Multicoated gratings: a differential formalism applicable in the entire optical region

Modal analysis of diffraction by snake gratings using a tensor product of pseudo-periodic functions and Legendre polynomials

The problem of diffraction by snake gratings is presented and formulated as an eigenvalue eigenvector problem. A numerical solution is obtained thanks to the method of moments where a tensor product of pseudo-periodic functions and Legendre polynomials is used as expansion and test functions. The method is validated by comparison with the usual Fourier modal method (FMM) as applied to crossed gratings. Our method is shown to be more efficient than the FMM in the case of metallic gratings.

Scattering by cylinders with an arbitrary cross-section using domain decomposition and polynomial expansions

In this paper, the electromagnetic field scattered by a cylinder with an arbitrary cross section is computed using a domain decomposition method in which the structure under consideration is enclosed with two fictitious circular cylinders. TE and TM polarizations are investigated. Our code is successfully validated by comparison with analytical results and with the finite element software COMSOL.

Electromagnetic response of corrugated multilayer systems inspired by the Dione vanillae butterfly scales

Inspired by the microstructures in the wing scales of the butterfly Dione vanillae, we investigate the optical response of two multilayer structures, which include one or two corrugated interfaces. The reflectance is calculated using the C-method and is compared with that of a planar multilayer. We perform a detailed analysis of the influence of each geometric parameter and study the angular response, which is important for structures exhibiting iridescence. The results of this study aim to contribute to the design of multilayer structures with predetermined optical responses.

Rayleigh method adapted for the study of the optical response of natural photonic structures

To study the electromagnetic response of natural structures that exhibit interesting optical properties, we developed a computational tool to solve the problem of electromagnetic scattering by a rough interface between two isotropic media, based on the Rayleigh method. The key aspect of the developed formalism is its capability of introducing the interface profile within the code by means of a digitalized image of the structure, which can be either obtained from an electron microscopy image or simply by design according to the complexity of the scattering surface. As application examples, we show the results obtained for surfaces taken directly from microscopy images of two different biological species. This approach constitutes a fundamental step in order to model the electromagnetic response of natural photonic structures.

Matched coordinates for the analysis of 1D gratings

The Fourier modal method (FMM) is certainly one of the most popular and general methods for the modeling of diffraction gratings. However, for non-lamellar gratings it is associated with a staircase approximation of the profile, leading to poor convergence rate for metallic gratings in TM polarization. One way to overcome this weakness of the FMM is the use of the fast Fourier factorization (FFF) first derived for the differential method. That approach relies on the definition of normal and tangential vectors to the profile. Instead, we introduce a coordinate system that matches laterally the profile and solve the covariant Maxwell's equations in the new coordinate system, hence the name matched coordinate method (MCM). Comparison of efficiencies computed with MCM with other data from the literature validates the method.

Understanding and optimizing diffraction gratings by the blazing analysis of total internal reflection

The diffraction grating is a classic and important optical element, and its design usually traverses the whole parameter space to search for an optimal solution, which is time consuming and inefficient. In order to specify the optimization direction of the grating to obtain clearer physical images and to improve the design efficiency, a new blazing model based on the total internal reflection (TIR) is proposed to analyze the diffraction behavior of the grating from a geometry perspective. The optical tunnel along the ridge direction can be used to understand and quantify the blaze of the grating. This TIR blazing model is demonstrated via three types of surface-relief grating with simple formulas, resulting in the solution space decreasing significantly. By utilization of the estimated upper limit of the diffraction efficiency and the range of the depth and slanted angle generated by the TIR blazing model, how the grating delivers the majority of the light energy to a required diffraction order is revealed. Binary and slanted gratings with >0.93 efficiency of T₁ order have been obtained with high probability within the calculated parameter range, regardless of the duty cycle and polarization. The reason why a transmission sawtooth grating cannot blaze the most energy to a high order at normal incidence has been clarified, and the method of using the first or second TIR blaze has also been provided. Through this TIR blazing model, the grating design could be simplified, and accommodation to various application requirements could be optimized as well.

