This paper attempts to review the major events in the development of diffraction gratings, the spectrometers that utilize them and some of their more esoteric applications. It is seen that from early beginnings both the design of gratings themselves as well as the instruments in which they are used have become simpler, smaller and less expensive without giving up utility. Ruled and Holographic gratings now co-exist as standard optical elements.

It is well known that gratings with high spatial frequency (spacings <EQ (lambda) /2) show form birefringence. Therefore, gratings formed in dielectric materials can act as a wave plate when the grating spacing is smaller than, or near to, half of the incident beam wavelength. Previous researchers used high frequency surface relief structures or sinusoidal gratings formed in photoresists to produce this effect. In this paper we show the performance of a volume holographic quarterwave plate formed in DCG operating at 632.8 nm. To our knowledge this is the first demonstration of a retardation plate exhibiting this magnitude of phase delay in a volume material. The fabrication techniques required to realize this element are also presented.

Sub-wavelength grating structures made in an isotropic medium induce form birefringence effects with the induced optical axis parallel to the grating vector. The phase shift between the two orthogonal electric field components exiting this grating varies linearly with the thickness of the grating. When a grating with sub-wavelength period is formed on a uniaxial birefringent material with the grating vector aligned parallel to is natural optical axis, the total effect is enhanced birefringence for the material. Smaller thickness of the material is required to achieve the same phase shift. If the natural optical axis and the induced optical axis lie within the surface plane and have an angle between them, the phase shift varies nonlinearly with the thickness of the grating.

Zeroth-order effective medium theory is applied to analyze the properties of volume holographic gratings that have periods much smaller than the illumination wavelength. These holograms, called zeroth order gratings, can be modeled as negative uniaxial films using the quasistatic field approximation. Exact analytic expressions for the form birefringence of gratings with sinusoidal, rectangular, and triangular permittivity profiles are obtained and compared. Approximate equations are derived that indicate a quadratic dependence of the form birefringences on the permittivity modulation. It is determined that the optimum rectangular profile yields the greatest form birefringence.

In this paper, the optical properties of broadband Lippmann-Bragg volume holographic mirrors are analyzed. These mirrors have a wavelength bandwidth much higher than their Bragg bandwidth, which is a result of Kogelnik's theory. While Kogelnik's model assumes uniform distribution of the distance between Bragg planes as a function of the vertical coordinate, the experimental results presented in this paper strongly demonstrate that Kogelnik's theory is not valid in the case of broadband Lippmann-Bragg volume holographic mirrors.

Bragg-Fresnel gratings and zone plates are etched into plane multilayers whose thicknesses may be hundreds of wavelengths. Similar situation is found for modulated multilayers deposited over a X-ray grating. Thus the analysis of such thick periodic stratified media through the classical differential method may present numerical instabilities linked with the growing of exponential functions associated with the evanescent orders during the integration process. There are two ways to avoid this contamination. They consist of cutting the modulated region into thin slices in which the numerical integration is stable and to combine the field diffracted by the thin slices via the Bremmer summation series of the R-matrix propagation algorithm. Both techniques are tried and compared, and the second one turns out to be more stable. It is then possible to analyze gratings with modulation depths ten times the groove spacing and thousand times the wavelength, or deep gratings supporting several hundreds of orders without numerical problems. The use of the R- matrix propagation algorithm opens new possibilities to the existing grating theories and, in particular to the differential method, in analyzing more and more complicated stratified media. As examples of the new possibilities of the Differential Method, Bragg-Fresnel zone plates and deep multilayer coated gratings for soft X-rays are investigated.

A brief review and discussion of ongoing research on radiation effects in key optoelectronic-photonic waveguide and periodic structures is presented. The review focuses on optoelectronic components composed of III-V and II-VI materials that are currently of interest in space applications. Reported and predicted radiation-induced responses in acousto-optic modulators, optical waveguide couplers, distributed Bragg reflectors, and organic materials are discussed.

Transmission properties of holographic Fabry-Perot filters are investigated. The effects of such filters on incident spatially partially coherent light are studied. In particular, the effects of such a filter on the intensity and the degree of spatial coherence of an incident partially coherent Gaussian Schell-model beam are analyzed. Numerical examples are presented.

