and add the following into the Abstract text field: This PDF file contains the front matter associated with SPIE Proceedings Volume 6994, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.

The numerical simulation of linear, lossless, paraxial, quadratic phase systems using the linear canonical transform (LCT) presents significant challenges due to the high sampling rate associated with the chirp function in the kernel. However, such simulations are significant for the design and analysis of optical systems and other signal processing purposes. Furthermore, such systems can be optically implemented using only lenses and free space. In this paper, we implement a recently proposed technique for calculating the discrete LCT. We review the existing literature on sampling the linear canonical transform. We apply a space-spatial frequency representation of the signal, the Wigner-Ville distribution function (WDF), and the space bandwidth product (SBP) of the signal (or system) to identify suitable sampling rates for simulation. We apply this method to simulate the effect on a 1D rectangular waveform of the fractional Fourier transform (FRT). The numerical results are compared with analytical expressions for the same system.

We propose an electro-optic time-lens (EOTL) model based on the coupled-mode theory. The model describes the propagation of a femtosecond pulse in an electro-optical crystal with parabolic refractive index modulation by a microwave. The proposed model integrates the second order dispersion approximation (β₂ ≠ 0) and takes into consideration the possible mismatch between the microwave phase velocity and the pulse group velocity. The coupled-mode theory uses the Hermite-Gaussian functions which are the modes of an ideal electro-optic time-lens. The model characterizes completely the performances of EOTL, including the aberrations, and it establishes the maximum velocity mismatch for which the pulse profile propagates through the crystal without significant distortion. The theoretical model is numerically implement considering the propagation of a short pulse in a Litium Niobate time-lens.

In succession of a benchmark study for the modeling of micro-optical components in the Network of Excellence on Micro-Optics (NEMO) we define a novel systematic approach for the evaluation of modeling results and the combination of different modeling approaches and modeling expertise. The method is applied for an optical bridge system, comprising both refractive and diffractive optical components. We work with different intermediate planes at which the field distributions obtained with different simulation tools are rigorously compared. Therefore all participating partners have programmed the necessary tools that allow the exchange of obtained field distributions. First evaluation results are discussed in detail.

Panoramic and hemispheric lens technologies represent new and exciting opportunities in both imaging and projection systems. Such lenses offer intriguing applications for the transportation/automotive industry, in the protection of civilian and military areas, business. In this paper we describe a new optical design technique that provides a greater degree of freedom in producing a variety of hemispheric spatial light distribution areas. This innovative optical design strategy, of generating and controlling image mapping, has been successful in producing high-resolution imaging and projection systems. This success has subsequently generated increased interest in the high-resolution camera/projector and the concept of absolute measurement with high-resolution wide-angle lenses. The new technique described in this paper uses optimization techniques to improve the performance of a customized wide-angle lens optical system for a specific application. By adding a custom angle-to-pixel ratio at the optical design stage, this customized optical system provides ideal image coverage while reducing and optimizing signal processing. This novel image formation technique requires the development of new algorithms in order to view the panoramic image on a display without any residual distortion.

A quite simple numerical model for the wave-optical simulation of the interference in a grating lateral shearing interferometer with a periodic light source and a large lateral shear is presented. Aberrations of the collimating lens will generate a spatially varying modulation in the interference pattern. The model assumes that the light source itself is completely spatially incoherent so that only the light from each point of the light source has to be propagated wave-optically through the optical system. Then, the intensity distributions of all light source points in the detector plane can just be added. The simulations are compared to theoretical calculations of partial coherence theory and also to experimental results.

Photopolymer materials are practical materials for use as holographic recording media, as they are inexpensive and self processing. By understanding the mechanisms present during recording in these materials their limitations for certain processes can be improved and a more efficient, environmentally stable material can be produced. In order to achieve this, it is necessary to develop material electromagnetic theory, which models these applications. In order to deal with electromagnetic diffraction by the resulting non-uniform slanted grating structures we develop first order analytic expressions governing the replay of such gratings.

