Modes In Gratings Research Articles

Excitation of surface phonon polariton modes in gold gratings with silicon carbide substrate and their potential sensing applications

We demonstrate the excitation of surface phonon polaritons (SPhPs) in the mid-infrared (mid-IR) Reststrahlen band (10.288μm-12.563μm) on patterned surfaces with silicon carbide (SiC) substrate and gold (Au) gratings. The very large negative permittivity of Au limits its applications in the mid-IR range, and to couple incident light to SPhPs modes, their momentum mismatch can be compensated by patterning Au grating onto the surface of SiC substrate. Samples were fabricated and characterized experimentally by Fourier transform infrared reflection (FTIR) spectroscopy. The optical properties were also simulated by the rigorous coupled wave analysis (RCWA) method. Reflection dips are observed for light polarized vertical to the grating lines (TM-polarized), which are attributed to the coupling of electromagnetic (EM) waves into the SPhP modes. In addition, we present small-volume index sensing with analyte specificity based on mid-IR SPhPs in the fabricated configuration.

Towards do-it-yourself planar optical components using plasmon-assisted etching.

In recent years, the push to foster increased technological innovation and basic scientific and engineering interest from the broadest sectors of society has helped to accelerate the development of do-it-yourself (DIY) components, particularly those related to low-cost microcontroller boards. The attraction with DIY kits is the simplification of the intervening steps going from basic design to fabrication, albeit typically at the expense of quality. We present herein plasmon-assisted etching as an approach to extend the DIY theme to optics, specifically the table-top fabrication of planar optical components. By operating in the design space between metasurfaces and traditional flat optical components, we employ arrays of Au pillar-supported bowtie nanoantennas as a template structure. To demonstrate, we fabricate a Fresnel zone plate, diffraction grating and holographic mode converter—all using the same template. Applications to nanotweezers and fabricating heterogeneous nanoantennas are also shown.

Subwavelength Grating Structure with High Aspect Ratio and Tapered Sidewall Profiles

ABSTRACTCMOS-compatible fabrication and etching processes are often used in subwavelength grating structures manufacturing, it normally generates tapered sidewall profile of the gratings. In this work, we have studied the impacts on resonance mode characteristics of subwavelength grating structures due to the tapered sidewall profile, as well as grating with high aspect ratio. Our simulation results have revealed that both of these two factors play important roles on the resonance mode behavior of subwavelength grating devices. We also discussed the mechanism between the guided mode resonance and the grating cavity mode resonance. Our study will provide guidance for a series of integrated photonics devices applications, such as compact optical filter, photonics amplifier, and lasers, while the realistic subwavelength grating structure is considered.

Periodicity Matters: Grating or lattice resonances in the scattering by sparse arrays of subwavelength strips and wires

This article reviews the nature and history of the discovery of high-quality natural modes existing on periodic arrays of many subwavelength scatterers; such arrays can be viewed as specific periodically structured open resonators. These grating modes (GMs), like any other natural modes, give rise to the associated resonances in electromagnetic-wave scattering and absorption. Their complex wavelengths are always located very close to (but not exactly at) the well-known Rayleigh anomalies (RAs), determined only by the period and the angle of incidence. This circumstance has long been a reason for their misinterpretation as RAs, especially in the measurements and simulations using low-resolution methods. In the frequency scans of the reflectance or transmittance, GM resonances usually develop as asymmetric Fano-shape spikes. In the optical range, if a grating is made of subwavelength-size noble-metal elements, then GMs exist together with better-known localized surface-plasmon (LSP) modes. Thanks to high tunability and considerably higher Q-factors, the GM resonances can potentially replace the LSP-mode resonances in the design of nanosensors, nanoantennas, and solar-cell nanoabsorbers.