We report the results of the experimental studies on the fabrication of Fabry-Perot filters using holographic methods. High finesse holographic Fabry-Perot (HFP) filters can be fabricated using low quality substrates and commercially available volume holographic recording materials. Several large aperture samples of HFP filters were successfully fabricated using glass and plastic (mylar) spacers of thickness ranging from 5 micrometers to 6.6 cm. The finesse of these HFP samples was sufficiently high (approximately equals 30) and limited only by the absorption of the presently available holographic materials.

Using the modal theory of perfectly conducting and finite conductivity lamellar gratings adapted to stratified media encountered in photolithographic transfer set-ups, we investigate a mounting patented 15 years ago and designed to obtain a faithful reproduction of a masks pierced with periodically distributed slits. We make a systematic study of the influence of the various parameters (incidence, mark-space ratio, groove spacing, groove depth, polarization, conductivity of the metal) on the field map below the mask. We discover a large tolerance over the parameters around the values stated in the patent. The result is that the set-up described in the patent can be used for duplicating non-periodic masks (e. g. linear Fresnel zone plates) as well as chirped gratings or gratings with non rectilinear grooves. Experiments have confirmed that predictions. Keywords: Grating mask transfer; Photolithography.

Waveguide output couplers fabricated in Norlund Optical Adhesive (NOA) #81 are investigated. The output coupler is implemented using periodic relief gratings on a planar waveguide. Design theory of the coupler is based ont he perturbation approach. Coupling of light from waveguide propagation modes to output radiation modes is described by coupled mode theory and the transmission line approximation of the perturbed area (grating structure). Using these concepts, gratings can be accurately designed to output a minimum number of modes at desired output angles. Waveguide couplers were designed using these concepts. The couplers were fabricated and analyzed for structural accuracy, output beam accuracy, and output efficiency. Applications for these couplers include databus and clock distribution system interfaces requiring coupling to out-of- plane detectors.

We present two types of polarizing holographic optical elements recorded in Du Pont's Omnidex film (reflection holograms). The first one takes benefit of the dry development process in order to respect the grating geometry associated with polarization properties. Thanks to that, we realized polarizing beam splitter with high diffraction efficiency and high polarization ratio. The second type of polarizer is an original polarizing mirror that is based on the polarization dependency of spectral and angular selectivities. The high index modulation of that polymer allows to record new holographic polarizers. Details about theoretical basis and experimental realization are given.

A novel integrated optical pressure sensor based on a distributed Bragg reflector structure was designed and simulated. The wavelength-selective device consists of AJ4 shifted distributed Bragg reflectors defined into the glass rib waveguide and a thin diaphragm anisotropically etched into the silicon substrate beneath the region between the reflectors. Pressure sensing is achieved through the detection of the light intensity change induced by the diaphragm deflection. The multilayered diaphragm structure was simulated by using an improved model and the finite-difference method. The effective index method was utilized for designing the rib waveguide. Numerical results revealed that a 1440 .tm long device presents 19.5 dB of extinction ratio with an insertion loss of 3.6 dB for TM polarization and an applied pressure difference of 1 .8 atm. Tenfold length reduction is achieved with the proposed device in relation to the interferometric sensors. The device can also be operated in tandem which is suitable for applications in wavelength division multiplexing sensor networks. Keywords: integrated optical sensors, distributed Bragg reflector, pressure sensors, silicon based sensors.

Interferometric etalons are of interest as wavemeters in the visible and the near IR to measure Doppler shifts from laser illuminated moving objects. Signal processing for estimating Doppler shifts is discussed in the context of three etalon-based methods of practical interest: the scanning Fabry-Perot interferometer, the 'edge' method, and the Fizeau interferometer. The semiclassical theory of photodetection is used to model the statistical properties of signal and background noise. Using the probability density functions that tend to govern the signal- and background-induced photocounts, we derive: the theoretical performance limit on unbiased estimators of the signal frequency (Cramer-Rao bound), as well as the maximum likelihood estimators, whose performance may approach this limit. Performance of the estimators is analyzed as a function of signal and background levels for the photocounts statistics. The paper provides a framework for the further development of signal processing theory for etalon wavemeters that operate in the low-light limit of the so-called photocounting regime.

In some white-light imaging applications it is desirable to make the optical elements extremely thin. Numerous practical advantages are derived if the lenses are one to two orders of magnitude thinner than conventional refractive lenses. For example, these lens systems provide minimal weight and compactness, and are potentially low cost. Although diffractive lenses are only a few microns thick, they have severe chromatic aberrations. Approaches are compared for making the lenses thinner and techniques are examined for correcting chromatic aberrations. There are basic limits to the polychromatic MTF and chromatic correction that can be achieved.