Coordinate transformation method for modeling three-dimensional photonic structures with curved boundaries

The coordinate transformation method (C method) is a powerful tool for modeling photonic structures with curved boundaries of discontinuities. As a modal method upon the Fourier basis, the C method has superior computational efficiency and rich physical intuitiveness compared to other full-wave numerical methods. But presently the C method is limited to two-dimensional (2D) structures if the boundaries between adjacent z-invariant layers are of generally different profiles [with (x,y,z) being the Cartesian coordinate]. Here we report a nontrivial extension of the C method to the general case of three-dimensional (3D) structures with curved boundaries of different profiles between adjacent layers. This extension drastically enlarges the applicability of the C method to the various interesting structures in nanophotonics and plasmonics. The extended 3D-C method adopts a hybrid coordinate transformation which includes not only the z-direction coordinate transformation in the classical C method but also the x- and y-direction matched coordinates adopted in the Fourier modal method (FMM), so as to exactly model the curved boundaries in all the three directions. The method also incorporates the perfectly matched layers (PMLs) for aperiodic structures and the adaptive spatial resolution (ASR) for enhancing the convergence. A modified numerically-stable scattering-matrix algorithm is proposed for solving the equations of boundary condition between adjacent z-invariant layers, which are derived via a transformation of the full 3D covariant field-components between the different curvilinear coordinate systems defined by the different-profile top and bottom boundaries of each layer. The validity of the extended 3D-C method is tested with several numerical examples.

Numerical instability of the C method when applied to coated gratings and methods to avoid it

We recently found that the coordinate transformation method (the C method) equipped with well-established recursive algorithms for solving the system of linear equations is numerically instable when it is applied to thinly coated gratings. The origin of this new kind of numerical instability is not the exponential dependence of the field in the coated layers but the ill condition of the eigenvector matrix of the C method when the truncation number is high. Two simple and effective methods to circumvent the new instability are recommended. We also found that the popular recursive matrix algorithms have different (poor) immunities to the new instability, and they all perform inferiorly to the full matrix (nonrecursive) algorithm.

Large positive and negative Goos-Hänchen shifts near the surface plasmon resonance in subwavelength grating

Diffraction of light of a visible spectral range by subwavelength metal gratings has been investigated experimentally and theoretically using rigorous electromagnetic calculations. It has been demonstrated that an effect of surface plasmon resonance (SPR), at which total absorption of light by metal grating can be observed, occurs under certain conditions. Large positive and negative Goos-Hänchen (GH) shifts occur near the SPR. It has been shown that the reflected beam is split into two parts, the relative powers of which depend on the incident beam width and the grating depth. The dependence of the GH shifts on the grating period and grating depth has been investigated for different incident beam widths. The high sensitivity of the GH shift on the incident angle of a light beam near the SPR has been demonstrated.

Massive Enhancement of Optical Transmission across a Thin Metal Film via Wave Vector Matching in Grating-Coupled Surface Plasmon Resonance

We demonstrate how distinct surface plasmon resonance modes on opposite sides of a metal-coated grating can be coupled across the metal film. This coupling occurs by matching the resonance conditions on each side of the grating by tuning the refractive index directly adjacent to the metal film. In the first example, we deposited a high refractive index layer of tin oxide on top of the grating to red-shift the front side surface plasmon until it coupled with the backside surface plasmon across a semitransparent ∼45 nm thin silver grating. By shifting the resonance condition of the nearby surface plasmon, this high refractive index coating creates an effective matching of wave vectors across the metal film, allowing them to couple and enhance the optical response. A massive increase in the magnitude of enhanced transmission is observed, increasing from a 6-fold transmission enhancement through a bare silver grating to a near 100-fold enhancement after deposition of a tin oxide layer of appropriate thickness (∼310 nm). This optical transmission enhancement is then probed through computational modeling and by experiments with liquids of various refractive index values. The matched system shows an increased amplitude sensitivity with respect to refractive index changes and a waveguide like behavior within the tin oxide film. As an alternative configuration, we also demonstrate coupling the front and back-side plasmon modes by using a lower refractive index substrate in order to blue-shift the back-side surface plasmon. Coupling between the two plasmon modes is then demonstrated by introducing aqueous solutions of various refractive index values. Under the proper conditions, this matched system also shows a substantial enhancement in transmission. This technique of wave vector matching provides a route to substantially increasing the plasmon enhanced optical transmission through metal gratings, which has potential application in improved plasmonic sensing, spectroscopy, and plasmon-based optical devices.

