Compound Gratings Research Articles

Dynamical Equivalent Circuit for 1-D Periodic Compound Gratings

Metallic compound gratings are studied in this work by means of an analytical equivalent circuit approach in order to obtain its transmission and reflection properties when illuminated by a TM-polarized plane wave. A compound grating consists of the periodic repetition of a finite number of slits carved out of a thick metal slab (reflection grating) or connecting two separated open regions through groups of slits in the metal slab (transmission grating). The equivalent circuit is rigorously obtained starting from a simplified version of the integral equation for the electric field at the slits apertures. That equivalent circuit involves transmission-line sections that account for the fundamental and lowest order diffracted modes (which does give the “dynamical” nature to the present equivalent circuit), and lumped components to model the effect of all the higher order diffracted modes. All the relevant and complex features of the spectra can be satisfactorily explained in terms of the topology and characteristics of the equivalent circuit. In contrast with some previously reported circuit models, all the dynamical and quasi-static circuit elements are analytically and explicitly obtained in terms of the geometric and electrical parameters of the grating. The accuracy of the approximate circuit model is very good over a very wide band, as it is demonstrated by comparison with full-wave data computed with commercial electromagnetic solvers.

Tunable Composite Graphene–Silica Pseudonoise Gratings

Graphene is a two-dimensional material with outstanding properties such as high electronic and thermal conductivities that may bring a revolution in the miniaturization of electronic and optical circuits. In this letter, we analyze a tunable grating structure that combines a graphene grating and a vertical silica grating based upon a pseudonoise function. We show that the properties of the compound grating can be tailored by applying an external voltage to the graphene grating.

Optical Waveguides with Compound Multiperiodic Grating Nanostructures for Refractive Index Sensing

The spectral characteristics and refractive index sensitivity of compound multiperiodic grating waveguides are investigated in theory and experiment. Compound gratings are formed by superposition of two or more monoperiodic gratings. Compared to monoperiodic photonic crystal waveguides, compound grating waveguides offer more degrees of design freedom by choice of component grating periods and duty cycles. Refractive index sensing is achieved by evaluating the wavelength or intensity of guided mode resonances in the reflection spectrum. We designed, fabricated, and characterized 24 different compound multiperiodic nanostructured waveguides for refractive index sensing. Simulations are carried out with the Rigorous Coupled Wave Algorithm (RCWA). The resulting spectra, resonance sensitivities, and quality factors are compared to monoperiodic as well as to three selected aperiodic nanostructures (Rudin-Shapiro, Fibonacci, and Thue-Morse). The refractive index sensitivity of the TE resonances is similar for all types of investigated nanostructures. For the TM resonances the compound multiperiodic nanostructures exhibit higher sensitivity values compared to the monoperiodic nanostructure and similar values as the aperiodic nanostructures. No significant influence of the compound grating duty cycles on the sensitivity is observed.

Cortical responses elicited by luminance and compound stimuli modulated by pseudo-random sequences: comparison between normal trichromats and congenital red-green color blinds.

Conventional pattern-reversal visual evoked cortical potential (VECP) shows positivity for luminance and chromatic equiluminant stimuli while conventional pattern-onset VECP shows positivity for luminance pattern-onset and negativity for chromatic pattern-onset. We evaluated how the presentation mode affects VECPs elicited by luminance and compound (luminance plus chromatic) pseudo-random stimulation. Eleven normal trichromats and 17 red-green color-blinds were studied. Pattern-reversal and pattern-onset luminance and compound (luminance plus red-green) gratings were temporally modulated by m-sequence. We used a cross-correlation routine to extract the first order kernel (K1) and the first and second slices of the second order kernel (K2.1 and K2.2, respectively) from the VECP response. We integrated the amplitude of VECP components as a function of time in order to estimate its magnitude for each stimulus condition. We also used a normalized cross-correlation method in order to test the similarity of the VECP components. The VECP components varied with the presentation mode and the presence of red-green contrast in the stimuli. In trichromats, for compound conditions, pattern-onset K1, K2.1, and K2.2, and pattern-reversal K2.1 and K2.2 had negative-dominated waveforms at 100 ms. Small negativity or small positivity were observed in dichromats. Trichromats had larger VECP magnitude than color-blinds for compound pattern-onset K1 (with large variability across subjects), compound pattern-onset and pattern-reversal K2.1, and compound pattern-reversal K2.2. Trichromats and color-blinds had similar VECP amplitude for compound pattern-reversal K1 and compound pattern-onset K2.2, as well as for all luminance conditions. The cross-correlation analysis showed high similarity between waveforms of compound pattern-onset K2.1 and pattern-reversal K2.2 as well as pattern-reversal K2.1 and K2.2. We suggest that compound pattern-reversal K2.1 is an appropriate response to study red-green color-opponent activity.