We developed an analytic framework to asses the performance of wind velocity measurements with the edge technique using a pulsed lidar. This technique is insensitive to frequency jitter and shifts of both laser and filter. This paper analyzes the applicability of the edge technique for a pulsed lidar. We show the velocity estimation with the edge technique is, in general, biased and that the bias depends on signal fading statistics, energy/pulse, and the number of pulses used for estimation. Two practical signal processing algorithms are considered for the wind velocity estimation. Analysis of their performance includes the trade-off between the number of pulses and energy/pulse. The effect of partial coherence of laser radiation is bounded by considering two limiting cases: (1) signal fading and its coherence can be neglected; and (2) signal fading is very strong and the effects of coherence degrade the lidar performance.

Computer-based analysis of fringe patterns in optical surface profilometry has become popular on account of the savings of time, increased ease of use, reduced operator error and increased range of analysis techniques available to the user. However,t he utility of fringe analysis software tools is often limited by their rigid demand for specific hardware or operating system components. This paper describes a range of portable computer-based tools for the processing of fringe patterns characterized by an underlying periodicity. The toolbox comprises a set of platform-independent Matlab 'm' files which may be used with the very popular Matlab engine installed under all standard operation systems. Image-acquisition hardware, a computer, the Matlab engine with its Image Processing Toolbox and the Fringe Pattern Analysis Toolbox described here can be used to implement flexible, adaptable fringe pattern analysis. The user-interface, processing, visualization, display and data storage tools may be modified or enhanced with ease and moved seemlessly between computer platforms.

A simple and intuitive formalism is presented to describe diffraction in multi-layered periodic structures. We use the well known results from scalar analysis (wave propagation in homogeneous layered media) and show that they can be generalized rather readily to vector problems such as diffraction analysis. Specifically, we derive: (1) generalized Fresnel equations appropriate for reflection and transmission from an infinitely thick grating, (2) a generalized Airy formula for thin-film to describe reflection and transmission of light through a lamellar grating and (3) a matrix propagation method akin that used for multi-layer thin film analysis. The results developed here complement the recent work on R- matrix propagation methods. The R-matrix technique is a modal method that has shown to be a numerically stable for calculating diffraction efficiencies from deep groove gratings. The formalism developed here, while equivalent to the R-matrix technique, is not identical and offers a number of advantages. We will discuss these and other related matters in this paper.

High Channel density broadband wavelength division multiplexers (WDMs) based on periodic grating structures are discussed. These so-called single-window WDMs transmit a large number (> 100) of independent wavelength channels through a single fiber and within a single fiber communications window in both singlemode and multimode fiber cases. In this paper, single-grating WDMs are analyzed in the context of the fundamental relation between channel density, crosstalk, power budget, and diffraction limited beam propagation. Also, the practical aspects of WDM-based fiber optic networks for high-speed (broadband) multimedia communication are discussed.

Review of dynamic or real time holography is given with emphasis on applications. Comparison of different materials for holographic recording (photorefractive crystals, photoconductive polymers, liquid- crystals, semiconductor) will be given.

A light-induced grating aperture (LIGA) is a semiconductor plate containing a periodic structure formed of nonequilibrium light-induced electron-hole plasma. The presence of excess charge carriers in a semiconductor medium locally changes the dielectric constant of the material. Such a light-induced periodic structure can serve as a diffraction grating for millimeter waves (MMW), and generates diffracted beams propagating in directions distinct from that of the incident beam. The angle between the incident and diffracted beams depends on the period (Lambda) of the light-induced grating, a parameter that can be controlled using a liquid crystal display (LCD). The effect is strong enough not only for academic study but for practical application as well. The authors fabricated a new scanning MMW antenna in which MMW is diffracted by a LIGA.

Transient grating reflection in non-instantaneous-response polymer media is analyzed. It is predicted that nanosecond-scale nonlinear polymers will exhibit strong grating reflection due to the phase lag between grating formation and coupled-beam propagation.

