Shallow Gratings Research Articles

Particle swarm optimizer for the surface plasmon resonance effect on metal gratings.

In this work, the spectral dependence of optimum parameters of the surface plasmon resonance (SPR) effect on metallized sinusoidal diffraction gratings, under normal incidence, was determined using the particle swarm optimization method. The method was chosen due to its simplicity and effectiveness in providing reliable results, relative to direct search or gradient methods. The Rayleigh's hypothesis, which restricts the analysis to the case of shallow gratings, is used to model the diffracted fields across the interface between the sensing medium and metal. A penalty function was applied to avoid the occurrence of singularities and violation of the validity of the Rayleigh hypothesis. Using this procedure, the optimum values of grating periodicity and amplitude that maximized the sensitivity function for gold, silver, copper, and aluminum-metals that yield high quality factor SPR effects-were determined in a wavelength range between 500 and 1600 nm, for both gaseous and aqueous sensing media.

Fabrication of nanometre sized gratings via ion irradiation

The damage caused by irradiation of crystalline material with ions results in localized volume changes. Here, swelling is utilized to fabricate nanostructured gratings with heights below 10 nm for extreme ultraviolet radiation. Irradiations were performed through a structured layer of photoresist shadowing parts of the sample from a broad ion beam. This enabled much shorter fabrication times than comparable direct write processes with a focussed ion beam. The study presents results from first systematic investigations regarding the fabrication of nanostructured gratings by irradiation of silicon with a broad beam of helium ions with energies of 30 keV. A smaller, scanned beam is used for comparison. Fluence was varied from 0.4 to 7.5×1016 ions/cm2. Fabricated structures were measured via atomic force microscopy. This yielded a controllable method to fabricate shallow gratings with heights in the range of 0 to 10 nm.

Transversal Kerr Effect Enhancement of Permalloy-Based Shallow Lamellar Magnetoplasmonic Crystals

This work demonstrates spectral dependencies of reflectivity and the transversal Kerr effect of a series of permalloy magnetoplasmonic crystals based on shallow lamellar diffraction gratings with a period of 500 nm, stripe’s width of 250 nm, and diffraction stripes’ heights of 28, 43, 67, and 88 nm. The fabricated magnetoplasmonic crystals show a monotonic increase of the transversal Kerr effect and the diffraction figure-of-merit with higher diffraction stripes. The maximum achieved modulation value of the transversal Kerr effect was found to be 0.78%, which can be further tuned by the periodicity and stripes width of the magnetoplasmonic crystals.

Wafer-scale high aspect-ratio sapphire periodic nanostructures fabricated by self-modulated femtosecond laser hybrid technology.

Sapphire nanostructures with a high aspect-ratio have broad applications in photoelectronic devices, which are difficult to be fabricated due to the properties of high transparency and hardness, remarkable thermal and chemical stability. Although the phenomenon of laser-induced periodic surface structures (LIPSS) provides an extraordinary idea for surface nanotexturing, it suffers from the limitation of the small depth of the nanostructures. Here, a high-efficiency self-modulated femtosecond laser hybrid technology was proposed to fabricate nanostructures with high aspect-ratios on the sapphire surface, which was combined backside laser modification and subsequent wet etching. Due to the refractive index mismatch, the focal length of the laser could be elongated when focused inside sapphire. Thus, periodic nanostructures with high-quality aspect ratios of more than 55 were prepared on the sapphire surface by using this hybrid fabrication method. As a proof-of-concept, wafer-scale (∼2 inches) periodic nanostripes with a high aspect-ratio were realized on a sapphire surface, which possesses unique diffractive properties compared to typical shallow gratings. The results indicate that the self-modulated femtosecond laser hybrid technology is an efficient and versatile technique for producing high aspect-ratio nanostructures on hard and transparent materials, which would propel the potential applications in optics and surface engineering, sensing, etc.

Theory of dipole-exchange spin-wave propagation in periodically corrugated films

We present a theory of spin-wave normal modes of a ferromagnetic film with periodically corrugated surfaces in Damon-Eshbach geometry. Two possibly different corrugations on the upper and lower film surface are considered. Both the surface mode and perpendicular standing modes are studied with the partial-wave method, adapted to take into account the modified boundary conditions, within the limit of validity of the Rayleigh's hypothesis. The theory, particularly suited to the case of shallow gratings, shows that the effect of corrugation on the dispersion curves is enhanced on asymmetrical structures, such as films with a sinusoidally corrugated top surface and flat bottom.

