A rigorous modified integral method applicable for diffraction grating analysis working from x-ray -up to millimeter range is presented. The changes have been made both in theory, and in numerical realization. In theory special attention has been given to power balance criterion generalization for the case of absorbing gratings and to forms of Green's function representations. in comparison with the well known integral method formulated by Maystre, a lot of fundamental improvements have been made in the following numerical sections: the forms of representation of a groove profile, choice of points for calculation of unknown functions, integration method, choice of numbers of collocation points and Green's function expansion terms and their derivatives. For the first time stable convergence for all types of gratings and wavelengths, including those with very deep profiles, high conductivity, small wavelength-to-period ratios, and, especially, for TM polarization has been achieved and demonstrated. Examples of results are given for a wide range of transmission and reflection gratings and parameters of light. Diffraction efficiencies calculated with the help of the developed method of analysis are compared with published data and calculations performed by other researchers. All results have been obtained using ordinary PC and commercially available program PCGrateTM 2000X.

The deep research of all types of echelle gratings, working from low (8) up to very high (143 1) diffraction orders with use of the rigorous modified integral method of the analysis is presented. The modified integral approach allows one, with the help of the standard program (PCGrateTM 2000X) and a rather small PC, to simulate one ofthe most hard-to-converge diffraction efficiency problems, what the behaviour of echelle is. In comparison with detailed paper of B. Loewen et al. "Echelles: scalar, electromagnetic, and real-groove properties" the significant difference was found in calculation values for some examples in TM polarization. The difference between the compared theoretical data with the same refractive index for 3 1 6 gr/mm r-2 echelle at 632.8 nm in the 9 order and for TM polarization is up to 25% of absolute efficiency. The difference between calculated curve and measured data for the same grating and polarization at 441.6 nm in 12 and 13 orders is small (one-two percents) in opposite to the data of E. Loewen et al. , where the difference is many times more because of weak convergence of their method. The appreciable difference also exists for the medium and high orders. The presented results for the given refractive indices (basically, taken from the book E. Palik) have the best coincidence to experiment in all cases. Numerical research of two largest monolithic echelles, made on the project SOFIA also is included. The new record of rigorous calculations for r-1O EXES echelle, working in 143 1 order was achieved at 1 0.6 tm. Because of the very small a wavelength-to-period ratios (O.OO1) it is necessary to increase truncation parameter for such a case up to such value, that in result the matrices with the order about three thousands turn out.

In this paper, a new method is developed to precisely control the key parameters for fabricating high quality diffractive optical elements, such as laser intensity and laser writing speed for the case of direct laser writing on photoresists. In order to obtain an accurate profile, the relationship between the final diffractive optical element relief profile and the required laser intensity is first characterized. Secondly, the designed diffractive optical elements' profile is divided into a M-stepped surface-relief profile, where M is decided by the process parameters. The spacing between two adjacent patterns is critical as overlapping of two adjacent traces could lead to over exposure and over development of the patterns. Hence, precise optimization of the fabrication parameters of each step is vital to avoid a rough and inaccurate surface. The computer control system has been programmed to compute the corresponding laser intensity incremental step and the spacing of adjacent patterns and control of process for fabricating diffractive optical elements. The compensation due to the laser variation has also been considered in the program. An example of a fabricated diffractive optical element and their optical performance are also demonstrated. It is proven that the method can control the process well to fabricate arbitrary surface relief profiles.

Optical Doppler shifts may be detected directly by filtering and dispersing the return light. The direct detection method is far more relaxed optically, requiring only "photon bucket" collection optics. A narrowband interference filter and two etalons are enough to distribute the frequency shifted light into the radial pattern ofonly one free spectral range ofthe last etalon. This paper describes a novel system using three hoes to perform transmission, collection, filtering and redistribution of the imaged zonal signal light onto a linear string of detectors. The light collection optic is a large area scanning and focusing hoe made in DCG. This optic may also serves as the laser transmitting optic. Holographically recorded etalons of medium finesse are made to do final filtering of the return signal down to picometer bandwidths. Finally a 24-channel circle to point converter has been fabricated in DCG and also transferred to resist and subsequently etched into a fused silica substrate. Reactive ion etching (RIE) was attempted using a Faraday cage to form tilted fringes in the silica. An Ion mill was rebuilt to perform a similar task. All components worked well when made in DCG but problems with dry etching were not all resolved. Circle-to-point conversion has been used for collecting the output of an etalon where a suitable detector of equal area circular zones was not readily available. The output is converted to a line of points so that it may be read with a simple and readily available linear photon counting detector.

In this paper, we employ a wavelet-based electromagnetic optimization algorithm to enhance multilevel diffractive lens performance. As we show in this paper, the optimized performance and iteration time is very much a function of the initial lens profile. To demonstrate this we analyze various types of initial profiles ranging from scalar-based lenses to flat and random structures. Additionally, we characterize the performance of replicated multilevel lenses fabricated using a soft lithographic technique known as nanoimprint lithography ( NIL) . Experimentalresults are presented.