Electro-optical switching of the diffraction efficiency in volume holographic gratings offers the possibility of real-time control and programmability of diffractive optic components. We have recently demonstrated efficient electro-optical control of the diffraction efficiency in gratings consisting of periodic polymer-dispersed liquid crystal (PDLC) planes. We analyze this system as a rectangular index modulation profile, with the low index region being pure polymer, and the high index region consisting of a distribution of ellipsoidal nematic liquid crystal droplets of sub-micrometer size. The results of coupled-wave theory are combined with an analysis of the electro- mechanical behavior of these droplets to model the field-dependent diffraction efficiency. The effects of system parameters on diffraction switching is explored, and a physical interpretation of the switching phenomena in PDLC gratings is elucidated. Insights to the design of practical switchable diffractive optical elements can be obtained from the model.

We suggest to use Lorentz force in crossed electric and magnetic fields for fast shifting of electron-hole gratings, induced by two interfering beams in semiconductors. Energy switching between coupling beams and possibility of electrical switching is described.

It was demonstrated experimentally, that recording of photorefraction gratings BaTiO₃ crystals can be realized with nonoverlapping in time 80 ps pulses of Nd:YAG laser ((lambda) equals 532 nm). This phenomenon of dynamic memory is explained by asymmetry of writing-reading mechanisms with simultaneous phase-conjugation.

The paper is concerned with second harmonic generation in optical resonators like prism or grating couplers when the depletion of the pump field is strong enough so that is can no longer be neglected. This means that we have to take into account the feedback between the signal field at 2(omega) circular frequency and the pump field at (omega) . Two different approaches are developed. The first one is a rigorous electromagnetic analysis based on the numerical integration of nonlinear Maxwell equations at both (omega) and 2(omega) frequencies, incorporated in a root-finding procedure to take the depletion into account. The second is based on a couple mode analysis which leads to a set of coupled mode equations governing the amplitudes of the pump and second harmonic frequency fields. These methods allow to predict that second- harmonic generation in prism or grating couplers can lead to optical bistability. Contrary to the Kerr-like bistability, this new type of bistability occurs not only at one side of the resonance maximum but on both sides provided the absolute value of the offset in the incident angle is above a threshold. The two approaches give numerical results in very good agreement. The coupled mode theory provides analytical predictions of the threshold value and brings physical insight on this new effect.

When an incident plane wave with circular frequency (omega) falls on a grating coated by a layer of nonlinear material, it generates a nonlinear polarization P^NL(2(omega) ) which acts as a source term and produces a second harmonic (SH) field called signal. The excitation of an electromagnetic resonance like surface plasmon or a guided wave increases the local field and thus the signal. The problem is to be able to compute and optimize the latter. We have developed a new theory which uses a coordinate transformation mapping the grating profile onto a plane. This simplifies the boundary conditions but complicates the propagation equation. Taking advantage of the psuedoperiodicity of the problem, the Fourier harmonics of the field are solution of a set of first order differential equations with constant coefficients. The resolution of this system via eigenvalue and eigenvector technique avoid numerical instabilities and lead to accurate results which agree perfectly with those found via the Rayleigh method or by the Differential method, when they work. A phenomenological approach is then developed to explain the unusual shape of the resonance lines at 2(omega) , which is based on the poles and zeros of the scattering operator S at (omega) and 2(omega) . It is shown that S(2(omega) ) presents 3 complex poles with 3 associated complex zeros. Their knowledge, plus the nonlinear reflectivity of the plane device allows predicting all the possible shapes of the 2(omega) signal as a function of angle of incidence. The phenomenological study explains an experimental result, found a few years ago, that if 2(omega) lies inside the absorption band of the guiding material instead of the transparent region, the enhanced second harmonic generation (SHG) is changed into a reduced one. It means that in the case phase matching can lead to a minimum instead of maximum. An algorithm is then proposed to maximize the signal intensity; with polyurethane as a guiding material a conversion factor of up to 40% is found when incident power is equal to 40 kW.

A critical analysis of grating behavior is presented over the entire spectrum, from millimeter waves to X rays. It concerns bare gratings used in resonance domain, VUV and XUV gratings used under near normal incidence, soft X-rays gratings used under grazing incidence, multilayer gratings and echelles for X rays, infrared and visible echelles, and transmission gratings. Polarization effects are pointed out and comparison between scalar theory and electromagnetic theory productions are done. It is shown that even under circumstances in which the wavelength-to-groove spacing ratio is less than 0.001, scalar theory can give erroneous predictions. The conclusion is that although scalar theory brings some physical insight and can be used as a starting point in optimizing a grating device, an accurate modelling should be made with the electromagnetic theory as a tool.