Self-trapping of optical beams in photorefractive (PR) materials at telecommunications wavelengths has been studied at steady state in insulators such as SBN [1] and in semiconductor InP:Fe [2], CdTe [3]. PR self-focusing and soliton interactions in semiconductors find interesting applications in optical communications such as optical routing and interconnections because of several advantages over insulators: their sensitivity to near-infrared wavelengths and shorter response time. Photorefractive self focusing in InP:Fe is characterized as a function of beam intensity and temperature. Transient self focusing is found to occur on two time scales for input intensities of tens of W/cm² (one on the order of tens of μs, one on the order of milliseconds). A theory developed describes the photorefractive self focusing in InP:Fe and confirmed by steady state and transient regime measurements. PR associated phenomena (bending and self focusing) are taking place in InP:Fe as fast as a μs for intensities on the order of 10W/cm² at 1.06 μm. Currently we are conducting more experiments in order to estimate the self focusing response time at 1.55μm, to clarify the temporal dynamic of the self focusing and to build up a demonstrator of fast optical routing by photorefractive spatial solitons interactions.

This paper presents the design, construction and testing of grounded Frequency Selective Surface (FSS) array as millimeter wave beam splitter. The phase dependence on slot length of grounded FSS demonstrates that the reflection phase of coherent mm-wave can be altered by using FSS array with different slot lengths. A beam splitter was designed with slot FSS array where the slot length is the main design parameter used to optimize the phase properties of the array. We simulated the FSSs with commercial CST Microwave studio software, fabricated them with etching technique and characterized with a free space MVNA and BWO with motorized detector setup.

We outline some general properties of the conerefracted (CR) beam - a beam passed along an optic axis of biaxial crystal. The intensity of the incident beam is assumed to have a propagation z-axis of cylindrical symmetry and a symmetry plane z = 0. The CR beam also has a symmetry plane Z = 0 and two kinds of axial symmetries with common Z-axis; besides, it possesses two focal planes Z = ±Z_F. The familiar light ring is best resolved at Z = 0. Some of the beam transformation rules can be "seen" as known from the geometrical or Gaussian optics. We present for the first time experiments with two consecutive crystal elements. In this case the exit beam splits in two CR beams and their parameterization is given by explicit formulas. The experimentally deduced rules are simple but not trivial.

Optical spectroscopy based on the use of fluorescent contrast agents has become an interesting tool to detect and localize diseased tissues from healthy structures in a harmless way. Herein, we present a numerical model based on the finite element method that allows to simulate time-resolved reflectance signals from a realistic compartmented two-dimensional model of a breast bearing a small-sized fluorescent inclusion. Results show that the depth location of the inclusion can be well inferred from the observation of the time to reach the half maximum intensity of the reflected signals. Improvements may be obtained if depth localization is provided by a dimensionless indicator based on a twoway reflectance determination.

In the framework of the depth detection of tumor using the diffusion equation, a finite element method is proposed in order to solve the time-dependent light propagation in highly scattering media. A tumor-like object is positioned in the media. The finite element method tacks into account Robin type air-tissue boundary conditions. This study is devoted to the depth localization of a tumor enclosed into a breast tissue-like slab. Cartesian coordinates are used in order to solve the time-dependent diffusion approximation. A short laser pulse of 1ps is considered. The transillumination technique is able to laterally detect the objects when the source and detector are moved together on the same axis. In order to perform the depth localization of the inclusion, we were interested in a non-coaxial transillumination technique conjugated to interesting contrast functions based on the mean time of flight of photons. These functions allow to localize axially the inclusion using the high scattering processes. Thus, we performed first results of a depth indicator of a tumor. We now perform a parametric study. The optical properties of the slab are varying. Furthermore, different sizes of the objects are tested. Thus, the influence and the variation of these parameters on the depth indicator are shown. Our study demonstrates the possibility to deeply localize a tumor enclosed in a breast tissue using the high scattering processes induced by a tumor. To enhance the scattering processes, an interesting way is then to use recent nanoparticles allowing to modify the scattering coefficient.