Design of a broadband high-efficiency two-port beam subwavelength grating splitter by modal method

On the basis of the comparison of diffraction efficiencies calculated by the simplified modal method to exact results predicted from rigorous coupled-wave analysis, the accuracy of modal method for subwavelength triangular-groove gratings is evaluated. It is revealed that a larger error exists in smaller grating period and lower groove depth. To enhance the validity of simplified modal method, we consider the reflection loss of propagating grating modes by using the optical thin film theory. Then, we design a highly efficient transmission two-port beam splitter grating with subwavelength triangular-grooves by using the enhanced simplified modal method. The physical mechanism of the designed grating splitter with a high transmitted performance over a broad spectrum and a wide angular spectrum can be explained by using the modal method with consideration of accumulated average phase difference of two excited propagating grating modes. Obviously, the designed splitter with triangular-grooves has higher transmitted diffraction efficiency and more broadband property than that with general rectangular ones. The broadband highly efficient transmission characteristic can be attributed to gradient effective index from air-grating interface to grating-substrate interface.

Flat grating lens utilizing widely variable transmission-phase via guided-modes.

We experimentally demonstrate a polarization-independent flat grating lens in the near-infrared region. The grating lens consists of ridges in the square lattice arrangement, and the ridge dimensions are gradually changed to distribute a phase map with focusing ability. It is well known that guided modes in gratings offer unity-reflection at a resonance, and therefore the transmission phase is widely varied around the resonance. We employ such transmission phase behavior and show that high transmittance is obtained in each unit cell for wide variation range of the transmission phase at the operation wavelength by sharpening the resonance. This enables us to accomplish a highly efficient transmissive grating lens.

Monitoring layer-by-layer assembly of polyelectrolyte multi-layers using high-order cladding mode in long-period fiber gratings

We have undertaken a combined theoretical and experimental investigation to illustrate and demonstrate the strong correlation between the order of the coupled cladding modes in long-period gratings (LPG) in conventional single mode fiber and their sensitivity to the process of layer-by-layer (LbL) assembly of polyelectrolyte multi-layers. We show that high-order cladding modes such as LP0,10 in LPG are significantly more sensitive than their lower-order counterparts such as LP0,2, with LP0,10 yielding a shift of 1.575nm in resonance wavelength per polyelectrolyte repeating unit of poly(vinyl pyrrolidone)/poly(methacrylic acid) bi-layer. The integrated LPG/LbL strategy as a robust LbL test-bed has broad ramifications in exploring and exploiting sensors and devices enabled by versatile, stimuli-responsive polyelectrolyte thin films.

Improvement of the validity of the simplified modal method for designing a subwavelength dielectric transmission grating

To accurately and easily design the diffraction characteristics of a rectangular transmission grating under the illumination of Littrow mounting, the validity and limitation of the simplified modal method is evaluated by a comparison of diffraction efficiencies predicted by the modal approach to exact results calculated with rigorous coupled-wave analysis. The influence of the grating normalized period, the normalized groove depth, and the fill factor on the accuracy of the modal method is quantitatively determined. More importantly, the reflection effect of two propagating grating modes with the optical thin-film model and the nonsymmetrical Fabry-Perot model is proposed and applied in the modal method to improve the accuracy of the calculated diffraction efficiencies. Generally, it is found that the thin-film model of reflection loss is valid at the smaller normalized period, but the Fabry-Perot model can exactly calculate the reflection loss of grating modes at the larger normalized period. Based on the fact that the validity of the modal approach is determined independently of the incident wavelength, the exact design and analysis of grating diffraction elements can be implemented at different wavelengths by simply scaling the grating parameters. Moreover, the polarization effect of diffraction properties on the limitation of the modal method without and with the reflection loss of grating modes is clearly demonstrated.

Nearly Total Omnidirectional Reflection by a Single Layer of Nanorods

It is shown that a single-layer array of high electric permittivity (high-ε) rods with a radius smaller than λ/10 is capable of reflecting more than 97% of the energy of optical waves with an arbitrary incident angle. Here, λ is the incident wavelength. The occurrence of the phenomenon depends on the construction of two particular grating modes (GMs) in the array which result in two corresponding transmitted wave components that cancel each other. The construction of the dominant GMs in the array benefits from the highly independent manipulability of the angular momenta components with opposite signs in high-ε particles. The effect offers the possibility to improve the optical elements integration level in on-chip optical circuits.

