Efficient hybrid method for the modal analysis of optical microcavities and nanoresonators

We propose a novel hybrid method for accurately and efficiently analyzing microcavities and nanoresonators. The method combines the marked spirit of quasinormal mode expansion approaches, e.g., analyticity and physical insight, with the renowned strengths of real-frequency simulations, e.g., accuracy and flexibility. Real- and complex-frequency simulations offer a complementarity between accuracy and computation speed, opening new perspectives for challenging inverse design of nanoresonators.

Nonuniqueness of the quasinormal mode expansion of electromagnetic Lorentz dispersive materials

Any optical structure possesses resonance modes, and its response to an excitation can be decomposed onto the quasinormal and numerical modes of a discretized Maxwell operator. In this paper, we consider a dielectric permittivity that is an N-pole Lorentz function of the frequency. Even for discretized operators, the literature proposes different formulas for the coefficients of the quasinormal-mode expansion, and this comes as a surprise. We propose a general formalism, based on auxiliary fields, which explains why and evidences that there is, in fact, an infinity of mathematically sound possible expansion coefficients. The nonuniqueness is due to a choice of the linearization of Maxwell's equations with respect to frequency and of the choice of the form of the source term. Numerical results validate the different formulas and compare their accuracy.

Quasinormal mode solvers for resonators with dispersive materials

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This raises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, with the perspective to elaborate standards for the computation of resonance modes.

[Prescription of furosemide in general medicine in Aquitaine: Prospective practice survey among universities general practitioners]

OBJECTIVES

Furosemide is essential in the management of patients with congestive heart failure, and provides important iatrogenic complications. We described the prescription of this treatment in general medicine, and tried to identify areas for optimizing its use.

PATIENTS AND METHOD

We carried out a prospective inventory of the prescription of furosemide with the general practitioners of the universities of Bordeaux, between May 1, 2017 and July 30, 2017.

RESULTS

We obtained data from 119 prescriptions of furosemide. The indications seemed well known, largely dominated by heart failure (67%) and its associated signs (24%). Clinical and biological follow-up (52%) and therapeutic education (42%) seemed relatively infrequent.

CONCLUSIONS

Our study confirms the central role of the general practitioner in the prescription of furosemide, the predominant place of heart failure in its indications and the iatrogeny observed. We identified areas of optimization of the safety and effectiveness of the treatment. The reinforcement of training concerning heart failure and its treatments, a better communication between specialties, the implementation of reference systems dedicated to the prescription of furosemide and prescription support software seem promising.

Photonic molecules: tailoring the coupling strength and sign

We demonstrate a large tuning of the coupling strength in Photonic Crystal molecules without changing the inter-cavity distance. The key element for the design is the "photonic barrier engineering", where the "potential barrier" is formed by the air-holes in between the two cavities. This consists in changing the hole radius of the central row in the barrier. As a result we show, both numerically and experimentally, that the wavelength splitting in two evanescently-coupled Photonic Crystal L3 cavities (three holes missing in the ΓK direction of the underlying triangular lattice) can be continuously controlled up to 5× the initial value upon ∼ 30% of hole-size modification in the barrier. Moreover, the sign of the splitting can be reversed in such a way that the fundamental mode can be either the symmetric or the anti-symmetric one without altering neither the cavity geometry nor the inter-cavity distance. Coupling sign inversion is explained in the framework of a Fabry-Perot model with underlying propagating Bloch modes in coupled W1 waveguides.

Anomalous light absorption around subwavelength apertures in metal films

In this Letter, we study the heat dissipated at metal surfaces by the electromagnetic field scattered by isolated subwavelength apertures in metal screens. In contrast to the common belief that the intensity of waves created by local sources should decrease with the distance from the sources, we reveal that the dissipated heat at the surface remains constant over a broad spatial interval. This behavior that occurs for noble metals at near infrared wavelengths is observed with nonintrusive thermoreflectance measurements and is explained with an analytical model, which underlines the intricate role played by quasicylindrical waves in the phenomenon. Additionally, we show that, by monitoring the phase of the quasicylindrical waves, the total heat dissipated at the metal surface can be rendered substantially smaller than the heat dissipated by the launched plasmon. This interesting property offers an alternative to amplification for overcoming the loss issue in miniaturized plasmonic devices.