Propagation of subnanosecond pulses over Metal-Insulator-Semiconductor (MIS) microstrip line has been reported to suffer from serious time- delay (the Slow-wave effect) in the microwave/millimeter wave frequency range (200approximately equals 4000 MHz) and in the substrate resistivity range of 10^-3 approximately equals 10² (Omega) cm (such as in silicon or gallium arsenide). This is primarily due to a huge equivalent capacitance generated by the thin insulation layer. This paper investigates the feasibility of employing a periodically corrugated surface at the oxide- semiconductor interface, which provides guided mode conversion (TM-to- Hybrid mode), to decrease the equivalent inductance of the microstrip line and compensates for the increase in parasitic capacitance. The price paid for speed increase in signal propagation is signal attenuation. It is predicted that for wiring length less than 3 mm signal attenuation will be in a tolerable range (less than 10%).

By evaporating an infinitely thin layer of perfectly conducting metal on the small facet of the groove of a dielectric echelette grating then by superimposing an adequate inhomogeneous layer on top of the large facet, it is shown that a theoretical efficiency of 100% is obtained in a transmitted order. A numerical proof of this theoretical prediction is achieved using a computer code based on a rigorous finite-elements method. The curves of efficiency near the blazing effect show remarkable widths.

Surface-phonon polaritons on a 1D SiC grating are studied by directional absorptivity measurement at 10.6 micrometers and variable angle reflectometry between 8 and 14 micrometers . Using a volume integral approach, numerical simulations of the electromagnetic scattering problem are carried out. The calculated reflectance spectra are in good agreement with the experimental observations.

The Far Ultraviolet Spectroscopic Explorer (FUSE) mission from NASA will explore the 900-1200 angstrom wavelength range with unequaled effective area and spectral resolving power (R equals 30,000). The optical solution relies on the single concave grating mount, which is the soundest design to keep a high throughput in the far UV, yet FUSE requires both groove efficiency and correction of aberrations to be pushed to their limits. A holographically corrected ellipsoidal prototype grating corresponding to the FUSE Phase A has been studied at Laboratoire d'Astronomie Spatiale (LAS) and recorded by Jobin-Yvon company. First, we show the results of the efficiency measurements compared with theoretical values and we discuss potential improvements allowed by ion etching process. Second, we present a spectrum of the molecular hydrogen recorded with a bidimensional delay line detector, and show that the 30,000 resolving power is reached for the most challenging channel (910-1030 angstrom) of the experiment.

Design concepts pertaining to resonant width in grating resonant filters are discussed. It is shown that the application of waveguide coupler concepts provides insight into polarization and angular/wavelength width trends.

Vector tensor theory results have been applied to optimization of selfdiffraction phenomena in photorefractive crystals of symmetry 23. The giant diffraction efficiency of 77% in doped and radiate BTO crystal is observed. The signal to noise ratio was 600. Optimization algorithm for improving this ratio is proposed. These results are applied to small size sensors for some engineering applications.

Daylighting techniques are an effective means of reducing both lighting and cooling costs; however, many of the standard techniques have flaws which reduce their effectiveness. Daylighting holograms are an efficient and effective method for diffracting sunlight up onto the ceiling, deep in a room, without diffracting the light at eye-level. They need only cover the top half of a window to produce significant energy savings. They may be used as part of a new glazing system or as a retrofit to existing windows. These holograms are broadband and are able to passively track the movement of the sun across the sky, throughout the day and year.

Recently, at the University of Massachusetts Lowell, promising Thermophotovoltaic (TPV) experimental results have been produced utilizing an experimental system that incorporates holographic optical elements and tubular geometry thermal sources. The results and concepts presented in this paper bring to light a unique merging of combustion and solar energy sources. The holographic elements provide a mechanism for spectral splitting, as well as concentration, while the tubular thermal source provides a flexible TPV photon emitter geometry that is capable of utilizing various thermal sources. The work reported here details the experiments as well as the concepts that indicate that such a TPV system could readily produce electricity utilizing 'dual' thermal sources. A tubular photon source was located in the focus of parabolic assembly to 'collimate' the photons emitted by a lamp simulating a TPV photon emitter. The collimated photons were directed onto the holographic element and spectrally redirected as a function of the photon energy. Components of a system constructed in this geometry can be readily converted to produce a highly concentrating solar photovoltaic electrical power source.