Application of Heisenberg uncertainty relation for the optimal modeling of surface diffraction

The modeling of the scattering of a plane wave at a rough aperiodic surface-as well as its diffraction by a microstructured surface-is possible only by limiting the infinite surface to a window of finite width D. We show that the scattering spectrum at infinity in the Fraunhofer zone can be obtained from the diffraction modeling of a grating of period D whose surface profile coincides with the aperiodic surface in this window. This is justified by adopting the corpuscular representation of light and resorting to Heisenberg's uncertainty relation applied to the photon's canonically conjugate variables momentum and position. This approach gives a deep and comprehensive representation of scattering phenomena, and also the limit of what can be meaningfully calculated and measured. Numerical examples of grating profiles demonstrate that results obtained under the widely used Beckmann-Kirchoff approximation are matched. The described approach can solve scattering problems that usual methods cannot, or face difficulties, such as when there is significant roughness with respect to the wavelength.

Highly confined surface plasmon polaritons in the ultraviolet region

Surface plasmon polaritons are commonly believed to be a future basis for the next generation of optoelectronic and all-optical devices. To achieve this, it is critical that the surface plasmon polariton modes be strongly confined to the surface and have a sufficiently long propagation length and a nanosize wavelength. As of today, in the visible part of the spectrum, these conditions are not satisfied for any type of surface plasmon polaritons. In this paper, we demonstrate that in the ultraviolet range, surface plasmon polaritons propagating along a periodically nanostructured aluminum-dielectric interface have all these properties. Both the confinement length and the wavelength of the mode considered are smaller than the period of the structure, which can be as small as 10 nm. At the same time, the propagation length of new surface plasmon-polaritons can reach dozens of its wavelengths. These plasmon polaritons can be observed in materials that are uncommon in plasmonics such as aluminum. The suggested modes can be used for miniaturization of optical devices.

Optical function of the finite-thickness corrugated pellicle of euglenoids

We explore the electromagnetic response of the pellicle of selected species of euglenoids. These microorganisms are bounded by a typical surface pellicle formed by S-shaped overlapping bands that resemble a corrugated film. We investigate the role played by this structure in the protection of the cell against UV radiation. By considering the pellicle as a periodically corrugated film of finite thickness, we applied the C-method to compute the reflectance spectra. The far-field results revealed reflectance peaks with a Q-factor larger than 10³ in the UV region for all the illumination conditions investigated. The resonant behavior responsible for this enhancement has also been illustrated by near-field computations performed by a photonic simulation method. These results confirm that the corrugated pellicle of euglenoids shields the cell from harmful UV radiation and open up new possibilities for the design of highly UV-reflective surfaces.

Polynomial modal analysis of slanted lamellar gratings

The problem of diffraction by slanted lamellar dielectric and metallic gratings in classical mounting is formulated as an eigenvalue eigenvector problem. The numerical solution is obtained by using the moment method with Legendre polynomials as expansion and test functions, which allows us to enforce in an exact manner the boundary conditions which determine the eigensolutions. Our method is successfully validated by comparison with other methods including in the case of highly slanted gratings.

Study of a reflection grating used in Littrow mount

The near and far fields of a finite conductivity metallic grating with symmetrical triangular facets, used in Littrow mount, are studied. A new Green's function approach, based on the Hertz vector, is introduced and used to propagate throughout a two-dimensional domain. The field quantity of primary interest is Poynting's vector; however, the stored power is also calculated. In assessing the fields generated by the propagator, a quasi-periodic dependence of output characteristics on the grating depth to period ratio, discussed in the literature, is also found in the present study. With a plane wave incident on the grating, geometrical relationships between the incident wave vector and the grating surfaces have interesting consequences.

Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings

We have formulated an asymptotic model for implementation in the finite-element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions, thereby eliminating the necessity of representing the grating layer by a fine mesh. The parameters defining the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions. Adoption of the asymptotic model will considerably reduce the computational cost of optimizing the grating shape because there is no need to re-mesh at every optimization step.

Coupling properties between plasmonic modes and cavity modes in corrugated metal–dielectric–metal waveguide

We investigate the coupling properties between plasmonic modes and cavity modes in corrugated metal–dielectric–metal structures.

Temperature and gain tuning of plasmonic coherent perfect absorbers

We experimentally demonstrate temperature-tuned and gain-assisted surface-plasmonic coherent perfect absorbers. In these devices, coherent perfect absorption (CPA) is supported by balancing the absorber's radiative and non-radiative decay rates under thermal tuning of free-electron collision frequency in the Ag layer and optical tuning of the amplification rate in the adjacent dielectric film with optical gain, respectively. The results show that these methods are experimentally feasible and applicable to various CPA configurations.