Photonic crystal-based flat lens integrated on a Bragg mirror for high-Q external cavity low noise laser

We demonstrate a high reflectivity (> 99%), low-loss (< 0.1%) and aberrations-free (2% of λ rms phase fluctuations) concave Bragg mirror (20mm radius of curvature) integrating a photonic crystal with engineered spherical phase and amplitude transfer functions, based on a III-V semiconductors flat photonics technology. This mirror design is of high interest for highly coherent high power stable external cavity semiconductor lasers, exhibiting very low noise. We design the photonic crystal for operation in the pass band. The approach incorporates spatial, spectral (filter bandwidth= 5nm) and polarization filtering capabilities. Thanks to the mirror, a compact single mode TEM(00) 2mm-long air gap high finesse (cold cavity Q-factor 10(6) - 10(7)) stable laser cavity is demonstrated with a GaAs-based quantum-wells 1/2-VCSEL gain structure at 1μm. Excellent laser performances are obtained in single frequency operation: low threshold density of 2kW/cm(2) with high differential efficiency (21%). And high spatial, temporal and polarization coherence: TEM(00) beam close to diffraction limit, linear light polarization (> 60dB), Side Mode Suppression Ratio > 46dB, relative intensity noise at quantum limit (< -150dB) in 1MHz-84GHz radio frequency range, and a theoretical linewidth fundamental limit at 10 Hz (Q-factor ∼ 3.10(13)).

Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure

We present a semi-analytical formalism capable of handling the coupling of electromagnetic sources, such as point dipoles or free-propagating fields, with various kinds of dissipative resonances with radiation leakage, Ohmic losses or both. Due to its analyticity, the approach is very intuitive and physically-sound. It is also very economic in computational resources, since once the resonances of a plasmonic or photonic resonator are known, their excitation coefficients are obtained analytically, independently of the polarization, frequency or location of the excitation source. To evidence that the present formalism is very general and versatile, we implement it with the commercial software COMSOL, rather than with our in-house numerical tools.

Coupling light into a slow-light photonic-crystal waveguide from a free-space normally-incident beam

We present a coupler design allowing normally-incident light coupling from free-space into a monomode photonic crystal waveguide operating in the slow-light regime. Numerical three-dimensional calculations show that extraction efficiencies as high as 80% can be achieved for very large group indices up to 100. We demonstrate experimentally the device feasibility by coupling and extracting light from a photonic crystal waveguide over a large group-index range (from 10 to 60). The measurements are in good agreement with theoretical predictions. We also study numerically the impact of various geometrical parameters on the coupler performances.

Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators

We provide a self-consistent electromagnetic theory of the coupling between dipole emitters and dissipative nanoresonators. The theory that relies on the concept of quasinormal modes with complex frequencies provides an accurate closed-form expression for the electromagnetic local density of states of any photonic or plasmonic resonator with strong radiation leakage, absorption, and material dispersion. It represents a powerful tool to calculate and conceptualize the electromagnetic response of systems that are governed by a small number of resonance modes. We use the formalism to revisit Purcell's factor. The new formula substantially differs from the usual one; in particular, it predicts that a spectral detuning between the emitter and the resonance does not necessarily result in a Lorentzian response in the presence of dissipation. Comparisons with fully vectorial numerical calculations for plasmonic nanoresonators made of gold nanorods evidence the high accuracy of the predictions achieved by our semianalytical treatment.

Plasmon switching: observation of dynamic surface plasmon steering by selective mode excitation in a sub-wavelength slit

We report a plasmon steering method that enables us to dynamically control the direction of surface plasmons generated by a two-mode slit in a thin metal film. By varying the phase between different coherent beams that are incident on the slit, individual waveguide modes are excited. Different linear combinations of the two modes lead to different diffracted fields at the exit of the slit. As a result, the direction in which surface plasmons are launched can be controlled. Experiments confirm that it is possible to distribute an approximately constant surface plasmon intensity in any desired proportion over the two launching directions. We also find that the anti-symmetric mode generates surface plasmons more efficiently than the fundamental symmetric mode.

Attenuation coefficient of single-mode periodic waveguides

It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate coefficient α=-⟨ln(T)⟩/L. In this Letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the group velocity decreases. This result, that contradicts common beliefs and experimental practices aiming at measuring α, is supported by a theoretical study of light transport in the limit of very small imperfections, and by numerical results obtained for two waveguide geometries that offer contrasted damping behaviors.