This paper investigates methods to launch high modes propagating along helix paths into a graded index fiber. These techniques may be particularly useful to avoid the central dip problem due to defects located in the center of the index profile of multimode fibers. Light was coupled into a graded index multimode fiber using the flat surface of side-polished or D-shaped fiber. The fibers were polished down to a few microns close to the core on a distance of about 3mm. The first method, active, is based on coupling the light from a D-shaped single mode fiber to a D-shaped graded index fiber. The two fibers are in contact through a film of index matching fluid and the coupling may be thought as the leakage from a fiber to a slab waveguide. The launching angle of the skew rays in the multimode fiber is controlled by the tilt between the fibers. Simulations using beam propagation method are presented. Analytical equations for the path of the skew rays in graded index fiber are also used for a parabolic index profile. The second method, passive, consists of etching a tilted grating on a side polished multimode fiber by means of focused-ion beam (FIB) technology. We discuss the fabrication of such a grating and the possibility of using FIB technology to etch diffractive elements on fused silica waveguides.

Photonic band gap structures and their applications have gained a great deal of interest in recent years, with the primary focus on designing structures that have specific optical characteristics. However, little attention has been given to solving the inverse problem of determining the optimum photonic lattice given a desired output. In this paper, we address this need using optimization techniques to design two-dimensional photonic crystals to arbitrarily guide light in two dimensions. By switching the rods of this lattice on and off (rod or no rod), the optimization algorithm arrives at a solution (distribution of the rod in this lattice) that minimizes the cost function. The performance of the optimization is driven by the proper selection of both the cost function and optimization algorithm.

Guided mode resonant filters (GMRFs) are potentially useful as wavelength selective devices for DWDM telecom and sensor applications. These elements consist ofa high frequency grating deposited on an optical waveguide. In this presentation we investigate several approaches to modeling the characteristics of finite aperture GMRFs. Experimental GMRFs were fabricated with photoresist gratings with different grating characteristics and apertures were deposited on planar waveguides with specific refractive indices and thickness in sol-gel materials. Good agreement between our model prediction and experimental data for the reflection efficiency and spectral bandwidth were found. Limiting the aperture of GMRF below a few millimeters reduces the diffraction efficiency and increases the spectral bandwidth.

Digilens is developing a new class of optical components based on the combination of Electrically Switchable Bragg Grating (ESBG) and waveguide technology. One or more optical waveguides are formed on a substrate which is used as one wall of a cell filled with an ESBG. The ESBG layer forms part of the waveguide cladding, such that the grating can interact with the evanescent field of the light energy traveling in the waveguide. This device architecture has been used to make Electrical Variable Optical Attenuators with more than 50 db of controllable range, flat attenuation over the optical communications C band, fast (<100 msecond) switching speed, and encouragingly low polarization dependent loss. Initial results on a variable wavelength-selective filter are also reported.

Colossal Storage Inc. has patents on new ways of non - contact reading and writing with non destructive reading of information to a ferroelectric molecule. These methods will be used to develop the worlds first 2 D / 3 D Area / Volume Holographic mass storage device. U.S. Patents, # 6,028,835 2/00 and # 6,046,973 4/00 for an integrated read/write head for ferroelectric optical media.

This paper demonstrates a MEMS (microelectromechanical systems) technology for the fabrication of a high-speed, phase-only spatial light modulator (SLM). An independently developed low temperature MEMS process for the vertical integration of MEMS directly onto VLSI substrates is presented. The low temperature process enables the use of standard VLSI wafers integrated with MEMS at the post-process level. A MEMS structure has been demonstrated that produces polarization-independent pixel-wise pure-piston phase delay with optically flat micromirrors fabricated on a mock VLSI substrate as a proof-of-concept device. The gray-scale phase modulation offers -pi to +pi dynamic range in the ultraviolet to near infrared spectrum without mechanical contact. Pixel sizes as small as 40 microns with 86% fill-factor have been demonstrated. In addition to high fill-factor, micromirror reflectivity exceeding 95% that significantly minimizes optical insertion loss and enables high power operation has also been confirmed with this novel process. Furthermore, single-pixel operating speeds in excess of 100 kHz have been verified. The high operating speeds enable electrically addressed framing rates that are limited by the electronic interface bandwidth as opposed to the optical modulating element. We are presently fabricating a monolithically integrated phase-only modulator on CMOS VLSI creating a compact, lightweight, low-cost SLM. The resulting 256x256, 4 kHz framing rate, gray-scale phase-only SLM has applications including adaptive optics, high-speed optical correlators, phased array beam steering and diffractive beam forming.

Optical Phased Array technology promises to reduce the size, weight, and power consumption of optical pointing and steering systems by replacing complex mechanically gimballed mirrors with small, lightweight, nonmechanical devices. This paper develops and describes several diagnostic techniques that can be used to evaluate the performance of Optical Phased Arrays (OPAs) and demonstrates their use by applying them to the evaluation of a commercially available liquid crystal device. Finally, the operation of this device is demonstrated by integrating it into a steered imaging system.

