}$ of ${\mathrm{CeO}}_{x}$ is due to the indirect $\mathrm{O}2\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{Ce}4f$ electronic transition along the L high-symmetry lines of the Brillouin zone and it is correlated with the $[{\mathrm{Ce}}^{3+}]$ content, explaining the redshift of ${E}_{g}$ in nanostructured ${\mathrm{CeO}}_{x},$ which is due to the ${\mathrm{Ce}}^{3+}$ at the grain boundaries and not due to the quantum-size effect itself We also correlate the energy position of the $\mathrm{O}2\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{Ce}4f$ electronic transition, which varies up to 160-meV wide, with the lattice constant of the ${\mathrm{CeO}}_{2}$ grains We also show that the higher-order transitions are more sensitive to film composition The refractive index, far below ${E}_{g},$ is explicitly correlated with the film density, independently of the ${\mathrm{Ce}}^{3+}/{\mathrm{Ce}}^{4+}$ and O concentrations, grain size, and lattice parameter The density is also found to be the major factor affecting the absolute value of the ${\ensuremath{\varepsilon}}_{2}$ peak, which corresponds to the $\mathrm{O}2\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{Ce}4f$ electronic transition

Structure-dependent electronic properties of nanocrystalline cerium oxide films

Synthesis of cerium oxide nanoparticles using Gloriosa superba L. leaf extract and their structural, optical and antibacterial properties

Ce3+ and oxygen vacancy mediated tuning of structural and optical properties of CeO2 nanoparticles

Violet/blue photoluminescence was observed from epitaxial cerium oxide films on silicon substrates. The films were deposited on silicon (111) substrates under ultrahigh vacuum conditions using pulsed laser ablation of a cerium oxide target and treated by rapid thermal annealing in argon. High resolution transmission electron microscopy and x-ray diffraction measurements indicated the formation of a single crystal cerium oxide phase Ce6O11 different from CeO2 in the annealed films. The emission might be due to charge transfer transitions from the 4f band to the valence band of the oxide.

Violet/blue emission from epitaxial cerium oxide films on silicon substrates

Multimode interference in optical waveguides has interesting self-imaging properties, which have extensively been investigated and utilized in many integrated optical devices. Although these investigations started with most interest in step-index integrated waveguides, they have later included graded-index waveguides, where the dependence of the interference images on the refractive index grading of the waveguides was observed and utilized in the design and optimization of devices. Later on, multimode interference has also been explored in optical fibers in order to realize fiber devices, including sensors. A basic structure of these devices has been the Single mode — Multimode — Single mode (SMS) fiber section concatenation, where multimode interference in the multimode section leads to the formation of a self-image of the single mode fiber excitation onto the output single mode fiber core. This paper reports on the investigation of the self-imaging properties of these optical fiber structures and their possible use as sensors. Self-imaging in symmetrically excited multimode optical fibers is analytically studied, revealing the effect of refractive index grading on the characteristics of SMS fiber devices. The theoretical results are verified by numerical simulations using the beam propagation method. The experimental investigation of an SMS structure proposed as a bending sensor is then described and a discussion of the results obtained and possible application of the device is presented.

Self-imaging in single mode-multimode-single mode optical fiber sensors

The measurement of vibrations is an important technique for the in-service evaluation and monitoring of machines and civil structures. For such measurement, optical fiber sensors are very promising candidates as optical fibers are electromagnetic interference- and hazard-free and their use enables the sensors to be operated remotely with the electronics and electrical connections situated away from the sensing sites, which is a major advantage in many applications. In this work, multimode optical fiber sensors are used to monitor the vibrations of an industrial sewing machine. The measurement is based on vibration sensing using multimode interference in a proposed sensor configuration which is simple in construction and straight forward to operate. The principle of operation, the results obtained and suggested further investigations of the proposed sensors are discussed.

Monitoring of vibrations using multimode optical fiber sensors

A comprehensive and rigorous study of the performance of MMI devices fabricated by ion exchange on a glass substrate is presented. The effect of both design and fabrication parameters on the performance of the devices is investigated and a physical interpretation of the effect of these parameters on the behavior of devices is given. A novel stable and efficient approach for solving the nonlinear ion exchange diffusion equation is proposed and exploited in this study. Based on this study an optimal design for a 3 dB ion-exchanged power splitter with low insertion loss and wide bandwidth is proposed.

Effect of the fabrication and design parameters on the performance of multimode interference devices made by ion exchange : a detailed study

An intensity-based optical fiber sensor using single-mode-multimode-single-mode fiber sections concatenation is proposed and investigated for use as an intrusion detector. The sensor is composed with simple FC/PC connections between the fiber sections. It is found to be sensitive to intrusion disturbances applied to the multimode fiber section. The transmission spectra of the device under different conditions are measured and its operation as intrusion detector is demonstrated using a single-mode laser source. More than 1 dB variation in the detected power level was observed at a wavelength of 1543 nm. The device proposed is a simple intensity-based sensor, which can be used as a stand-alone device to detect intrusion events over its length or possibly interrogated in a quasidistributed intrusion detection system based on optical time domain reflectometry.

Ahmed Hisham Morshed

Papers

Violet/blue emission from epitaxial cerium oxide films on silicon substrates

Self-imaging in single mode-multimode-single mode optical fiber sensors

Monitoring of vibrations using multimode optical fiber sensors

Effect of the fabrication and design parameters on the performance of multimode interference devices made by ion exchange : a detailed study

Intensity-based optical fiber intrusion detector