The generalized source method is shown to give the exact solution to an unsolved electromagnetic problem from the complete solution to another solved problem even when the solution to the known problem is approximate. This is illustrated with the example of a binary grating where an exact solution exists.

The diffraction by periodic structures using a representation of the field in some functional basis leads to a set of ordinary differential equations, which can be solved by numerical integration. When the basic functions are the exponential harmonics (Fourier decomposition) one arrives at the well-known classical differential method. In the case of simple lamellar profiles, the numerical integration can be substituted by eigenvalue-eigenvector technique, known in the field of diffraction by periodic systems under the name of rigorous coupled-wave analysis or method of Moharam and gaylord. When the basis functions are searched as the rigorous solutions of the diffraction problem inside the lamellar grooves, the theory is known under the name of modal method. A comparative analysis of the three methods is made to reveal the convergence rate for an arbitrary shaped grating using the staircase approximation. It is shown that in TM polarization this approximation leads to sharp peaks of the electric field near the edges. A higher number of fourir harmonics is then required to describe the field, compared with the case of a smooth profile, and a poor convergence is observed. The classical differential method, which does not use the staircase approximation does not suffer from this problem.

We establish the most general differential equations satisfied by the Fourier components of the electromagnetic field diffracted by an arbitrary periodic anisotropic medium. The equations are derived using the recently published Fast Fourier Factorization (FFF) method, which ensures fast convergence of the Fourier series of the field. The diffraction by classical isotropic gratings arises as a particular case of the derived equations, while the case of anisotropic classical gratings has been published in a separate paper. The equations can be resolved either through the classical differential theory or through the modal method after staircase approximation of the groove profile. The new equations improve both methods in the same way. Crossed gratings, among which are grids and two- dimensional (2-D) arbitrary-shaped periodic surfaces, appear as particular cases of the theory, as well as three- dimensional photonic crystals. The method can be extended to non-periodic media through the use of Fourier transform.

FEM for electromagnetic simulation with absorbing boundary condition is applied to the design of polarizers, and the characteristics of metal sheet polarizers has been studied numerically. The dimensions of Au and Al metal sheet polarizers, which give enough performance as practical polarizers with much thinner structure than conventional polarizers, are presented. An Al metal sheet polarizer with comparable performance to Au metal sheet polarizer can be achieved by applying thinner Al metal sheets than the thickness of Au metal sheets. However, the performance given by Al metal sheet polarizer should be taken care, because the relative permittivity of Al film varies largely according to the film condition. Though Au and Al metal sheet polarizers exhibit high performance, the reflectance of TE polarization is higher than that of conventional polarizers. Therefore, the stray light should be paid attention more than conventional ones. The metal sheet polarizer exhibits enough high polarization performance for wide range of wavelength over 5 times as large as the distance between the metal sheets. The characteristics of metal fiber polarizers are also simulated. The metal fiber polarizers need much finer and thicker structure than metal sheet polarizers to exhibit enough performance.

Photonic crystals have been a subject of intensive study during the last years in view of their wide bandgap, which is almost independent of the incident angle and thus enables light confinement in one, two, or three dimensions. The present work discusses another much less known property of photonic crystals to diffract light like diffraction gratings, due to their periodicity. Several examples are given to illustrate the possibility of perfect blazing in unpolarized light, a property that is quite useful for light demultiplexing.

The availability of periodic surface-relief structures with grating constants from 200 nm to 100 microns on large areas leads to a wide field of applications. Effects of interest are the antireflection properties of high aspect ratio subwavelength gratings and the light management by structures in the micrometer scale. The size of the homogeneously structured area and the ease of producability is decisive for the commercialization of such functional surfaces. Microstructures like these can be produced on large areas by holographic exposure processes. Subsequent holographic exposures with differing parameters lead to combined structures with distinct properties. Master structures in photoresist can be used to fabricate nickel stampers. Techniques like UV roller casting and hot embossing can be employed to replicate such microstructures on large areas with high precision. With such replication processes a very cost effective mass production is possible. With our holographic set-up periodic surface relief structures with various grating types and profile shapes can be realized with a good homogeneity on an area with dimensions up to 600 x 800 mm². The combination of stochastic and periodic structures offers the chance to obtain a multifunctional surface with antiglare and broadband antireflection properties. The possible applications are solar energy systems, lighting or displays.