We propose a generalized method for analyzing the polarization modulation of different types of liquid-crystal spatial light modulators. In our method, we use a Jones matrix representation for the polarization state of the modulated light. Contrary to previous investigations we are not restricted to a particular orientation of the fast axis of the spatial light modulator giving us a unique possibility for a complete polarization performance analysis. We show a method for spatially encoding the state of polarization in a two-dimensional wavefront with elliptically polarized light, controlling both the ellipticity and rotation angle of the major axes of the ellipse. We have constructed a demonstration system using two optically addressable phase-only spatial light modulators, where it is possible to control the relative phase of each modulation cell in the spatial light modulator. This gives a full two-dimensional control over the state of polarization and results are presented for the generation of arbitrary elliptically polarized two-dimensional wavefronts. The experimental performance of the system has been analyzed and found to be in good agreement with the theoretical analysis.

Liquid crystal displays, operating in a linearized phase mode, can achieve a performance to be applicable as diffractive elements. We built up a Fourier-system with a Sony-LCD based spatial light modulator in order to realize dynamic diffraction patterns. The quality measures of our DOE in the output plane of the system are promising for a wide range of applications. The performance oftechnical beam splitters, realized as binary or 8-256 level diffractive elements will be discussed in the paper. Here we will focus on parameters as diffraction efficiency, signal to noise ratio and also speckle effects. Since the display is addressed directly from the graphics card series of diffraction patterns and animations can be realized. Furthermore, beam shaping elements, two-dimensional holograms and the reconstruction of digital holograms will be shown. The latter opens new possibilities for non-destructive testing devices especially in the field of holographic interferometry. The limiting parameters of the performance are mostly due to physical boundary conditions, such as pixel number and size, response time, transmission etc. . We can assume that the fast growing micro-structuring technology will serve us soon with displays of higher resolutions and efficiency. A discussion concerning requirements for medial or micro-fabrication applications, particularly due to the limited efficiency and the intensity-dependent modulation, will finish the paper.

In this paper, the dependences of both multiplexing selectivity and diffraction efficiency in the holographic data storage on the speckle size are derived respectively. Based on these dependences, a new characteristic parameter of speckle holographic storage is defined as the optimization criterion. Then the speckle size is optimized to compromise its influence on the multiplexing selectivity and the diffraction efficiency. The simulated calculation results show that the speckle size should be neither too big nor too small in order to get the best performance of the high-density volume holographic storage with speckle reference beam. In addition, the intensity ratio between the signal beam and the illumination beam that is used to produce speckle reference beam also influences the optimization.

The concept of nondiffracting beams was first introduced by Durnin. The beam spot of nondiffracting beam undergoes diffraction-free spreading over a long propagating distance. Therefore, nondiffracting beams could have potential applications in precision alignment, optical interconnections, and power transport. In this paper, hybrid genetic algorithms that combine genetic algorithms (GAs) with traditional gradient-based local search techniques are proposed for the optimization design of diffractive optical elements (DOE's) for the generation of nondiffracting beams. In the hybrid genetic algorithms, an offspring obtained by genetic operators, such as crossover and mutation, is not included in the next generation directly but used as a seed for the sequent local search. The local search method searches the neighborhood of each offspring, and selects a better point, which is included in the next generation. In such a manner, the efficient exploitation of local information is provided by the incorporated local search procedure and the reliable locating of the global minimum is provided by the use of mechanisms of nature selection. The proposed hybrid methods exploit the global nature of the GAs as well as the local improvement capabilities of the gradient-based local search techniques, and will perform a more improved search while comparing with both of the single ones. The incorporated local search technique we used here is the Davidon-Fletcher-Powell (DFP) method, which is well known for its good convergence property. Numerical results demonstrate that the designed DOE's can successfully produce both zero-order and high-order nondiffracting beams.

We developed a novel design technique for multi-fanout surface-relief diffractive optical elements (DOEs) with high diffraction efficiencies. This technique also has the possibility for controlling both the directions and power ratio for output beams. It easily provides us phase distributions of DOEs, because iterative calculation procedures are not used. The design concept includes combining with blazed gratings to a crossed grating. Each blazed grating has its own phase distribution to achieve its diffraction efficiency high. The multi-fanout DOEs are accomplished by overlapping the blazed gratings. This design technique provides DOEs with high diffraction efficiency of more than 82 % by computer simulations based on the Fresnel-Kirchhoff diffraction. The diffraction efficiency has its minimum value when the output-beam power ratio is even. We fabricated two fan-outs DOEs with 1:16 output-beam power ratio designed by this technique. The measured diffraction efficiency is well agreed with the simulation result of 88 %. This technique may be suitable for designing large-core beam-couplers with unequal output-beam power ratio.