# Electrical and Electronic Engineering Research Collection

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- PublicationDiffraction by volume gratings : approximate solution in terms of boundary diffraction coefficientsAn approximate analytic method is presented that permits the calculation of all the output waves, both backward and forward traveling, for slanted, transmission-type volume gratings replayed at the Bragg angle and perfectly index matched to their surroundings. The predictions of the resulting analytic expressions are compared with numerical results produced by using the rigorous coupled-wave method and found to be accurate over a large range of parameters to the first order of the permittivity variation of the volume grating, all second order terms being assumed negligible.
329Scopus© Citations 11 - PublicationDiffractive beam splitter for laser Doppler velocimetry(Optical Society of America, 1992-09-01)
; ; ; ; ; ; A miniaturized sensor head for the optical measurement of velocities of fluids based on laser Doppler velocimetry is demonstrated. Holographic optical elements mounted on a glass substrate are used for beam splitting and deflection. Volume holograms in dichromated gelatin exhibit good optical efficiency (75% transmission of a cascade of two holographic optical elements). With diffractive devices one can achieve achromatic behavior that makes the sensor insensitive to wavelength drifts or mode hopping of a semiconductor laser.433Scopus© Citations 44 - PublicationCoherent imaging of periodic thick fine isolated structuresThe diffraction orders and coherent bright and dark field images produced by isolated steps and grooves (notches and trenches) are examined. The isolated structures are approximated by means of a grating with a large period that contains small, widely separated, lamellar structures. The rigorous modal method for TE polarized incident light is used for the numerical calculations. Structures in two types of dielectric material, refractive index n = 1.5 and n = 4.0, are discussed. The images are examined for variations with several parameters, including width and thickness of the structure and focus position. Several approximate methods for calculating these images, based on first-order approximations, are suggested.
332Scopus© Citations 19 - PublicationDielectric binary blazed gratingsArtificial index gratings, which are composed of binary microstructures of sizes less than the incident wavelength, are analyzed as functions of the filling factor or duty cycle of the microstructures. Different models for calculating the optimum duty cycles to produce high blazed diffraction efficiency are compared. Blazed binary grating designs in a material with a refractive index n = 2 show theoretical diffraction efficiencies as high as η = 80%. In the semiconductor material silicon, which has a refractive index n = 3.4, theoretical diffraction efficiencies as high as η = 70% are predicted.
392Scopus© Citations 27 - PublicationGeneralization of the boundary diffraction method for volume gratingsThe boundary diffraction method (BDM) is an approximate method that permits the derivation of analytic solutions for the output beams, both forward and backward propagating, that arise from the fundamental nature of holographic gratings. The method is based on the assumption that the volume scatter inside the grating can be supplemented by boundary diffraction coefficients. The boundary diffraction method is used for analysis of thick transmission geometry gratings in a unified way that deals with both the slanted and the unslanted cases. During the analysis, evidence emerges for the superiority of the first-order two-wave beta-value method over the Kogelnik k-vector closure method. The BDM is then further generalized to the case of a volume transmission grating, index matched to its surroundings, and replayed normally on-Bragg, i.e., satisfying the Bragg condition for normal incidence. The analytic equations derived are compared with results calculated with the rigorous coupled-wave method.
263Scopus© Citations 11 - PublicationGeneralization of the boundary diffraction method for volume gratingsThe boundary diffraction method (BDM) is an approximate method that permits the derivation of analytic solutions for the output beams, both forward and backward propagating, that arise from the fundamental nature of holographic gratings. The method is based on the assumption that the volume scatter inside the grating can be supplemented by boundary diffraction coefficients. The boundary diffraction method is used for analysis of thick transmission geometry gratings in a unified way that deals with both the slanted and the unslanted cases. During the analysis, evidence emerges for the superiority of the first-order two-wave beta-value method over the Kogelnik k-vector closure method. The BDM is then further generalized to the case of a volume transmission grating, index matched to its surroundings, and replayed normally on-Bragg, i.e., satisfying the Bragg condition for normal incidence. The analytic equations derived are compared with results calculated with the rigorous coupled-wave method.