To deviate and focus of the beams of the future Laser Integration Line (LIL) and Megajoule laser (LMJ), CEA has chosen an original setup using two large 420 x 470 mm² transmission gratings. The first grating is an holographic plano transmission master grating with straight and equispaced ruling, 25 degree(s) incidence angle and working at 1.053 micrometers . The second one is an holographic plano transmission master grating, with curved and non equispaced ruling, 25 degree(s) incidence angle which combines both focusing and deviation properties. Groove profile of both gratings is deep laminar. High damage threshold, improved wavefront quality and high efficiencies are the main issues for those two gratings. Jobin Yvon's was selected by CEA in 1999 to develop, industrialize and manufacture gratings reaching LIL/LMJ specifications. A dedicated plant and facilities were built to manufacture the gratings directly engraved into the fused silica substrates provided by CEA. After process developments, Jobin Yvon manufactured the two first 1(omega) and 3(omega) gratings in mid 2001. After a short summary of the specification of these gratings, we present in this paper the production process and the performances of the 1(omega) and 3(omega) gratings manufactured. Wavefront data, efficiency measurements and damage threshold performances are detailed.

Many techniques have been described in the literature for generating spot arrays from a single input beam. When such a device is used for image replication (IR), the finite field of view unavoidably introduces optical aberrations that reduce the fidelity of the replicated images. Fourier array generators offer a low-cost and flexible method of image replication with lower optical aberrations than other methods and aberrations that are sufficiently low for replication of extended images. Using multicriteria optimization, two-dimensional Fourier array generator-based optical systems can be designed with high diffraction efficiency and near-diffraction-limited imaging performance across an extended field of view.

Recent experimental results clearly evidence that blazed-binary diffractive elements, a family of diffractive components composed of subwavelength binary features, offers unusual and attractive properties in the resonance domain. In this paper, we provide further insight into the field-angle behavior of these diffractive elements. We show that blazed-binary gratings operate efficiently under symmetrical mount and over a wide field-angle interval. This interesting feature makes blazed-binary diffractive elements attractive candidates for imaging systems.

An electromagnetic analysis of a two-dimensional metallic grating is used to explain the extraordinary optical transmission of a metallic film pierced by a two-dimensional subwavelength hole array, observed three years ago. The analysis is based on the Fourier-modal method extended to crossed gratings, which reduces the diffraction problem to the search of eigenvalues and eigenvectors of a particular matrix. The computation of the eigenvalues allows finding a new channel for light transmission through the subwavelength holes, which differs from the transmission channel in the one dimensional case (lamellar or rectangular-rod grating). It is demonstrated that the enhanced transmission is due to the excitation of a surface plasmon on the lower metallic surface.

Surveys of the natural world reveal an extensive array of optical effects in a broad range of animal and insect species. While the aesthete may simply take delight in such phenomena, students of photonics have increasingly been prepared to look more closely; deriving understanding and inspiration from nature's optical ingenuity. By describing specific structural color examples in detail, within a general context of Lepidopteran microstructure classification, this review paper seeks to present an introduction to current work on butterfly photonics. Additionally, new but preliminary results and analysis are presented, that describe the structural color of a butterfly that exhibits a distinct 3D photonic crystal structure.

We describe a multilayered dielectric stack configuration designed specifically for use as a transmissive phase modulator for broadband optical signals. Applications for this device range from full aperture wavefront correction to nonmechanical beam steering arrays for free space optical communication links. Our implementation employs alternating GaAs and AlAs layers of varying thickness on a GaAs substrate to create a bandpass region of high average transmission in the near infrared. Within this transmission bandpass, the phase component of the complex transmission coefficient varies in a near-linear fashion with respect to wavelength. The transmission bandpass is designed to have a bandwidth of 21.0 nm (or 6.3THz frequency bandwidth) and to have an edge-to-edge relative phase change of greater than 4p radians. Modification of the stack materials' optical properties causes the transmission profile to shift spectrally, resulting in a phase modulation for specific bands of transmitted frequencies. Our broadband phase modulator imparts nearly a full-cycle of phase modulation with low loss and low group velocity dispersion. A sample comprising 91 alternating layers has been fabricated to exhibit the bandpass properties required for optical signal phase modulation. We experimentally characterize the sample using an interferometer and spectrometer to measure the spectral transmission and relative phase profiles and to assess the relative phase modulation in response to a variable angle of incidence. We compare the experimental data to computational predictions and discuss the results.