Gain-assisted critical coupling for high-performance coherent perfect absorbers

Balanced radiation and absorption rates of an optical resonator are necessary for coherent perfect light absorption in many active device applications. This balance is referred to as critical coupling condition. We propose a gain-assisted method for exact access to critical coupling conditions without altering any structure parameters. In a coherent absorber with additional internal gain media, critical coupling with arbitrarily high coherent signal extinction can be obtained by continuously tuning optical pumping density. Assuming a surface-plasmon resonance grating covered by a gain layer as a promising architecture, we numerically demonstrate gain-assisted continuous access to its critical coupling point with experimentally probable settings. In addition, the gain tuning further introduces switching of the coherent-absorber's functionality to a conventional lossless beam splitter.

Surface plasmon hurdles leading to a strongly localized giant field enhancement on two-dimensional (2D) metallic diffraction gratings

An extensive numerical study of diffraction of a plane monochromatic wave by a single gold cone on a plane gold substrate and by a periodical array of such cones shows formation of curls in the map of the Poynting vector. They result from the interference between the incident wave, the wave reflected by the substrate, and the field scattered by the cone(s). In case of a single cone, when going away from its base along the surface, the main contribution in the scattered field is given by the plasmon surface wave (PSW) excited on the surface. As expected, it has a predominant direction of propagation, determined by the incident wave polarization. Two particular cones with height approximately 1/6 and 1/3 of the wavelength are studied in detail, as they present the strongest absorption and field enhancement when arranged in a periodic array. While the PSW excited by the smaller single cone shows an energy flux globally directed along the substrate surface, we show that curls of the Poynting vector generated with the larger cone touch the diopter surface. At this point, their direction is opposite to the energy flow of the PSW, which is then forced to jump over the vortex regions. Arranging the cones in a two-dimensional subwavelength periodic array (diffraction grating), supporting a specular reflected order only, resonantly strengthens the field intensity at the tip of cones and leads to a field intensity enhancement of the order of 10 000 with respect to the incident wave intensity. The enhanced field is strongly localized on the rounded top of the cones. It is accompanied by a total absorption of the incident light exhibiting large angular tolerances. This strongly localized giant field enhancement can be of much interest in many applications, including fluorescence spectroscopy, label-free biosensing, surface-enhanced Raman scattering (SERS), nonlinear optical effects and photovoltaics.

Laser-driven Rayleigh-Taylor instability: plasmonic effects and three-dimensional structures

The acceleration of dense targets driven by the radiation pressure of high-intensity lasers leads to a Rayleigh-Taylor instability (RTI) with rippling of the interaction surface. Using a simple model it is shown that the self-consistent modulation of the radiation pressure caused by a sinusoidal rippling affects substantially the wave vector spectrum of the RTI, depending on the laser polarization. The plasmonic enhancement of the local field when the rippling period is close to a laser wavelength sets the dominant RTI scale. The nonlinear evolution is investigated by three-dimensional simulations, which show the formation of stable structures with "wallpaper" symmetry.

Local transformation leading to an efficient Fourier modal method for perfectly conducting gratings

We present an efficient Fourier modal method for wave scattering by perfectly conducting gratings (in the two polarizations). The method uses a geometrical transformation, similar to the one used in the C-method, that transforms the grating surface into a flat surface, thus avoiding to question the Rayleigh hypothesis; also, the transformation only affects a bounded inner region that naturally matches the outer region; this allows applying a simple criterion to select the ingoing and outgoing waves. The method is shown to satisfy reciprocity and energy conservation, and it has an exponential rate of convergence for regular groove shapes. Besides, it is shown that the size of the inner region, where the solution is computed, can be reduced to the groove depth, that is, to the minimal computation domain.

Plasmonic band gap engineering of plasmon-exciton coupling

Controlling plasmon-exciton coupling through band gap engineering of plasmonic crystals is demonstrated in the Kretschmann configuration. When the flat metal surface is textured with a sinusoidal grating only in one direction, using laser interference lithography, it exhibits a plasmonic band gap because of the Bragg scattering of surface plasmon polaritons on the plasmonic crystals. The contrast of the grating profile determines the observed width of the plasmonic band gap and hence allows engineering of the plasmonic band gap. In this work, resonant coupling between the molecular resonance of a J-aggregate dye and the plasmonic resonance of a textured metal film is extensively studied through plasmonic band gap engineering. Polarization dependent spectroscopic reflection measurements probe the spectral overlap occurring between the molecular resonance and the plasmonic resonance. The results indicate that plasmon-exciton interaction is attenuated in the band gap region along the grating direction.