Theory of fishnet negative-index optical metamaterials

We theoretically study fishnet metamaterials at optical frequencies. In contrast with earlier works, we provide a microscopic description by tracking the transversal and longitudinal flows of energy through the fishnet mesh composed of intersecting subwavelength plasmonic waveguides. The analysis is supported by a semianalytical model based on surface-plasmon coupled-mode equations, which provides accurate formulas for the fishnet refractive index, including the real-negative and imaginary parts. The model simply explains how the surface plasmons couple at the waveguide intersections, and it shines new light on the fishnet negative-index paradigm at optical frequencies. Extension of the theory for loss-compensated metamaterials with gain media is also presented.

Loss engineered slow light waveguides

Slow light devices such as photonic crystal waveguides (PhCW) and coupled resonator optical waveguides (CROW) have much promise for optical signal processing applications and a number of successful demonstrations underpinning this promise have already been made. Most of these applications are limited by propagation losses, especially for higher group indices. These losses are caused by technological imperfections ("extrinsic loss") that cause scattering of light from the waveguide mode. The relationship between this loss and the group velocity is complex and until now has not been fully understood. Here, we present a comprehensive explanation of the extrinsic loss mechanisms in PhC waveguides and address some misconceptions surrounding loss and slow light that have arisen in recent years. We develop a theoretical model that accurately describes the loss spectra of PhC waveguides. One of the key insights of the model is that the entire hole contributes coherently to the scattering process, in contrast to previous models that added up the scattering from short sections incoherently. As a result, we have already realised waveguides with significantly lower losses than comparable photonic crystal waveguides as well as achieving propagation losses, in units of loss per unit time (dB/ns) that are even lower than those of state-of-the-art coupled resonator optical waveguides based on silicon photonic wires. The model will enable more advanced designs with further loss reduction within existing technological constraints.

Metal-coated nanocylinder cavity for broadband nonclassical light emission

A novel metal-coated nanocylinder-cavity architecture fully compatible with III-V GaInAs technology and benefiting from a broad spectral range enhancement of the local density of states is proposed as an integrated source of nonclassical light. Because of a judicious selection of the mode volume, the cavity combines good collection efficiency (≈45%), large Purcell factors (≈15) over a 80 nm spectral range, and a low sensitivity to inevitable spatial mismatches between the single emitter and the cavity mode. This represents a decisive step towards the implementation of reliable solid-state devices for the generation of entangled photon pairs at infrared wavelengths.

Statistical fluctuations of transmission in slow light photonic-crystal waveguides

We report statistical fluctuations for the transmissions of a series of photonic-crystal waveguides (PhCWs) that are supposedly identical and that only differ because of statistical structural fabrication-induced imperfections. For practical PhCW lengths offering tolerable -3dB attenuation with moderate group indices (n(g) approximately 60), the transmission spectra contains very narrow peaks (Q approximately 20,000) that vary from one waveguide to another. The physical origin of the peaks is explained by calculating the actual electromagnetic-field pattern inside the waveguide. The peaks that are observed in an intermediate regime between the ballistic and localization transports are responsible for a smearing of the local density of states, for a rapid broadening of the probability density function of the transmission, and bring a severe constraint on the effective use of slow light for on-chip optical information processing. The experimental results are quantitatively supported by theoretical results obtained with a coupled-Bloch-mode approach that takes into account multiple scattering and localization effects.

Understanding the electric and magnetic response of isolated metaatoms by means of a multipolar field decomposition

We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as known from Mie's theory. By relating these cylindrical harmonics to the field radiated by Cartesian multipoles, the contribution of the lowest order electric and magnetic multipoles can be identified. Revealing these multipoles is essential for the design of metamaterials because they largely determine the character of light propagation. In particular, having this information at hand it is straightforward to distinguish between effects that result either from the arrangement of the metaatoms or from their particular design.

Surface plasmon polaritons locally excited on the ridges of metallic gratings

With the perspective to achieve an in-depth understanding of metallic periodic surfaces, we study the surface plasmon polaritons that are locally excited on the ridges (between the indentations) of metallic lamellar gratings composed of slits or grooves. An approximate model and fully vectorial computational results show that the normalized excitation rate is rather small for slit arrays (approximately 10 at maximum) and is surprisingly weakly dependent on the metal permittivity. Additionally, the analysis is supported by an intuitive microscopic model that shines new light on the role of surface plasmons in the transmission and resonance anomalies of periodic metallic surfaces.