Pulse-width of ultrashort laser is a very important parameter for the wide applications of ultrashort pulse. Various methods have been proposed to measure pulse-width, such as second harmonic generation method, third harmonic generation method and frequency resolved optical gating method. Despite of the benefits they hold, they share a vital drawback: they all employ nonlinear effects of ultrashort pulse, which means that the input power must be large enough to generate nonlinear effect, and the central wavelength of the pulse must correspond to the sensitivity range of nonlinear crystal. In this paper we present a new method of measuring pulse-width based on the Talbot effect of ultrashort laser pulse. The ultrashort pulse can be treated as a series of waves of different wavelengths, so at certain Talbot distances, the diffraction of the ultrashort laser pulse reshapes the energy distribution. Thus it gives us the possibility to determine the pulse-width by means of the diffraction. Taking advantages of Talbot effect, the method has the features of large measuring wavelength range, accurate measurement and simple structure. As the basis of the method is diffraction rather than nonlinear effect, all the problems related to nonlinear effect are avoided, such as high incident power and wavelength requirement. Both single and multiple shot pulse are suitable for this method. Numerical analysis has shown that pulse-width from 1 to 100fs can be measured with error of less than 1fs, at wavelength of 800nm. As there is just one Talbot grating between the light source and the detector, we can make the conclusion that this very simple method of pulse-width measuring should be highly interesting for practical application.

The parametric Fourier Modal Method is extended to the case of lamellar gratings that are periodic in two directions. We provide numerical evidence that improved convergence rates can be obtained. As an example, we calculate the optical transmission of a gold grating and rather good agreement with Ebbessen's experimental data is observed.

A Fourier modal method for analyzing crossed anisotropic gratings is presented. No restriction is imposed on the permittivity tensor of the medium in the grating region. A skew Cartesian coordinate system with skew angles both in and out of the grating plane is used in the mathematical derivation, which gives the formulation a greater generality. However, the facets of the crossed gratings are required to be parallel to the skew coordinate surfaces. Correct Fourier factorization of Maxwell's equations is carried out with aid of two efficient operators that greatly simplify otherwise complicated notation. Numerical curves are presented to demonstrate the convergence of the method, and numerical values are tabulated to provide reference data.

This contribution concentrates on modeling of diffraction processes in optical diffraction gratings (ODG). First, the characterization of mechanism and diffraction processes is briefly presented, together with the regions with typical diffraction regimes. Different types of volume phase synchronism are then described, and their periodicity and characteristic properties are explained and physically interpreted. Different situations are analyzed and compared concerning ODG of different types (surface-relief, planar holographic, metallic), different refractive index/relief modulation profiles (binary, sinusoidal, triangular), various modulation strengths, and incident wave polarization influence. As rigorous modeling tools, both rigorous coupled wave analysis, and coordinate transformation methods are used, implemented and modified. Some new and interesting results concerning resonant and threshold effects in diffraction process are also presented.

An overview of results concerning diffraction by periodic structures under conditions of surface plasmon polaritons excitation is presented. The possibility of the detailed analytical investigation of the problem is based upon the restriction for the case of weak scattering. In spite of this restriction, it is shown that resonance may be strong. The simple analytical approach based upon the modified perturbation theory allows presenting results in explicit analytical form. We consider both the in-plane diffraction (i.e., the wavevector of the periodic structure is parallel to the plane of incidence) and diffraction in general geometry (conical mounting). The systematization of the resonances is presented for diffraction from the grating on the surface of high reflecting media. It is shown that the behavior of the complex amplitudes of all diffracted waves in the resonance vicinity possesses universality, namely, the results may be presented in a scaled form and thus are self-similar. The difference between various media consists in the resonance position and scaling factors. For the conical mounting, the dependence of the diffracted wave intensities, amplitudes and phases on the parameters of the incident wave and media properties are investigated. The theoretical results obtained show good agreement with the experimental data. The possibilities of new experiments based on the theoretical predictions and possible generalizations are discussed.