We describe a theoretical analysis of broadband stimulated Brillouin scattering (SBS) slow light delay in a single-mode optical fiber. A flat-top broadband SBS gain spectrum can be constructed by use of two broadband pump beams. We propose two schemes of the double broadband pumping. We show that, for each scheme, the spectral profile of the total SBS gain becomes wide and symmetric when the appropriate architecture of the two broadband pump beams is adopted accordingly. Our schemes can effectively reduce or even eliminate the broadening of signal pulse. It provides the use of shorter signal pulses for slow light control.

This paper proposes a non-invasive optical scrambling technique to secure optical transmissions at high data rates (>10Gb/s). The proposed method belongs to the optical code-division multiple access (OCDMA) technique, using spectral phase encoding, based on overlapping of adjacent scrambled/spread pulses to encrypt transmitted data. In our system, data confidentiality is directly related to scrambled/spread pulse interference, avoiding direct detection by a power detector, in contrast to network access application (OCDMA), where this overlapping should be avoided. Our goal is to secure data transmission without impacting the physical layer, by guaranteeing the optical transparency of the encryption technique with respect to conventional transmission equipments. Therefore, we simulated the system penalty as a function of the transmission distance for a bit error rate (BER) target of 10-9 to estimate the impact of the linear and non-linear transmission effects on our encryption technique. We consider a point-to-point span for mono-channel and multi-channel setups where self-phase modulation (SPM) and cross-phase modulation (XPM) become significant. In the last section, we discuss the resilience of our encryption technique to some realistic attack scenarios. The eavesdropper can use the linear optical sampling (LOS) technique, which with coherence conditions on the waveform under test, permits to extract the amplitude and the phase of each spectral compound, enabling, to determinate the phase filter used to encrypt. Determining the necessary time to crack the mask allows us to establish the mask refreshment to guarantee data confidentiality.

One of the most successful experimental technique for determining nonlinear properties of optical materials is the Z-scan technique. Interaction between a high intensity beam with a Kerr medium gives rise to a lensing effect that implies focusing or defocusing of the beam which is transformed into transmittance variations of a diaphragm set in the far-field. In other words, one can consider Z-scan technique as a diagnostic of beam divergence variations and its ultimate sensitivity depends on the smallest transmittance change that can be measured. In this paper we propose a new technique allowing to multiply the sensitivity of the Z-scan technique by a factor greater than one hundred. The basic idea is to "amplify" the divergence variation, by a Diffractive Optical Element.

Liquid Crystal on Silicon (LCoS) displays can be very useful in numerous optical applications due to some technical features of these devices, like the large fill factor and resolution. Here, we have developed a study related to the performance of the LCoS displays. It has been demonstrated that the LCoS display produces certain amount of depolarized light and the Mueller-Stokes formalism has been required for a full polarimetric characterization. In a previous paper we obtained the experimental Mueller matrix of the LCoS display as a function of the addressed gray level, at the very small angle of 2 degrees between the incident beam and the LCoS display normal, and for the wavelength of 633 nm. In the present paper we extend this study to different angles of incidence in order to analyze the influence of this parameter on the performance of the LCoS display. We also analyze the influence of the angle of incidence on the degree of polarization of the reflected beam. A comparison between the obtained results is presented in this paper.

In this work we present a characterization of the phase shift chromatic dispersion introduced by a ferroelectric liquid crystal modulator. Maximum optical contrast is obtained when the proper design wavelength illuminates the device. In this situation the modulator acts as a perfect half-wave plate. However, for many applications the illuminating sources available are different from the design one and the optical contrast is reduced. In a previous work we proposed an optimization method to increase the optical contrast ratio by illuminating the device with an optimal elliptically polarized light. Here, we explore further the optimization of the ferroelectric modulator performance as an optical switching device for different monochromatic and polychromatic sources. For that purpose we use an achromatic quarter wave-plate placed in front of the modulator. For the optimal situations, the two output states of the modulator will be almost linear and orthogonal providing a highly contrasted modulated optical signal. Experimental results are obtained using a commercially available single pixel ferroelectric liquid crystal modulator from CRL-Opto, model LCS2N-G, with an active area of 25.5×25.5 mm².