Effects of Dielectric Environment on Phase Resonance in Compound Grating

Effects of dielectric environment on phase resonance in compound grating are investigated theoretically and numerically. Transmission characteristics can be effectively tailored by changing the dielectric environment. When the dielectric constants between the two slits are slightly different, the transmission spectra show obvious dips for all modes, and values of the dips are near to zero, and photon forbidden band gaps emerge with larger difference of dielectric environment. The corresponding physical mechanisms are discussed by means of effective refractive index and effective length based on F‐P‐like and phase resonant mechanisms. In addition, the electric field for the peak at the shorter wavelength of the dip is mainly concentrated on the slit filled with smaller dielectric constant, while the electric field located on the slit filled with larger dielectric constant for the peak at the longer wavelength of the dip. By selecting a proper dielectric environment, the channel selecting device can be constructed by using the dielectric compound grating.

Multiple excitations of surface-plasmon-polariton waves in an amorphous silicon p-i-n solar cell using Fourier harmonics and compound gratings

In an amorphous silicon p-i-n solar cell, back contact Fourier harmonics (FH) and compound gratings were studied theoretically, using the rigorous coupled-wave analysis. The FH grating was found to enable more efficient multiple surface-plasmon-polariton (SPP) wave excitations compared with a compound grating, while both of them are made of the same constituting simple gratings. The incident plane wave was considered to be TM-polarized. The FH and compound gratings were designed to excite multiple SPP waves at desirable wavelengths by solving a canonical boundary-value problem. The excitation of SPP waves is indicated by the presence of peaks in the absorptance plots. The multiple SPP waves excited by the FH grating were found to increase the external quantum efficiency.

Mixing of Chromatic and Luminance Retinal Signals in Primate Area V1

Vision emerges from activation of chromatic and achromatic retinal channels whose interaction in visual cortex is still poorly understood. To investigate this interaction, we recorded neuronal activity from retinal ganglion cells and V1 cortical cells in macaques and measured their visual responses to grating stimuli that had either luminance contrast (luminance grating), chromatic contrast (chromatic grating), or a combination of the two (compound grating). As with parvocellular or koniocellular retinal ganglion cells, some V1 cells responded mostly to the chromatic contrast of the compound grating. As with magnocellular retinal ganglion cells, other V1 cells responded mostly to the luminance contrast and generated a frequency-doubled response to equiluminant chromatic gratings. Unlike magnocellular and parvocellular retinal ganglion cells, V1 cells formed a unimodal distribution for luminance/color preference with a 2- to 4-fold bias toward luminance. V1 cells associated with positive local field potentials in deep layers showed the strongest combined responses to color and luminance and, as a population, V1 cells encoded a diverse combination of luminance/color edges that matched edge distributions of natural scenes. Taken together, these results suggest that the primary visual cortex combines magnocellular and parvocellular retinal inputs to increase cortical receptive field diversity and to optimize visual processing of our natural environment.