Analysis is made of transient-grating reflection from a split- polarization device based on a Kerr medium with and without absorption. It is found that strong grating reflection, hence attenuation of high- intensity incident pulsed radiation, can occur when absorption is present.

The present paper deals with new results ont he development of a holographic nonspatial filter to be used for laser beam clean up. An analysis of thick holographic materials suitable for recording of such elements is carried out. The experimental setups for hologram recording and evaluation are described. The results on measurements of angular selectivity contour of such holographic filters are presented.

Radiation form waveguide gratings are found via a bounded approach. The grating is enclosed by a metallic box to sample the continuous radiation spectrum. Then physical optics and generalized transmission matrix is used for analysis of grating.

Optimization of resonant periodic gain structures relies on maximizing the overlap between the standing wave electric field and the gain medium at the peak gain wavelength. Traditional techniques which place the gain regions one-half wave apart do not account for reflections between gain and spacer regions. They result in a standing wave pattern in which the wavelength differs from the design wavelength and which is not uniform across the quantum wells. A simple theoretical model based on a perfectly resonant cavity will show how to correctly design resonant periodic gain devices to account for these effects. The model is subsequently generalized to facilitate multiple quantum well resonant periodic gain designs.

The discussion on binary subwavelength gratings has recently been increased due to its simple fabrication procedure and potential applications in a variety of optoelectronic fields. Most designs of binary subwavelength gratings have been confined in the way that the grating ridges and/or channels are chirped and the defined grating period does not change during the design process. For some applications (e.g. interconnections), however, a dynamic diffraction pattern may be more desirable. In these cases, the variation of the diffraction angle and/or multiple diffraction beam pattern may be required. Therefor the rearrangement of the grating ridges and/or channels becomes a necessary. The newly arranged profile of the grating ridges and/or channels may be total different from the original one and may need to be changed into another profile later. This paper proposes a design method which optimize the diffraction efficiency at a desired angle and/or optimize the diffraction efficiencies at a multiangle pattern by forming a dynamic 'subperiod' within the initial defined grating period. Some design examples have been provided to prove the design concept.

Conventional methods for detecting the release of foreign substances into the atmosphere are often slow, expensive, and only give an actual reading for a small section of the area of interest. The Environmental Interferometer can allow inexpensive, real time monitoring of a large area. The principle behind the Environmental Interferometer is the use of a fringe locked Michelson Interferometer scanning throughout a continuous range of colors at an intermediate bandwidth (50-100 nm). The fringe locking allows a the beam in a test arm to be reflected through a test area for about 1 kilometer of distance, while a reference arm is kept in a controlled environment (perhaps fiber optics or a multiple reflected air path) and retain a suitable interference pattern. The use of intermediate bandwidth light allows the central fringe to be located, and thus allows fast scanning through a continuous range of colors. Sampling at n different colors allows the discrimination of n different sources of optical pathlength change. This allows easy discrimination against moisture content change, air turbulence, ground vibrations, and the like, because of their characteristic pathlength change frequencies. The fringe locking allows for the electronic interpretation of a signal and enhances the accuracy of the instrumentation so that small optical pathlength changes can be easily measured and interpreted. A demonstration unit has been created using a 670 nm laser instead of a filtered white light source. Absolute index measurements of test gases injected into a 3 cm pollution chamber were made with the demonstration unit with errors of less than 1%. The fringe locker used in the demonstration unit was able to keep the fringe pattern stable during table oscillations, moderately fast introduction of test gases, and simulated air turbulence.

We describe a new concept for producing, on a single substrate, a 2D array of optical interference filters where the pass-band of each element can be independently specified. The interference filter is formed by optically contacting two dielectric mirrors so that the top quarter-wave films of the two mirrors form a Fabry-Perot cavity having a half-wave thickness. In the new device, we propose to etch an array of subwavelength patterns into the top surface of one of the mirrors before forming the cavity. The patterns must have a pitch shorter than the operational wavelength in order to eliminate diffraction. By changing the index of refraction of the half-wave layer, or the optical thickness of the cavity, the patterning is used to shift the pass-band and form an array of interference filters. One approach to producing the array is to change the fill factor of the pattern. Once the filter array is produced it may be mated to a 2D detector array to form a miniature spectrophotometer.