Well-confined surface plasmon polaritons for sensing applications in the near-infrared

The surface plasmon polariton (SPP) dispersion at the interface between a dielectric half-space and a layered metallodielectric metamaterial is investigated. By varying the material constituants, it is shown that the SPP resonance frequency can be readily shifted to the near-IR. Through numerical simulations, the validity domain of homogenization and the effects of the finite number of layers in the metamaterial are studied. It is found that as few as N=2 periods are sufficient for practical operation. These results reveal the potential of employing metallodielectric stacks for sensing applications in the near-IR regime.

Disorder-induced multiple scattering in photonic-crystal waveguides

In this Letter, we study slow-light transport in photonic-crystal waveguides in the presence of structural imperfections. In contrast with previous theoretical works that rely on perturbation theories, the present formalism takes into account multiple scattering and localization effects. It allows for a quantitative prediction of the main statistical transport coefficients, including averaged values as well as probability distributions. In particular, we evidence that, as the group velocity decreases, the attenuation probability distribution exhibits a rapid broadening that one should consider for designing slow-light devices.

Cross conversion between surface plasmon polaritons and quasicylindrical waves

The optical properties of textured metallic surfaces are governed by the scattering of surface plasmon polaritons (SPPs) and of quasicylindrical waves (CWs), which are both excited by the nano-objects located on the surface. We study here a fundamental scattering process of these fields, namely, the cross conversion of a CW into a SPP. We first show that this inelastic process is inevitable in multi-nano-object ensembles and then propose a procedure enabling a rigorous calculation of the cross conversion scattering coefficients. Additionally, by mapping this intricate process to a much simpler one, we derive general and simple expressions for the cross conversion efficiency. All predictions are carefully supported by fully vectorial computational results.

Solid-state single photon sources: the nanowire antenna

We design several single-photon-sources based on the emission of a quantum dot embedded in a semiconductor (GaAs) nanowire. Through various taper designs, we engineer the nanowire ends to realize efficient metallic-dielectric mirrors and to reduce the divergence of the far-field radiation diagram. Using fully-vectorial calculations and a comprehensive Fabry-Perot model, we show that various realistic nanowire geometries may act as nanoantennas (volume of approximately 0.05 lambda(3)) that assist funnelling the emitted photons into a single monomode channel. Typically, very high extraction efficiencies above 90% are predicted for a collection optics with a numerical aperture NA=0.85. In addition, since no frequency-selective effect is used in our design, this large efficiency is achieved over a remarkably broad spectral range, Deltalambda=70 nm at lambda=950 nm.

Efficient photonic mirrors for semiconductor nanowires

Using a fully vectorial frequency-domain aperiodic Fourier modal method, we study nanowire metallic mirrors and their photonic performance. We show that the performance of standard quarter-wave Bragg mirrors at subwavelength diameters is surprisingly poor, while engineered metallic mirrors that incorporate a thin dielectric adlayer may offer reflectance larger than 90% even for diameters as small as lambda/5.

Hybridization of electromagnetic numerical methods through the G-matrix algorithm

For the sake of numerical performance, we hybridize two common approaches often used in electromagnetic computations, namely the finite-element method and the aperiodic Fourier modal method. To that end, we propose an extension of the classical S-matrix formalism to numerical situations, which requires handling different mathematical representations of the electromagnetic fields. As shown with a three-dimensional example, the proposed G-matrix formalism is stable and allows for an enhanced performance in terms of numerical accuracy and efficiency.

Ultra-High Q/V Fabry-Perot microcavity on SOI substrate

We experimentally demonstrate an ultra high Q/V nanocavity on SOI substrate. The design is based on modal adaptation within the cavity and allows to measure a quality factor of 58.000 for a modal volume of 0.6(lambda/n)(3) . This record Q/V value of 10(5) achieved for a structure standing on a physical substrate, rather than on membrane, is in very good agreement with theoretical predictions also shown. Based on these experimental results, we show that further refinements of the cavity design could lead to Q/V ratios close to 10(6).