Fano phase resonances in multilayer metal-dielectric compound gratings

Phase resonances in multilayer metal-dielectric compound gratings are numerically modeled and described. Additional grating layers allow for more complex types of phase resonances in which light travels in different, circuitous routes through the structure. It is shown that phase resonances produce highly enhanced fields, have a very narrow bandwidth, are Fano resonances with asymmetric line shapes of their reflectance, and produce a complete inversion in the transmittivity and opacity of low loss structures. Several multigrating structures are numerically modeled that show the addition of more complicated phase resonances as more layers are added to the structure. The dispersion curves of the multiple bands of phase resonances are predicted using an analytical approach and numerical modeling. Applications of the resonance effects are described for optical filters.

Tailoring the Optical Transmission Spectra of Double-Layered Compound Metallic Gratings

The transmission resonance characteristics of a gold double-layered compound grating (DCG) are investigated numerically using the rigorous coupled-wave analysis (RCWA) method. The DCG is assumed to comprise two identical single-layered gratings separated by an air gap with a thickness of 0 ~ 250 mm. Furthermore, each grating is assumed to comprise two slits with different widths (w) within each period. The physical origins of the transmission features of the DCG structures are examined using the finite-difference time-domain (FDTD) method. The RCWA results show that the optical transmission spectra of the considered DCG structures can be tailored over a wide range of wavelengths via a suitable adjustment of the air gap thickness. Moreover, it is shown that, for values of the air gap thickness greater than 100 nm, the transmission spectrum of the DCG structure converges toward that of a single-layered compound grating (SCG). Overall, the results presented in this paper show that the optical transmission properties of a metallic DCG are highly sensitive to the thickness of the air gap between the two grating structures. As such, DCG structures are ideally suited to the realization of proximity sensors and other photonic-based optical devices.

Extraordinary light circulation and concentration of s- and p-polarized phase resonances

Both s-polarized and p-polarized phase resonances in one-dimensionally compound transmission gratings are analyzed, modeled, and measured. We demonstrate that s-polarized phase resonances occur with similar characteristics of p-polarized phase resonances, with narrow bandwidths, high Q values, and highly amplified fields. The phase difference of π radian between the fields in the coupled cavities produces light circulation and an inversion of the transmissivity/opacity of the structure. The dependencies of bandwidth and wavelength of the resonances on structural and material properties are described, as well as the way light flows in the structure when the phase resonances are excited.

EIGENMODES AND RESONANCE PROPERTIES OF ONE‐DIMENSIONALLY PERIODIC METALLIC BAR GRATINGS. PART 1: CLASSICAL GRATING

The interest shown today toward resonance properties of perforated metal gratings has been renewed owing to the effect known as the "enhanced transmission phenomena" which was investigated, interpreted and found promising for practical applications. Based on the works of the V. Shestopalov school, the paper is aimed at analyzing properties of one‐dimensionally periodic gratings, i.e. at investigating eigenmode spectra and principles of their formation which are determined in particular by the structure of the grating period, and then at analyzing the impact of these spectra on the resonance characteristics. The effects arising in the case of scattering of an H‐polarized plane wave by a one‐dimensionally periodic metallic bar grating are considered. Specific features of the resonance interaction are treated in terms of the spectral theory of open periodic resonant cavities. A classification is suggested for the spectra of classical and compound gratings. The spectrum of lower‐order eigenmodes of the classical grating is investigated in dependence on the grating geometry, and motion of the eigenfrequencies along a multisheeted Riemann surface is analyzed as the grating thickness decreases to zero. It is shown that the limiting points of frequencies of antisymmetric modes correspond to the cutoff points of the higher‐order Floquet harmonics; the greater the number of eigenmode field variations, the higher order of the harmonic. Eigenfrequency paths on upper sheets and regularities of their crossing the real axis where the wave packet conversion takes place are investigated. The resonance behavior of the grating is described in terms of the unified spectral theory which makes it possible not only to establish the interrelation between different resonance effects but also to determine the source of such a behavior conditioned by excitation of certain eigenmodes.