Application of rigorous integral method for computing the efficiency of arbitrary profile relief gratings used in all the optical spectral range is presented in this paper. The main progress of the method and the programs lays in numerical solution algorithm. In particular, an approximation of Green-function and its normal derivative is used providing a sufficient accuracy for common practice simultaneously with satisfactory computation time. There is a very important peculiarity of the algorithm, namely both distribution of points of collocation and choice of the number of terms in Green-function expansion are used. These characteristics are different for each special case: perfect conductivity, finite conductivity, transmission gratings and gratings for X-ray and XUV. Such programs can be used as a mathematical model to design and calculate complex multielement optical systems with diffraction gratings.

Nonlinear periodic structures in a broad aperture Fabry-Perot interferometer with Kerr nonlinear medium are investigated. We discuss spectrum of collective excitations and stability of the periodic structures. The new mechanism of the quasi-periodic structures forming- self- building- is demonstrated. The structures appear after finite amplitude disturbances, when initial homogeneous state is stable with respect to the small fluctuations.

The new concept of single-mode resonator for single-frequency distributed feedback (DFB) lasers is presented. This concept is based on embedded nonharmonic distributed Bragg structure with sinusoidally modulated coupling coefficient, which is a combination of two superimposed sinusoidal Bragg gratings of equal heights and slightly different periods. Resonant frequencies and corresponding threshold gains of such distributed resonator are calculated theoretically by using the coupled-mode theory. The designed resonator provides stable single-frequency oscillation and has lasing characteristics (frequencies and thresholds) very similar to those of well-known distributed resonator with quarter-wavelength shift. The developed concept of resonator with sinusoidally modulated coupling coefficient can be applied both to semiconductor laser diodes with incorporated Bragg relief grating and to DFB fiber lasers with refractive index grating. The important advantage of designed new single-mode Bragg structure, as compared to quarter-wavelength-shifted structure, is that it can be fabricated very easily on semiconductor surfaces and in photosensitive fibers by direct three-beam holographic writing.

We report the design and performance of an InGaAsP/InP multiquantum well tunable distributed Bragg reflector optical intensity modulator module for wavelength division multiplexing systems operation near 1.55 micrometers . The module is composed of three wavelength-selective electrorefraction type modulators in tandem. The device presents for 1.54 micrometers an extinction ratio of 18.3 dB at 3.0 V and an insertion loss of 4.0 dB with 3.0 V applied to the other two modulators. Optical tuning of 5 angstrom is obtained with the application of 3.0 V to the Bragg reflector sections. The modulation and tuning bandwidth of 30 and 14 GHz is predicted for a modulator length of 220 micrometers . The total module length is only 675 micrometers .

A precise and accurate technique for the characterization of periodic line/space gratings is presented. The technique, known as scatterometry, derives its sensitivity and robustness from the wealth of information present in diffracted optical radiation. Scatterometry is capable of determining width, height, and overall shape of sub-half micron lines as well as the thickness of underlying thin films. The characterization process consists of three elements: a diffraction measurement apparatus, a model built on calibration data, and a statistical analysis routine that uses the model to correlate empirical data to the unknown parameters of the structure. The measurement technique was evaluated on twenty five wafers fabricated with deliberate deviation in focus, exposure dose, and underlying thin film thickness. Each wafer consisted of developed photoresist lines on an antireflecting layer, placed on layers of polycrystalline silicon on gate oxide on a silicon substrate. Scatterometry was used to simultaneously determine the width and height of the nominal 0.25 micrometers and 0.35 micrometers photoresist lines, as well as the thickness of underlying layers. Comparison of results obtained using reference methods (ellipsometry and scanning electron microscopy) are included.

The aim of this paper is to inform practical people of what can be done to compute the efficiencies of finite conductivity gratings when the incident wave vector is not perpendicular to the grooves. We recall the principle of the method of fictitious sources, and give some numerical results as a way of illustration.

Computationally efficient and stable implementations of rigorous coupled-wave analysis for 1D and 2D surface-relief gratings are presented. The eigenvalue problem for a 1D grating in a conical mounting is reduced to two eigenvalue problems in the corresponding nonconical mounting. The matrix in the eigenvalue problem of 2D gratings is reduced in size by a factor of two. These simplifications reduce the computation time for the eigenvalue problem by 8 to 32 times compared to the original computation time. The required computer memory is also decreased thus complicated grating diffraction problems can be solved efficiently.