Coupling into slow-mode photonic crystal waveguides

We study efficient injectors for coupling light from z-invariant ridge waveguides into slow Bloch modes of single-row defect photonic crystal waveguides. Two-dimensional vectorial computations performed with a Bloch mode theory approach predict that very high efficiencies (>90%) can be achieved for injector lengths of only a few wavelengths in length, even for small group velocities in the range of c/100-c/400. This result suggests that photonic crystal devices operating with slow waves can be interfaced with classical waveguides without sacrificing compactness.

Theoretical and computational concepts for periodic optical waveguides

We present a general, rigorous, modal formalism for modeling light propagation and light emission in three-dimensional (3D) periodic waveguides and in aggregates of them. In essence, the formalism is a generalization of well-known modal concepts for translation-invariant waveguides to situations involving stacks of periodic waveguides. By surrounding the actual stack by perfectly-matched layers (PMLs) in the transverse directions, reciprocity considerations lead to the derivation of Bloch-mode orthogonality relations in the sense of E x H products, to the normalization of these modes, and to the proof of the symmetrical property of the scattering matrix linking the Bloch modes. The general formalism, which rigorously takes into account radiation losses resulting from the excitation of radiation Bloch modes, is implemented with a Fourier numerical approach. Basic examples of light scattering like reflection, transmission and emission in periodic-waveguides are accurately resolved.

Very large spontaneous-emission Beta factors in photonic-crystal waveguides

Through a new rigorous Bloch-mode formalism, we theoretically study the generation of photons in single-row-defect photonic-crystal waveguides. In contrast with previous related works relying on a reinforcement of the spontaneous emission (SE) through microcavity effects, we explore situations for which the SE into radiation modes is reduced to a very low level while the SE into the guided mode is maintained at a level comparable to that in the bulk material. Remarkably large SE beta factors in excess of 95% are obtained, and since no resonance effect is involved, this efficiency is achieved over a 40-nm-large spectral interval at lambda approximately 950 nm.

Compact and efficient injection of light into band-edge slow-modes

We design compact (a few wavelength long) and efficient (>99%) injectors for coupling light into slow Bloch modes of periodic thin film stacks and of periodic slab waveguides. The study includes the derivation of closed-form expressions for the injection efficiency as a function of the group-velocity of injected light, and the proof that 100% coupling efficiencies for arbitrary small group velocities is possible with an injector length scaling as log(c/vg). The trade-off between the injector bandwidth and the group velocity of the injected light is also considered.

Near-field analysis of surface waves launched at nanoslit apertures

With the aim of analyzing the properties of the waves that are scattered by nanoslits on metallic surfaces, we provide a direct observation of the near-field in a slit-doublet experiment at optical wavelengths. We show that two distinct waves are involved: a surface plasmon polariton and another wave with a free-space character. From the recorded data, we have extracted the amplitudes and phases of these waves, their damping characteristic lengths and their relative weights as a function of the separation distance from the slit. The analysis is fully supported by a quantitative agreement with vector-theory computational results.

Approximate model for surface-plasmon generation at slit apertures

We present a semianalytical model that quantitatively predicts the scattering of light by a single subwavelength slit in a thick metal screen. In contrast to previous theoretical works related to the transmission properties of the slit, the analysis emphasizes the generation of surface plasmons at the slit apertures. The model relies on a two-stage scattering mechanism, a purely geometric diffraction problem in the immediate vicinity of the slit aperture followed by the launching of a bounded surface-plasmon wave on the flat interfaces surrounding the aperture. By comparison with a full electromagnetic treatment, the model is shown to provide accurate formulas for the plasmonic generation strength coefficients, even for metals with a low conductivity. Limitations are outlined for large slit widths (>lambda) or oblique incidence (>30 degrees ) when the slit is illuminated by a plane wave.

Theory of surface plasmon generation at nanoslit apertures

In this Letter, we study the scattering of light by a single subwavelength slit in a metal screen. In contrast with previous theoretical works, we provide a microscopic description of the scattering process by emphasizing the generation of surface plasmons at the slit apertures. The analysis is supported by a rigorous formalism based on a normal-mode-decomposition technique and by a semianalytical model that provides accurate formulas for the plasmonic generation strengths. The generation is shown to be fairly efficient for metals with a low conductivity, such as gold in the visible regime. Verification of the theory is also shown by comparison with recent experimental data [H. F. Schouten, Phys. Rev. Lett. 94, 053901 (2005)].

Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities

When a guided wave is impinging onto a Photonic Crystal (PC) mirror, a fraction of the light is not reflected back and is radiated into the claddings. We present a theoretical and numerical study of this radiation problem for several three-dimensional mirror geometries which are important for light confinement in micropillars, air-bridge microcavities and two-dimensional PC microcavities. The cause of the radiation is shown to be a mode-profile mismatch. Additionally, design tools for reducing this mismatch by tuning the mirror geometry are derived. These tools are validated by numerical results performed with a three-dimensional Fourier modal method. Several engineered mirror geometries which lower the radiation loss by several orders of magnitude are designed.

Use of grating theories in integrated optics

Recently [Opt. Lett. 25, 1092 (2000)], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.

Stochastic artificial retinas: algorithm, optoelectronic circuits, and implementation

An analogy can be established between image processing and statistical mechanics. Many early- and intermediate-vision tasks such as restoration, image segmentation, and motion detection can be formulated as optimization problems that consist in finding the ground states of an energy function. This approach yields excellent results, but, once it is implemented in conventional sequential workstations, the computational loads are too extensive for practical purposes, and even fast suboptimal optimization approaches are not sufficient. We elaborate on dedicated massively-parallel integrated circuits, called stochastic artificial retinas, that minimize the energy function at a video rate. We consider several components of these artificial retinas: stochastic algorithms for restoration tasks in the presence of discontinuities, dedicated optoelectronic hardware to implement thermal motion by photodetection of speckles, and hybrid architectures that combine optoelectronic, asynchronous-analog, and clocked-digital circuits.

Wide-field-angle behavior of blazed-binary gratings in the resonance domain

Blazed-binary gratings for which a blazed effect with binary etches is achieved under normal incidence offer first-order diffraction efficiencies larger than those of blazed-échelette gratings in the resonance domain [Opt. Lett. 23 1081 (1998)]. We provide further insight into the behavior of blazed-binary gratings and show that they operate efficiently under symmetrical mounting and over a wide field-angle interval. These properties are illustrated with theoretical and experimental results obtained for an approximately 1000-line/mm grating at 633 nm.

Fourier-modal methods applied to waveguide computational problems

Rigorous coupled-wave analysis (also called the Fourier-modal method) is an efficient tool for the numerical analysis of grating diffraction problems. We show that, with only a few modifications, this method can be used efficiently for the numerical analysis of aperiodic diffraction problems, including photonic crystal waveguides, Bragg mirrors, and grating couplers. We thus extend the domain of applications of grating theories.

Blazed-binary diffractive elements with periods much larger than the wavelength

Blazed-binary optical elements with only binary ridges or pillars are diffractive components that mimic standard blazed-echelette diffractive elements. We report on the behavior of one-dimensional blazed-binary optical elements with local periods much larger than the wavelength. For this purpose, an approximate model based on both scalar and electromagnetic theory is proposed. The model is tested against electromagnetic-theory computational results obtained for one-dimensional blazed-binary gratings with large periods. An excellent agreement is obtained, showing that the model is able to predict quantitatively the wavelength and the incidence-angle dependences of the diffraction efficiency of blazed-binary structures.

Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings

The numerical performance of a finite-difference modal method for the analysis of one-dimensional lamellar gratings in a classical mounting is studied. The method is simple and relies on first-order finite difference in the grating to solve the Maxwell differential equations. The finite-difference scheme incorporates three features that accelerate the convergence performance of the method: (1) The discrete permittivity is interpolated at the lamellar boundaries, (2) mesh points are located on the permittivity discontinuities, and (3) a nonuniform sampling with increased resolution is performed near the discontinuities. Although the performance achieved with the present method remains inferior to that achieved with up-to-date grating theories such as rigorous coupled-wave analysis with adaptive spatial resolution, it is found that the present method offers rather good performance for metallic gratings operating in the visible and near-infrared regions of the spectrum, especially for TM polarization.

Interferometric characterization of subwavelength lamellar gratings

We propose a new, to our knowledge, method for determining the two main critical parameters of periodic one-dimensional lamellar structures, namely, linewidths and etched depths. The method is simple and requires only two measurements for the phase of the zero-transmitted order under two orthogonal polarizations. It is inspired by the analogy between subwavelength gratings and anisotropic homogeneous thin films. The method is tested with experimental data obtained with a Mach-Zehnder interferometer. Etched depths and linewidths derived from the interferograms and electromagnetic theory are compared with scanning-electron-microscope observations.