The light filtering and guiding properties of high finesse phase resonant compound gratings

Phase resonances in compound gratings are studied in the frequency and time domains, with the gratings having two dissimilar grooves within the unit cell that each support waveguide cavity modes that couple. Described in this work are the dependence of the phase resonances' Q on the degree of difference between the grooves in the unit cell, their optical properties, a closed-form expression describing their dispersion, their excitation, and the extraction of energy from the phase resonances into free space and into a waveguide. Application to optical filters and corrugated surface antennas are discussed.

Psychophysical and physiological responses to gratings with luminance and chromatic components of different spatial frequencies

Gratings that contain luminance and chromatic components of different spatial frequencies were used to study the segregation of signals in luminance and chromatic pathways. Psychophysical detection and discrimination thresholds to these compound gratings, with luminance and chromatic components of the one either half or double the spatial frequency of the other, were measured in human observers. Spatial frequency tuning curves for detection of compound gratings followed the envelope of those for luminance and chromatic gratings. Different grating types were discriminable at detection threshold. Fourier analysis of physiological responses of macaque retinal ganglion cells to compound waveforms showed chromatic information to be restricted to the parvocellular pathway and luminance information to the magnocellular pathway. Taken together, the human psychophysical and macaque physiological data support the strict segregation of luminance and chromatic information in independent channels, with the magnocellular and parvocellular pathways, respectively, serving as likely the physiological substrates.

Contrast and stimulus complexity moderate the relationship between spatial frequency and perceived speed: Implications for MT models of speed perception

Area MT in extrastriate visual cortex is widely believed to be responsible for the perception of object speed. Recent physiological data show that many cells in macaque visual area MT change their speed preferences with a change in stimulus spatial frequency (N. J. Priebe, C. R. Cassanello, & S. G. Lisberger, 2003) and that this effect can accurately predict the dependence of perceived speed on spatial frequency demonstrated in a related psychophysical study (N. J. Priebe & S. G. Lisberger, 2004). For more complex compound gratings and high contrast stimuli, MT cell speed preferences show sharper tuning and less dependence on spatial frequency (Priebe et al., 2003), allowing us to predict that such stimuli should produce speed percepts that are less vulnerable to spatial frequency variations. We investigated the perceived speed of simple sine wave gratings and more complex compound gratings (formed from 2 sine wave components) in response to changes in contrast and spatial frequency. In all cases, high contrast stimuli appeared to translate more rapidly. In addition, high spatial frequencies appeared faster-the opposite effect to that predicted by changes in MT cell spatial frequency preferences. Complex grating stimuli were somewhat "protected" from the effect of spatial frequency (compared to simple gratings), as predicted. However, contrary to predictions, the effect of spatial frequency was larger in high (compared to low) contrast gratings. Our data demonstrate that the previously established links between changes in MT cells' speed preferences and human speed perception are more complex than first thought.

Attention to hierarchical level influences attentional selection of spatial scale.

Ample evidence suggests that global perception may involve low spatial frequency (LSF) processing and that local perception may involve high spatial frequency (HSF) processing (Shulman, Sullivan, Gish, & Sakoda, 1986; Shulman & Wilson, 1987; Robertson, 1996). It is debated whether SF selection is a low-level mechanism associating global and local information with absolute LSF and HSF content, or whether it is a higher level mechanism involving a selective process that defines the SF range in which global and local can then be relatively defined. The present study provides support for the latter claim by demonstrating that allocating attention to global or local levels of hierarchical displays biased selection of LSFs or HSFs, respectively, in subsequently presented compound gratings. This bias occurred despite a change in the response dimension (from letter identification in the hierarchical stimulus to orientation discrimination in the grating) and despite a difference in retinal location of the hierarchical stimuli and the grating stimulus. Moreover, the bias was determined by the relationship between the 2 SFs in the compound grating (i.e., their relative frequency) rather than the absolute SF values.