Modeling of surface grating-loaded VCSEL with slowing light

We propose single-mode vertical cavity surface-emitting lasers (VCSEL) based on the surface grating with various cavity lengths ranging from 10 μm to 1 cm. We present the modeling of surface grating-loaded VCSEL based on the coupled-mode theory with slowing light. Thanks to the low effective index caused by the slow-wave propagation, a shallow surface grating of a few tens nm provides large optical feedback. A narrow stop band in the surface grating-loaded VCSEL waveguide appears because of the large waveguide dispersion of slow-waves. The numerical results on coupling coefficient, mode selectivity and threshold gain are given for single-mode, long-cavity and short-cavity grating-loaded VCSELs with different grating parameters. A wide range of grating coupling strength enables a short cavity of 10 μm and a long cavity of 1 cm with a single-mode operation. The proposed VCSEL structure may open up new VCSEL platforms for low-power consumption and high-power applications.

Towards Ultrafast Laser Micromachining of X-Ray Gratings and Creation of Sub-Micron Hole Patterns, Comparison of Results With Bessel and Gaussian Beams

We compare micromachining results with Gaussian and Bessel beams using an UV picosecond laser system and demonstrate feasibility to produce tungsten gratings for x-ray interferometry medical imaging, and sub-micrometer size hole patterns. The advantages of Bessel beams compared to Gaussian beams, are demonstrated for micromachining of rectangular shallow profile gratings with sharp edges. The high-aspect ratio grating (10 microns wide and 200 microns deep) from tungsten foil could only be obtained with the Gaussian beam and focusing with an F-Theta type lens. Bessel beams contain significant amount of energy in the side lobes in comparison with the central peak. The limited amount of the pulse energy in the central, 2-micron peak of the beam and destruction of the Bessel beam structure due to the narrow slit clipping the side lobes, prevented the Bessel beam deeper penetration. On the other hand, the axicon lens and the Bessel beam shape enable creation of shallow sub-micron size structures.

Deepening of nanograting structures on Si by a two-step laser spatial-selective amorphization strategy combined with chemical etching

Femtosecond laser induced periodic surface structures (LIPSSs) have been implemented on various materials. However, its further development in manipulation of optical properties is hindered by the shallow depth. Herein, the paper proposes a novel method of two-step spatial-selective amorphization for producing the deep regular nanogratings on silicon by femtosecond laser and chemical etching with HF acid. In the first step, the spatially periodic amorphization of silicon surface is fabricated by the surface plasmon excitation of the incident femtosecond laser, the chemical etching of which produces the shallow gratings with a period of 765 nm, or so-called prefabricated-LIPSSs (pre-LIPSSs). During the second step, the spatial-selective amorphization of sample takes place by exploiting the local field enhancement of laser irradiation within the grooves. After chemical etching, the deep local field enhancement assisted LIPSSs (LFE-LIPSSs) are formed, with a three-fold larger depth of 155 nm but an invariable period. Comparing with the pre-LIPSSs, the LFE-LIPSSs show 45% increase in anti-reflection performance at around 700 nm and surface-enhanced Raman scattering (SERS) anisotropy ratio is increased about four times with 4-MBA molecules as probe molecules. This work provides a promising approach to fabricate deeper LIPSSs for more effectively controlling the optical properties of materials by femtosecond laser.

Effect of roughness on surface plasmons propagation along deep and shallow metallic diffraction gratings.

The roughness of shallow or deep metallic diffraction gratings modifies the propagation of surface plasmon mode along the metallic-air interface. The scattering losses lead to a spectral or angular broadening of the surface plasmon resonance (SPR) and to a shift of the resonance wavelength and coupling angle. This mechanism is deeply analyzed both experimentally and theoretically to overcome these effects when such structures, in particular deep ones, are used as SPR-based sensors.

High-power operations of single-mode surface grating long oxide aperture VCSELs

A high-power single-mode vertical cavity surface emitting laser (VCSEL) based on a slow light mode (SLM) concept is demonstrated. Shallow surface gratings were implemented to select a single slow light mode in mm long oxide aperture VCSELs. The vertical structure and well-established fabrication processes are unchanged from those of conventional 850 nm VCSELs. An electron-beam lithography is used to form a 1st-order shallow grating on the surface. Thanks to the low effective index and the intensity penetration of the SLM to the surface, the grating fabrication process is much easier than conventional guided mode distributed feedback lasers. A stable single mode with a high side suppression ration of more than 30 dB is obtained for the entire current range under CW operations. A narrow divergence of 0.038° in far field patterns is achieved for a 6 mm long device. A record single-mode power of more than 5 W is realized before saturation under 50 ns pulse operations. Unlike long cavity in-plane edge emitting lasers, a SLM-based VCSEL can provide higher output powers without limitation of catastrophic optical mirror damage. The high power, superior mode stability, and good beam quality of our unique design paves a way for VCSELs to be used for wide ranges of high-power applications.