279Scopus© Citations 11 - PublicationBinary blazed reflection gratings(Optical Society of America, 1994-06-01)
; ; ; ; ; ; ; A reflection grating with a binary surface profile is presented that has high diffraction efficiency. The measured intensity for the + 1st diffracted order was 77%. The binary grating is composed of a minilattice with feature sizes comparable with the wavelength of the incident light. The overall structure is designed in such a way that it imitates a conventional blazed grating. The grating also has interesting polarization properties. The main part of the TE-polarized light is diffracted into the 1st diffracted order, and most of the TM-polarized light remains in the 0th diffracted order. The measurements of the grating are compared with rigorous diffraction theory and found to be in reasonable agreement.734Scopus© Citations 1 - PublicationOptical operations on wave functions as the Abelian subgroups of the special affine Fourier transformationThe special affine Fourier transformation (SAFT) is a generalization of the fractional Fourier transformation (FRT) and represents the most general lossless inhomogeneous linear mapping, in phase space, as the integral transformation of a wave function. Here we first summarize the most well-known optical operations on lightwave functions (i.e., the FRT, lens transformation, free-space propagation, and magnification), in a unified way, from the viewpoint of the one-parameter Abelian subgroups of the SAFT. Then we present a new operation, which is the Lorentz-type hyperbolic transformation in phase space and exhibits squeezing. We also show that the SAFT including these five operations can be generated from any two independent operations.
572Scopus© Citations 190 - PublicationInterferometric resolution examined by means of electromagnetic theoryInterferometric methods are widely used in surface metrology. A question that arises is how much information about the surface can be extracted from a given interferogram. For examination of the resolution limit of interferometry with coherent monochromatic light, interferograms of several surface relief gratings calculated with the use of approximate and rigorous theories are presented. The limits of the usefulness of scalar theory based on the use of the Fourier transform are indicated. Interferograms of dielectric and metallic structures are examined, including simple lamellar gratings and gratings made up of trapezoidal steps with varying slopes and depths. In all cases TE illumination is assumed. The effects of changing numerical aperture and defocus on the interferograms are also examined.
334Scopus© Citations 11 - PublicationRandom fractional Fourier transform : stochastic perturbations along the axis of propagationThe fractional Fourier transform (FRT) is known to be optically implementable with use of a medium with a perfect radial quadratic-index profile. Using the quantum-mechanical operator formalism, we examine the effects on the FRT action of such a medium that are due to small random inhomogeneities in the longitudinal direction, the direction of propagation, and we formulate the random fractional Fourier transform (RFRT). Applying the RFRT to a self-fractional Fourier function, a Gaussian function, we discuss both the total power and the variance. The random Fourier transform is examined as a special limiting case.
329Scopus© Citations 6 - PublicationHolographic interferometry and the fractional Fourier transformationThe fractional Fourier transform (FRT) is shown to be of potential use in analyzing the motion of a surface by use of holographic interferometry. The extra degree of freedom made available by the use of the FRT allows information regarding both translational and tilting motion to be obtained in an efficient manner.
360Scopus© Citations 39 - PublicationNonlocal-response diffusion model of holographic recording in photopolymerThe standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The resulting nonlocal diffusion equation is then solved numerically, in low-harmonic approximation, to describe grating formation. The effects of the diffusion rate, the rate of polymerization, and a new parameter, the nonlocal response length, are examined by using the predictions of the model. By applying the two-wave coupled-wave model, assuming a linear relationship between polymerized concentration and index modulation, the resulting variation of the grating diffraction efficiency is examined.
475Scopus© Citations 245 - PublicationThickness variation of self-processing acrylamide-based photopolymer and reflection holography(Society of Photo-Optical Instrumentation Engineers, 2001-04)
; ; There are many types of holographic recording material. The acrylamide-based recording material examined here has one significant advantage: it is self-processing. This simplifies the recording process and enables holographic interferometry to be carried out without the need for complex realignment procedures. However, the effect that the polymerization process has on the grating thickness must be examined. This question is fundamental to the material’s use in holographic optical elements, as thickness variations affect the replay conditions of the produced elements. This paper presents a study of this thickness variation and reports for the ﬁrst time the production of reﬂection holographic gratings in this material.469Scopus© Citations 45 - PublicationDigital Deep-Submicron CMOS Frequency Synthesis for RF Wireless ApplicationsTraditional designs of commercial frequency synthesizers for multi-GHz mobile RF wireless applications have almost exclusively employed the use of a charge-pump phase-locked loop (PLL), which acts as a local oscillator (LO) for both transmitter and receiver. Unfortunately, the circuits and techniques required are extremely analog intensive and utilize a process technology which is incompatible with a digital baseband. The author's research related to low-power and low-cost radio solutions has led to a novel all-digital synthesizer architecture that exploits strong advantages of a deep-submicron digital CMOS process technology as well as advances in digital very large scale of integration (VLSI) field. Its underlying theme is to maximize digitally-intensive implementation by operating in a synchronous phase domain. Chief benefit obtained with this architecture is to allow to integrate the RF front-end with the digital back-end onto a single silicon die. The presented frequency synthesizer naturally combines the transmitter modulation capability implemented in an all-digital manner. The pulse-shaping transmit filter and a class-E power amplifier are included to demonstrate the use of the proposed synthesizer in a targeted RF application. The ideas developed in this research project have been implemented in a Texas Instruments' deep-submicron CMOS process and demonstrated in a working silicon of Bluetooth transmitter for short-range communications.