Multi-resonant plasmonic nanodome arrays for label-free biosensing applications

The characteristics and utility of plasmonic nanodome arrays capable of supporting multiple resonance modes are described. A low-cost, large-area replica molding process is used to produce, on flexible plastic substrates, two-dimensional periodic arrays of cylinders that are subsequently coated with SiO2 and Ag thin films to form dome-shaped structures, with 14 nm spacing between the features, in a precise and reproducible fashion. Three distinct optical resonance modes, a grating diffraction mode and two localized surface plasmon resonance (LSPR) modes, are observed experimentally and confirmed by finite-difference-time-domain (FDTD) modeling which is used to calculate the electromagnetic field distribution of each resonance around the nanodome array structure. Each optical mode is characterized by measuring sensitivity to bulk refractive index changes and to surface effects, which are examined using stacked polyelectrolyte layers. The utility of the plasmonic nanodome array as a functional interface for biosensing applications is demonstrated by performing a bioassay to measure the binding affinity constant between protein A and human immunoglobulin G (IgG) as a model system. The nanoreplica molding process presented in this work allows for simple, inexpensive, high-throughput fabrication of nanoscale plasmonic structures over a large surface area (120 × 120 mm(2)) without the requirement for high resolution lithography or additional processes such as etching or liftoff. The availability of multiple resonant modes, each with different optical properties, allows the nanodome array surface to address a wide range of biosensing problems with various target analytes of different sizes and configurations.

Calculation and simulation of optical fiber core and cladding mode effective refractive index

The accurate computation of effective refractive index of optical fiber core and the cladding mode are needed for the fiber structure design, mode dispersion analysis and fiber grating mode coupling research. In this paper, based on three layered optical fiber waveguide model and its accurate eigenvalue equation, by using the cut string algorithm the effective refractive index of core mode is solved. At the same time the computation results are verified by using COMSOL software. By using interval traversal algorithm the effective refractive index of cladding mode is computed. Compared with the existing algorithms, this method can avoid the loss of root during the calculation. It can also avoid the generation of odd point and can keep the normality of each mode. The simulation is based on Mathematica software. The curves relating effective refractive index of core and cladding mode to wavelength are obtained.

Theoretical analysis of a tilted fiber grating polarizer by the beam tracing approach

Using the new beam tracing approach of dividing a fiber grating into a pile of infinitesimally thin films and calculating the multiple beam interference of the Fresnel reflections from the thin-film interfaces, a tilted fiber grating based polarizer is theoretically investigated. On the Gaussian fiber mode model, new analytical formulas for expressing the characteristics of the 45° tilted fiber grating polarizer are obtained as the explicit functions of the fiber grating and fiber mode parameters. The present approach provides a clear understanding and fine perspective of all the properties of the tilted fiber grating polarizer, as well as making their quantitative evaluation much easier, as compared with previous works. Our numerical result is shown to be in good agreement with the numerical solution by the volume current method. The achievable polarization performance with different grating parameters is numerically examined and discussed.

Design and fabrication of a polarization-independent wideband transmission fused-silica grating

A fused-silica polarization-independent wideband transmission grating used in the -1st order (Littrow mounting) for chirped-pulse-amplification, high-power lasers is designed and manufactured. An approximate grating profile can be obtained by using the simplified modal method with consideration for the corresponding accumulated phase difference of two excited propagating grating modes. An exact grating profile is optimized by using the rigorous coupled-wave analysis. With the optimized profile parameters, the gratings can theoretically exhibit diffraction efficiencies of greater than 97% at a wavelength of 800 nm for both of TE- and TM-polarized waves. Diffraction efficiencies of greater than 92% can be obtained in a 100 nm bandwidth (from 750 to 850 nm) for both TE- and TM-polarized waves. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results agree well with the theoretical values.

Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm

We describe polarization-independent triangular-groove fused-silica gratings illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. The physical mechanisms of the grating can be shown clearly by using the simplified modal method with consideration of the corresponding accumulated average phase difference of two excited propagating grating modes, which illustrates that the grating structure depends mainly on the ratio of the average effective indices difference to the incident wavelength. Exact grating profile is optimized by using the rigorous coupled-wave analysis (RCWA). With the optimized grating parameters, the grating exhibits diffraction efficiencies of greater than 90% under TE- and TM-polarized incident lights for 101 nm spectral bandwidths (1500–1601 nm) and it can reach an efficiency of more than 99% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, coating of dielectric film layers, the designed triangular-groove fused-silica grating should be of great interest for DWDM application.