Subwavelength diffractive color beam combiner

A high-efficiency subwavelength diffractive beam combiner operating in a visible spectral range is designed, fabricated, and demonstrated. Such a device combines red, green, and blue color beams into one output light beam. Diffraction efficiencies of different types of gratings are calculated for various materials, incidence angles, and polarizations of light. It is shown that the plasmon resonance via a grating coupling occurs at the determined conditions. Subwavelength gratings with a period of 400 nm are fabricated and tested using laser and laser diode sources.

Strong three-dimensional field localization and enhancement on deep sinusoidal gratings with two-dimensional periodicity

The study of total light absorption due to excitation of localized surface plasmons on deep metallic crossed gratings having a sinusoidal profile with a two-dimensional periodicity shows a very strong increase in the electric field intensity, reaching 800 times the incident intensity. The region with high intensity is strongly localized at the groove top and is characterized by a volume much smaller than the diffraction limit, both in transverse direction along the grating plane, and in longitudinal direction when going away from the grating surface. The field enhancement and its localization are much more pronounced than in shallow gratings.

A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applications

In this paper we demonstrate that rigorous high-order perturbation of surfaces (HOPS) methods coupled with analytic continuation mechanisms are particularly well-suited for the assessment and design of nanoscale devices (e.g., biosensors) that operate based on surface plasmon resonances generated through the interaction of light with a periodic (metallic) grating. In this connection we explain that the characteristics of the latter are perfectly aligned with the optimal domain of applicability of HOPS schemes, as these procedures can be shown to be the methods of choice for low to moderate wavelengths of radiation and grating roughness that is representable by a few (e.g., tens of) Fourier coefficients. We argue that, in this context, the method can, for instance, produce full and precise reflectivity maps in computational times that are orders of magnitude faster than those of alternative numerical schemes (e.g., the popular "C-method," finite differences, integral equations or finite elements). In this initial study we concentrate on the description of the basic principles that underlie the solution scheme, including those that relate to analytic continuation procedures. Within this framework, we explain how, in spite of conventional wisdom to the contrary, the resulting perturbative techniques can provide a most valuable tool for practical investigations in plasmonics. We demonstrate this with some examples that have been previously discussed in the literature (including treatments of the reflectivity and band gap structure of some simple geometries) and extend this to demonstrate the wider applicability of the proposed approach.

Enhanced method for determining the optical response of highly complex biological photonic structures

We present a set of techniques that enhances a previously developed time domain simulation of wave propagation and allows the study of the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological structures, especially due to the simple and intuitive way of defining the setup and the photonic structure to be simulated, which can be done via a digital image of the structure. The presented techniques include a direction filter that permits the decoupling of waves traveling simultaneously in different directions, a dynamic differential absorber to cancel the waves reflected at the edges of the simulation space, and a multifrequency excitation scheme. We also show how the simulation can be adapted to apply a near to far field method in order to evaluate the resulting wavefield outside the simulation domain. We validate these techniques, and, as an example, we apply the method to the complex structure of a microorganism called Diachea leucopoda, which exhibits a multicolor iridescent appearance.

Fano resonance formula for lossy two-port systems

We provide a modified Fano resonance formula applicable to dissipative two-port resonance systems. Based on a generic coupled-resonator model, the formula embodies loss-related correction terms and fundamental resonance parameters that can be determined by an analytic method or experimentally as opposed to finding phenomenological parameters by fitting to numerical results. The theory applies physically meaningful resonance parameters including resonance frequency, total decay rates, and partial radiation probabilities. For example, it shows that the classic Fano shape parameter q is given directly in terms of the phase difference between the resonant and non-resonant transmission pathways. Our new resonance formula quantitatively expresses the resonance spectra pertaining to modal nanophotonic and surface-plasmonic thin-film structures as verified by comparing with exact numerical models.