Numerical study on the optical absorption of one dimension metallic gratings

We investigate the reflected response of one-dimensional metallic grating with rigid coupled-wave analysis. Three types of resonance absorptions, i.e., Rayleigh anomaly, surface plasmon polariton (SPP) standing wave resonance and geometric resonance, are identified in the gray-scale map of the reflectivity as a function of two structural parameters: grating period and groove depth. Furthermore, the interactions among these resonances are discussed. Our calculation reveals that a hybrid mode of SPP standing wave resonance and geometric resonance can be found, while no hybrid mode of Rayleigh anomaly and geometric resonance exists. In the analysis of compound gratings, we find phase resonance. How the phase resonance changes the reflection and the absorption of compound metallic gratings is also discussed. When the wavelength of incident light is less than grating period, sharp dip is found in reflectivity as a function of groove depth. In the other case, i.e. Wavelength greater than grating period, phase resonance results in a split of the hybrid absorption branch of SPP standing wave resonance and geometric resonance.

Segregation of chromatic and luminance signals using a novel grating stimulus

Segregation of chromatic and luminance signals in afferent pathways are investigated with a grating stimulus containing luminance and chromatic components of different spatial frequencies. Ganglion cell recordings were obtained from the retinae of macaques (Macaca fascicularis). Cell responses to the 'compound' gratings were compared to responses to standard chromatic and luminance gratings. Parvocellular (PC) pathway cell responses to compound and chromatic gratings were very similar, as were magnocellular (MC) cell responses to compound and luminance gratings. This was the case over a broad range of spatial and temporal frequencies and contrasts. In psychophysical experiments with human observers, discrimination between grating types was possible close to detection threshold. These results are consistent with chromatic and luminance structure in complex patterns being strictly localized in different afferent pathways. This novel stimulus may prove useful in identifying afferent inputs to cortical neurons.

Infrared reflectance from a compound grating and its alternative componential gratings

This work both numerically and experimentally investigates reflectance spectra from a metallic compound grating and its alternative sets of componential gratings at wavelengths between 2.5 and 25 μm. The numerical algorithm is based on the rigorous coupled-wave analysis, and the specular reflectance is measured with Fourier-transform infrared spectrometry. The impact dominance of each componential grating on the compound grating reflectance is thoroughly discussed considering the incidence polarization, grating geometry, and rules for profile synthesis. Tailored spectra by individual Wood’s anomaly and their interplay associated with the profile synthesis are also studied.

Anomalous optical absorption in metallic gratings with subwavelength slits

The absorption in metallic gratings with subwavelength slits is theoretically investigated. Anomalous optical absorption occurs over a wide range of incident angles for both polarizations. In particular, a nearly perfect absorbance up to 99.5% with a significant bandwidth is attained for TM polarization with compound slits. Enhanced absorption is associated with extreme concentration of fields inside the structure. The respective field pattern depicts a special feature of surface plasmons excited on single interface only, which are identified as semibonding modes. The anomalous absorption is also achieved for TE polarization, when the compound grating is reduced to a simple grating. For this polarization, the nomalous absorption is attributed to the occurrence of trapped modes, with a slightly smaller absorbance (98.4%).

Attention to hierarchical level influences attentional selection of spatial scale

Ample evidence suggests that global perception may involve low spatial frequency (LSF) processing and that local perception may involve high spatial frequency (HSF) processing (Shulman, Sullivan, Gish, & Sakoda, 1986; Shulman & Wilson, 1987; Robertson, 1996). It is debated whether SF selection is a low-level mechanism associating global and local information with absolute LSF and HSF content, or whether it is a higher level mechanism involving a selective process that defines the SF range in which global and local can then be relatively defined. The present study provides support for the latter claim by demonstrating that allocating attention to global or local levels of hierarchical displays biased selection of LSFs or HSFs, respectively, in subsequently presented compound gratings. This bias occurred despite a change in the response dimension (from letter identification in the hierarchical stimulus to orientation discrimination in the grating) and despite a difference in retinal location of the hierarchical stimuli and the grating stimulus. Moreover, the bias was determined by the relationship between the 2 SFs in the compound grating (i.e., their relative frequency) rather than the absolute SF values.