Unified design of wavelength-independent deep-etched fused-silica gratings

We present a unified design of wavelength-independent deep-etched fused-silica gratings as polarizing beam splitters and polarization-independent two-port beam splitters by using the simplified modal method. By defining unified grating parameters as the ratio of incident wavelength to grating period and the ratio of groove depth to grating period, unified grating structures are found to be approximately wavelength-independent, which is based on the modal view of the accumulated phase difference of two excited propagating grating modes. Diffraction efficiencies given by the rigorous coupled-wave analysis (RCWA) verified this unified design at the wavelength of 1064 nm. It should be noted that this unified design of wavelength-independent gratings is an analytic result, which is impossible to be derived with the well-known numerical RCWA. Modal method is powerful and presents a clear physical picture for us to obtain this unified design. Therefore, this unified design can be used as a general guideline for designing deep-etched fused-silica gratings as beam splitters for practical applications from ultraviolet to near infrared.

Analysis of coupling from core mode to counter-propagating radiation modes in tilted fiber Bragg gratings

Radiation-mode coupling is stronger and more efficient in tilted fiber Bragg gratings than in other fiber gratings; it has good advantage in such fields as optical communication and optical sensors. A simplified coupled-mode theory (CMT) approach is proposed for what we believe to be the first time, whose validity is demonstrated by comparing its simulation results with that of the complete CMT equations. With the simplified CMT approach, a theoretical spectral analysis of coupling from core mode to counter-propagating radiation modes in reflective tilted fiber Bragg gratings is presented. The influence of grating length, refractive index modulation amplitude and tilt angle is exhaustively investigated on the transmission spectrum characteristics. The different dependences between s-polarized and p-polarized radiation-mode coupling on grating tilt angle are discussed, and the coupling strength of 45°-tilted gratings shows the greatest polarization dependence with the limitation of backward-propagating radiation-mode coupling.

Enhancement of optical absorption in thin-film organic solar cells through the excitation of plasmonic modes in metallic gratings

We theoretically investigate the enhancement of optical absorption in thin-film organic solar cells in which the top transparent electrode is partially substituted by a periodic metallic grating. We show that the grating can result in broadband optical absorption enhancement for TM-polarized light, due to the large field enhancement in the vicinity of the strips of the grating, associated with the excitation of plasmonic modes. The overall optical absorption in the organic layers can be greatly enhanced up to ∼50% for such solar cell structures.

Coherent electronic grating cavity modes in corrugated ultrathin metal films

Stepped semiconductor substrates can serve as a template for growing metal films with a corrugated structure at the nanoscale. The corrugation modulates the electron motion and thus modifies the electronic properties of the system. This work is a study of corrugated films of Ag and Pb using angle-resolved photoemission. Our measurements show that the valence electrons form coherent grating cavity modes defined by the corrugation geometry and the photoemission patterns are governed by quantum interference.

Design and fabrication of a polarization-independent two-port beam splitter

We design and manufacture a fused-silica polarization-independent two-port beam splitter grating. The physical mechanism of this deeply etched grating can be shown clearly by using the simplified modal method with consideration of corresponding accumulated phase difference of two excited propagating grating modes, which illustrates that the binary-phase fused-silica grating structure depends little on the incident wavelength, but mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These analytic results would also be very helpful for wavelength bandwidth analysis. The exact grating profile is optimized by using the rigorous coupled-wave analysis. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results agree well with the theoretical values.

Beam splitting of low-contrast binary gratings under second Bragg angle incidence

Beam splitting of low-contrast rectangular gratings under second Bragg angle incidence is studied. The grating period is between lambda and 2lambda. The diffraction behaviors of the three transmitted propagating orders are illustrated by analyzing the first three propagating grating modes. From a simplified modal approach, the design conditions of gratings as a high-efficiency element with most of its energy concentrated in the -2nd transmitted order (~90%) and of gratings as a 1 x 2 beam splitter with a total efficiency over 90% are derived. The grating parameters for achieving exactly the splitting pattern by use of rigorous coupled-wave analysis verified the design method. A 1 x 3 beam splitter is also demonstrated. Moreover, the polarization-dependent diffraction behaviors are investigated, which suggest the possibility of designing polarization-selective elements under such a configuration. The proposed concept of using the second Bragg angle should be helpful for developing new grating-based devices.