Polytetrafluoroethylene (PTFE) is an ideal material for use in industrial, automotive and consumer electronics. Specifically, PTFE has outstanding physical properties; such as chemical inertness and resistance to chemical corrosion, even when exposed to a strong acid, alkali and oxidants. Its properties provide for superior electrical insulation and thermal stability, which is not affected by wide ranges in temperature and frequency. Its non-absorption of moisture makes it a perfect material for consideration in micro optical, retro-reflector or diffuser type devices used in optical sensor applications in harsh environments as well as in automotive, aerospace, industrial and home lighting. This paper presents an overview of a unique fabrication method that incorporates a variety of technologies to establish a processing technique that can form micro scale diffractive and retro-reflective structures into fused and semi-fused PTFE materials. Example structures and a single design will that was function tested will be presented with comparison metrology of the micro-structure geometry formed on the sample as compared to the original design mandrel geometry.

Photopolymer materials are practical materials for use as holographic recording media. In order to further develop such materials, a deeper understanding of the photochemical mechanisms present during the formation of holographic gratings in these materials has become ever more crucial. This is especially true of the photoinitiation process, which has already received much attention in the literature. Typically the absorption mechanism varies with exposure time. This has previously been investigated in association with several effects taking place during recording. Since holographic data storage requires multiple short exposures, it is necessary to verify the temporal change in photosensitizer concentration. Post exposure effects have also been discussed in the literature; however, they do not include post exposure effects such as the photosensitizer recovery. In this paper we report experimental results and theoretical analysis to examine the effects of the recovery and bleaching mechanisms which arise during exposure.

The one-dimensional diffusion equation, which governs the temporal evolution of holographic grating formation in photopolymers, which includes the non-local material response, the generalized dependence of the rate of polymerization on the absorbed illuminating intensity and the inclusion of our material's response to initiation and inhibition effects has been previously studied and presented. The resulting analytic expressions for the monomer and polymer concentrations have been derived and their validity tested against experimental data using a four-harmonic, numerical fitting regime. In this paper we examine the spatial frequency response of our photopolymer material and using our improved NPDD model we fit experimentally obtained data and extract estimates for material parameters. We attempt to improve our material's spatial frequency response with the addition of chain transfer agents to reduce the polymer chain length formed and the non-local chain-length variance. Achieving this should increase the locality of the polymer chains and hence cause an improvement in the spatial frequency response of the material. It is a material's response to high spatial frequencies, which determines a material's resolution and data storage density.

The first results on the use of the hot stamping technique for fabricating a diffraction grating on the end face of the polycrystalline IR fibers (PIR-fibers) were reported in before. This paper presents a continuation of the research in this direction. In particular, we look into the possibility of using the hot stamping technique for fabricating antireflection subwavelength structures on the end faces of the silver halide PIR-fibers.

We report on measurements of thermal expansion coefficients and temperature-dependent refractive indices of nanoparticle-polymer composite films in which plane-wave volume holograms are recorded. These physical constants are evaluated for photopolymer films with the incorporation of inorganic nanoparticles or binder polymer. We show that the incorporation of inorganic nanoparticles in photopolymer is a very effective method to suppress temperature-dependent film-thickness and refractive-index changes as well as to increase the refractive index modulation and reduce polymerization shrinkage.

Contact techniques exist to measure low amplitude low frequency mechanical vibration, however, by mechanically loading the system of interest, they affect the measured results. In this paper, we design a compact non-contact optical fiber speckle interferometer to measure inplane displacements. We implement this under laboratory conditions, and present our calibration results, measuring low-amplitude microvibrations from 0.34 nm to 1.5 μm over a frequency range from 10 Hz to 150 Hz.

When a digital hologram is reconstructed only points on objects within the depth of focus at the reconstruction distance are in focus. For complex scenes, scenes containing multiple objects or multiple object features located at different depths, this can lead to a reconstruction with large blurred regions. Using a depth-from-focus algorithm we have developed an approach to extract an objects depth information in the form of a depth map from volumes of reconstructions, where each reconstruction in the volume is a reconstruction at a different focal plane. By combining the depth map with the volume of reconstructions used to calculate the depth map we can create an image, an extended focus image, where the full scene is in focus. To our knowledge, this is the first technique which creates extended focused images of digital holograms encoding macroscopic objects. We present results for digital holograms containing low and high contrast macroscopic objects.