Resonant coupling from a new angle: coherent control through geometry

We demonstrate that interference of absorption pathways can be used to control resonant coupling of light to guided modes in a manner analogous to quantum coherent control or electronically induced transparency. We illustrate the control of resonant coupling that interference affords using a plasmonic test system where tuning the phase of a grating is sufficient to vary the transfer of energy into the surface plasmon polariton by a factor of over 10(6). We show that such a structure could function as a one-way coupler, and present a simple explanation for the underlying physics.

Designing optimized nano textures for thin-film silicon solar cells

Thin-film silicon solar cells (TFSSC), which can be manufactured from abundant materials solely, contain nano-textured interfaces that scatter the incident light. We present an approximate very fast algorithm that allows optimizing the surface morphology of two-dimensional nano-textured interfaces. Optimized nano-textures scatter the light incident on the solar cell stronger leading to a higher short-circuit current density and thus efficiency. Our algorithm combines a recently developed scattering model based on the scalar scattering theory, the Perlin-noise algorithm to generate the nano textures and the simulated annealing algorithm as optimization tool. The results presented in this letter allow to push the efficiency of TFSSC towards their theoretical limit.

Surface-plasmon-enhanced GaN-LED based on a multilayered M-shaped nano-grating

A multilayered metallic M-shaped nano-grating is proposed to enhance the internal quantum efficiency, light extraction efficiency and surface-plasmon (SP) extraction efficiency of the gallium nitride-based light emitting diodes. This structure is fabricated by the low-cost nano-imprint lithography. The suitable grating based on quasi-symmetrical-waveguide structure has a high transmission in the visible region. The properties of SP mode and the Purcell effect in this type of LED is investigated. The experimental results demonstrate that its peak photoluminescence intensity of the proposed LED is over 10 times greater than that from a naked GaN-LED without any nanostructure.

Short and long range surface plasmon polariton waveguides for xylene sensing

Nanostructured plasmonic sensors are fabricated as sinusoidal surface plasmon metallic gratings (SPGs) embedded in a functional and porous hybrid sol-gel material, phenyl-bridged polysilsesquioxane (ph-PSQ). The metal layer is in contact with the environment through the sol-gel film, which works as sensitive element, changing its dielectric properties upon interaction with aromatic hydrocarbons. The combination of sensitivity, transparency and patternability offered by ph-PSQs gives the exceptional possibility to fabricate innovative optical sensors with straightforward processes. An embedded SPG is a thin metal slab waveguide, in which the surface plasmon polaritons (SPPs) at the two metal-dielectric interfaces superpose, resulting in two physical coupled modes: the long range SPPs (LRSPPs) and the short range SPPs (SRSPPs). An extended experimental and theoretical characterization of the optical properties of the plasmonic device was performed. The sensor performance was tested against the detection of 30 ppm xylene, monitoring the influence of the target gas on the SPPs modes. A reversible red-shift of the reflectance dips of both LRSPP and SRSPP resonances in the 1.9-2.9 nm range was observed and correlated to the interaction with the analyte. An enhancement in sensitivity associated with the rotation of the grating grooves with respect to the scattering plane (azimuthal rotation) was verified within the experimental errors. Collected data are compatible with theoretical predictions assuming a variation of the film refractive index of 0.011 ± 0.005.

Measurement and modeling of a complete optical absorption and scattering by coherent surface plasmon-polariton excitation using a silver thin-film grating

We demonstrate the plasmonic analogue of a coherent photonic effect known as coherent perfect absorption. A periodically nanopatterned metal film perfectly absorbs multiple coherent light beams coupling to a single surface plasmon mode. The perfect absorbing state can be switched to a nearly perfect scattering state by tuning the phase difference between the incident beams. We theoretically explain the plasmonic coherent perfect absorption by considering time-reversal symmetry of surface plasmon amplification by stimulated emission of radiation. We experimentally demonstrate coherent control of the plasmonic absorption in good agreement with a coupled-mode theory of dissipative resonances. Associated potential applications include absorption-based plasmonic switches, modulators, and light-electricity transducers.

Fluorescence enhancement from nano-gap embedded plasmonic gratings by a novel fabrication technique with HD-DVD

We demonstrate strong electromagnetic field enhancement from nano-gaps embedded in silver gratings for visible wavelengths. These structures fabricated using a store-bought HD-DVD worth $10 and conventional micro-contact printing techniques have shown maximum fluorescence enhancement factors of up to 118 times when compared to a glass substrate under epi-fluorescent conditions. The novel fabrication procedure provides for the development of a cost-effective and facile plasmonic substrate for low-level chemical and biological detection. Electromagnetic field simulations were also performed that reveal the strong field confinement in the nano-gap region embedded in the silver grating, which is attributed to the combined effect of localized as well as propagating surface plasmons.