604 - PublicationComparison of holographic photopolymer materials by use of analytic nonlocal diffusion models(Optical Society of America, 2002-02-01)
; ; The one-dimensional diffusion equation governing holographic grating formation in photopolymers, which includes both nonlocal material response and generalized dependence of the rate of polymerization on the illuminating intensity, has been previously solved under the two-harmonic expansion assumption. The resulting analytic expressions for the monomer and polymer concentrations have been derived and their ranges of validity tested in comparison with the more accurate numerical four-harmonic case. We used these analytic expressions to carry out a study of experimental results presented in the literature over a 30-year period. Automatic ﬁtting of the data with these formulas allows material parameters, including the nonlocal chain-length variance σ, to be estimated. In this way, (i) a quantitative comparison of different materials can be made, and (ii) a standard form of experimental result presentation is proposed to facilitate such a procedure.349Scopus© Citations 58 - PublicationAdjusted intensity nonlocal diffusion model of photopolymer grating formation(Optical Society of America, 2002-04-01)
; ; Diffusion-based models of grating formation in photopolymers have been proposed in which the rate of monomer polymerization (removal) is directly proportional to the illuminating intensity inside the medium. However, based on photochemical considerations, the rate of polymerization is proportional in the steady state to the square root of the interference intensity. Recently it was shown that, by introducing a nonlocal response function into the one-dimensional diffusion equation that governs holographic grating formation in photopolymers, one can deduce both high-frequency and low-frequency cutoffs in the spatial-frequency response of photopolymer materials. Here the ﬁrst-order nonlocal coupled diffusion equations are derived for the case of a general relationship between the rate of polymerization and the exposing intensity. Assuming a twoharmonic monomer expansion, the resultant analytic solutions are then used to ﬁt experimental growth curves for gratings fabricated with different spatial frequencies. Various material parameters, including monomer diffusion constant D and nonlocal variance s, are estimated.363Scopus© Citations 89 - PublicationOptical image encryption by random shifting in fractional Fourier domainsA number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.
1104Scopus© Citations 420 - PublicationQuantifying reserve demands due to increasing wind power penetrationWith wind power penetration increasing in many systems worldwide, operational issues are beginning to emerge due to the uncertain nature of wind power. One of these issues is the provision of reserve for system security. To analyse this, one must consider generator outage rates, system load forecast errors and wind power forecast errors in such a way as to directly relate the system reserve level to the security of the system. In this paper a new methodology is proposed for the analysis and provision of system reserve levels. The methodology considers the provision of both reserve (on-line) and replacement reserve (offline). The proposed methodology is then applied to the IEEE reliability test system incorporating other influencing factors like wind farm size and numbers and forecast periods. Results illustrate the impact increasing wind power penetration has on reserve.
1038Scopus© Citations 70 - PublicationMotion detection, the Wigner distribution function, and the optical fractional Fourier transformIt is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior information is known about the motion.
314Scopus© Citations 29 - PublicationNon-local polymerization driven diffusion based model : general dependence of the polymerization rate to the exposure intensity(Optical Society of America, 2003-08-11)
; ; ; ; ; ; ; The nonlocal diffusion model proposed by Sheridan and coworkers has provided a useful interpretation of the nature of grating formation inside photopolymer materials. This model accounts for some important experimental facts, such as the cut-off of diffraction efficiency for high spatial frequencies. In this article we examine the predictions of the model in the case of a general dependence of the polymerisation rate with respect to the intensity pattern. The effects of this dependence on the different harmonic components of the polymerisation concentration will be investigated. The influence of the visibility on the different harmonic components will also be studied. These effects are compared to the effects of varying RD and σD.247Scopus© Citations 20