Devices for document security consisting of a thin metallic film the boundaries of which are undulated with a relief of a rainbow hologram, with the lower boundary facing to a lossless medium and the upper one facing (i) to a lossless medium with the same refractive index or (ii) to a thin dielectric film with a higher refractive index, are proposed. When viewed through in collimated and monochromatic light, they exhibit unique angular variation of appearance - a marked succession of dark and bright areas if the incident beam is polarized in the plane of recording of the hologram (the s-polarization). The devices are modelled as single-film and double-film structures that are composed either of a 30 nm thick silver film, which is sandwiched between two photoresist layers, or of a 30 nm thick silver film, which is deposited on a photoresist layer, and a 60 nm thick overlay film of titanium dioxide. Sensitivity to the polarization and the unique angular variation for the s-polarization follow from theoretical calculations, assuming a sinusoidal modulation of the surface relief, and they are demonstrated experimentally by capturing intensity distributions of light transmitted through realized samples in the zero diffraction order.

In the paraxial limit, optical systems can be well described as ABCD systems, which are linear, lossless systems and can be well modeled using the Linear Canonical Transform (LCT). In theory, their effects are perfectly reversible. In practice, finite component sizes mean that a system designer must be aware that a waveform passing through a practical implementation of such a system may lose information due to walk-off and apertures, and make allowances accordingly. Such limitations also place restrictions on the bandwidth of a waveform which may be propagated through a system. These considerations are also very important from the point of view of attempting to simulate such systems for design or analysis. We consider the parameters of a system which result in low loss due to this factor, demonstrating the parameters which result in lossless systems for particular types of signal. We offer mathematical proof that certain classes of two-parameter LCTs preserve bandwidth or compact support, or transform one into the other. We propose a matrix-based methodology for minimizing aperture effects in ABCD systems.

We have successfully demonstrated a holographic memory in a single LiNbO₃ crystal with two simultaneous but individual readout channels. A special scheduled exposure model is derived to obtain equal diffraction efficiency of each hologram in this memory. The simultaneous readout technique is achieved in a hybrid-multiplexed memory using angular multiplexing and the polarization multiplexing. Polarization multiplexing offers the mechanism of simultaneous readout for two individual orthogonally polarized images. In each angular position of the holographic memory, these two orthogonally polarized images can be reconstructed simultaneously and each of them can be viewed independently. After our proposed scheduled exposure, experimental result of diffraction efficiency in each hologram becomes equal and the result is consistent with our prediction.

We first study features of optical periodic lattices generated with mismatched cascade three-wave interaction in quadratically nonlinear media. We elaborate the theory of parametric waveguides arrays induced by two crossing pump waves together with exited sum wave. As the signal wave spreads due to the diffraction the induced lattice appears and its transverse dimension increases. Note the parametric periodic grating becomes apparent since launching any signal beam. It's likely to be the leading peculiarity of cascaded induced lattices. Parametric inhomogeneity depends on wave vector mismatch sign, and its modulation depth can be controlled by pump beam intensity. We observed a transformation from the discrete diffraction into the waveguiding of one or several signal beams with the increasing of pump intensity. The discrete diffraction dynamics dependence on pump intensity, spatial period, and signal beam tilting is analyzed when one or few central waveguides are exited at the input. At the certain incidence diffractionless propagation of signal beam takes place. The similar discrete diffraction effects in 2D cascaded lattices with various pump structure geometries have been studied. The additional degree of freedom gives novel properties to the effect of discrete diffraction.

This study explores the effectiveness of wavelet analysis techniques on digital holograms of real-world 3D objects. Stationary and discrete wavelet transform techniques have been applied for noise reduction and compared. Noise is a common problem in image analysis and successful reduction of noise without degradation of content is difficult to achieve. These wavelet transform denoising techniques are contrasted with traditional noise reduction techniques; mean filtering, median filtering, Fourier filtering. The different approaches are compared in terms of speckle reduction, edge preservation and resolution preservation.