Coordinate transformation formulation of electromagnetic scattering from imperfectly periodic surfaces

This paper considers the electromagnetic scattering problem of periodically corrugated surface with local imperfection of structural periodicity, and presents a formulation based on the coordinate transformation method (C-method). The C-method is originally developed to analyze the plane-wave scattering from perfectly periodic structures, and uses the pseudo-periodic property of the fields. The fields in imperfectly periodic structures are not pseudo-periodic and the C-method cannot be directly applied. This paper introduces the pseudo-periodic Fourier transform to convert the fields in imperfectly periodic structures to pseudo-periodic ones, and the C-method becomes then applicable.

Toward a cylindrical cloak via inverse homogenization

An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighborhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic material, characterized by positive-definite constitutive dyadics. It can arise from the homogenization of component materials that are remarkably simple in terms of their structure and constitutive relations. For example, the components can be two isotropic dielectric-magnetic materials, randomly distributed as oriented spheroidal particles. By carefully controlling the spheroidal shape of the component particles, a high degree of HCM anisotropy may be achieved which is necessary for the cloaking effect to be realized. The inverse Bruggeman formalism can provide estimates of the shape and constitutive parameters for the component materials, as well as their volume fractions.

Surface-plasmon mediated total absorption of light into silicon

We report surface-plasmon mediated total absorption of light into a silicon substrate. For an Au grating on Si, we experimentally show that a surface-plasmon polariton (SPP) excited on the air/Au interface leads to total absorption with a rate nearly 10 times larger than the ohmic damping rate of collectively oscillating free electrons in the Au film. Rigorous numerical simulations show that the SPP resonantly enhances forward diffraction of light to multiple orders of lossy waves in the Si substrate with reflection and ohmic absorption in the Au film being negligible. The measured reflection and phase spectra reveal a quantitative relation between the peak absorbance and the associated reflection phase change, implying a resonant interference contribution to this effect. An analytic model of a dissipative quasi-bound resonator provides a general formula for the resonant absorbance-phase relation in excellent agreement with the experimental results.

Investigation of the wave behaviors inside a step-modulated subwavelength metal slit

In this paper, we applied the modal expansion method (MEM) to investigate the wave behaviors inside a step-modulated subwavelength metal slit. The physical mechanism of the surface plasmon polariton (SPP) transmission is investigated in detail for slit structures with either dielectric or geometric modulation. The applicability of the effective index method is discussed. Moreover, as a special case of the geometric modulation, the evanescent-wave assisted transmission is demonstrated in a thin-modulated slit. We emphasize that a complete set is necessary in order to expand the wave functions in these kinds of structures. All the calculated results by the MEM are well retrieved by the finite-difference time-domain calculation.

Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings

Despite the progress in the engineering of structures to enhance photocurrent in thin film solar cells, there are few comprehensive studies which provide general and intuitive insight into the problem of light trapping. Also, lack of theoretical propositions which are consistent with fabrication is an issue to be improved. We investigate a real thin film solar cell with almost conformal layers grown on a 1D grating metallic back-reflector both experimentally and theoretically. Photocurrent increase is observed as an outcome of guided mode excitation in both theory and experiment by obtaining the external quantum efficiency of the cell for different angles of incidence and in both polarization directions. Finally, the effect of geometrical parameters on the short circuit current density of the device is investigated by considering different substrate shapes that are compatible with solar cell fabrication. Based on our simulations, among the investigated shapes, triangular gratings with a very sharp slope in one side, so called sawtooth gratings, are the most promising 1D gratings for optimal light trapping.

Critical coupling in dissipative surface-plasmon resonators with multiple ports

We theoretically investigate resonant absorption in a multiple-port surface-plasmon polaritons (SPP) resonator near the condition of critical coupling at which internal loss is comparable to radiation coupling. We show that total absorption is obtainable in a multiple-port system by properly configuring multiple coherent lightwaves at the condition of critical coupling. We further derive analytic expressions for the partial absorbance at each port, the total absorbance, and their sum rule, which provide a non-perturbing method to probe coupling characteristics of highly localized optical modes. Rigorous simulation results modeling a surface-plasmon resonance grating in the multiple-order diffraction regime show excellent agreements with the analytic expressions.