Integration of photonic crystals on standard SOI wafers used in microelectronics seems very attractive due to the large demand for optical and opto-electronic components in telecommunications. The 200nm thick silicon superficial layer which can be an interesting monomode waveguide for the wavelengths of interest presents important draw-backs and characterization of elementary blocks is not easy as reliable coupling of light in such thin films is still a challenge. We propose here a demonstrator made of an elementary photonic crystal and its associated grating couplers introduced for characterization purposes carried out in single step lithography process. Dimensions have been defined in order to realize an omnidirectional mirror in the 1.3-1.5micrometers range.

A more actual situation is studied on the effects of both inclined grating planes in Talbot interferometry illuminated by a plane wave. In the situation, the two grating planes are first rotated around their own axis parallel to the line direction, and then detector grating is rotated by an angle around the normal of the grating plane. Theoretical analyses indicate that the tilt-angle of the moire fringes is sensitive to the inclination. The results in this paper are also compared with those in one of our earlier works.

Photonic crystals have been a subject of intensive study during the last years in view of their wide bandgap, which is almost independent of the incident angle and thus enables light confinement in one, two, or three dimensions. The present work discusses another much less known property of photonic crystals to diffract light like diffraction gratings, due to their periodicity. Several examples are given to illustrate the possibility of perfect blazing in unpolarized light, a property that is quite useful for light demultiplexing.

Talbot array illuminator (TAIL) based on fractional Talbot effect is useful for illuminating very large array, the number of phase levels of TAIL is a very important factor for estimation of practical fabrication complexity and cost. Based on the symmetry of the phase distribution, we can obtain the maximum phase level number for a given fractional Talbot distance. But because of the redundant equal phase, the exact phase level number is still unpredictable for an arbitrary opening ratio (1/M) of the illumination array. In this paper, we'll show that there is a simple decomposing rule to predict the number of phase levels of two-dimensional Talbot array illuminator (2D-TAIL) with the opening ratios (1/M_x), (1/M_y) in two dimensions, respectively. In the condition that the output array is alternatively (pi) -phase-modulated, there are similar simple relations. These results are generally applicable and should be interesting for practical use. Based on the joint-Talbot effect, we realized a separable 2D-TAIL by using two crossly placed 1D-TAIL. The 1D-TAIL is fabricated with the usual binary-optics technique and the number of phase levels in this experiment can be well explained by our theoretical results.

Finite-difference time-domain technique of numerical modeling is applied to investigate scattering of plane linearly polarized monochromatic wave by sinc variations of dielectric surface relief. Results of modeling include 1) space distribution of scattered light, 2) dependence of field amplification on ratio of roughness amplitude to laser wavelength, and 3) dependence of field amplification on ratio of roughness period to laser wavelength. Obtained results show that for TE polarization a)transmitted signal is more sensitive to roughness parameters than reflected one, b) there is narrow resonance in dependence of amplitude of scattered field on laser wavelength and roughness period, c) dependence of amplitude of scattered field on roughness amplitude is described by parabolic function for small values of relief amplitude. Depending on relief amplitude and period, scattering by sine roughness can result in formation of inhomogeneous space field distribution consisting of periodic field maxima inside dielectric or formation of homogeneous distribution such that both transmitted and reflected signals are close to plane wave. We consider the following applications of obtained results: 1) possibility to develop a new technique for in-situ surface roughness characterization, 2) possible mechanisms of feedbacks during laser-induced formation of surface ripples, and 3) anti-reflection effect.

The out-of-plane losses experienced in conventional photonic crystals waveguides are an essential limitation for theirs future applications. This article presents a theoretical study of this losses for one-dimensional photonic crystals waveguides. Our numerical results are obtained using a new and powerful algorithm based on an extension of the rigorous coupled wave analysis. The origins of the losses are highlighted qualitatively in terms of effective medium theory and quantitatively in terms of mode mismatch. From these insights, a generic approach based on an adiabatic mode conversion is proposed and validated numerically for cavities with large quality factors and large peak transmissions.