Extremely asymmetrical scattering in gratings with varying mean structural parameters

Extremely asymmetrical scattering (EAS) is an unusual type of Bragg scattering in slanted periodic gratings with the scattered wave (the +1 diffracted order) propagating parallel to the grating boundaries. Here, a unique and strong sensitivity of EAS to small stepwise variations of mean structural parameters at the grating boundaries is predicted theoretically (by means of approximate and rigorous analyses) for bulk TE electromagnetic waves and slab optical modes of arbitrary polarization in holographic (for bulk waves) and corrugation (for slab modes) gratings. The predicted effects are explained using one of the main physical reasons for EAS—the diffractional divergence of the scattered wave (similar to divergence of a laser beam). The approximate method of analysis is based on this understanding of the role of the divergence of the scattered wave, while the rigorous analysis uses the enhanced T-matrix algorithm. The effect of small and large stepwise variations of the mean permittivity at the grating boundaries is analysed. Two distinctly different and unusual patterns of EAS are predicted in the cases of wide and narrow (compared to a critical width) gratings. Comparison between the approximate and rigorous theories is carried out.     

Grazing angle scattering of electromagnetic waves in gratings with varying mean parameters

Abstract

Highly unusual sensitivity of wave scattering in thick periodic gratings to small step-like variations of mean structural parameters at the grating boundaries is predicted and described for the case when the scattered wave (the +1 diffracted order) propagates almost parallel to the front grating boundary (the geometry of GAS — grazing-angle scattering). The analysis is carried out for GAS of bulk TE electromagnetic waves in holographic gratings with varying mean permittivity, and GAS of optical modes guided by a slab with a periodic groove array and varying mean thickness. In particular, it is shown that variations of the mean permittivity by ～0.007% may result in several times variations in the scattered wave amplitude in the grating. At the same time, it is also demonstrated that near the main GAS resonance, the scattered wave amplitudes are only weakly dependent on small variations of mean structural parameters. Physical explanations of the predicted effects are presented. Possible ways of enhancing and, vice versa, reducing (compensating for) the unusual sensitivity of GAS are indicated. Feasible applications of the predicted effects for the design of new highly sensitive sensors and measurement techniques are discussed.     

Analysis of leaky-surface-wave propagating under periodic metal grating

A detailed field analysis is presented for a leaky surface wave propagating under a periodic metal grating, using a theory that neglects the effect of mass loading due to the grating. The approach is based on Floquet's theorem and the coupled equations of wave motion with unperturbed mechanical and perturbed (or periodic) electrical boundary conditions, yielding a general field solution applicable to any material and to arbitrary connections to the grating. As a key step, the periodic boundary equations are solved by combining them into a set of infinite homogeneous equations through algebraic treatment and performing orthogonal integration with respect to space harmonics. The advantage in using this method results from there being no need to use assumptions or complicated expressions anticipating an accurate solution if sufficient space harmonics are considered. It is shown that the theory proposed here can be directly extended to solve simpler SAW problems. An analysis is carried out for LiNbO(3) for both the leaky wave and Rayleigh wave, taking into account dispersion relations, propagation attenuation of the leaky wave, and other field distributions. Theoretical and experimental results for the width of the first stopband are discussed.     

Optical fiber Bragg gratings. Part II. Modeling of finite-length gratings and grating arrays

A model of both uniform finite-length optical fiber Bragg gratings and grating arrays is presented. The model is based on the Floquet-Bloch formalism and allows rigorous investigation of all the physical aspects in either single- or multiple-periodic structures realized on the core of a monomodal fiber. Analytical expressions of reflectivity and transmittivity for both single gratings and grating arrays are derived. The influence of the grating length and the index modulation amplitude on the reflected and transmitted optical power for both sinusoidal and rectangular profiles is evaluated. Good agreement between our method and the well-known coupled-mode theory (CMT) approach has been observed for both single gratings and grating arrays only in the case of weak index perturbation. Significant discrepancies exist there in cases of strong index contrast because of the increasing approximation of the CMT approach. The effects of intragrating phase shift are also shown and discussed.     

Optical interference from pairs and arrays of nanowires

The angle dependence of the scattered light from pairs and one-dimensional arrays of nanowires was studied. The intensity of the scattered light varied distinctly during rotation of the structure. The results could be theoretically modeled by treating a pair of nanowires as a double slit and an array of nanowires as a grating. The correspondence between theory and experimental results conclusively proves that the variations are due to the proposed interference effects.     

Diffraction by a microrelief grating

A model is proposed that describes diffraction by a microrelief grating. A microrelief grating is a grating of large period with grooves containing a periodic microrelief with a period considerably smaller than the period of the grating. In the model the interaction of the incident wave with the fine structure is taken into account rigorously while features of the grating that are large compared with the wavelength are modeled as phase or amplitude objects.     