Generation of adaptive coordinates and their use in the Fourier Modal Method

We present an improvement of the standard Fourier Modal Method (FMM) for the analysis of lamellar gratings that is based on the use of automatically generated adaptive coordinates for arbitrarily shaped material profiles in the lateral plane of periodicity. This allows for an accurate resolution of small geometric features and/or large material contrasts within the unit. For dielectric gratings, we obtain considerable convergence accelerations. Similarly, for metallic gratings, our approach allows efficient and accurate computations of transmittance and reflectance coefficients into various Bragg orders, the spectral positions of Rayleigh anomalies, and field enhancement values within the grating structures.

Optimization of nonbinary slanted surface-relief gratings as high-efficiency broadband couplers for light guides

We propose and investigate the use of slanted surface-relief gratings with nonbinary profiles as high-efficiency broadband couplers for light guides. First, a Chandezon-method-based rigorous numerical formulation is presented for modeling the slanted gratings with overhanging profiles. Then, two typical types of slanted grating couplers--a sinusoidal one and a trapezoidal one--are studied and optimized numerically, both exhibiting a high coupling efficiency of over 50% over the full band of white LED under the normal illumination of unpolarized light. Reasonable structural parameters with nice tolerance have been obtained for the optimized designs. It is found that the performance of the couplers depends little on the grating profile shape, but primarily on the grating period and the slant angle of the ridge. The underlying mechanism is analyzed by the equivalence rules of gratings, which provide useful guidelines for the design and fabrication of the couplers. Preliminary investigation has been performed on the fabrication and replication of the slanted overhanging grating couplers, which shows the feasibility of fabrication with mature microfabrication techniques and the perspective for mass production.

Statistical study of radiation loss from planar optical waveguides: the curvilinear coordinate method and the small perturbation method

This article presents an original method for the theoretical analysis of the intensity radiated by a dielectric waveguide with rough walls. The method is based on Maxwell's equations under their covariant form written in nonorthogonal coordinate systems adapted to the geometry of the waveguide. The solutions are found by using a perturbation method starting from a guide with smooth walls. The statistical characteristics of the radiant intensity, the mean value, and the probability density function are analytically determined.

Dependence of surface plasmon polarization conversion on the grating pitch

A polarization conversion of linearly polarized light incident on a cross-corrugated metal surface may occur due to the optical energy exchange between the surface plasmon (SP) resonances at the metal-dielectric interface. In this paper, the angular and wavelength dependence of the SP-induced polarization conversion was studied in transmission as a function of the grating pitch of two perpendicular surface relief diffraction gratings. A theoretical model based on graphical representations in momentum space of the traveling light beam through the specimen was developed and successfully applied to the experimental results.

Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method

For analyzing diffraction gratings, a new method is developed based on dividing one period of the grating into homogeneous subdomains and computing the Neumann-to-Dirichlet (NtD) maps for these subdomains by boundary integral equations. For a subdomain, the NtD operator maps the normal derivative of the wave field to the wave field on its boundary. The integral operators used in this method are simple to approximate, since they involve only the standard Green's function of the Helmholtz equation in homogeneous media. The method retains the advantages of existing boundary integral equation methods for diffraction gratings but avoids the quasi-periodic Green's functions that are expensive to evaluate.

Analysis of biomolecules using surface plasmons

Surface plasmon resonance (SPR) biosensors are optical sensors that use special electromagnetic waves (surface plasmon-polaritons) to probe interactions between an analyte in solution and a biomolecular recognition element immobilized on the SPR sensor surface. Major application areas include the detection of biological analytes and analysis of biomolecular interactions, where SPR biosensors provide benefits of label-free real-time analytical technology. The information obtained is both qualitative and quantitative and it is possible to obtain the kinetic parameters of the interaction. This new technology has been used to study a diverse set of interaction partners of biological interest, such as protein-protein, protein-lipids, protein-nucleic acids, or protein and low molecular weight molecules such as drugs, substrates, and cofactors. In addition to basic biomedical research, the SPR biosensor has recently been used in food analysis, proteomics, immunogenicity, and drug discovery. This chapter reviews the major developments in SPR technology. The main application areas are outlined and examples of applications of SPR sensor technology are presented. Future prospects of SPR sensor technology are discussed.