Propagation of longitudinal leaky surface waves under periodic SiO (2)/Al structure on Li(2)B(4)O(7) substrate

The properties of longitudinal leaky surface waves (LLSW) under a periodic SiO(2)/Al structure on Li(2)B(4)O (7) (LBO) substrate, were investigated theoretically and experimentally, in order to improve the high propagation losses of LLSWs under a periodic Al grating with the normalized thickness over 2%. In the theoretical analysis, the previously presented method based on the boundary integral equations for the periodic metal grating structure on the substrate was extended to include the dielectric layer. In the experiments, devices with Al electrodes recessed into a SiO(2) groove on LBO were fabricated, and the propagation losses of them were estimated. As a result, it was shown that, when the surface of the structure was flattened, the propagation losses were sufficiently low and the first Bragg stopband width decreased.     

Interferometric lithography for nanoscale feature patterning: a comparative analysis between laser interference, evanescent wave interference, and surface plasmon interference

In this paper, we experimentally demonstrate and compare single-exposure multiple-beam interference lithography based on conventional laser interference, evanescent wave interference, and surface plasmon interference. The proposed two-beam and four-beam interference approaches are carried out theoretically and verified experimentally, employing the proposed configurations so as to realize the patterning of one- and two-dimensional periodic features on photoresists. A custom-fabricated grating is employed in the configuration in order to achieve two- and four-beam interference.     

Self-pumped phase-conjugate interferometer with a photorefractive iron-doped lithium-niobate crystal

A single object wave is amplitude divided by a beam splitter into two waves of equal intensity that are made to interfere at the back surface of an iron-doped lithium-niobate crystal so that the normal to the back surface is the angular bisector of the input waves. The interference results in the formation of a phase grating (Bragg grating) in the volume of the crystal. These waves are diffracted at the Bragg grating on both the front focal plane and the back focal plane of the crystal. The wave diffracted in the back focal plane from the Bragg grating and counterpropagating to the incident wave is observed to be the phase conjugate of the input object wave. The wave diffracted in the front focal plane of the Bragg grating is incorporated into the design of an interferometer to measure a specific in-plane displacement of the object wave. It is theoretically evaluated and experimentally demonstrated that interferometers such as those that incorporate conjugate-wave pairs are highly sensitive.     

Electrically reconstructable phonon crystal based on a coplanar waveguide with a nanodimensional ferroelectric film

Electrically reconstructable one-dimensional photon crystal, which is formed based on a coplanar wave guide with periodic modulation of wave resistance, is investigated. To ensure electrical reconstruction of the photon crystal, the coplanar wave guide is formed based on the Ba_0.8Sr_0.2TiO₃-magnesia heterostructure. The possibility of controlling the amplitude and phase-sensitive characteristics of the device under study is shown.     

Diffraction effects in the propagation of radiation in polarizable layers

The very low transmission of light through holes smaller than the wavelength has been found to be enhanced for subwavelength apertures in metallic surfaces with periodic corrugations. This effect has been attributed to the interaction of light with surface plasmons. Similar effects obtained subsequently for non-metallic surfaces have been attributed to evanescent waves on the surface produced by the diffracted Bloch waves from different points in the array. We present an exact solution of Maxwell's equations in the discrete dipole approximation (DDA) for a periodic array of polarizable point dipoles in a layer. Metallic as well as non metallic layers are described. When the wavelength is smaller than the lattice period there is a Bragg's scattered wave, while for subwavelength conditions an evanescent wave on the surface appears. The transmission/reflection coefficients are found to oscillate as a function of frequency, with resonances occurring in a broad range of frequencies depending on the polarizability, at which the evanescent field is enhanced. A detailed study is presented for nanostructured arrays. We find that this model agrees with features observed in experiments through hole arrays supporting the role played by diffraction during light transmission through such arrays without invoking surface plasmons and providing a base to analyze more complex geometries.     

Lamb wave generation and reception with time-delay periodic linear arrays: a BEM simulation and experimental study

A time-delay periodic linear array model has been proposed for Lamb wave generation and reception in plates. The unilateral guided wave emitting and receiving have been achieved by applying the interference principle in the array designs. A hybrid BEM technique has been developed and applied to simulate the wave generation procedure with such arrays and to analyze the performance. Experimental results also are presented for two typical time-delay periodic arrays to qualitatively validate the theoretical designs. The effects of the array parameters on the array performance, such as the selectivity of Lamb modes and effectiveness of Lamb wave generation, are investigated through the 2-D phase velocity-frequency spectrum analyses as well as Lamb mode wave structure calculations.     

Efficient and monolithic polarization conversion system based on a polarization grating

We introduce a new polarization conversion system (PCS) based on a liquid-crystal polarization grating (PG) and louvered wave plate. A simple arrangement of these elements laminated between two microlens arrays results in a compact and monolithic element, with the ability to nearly completely convert unpolarized input into linearly polarized output across most of the visible bandwidth. In our first prototypes, this PG-PCS approach manifests nearly 90% conversion efficiency of unpolarized to polarized for ±11° input light divergence, leading to an energy efficient picoprojector that presents high efficacy (12 lm/W) with good color uniformity.     

Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides

A plasmon-polariton Bragg grating (PPBG) concept, based on the propagation of the long-range ss0b mode in structures comprising a thin metal film of finite width embedded in a homogeneous background dielectric, is discussed theoretically. The PPBGs are operated in an end-fire arrangement with access plasmon-polariton waveguides or optical fibers being directly butt-coupled to their input and output ports. A model for the PPBGs, which was recently proposed and validated experimentally for third order structures, is used to generate theoretical results describing their expected performance for various architectures. First order uniform periodic, interleaved, and apodized grating structures are considered and compared. Third order uniform periodic designs are also considered. The gratings investigated are based on a 20 nm thick Au film embedded in SiO2 and have a Bragg wavelength near 1550 nm. First order uniform periodic gratings provide the strongest reflection, with a maximum reflectance of about 97% being achievable over a length of a few millimeters and over a full width at half-maximum bandwidth of about 0.8 nm. The off-resonance insertion loss of the gratings can be as low as a few decibels. Specific Bragg wavelengths can easily be attained using interleaving without requiring extraordinary resolution from the fabrication process. Apodized designs providing low sidelobe levels are also investigated.     

Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit

Scatterometry is now proven to be a very powerful technique for measurement of subwavelength periodic structures. However it requires heavy numerical calculations of the scattered optical waves from the structure. For periodic nanoarrays with feature size less than 100 nm, it is possible to simplify this using the Rytov near-quasi-static approximation valid for feature periods only few time less than the wavelength. The validity is investigated by way of comparison with exact numerical results obtained with the eigenfunctions approach. It is shown to be adequate for the determination of the structure parameters from the specularly reflected or transmitted waves and their polarization or ellipsometric properties. The validity of this approach is applied to lamellar nanoscale grating photoresist lines on Si substrate. The high sensitivity of the signals to the structure parameters is demonstrated using wavelengths of only few times the period.     

Beam steering with segmented annular arrays

Two-dimensional (2-D) arrays of squared matrix have maximum periodicity in their main directions; consequently, they require half wavelength (lambda/2), interelement spacing to avoid grating lobes. This condition gives rise to well-known problems derived from the huge number of array elements and from their small size. In contrast, 2-D arrays with curvilinear configuration produce lower grating lobes and, therefore, allow the element size to be increased beyond lambda/2. Using larger elements, these arrays have the advantage of reducing the number of elements and of increasing the signal-to-noise ratio (SNR). In this paper, the beamforming properties of segmented annular phased arrays are theoretically analyzed and compared with the equivalent squared matrix array. In the first part, point-like elements are considered in order to facilitate the field analysis with respect to the array structure. Afterward, the effect of the element size on the steered beam properties also is presented. In the examples, it is shown that the segmented annular array has notably lower grating lobes than the equivalent squared matrix array and that it is possible to design segmented annular arrays with interelement distance higher than lambda whose beam characteristics are perfectly valid for volumetric imaging applications.     

Perturbed Talbot patterns for the measurement of low particle concentrations in fluids

Behind periodic amplitude or phase objects, the object transmittance is repeated at the so-called Talbot distances. In these planes perpendicular to the propagation direction, Talbot self-images are formed. In the case of plane wave illumination, the distances between the self-images are equally spaced. A periodic pattern called optical carpet or Talbot carpet is formed along the propagation direction. We show theoretically how the presence of spherical particles (10 to 100 μm in diameter) behind gratings of 20 and 50 μm period affects the formation of Talbot carpets and Talbot self-images at 633 nm illumination wavelength. The scattering of the particles is modeled by the Fresnel diffraction of its geometrical shadow. We analytically calculate the interference of the diffraction orders of rectangular and sinusoidal amplitude gratings disturbed by the presence of particles. To verify our model, we present measurements of Talbot carpets perturbed with both opaque disks and transparent spheres, and discuss the effects for various size parameters. We present an approach to simulate the movement of particles within the Talbot pattern in real time. We simulate and measure axial and lateral particle movements within a probe volume and evaluate the effect on the signal formation in a Talbot interferometric setup. We evaluate the best system parameters in terms of grating period and particle-detector-distance for a prospective measuring setup to determine characteristics of flowing suspensions, such as particle volume concentration or particle size distribution.     

Sampling time effects in the ACT device

The signal-dependent sampling process in an acoustic charge transport (ACT) device is demonstrated. Theoretical calculations and experimental measurements show the direct effect of gate voltage, wave amplitude, and transport depth on the sampling interval. A decrease in gate voltage and transport depth, and an increase in wave amplitude, are shown to reduce the increase in sampling time delay for a fixed transport current. An analysis of the distortion generated by this nonuniform sampling is performed, and a channel-current-intercept value is computed for a typical ACT device.     

Spherical wave scattering by slender bodies

The problem of the scattering of a spherical acoustic wave by rigid slender bodies of revolution is investigated theoretically from a formalism based on the matched asymptotic expansion method. It is an extension of a formulation that was originally derived for incident plane waves with the so-called slender-body approximation. Simple and practical formulas are obtained for the scattered pressure in the near- and far-fields: they are valid at low and medium frequencies when the reduced wavenumber Ka is less or of the order of unity. Computations of the monostatic and bistatic angular distributions for a spheroid are presented to illustrate the sensitivity of the scattered field with respect to the distance source and observation point.