Fabrication and characterization of aluminum, gold-tin and titanium-tungsten alloys for mid-infrared plasmonic applications

We numerically and experimentally investigate aluminum metal (Al), gold-tin (AuSn) and titanium-tungsten (TiW) metallic alloys as plasmonic materials in the mid-infrared (MIR) region using spectroscopic ellipsometry and reflection measurements of gratings. The angle dependence of the specular reflectance of shallow gratings is investigated using a free-beam measurement setup and compared to simulations. It is shown that the deep and narrow resonances observed for all three materials match the associated prediction from simulations.

High power surface grating slow-light VCSEL

We report on a novel high power vertical cavity surface emitting laser (VCSEL) with high order shallow surface grating, which enables a single mode operation even for 6 mm long devices. A high single mode power of over 3 W is obtained under pulsed operations for a 6 mm long oxide aperture. A fan-shape beam with sub-degree narrow divergence is obtained up to high injection currents of 5 A. Thanks to the low effective index of slow-light modes in a VCSEL structure, the grating pitch is over 2.5 μm, which can be made by using a standard photo-lithography. The simple fabrication process and potentials of high power and high beam quality could make the proposed laser to be a good candidate for 3D optical sensing and imaging applications.

Excitation of plasmonic and photonic modes in metallic lamellar gratings

We study the optical properties of metallic lamellar gratings with sub-wavelength period as a function of the groove depth and width, in situations in which there is only one propagating order (order zero or specular). The reflected light is calculated with an integral equation method for periodic surfaces. Under p-polarized illumination, different kinds of anomalies are observed as the angle of incidence or the grating parameters are changed. These are due to the excitation of surface plasmon polaritons (SPPs) and their interaction with the plasmonic and photonic modes supported by the grating grooves. We find that the propagation constant of the SPPs supported by shallow gratings is affected by the presence of the corrugations. As the groove depth increases, the formation of an energy gap inhibits the excitation of SPPs. However, for grooves deeper than about half a wavelength, new resonances appear. These are due to the coupling of the SPP excitations with the photonic and plasmonic modes supported by the grating grooves.

Spatial coherence of hybrid surface plasmon-phonon-polaritons in shallow n-GaN surface-relief gratings.

Dispersion characteristics of hybrid surface plasmon-phonon-polaritons (SPPhPs) on the air/polar semiconductor interface were investigated by means of shallow surface relief grating using emission spectroscopy methods. A set of grating structures with optimal 1 µm depth and periods from 8 to 22 µm was developed on a heavily-doped GaN crystal. The SPPhPs were excited by thermal heating or electrical biasing of the samples which radiated directive polarized features in an extremely narrowband spectrum range. Detailed analysis of damping factors and propagation losses revealed maximum values of quality factor and spatial coherence of hybrid SPPhPs modes. Highest quality factor was found to be practically independent on the period of the shallow grating, as it was always detected near the frequency of transverse optical phonon, demonstrating values as high as 88 and 200 in experiment and theory, respectively. Meanwhile, the largest values of coherence length strongly depended on the grating as the propagation losses of hybrid SPPhP modes showed a tendency to accumulate with the wavevector increase. The sample with 22 µm grating period demonstrated the highest coherence of hybrid polaritons with the experimental (theoretical) coherence length values as high as 1.6 mm (2.3 mm).

An asymptotic model based on matching far and near field expansions for thin gratings problems

In this paper, we devise an asymptotic model for calculating electromagnetic diffraction and absorption in planar multilayered structures with a shallow surface-relief grating. Far from the grating, we assume that the solution can be written as a power series in terms of the grating thickness δ, the coefficients of this expansion being smooth up to the grating. However, the expansion approximates the solution only sufficiently far from the grating (far field approximation). Near the grating, we assume that there exists another expansion in powers of δ (near field approximation). Moreover, there is an overlapping zone where both expansion are valid. The proposed model is based on matching the two expansions on this overlapping domain. Then, by truncating terms of order δ2 or higher, we obtain explicitly the equations satisfied by the lowest order terms in the power series. Under appropriate assumptions, we prove second order convergence of the error with respect to δ. Finally, an alternative form, more convenient for implementation, is derived and discretized with finite elements to perform some numerical tests.

Investigation of n-type gallium nitride grating for applications in coherent thermal sources

In this study, polarized reflection and emission spectroscopy was employed in order to describe experimentally and numerically the coherent behavior of surface plasmon phonon polaritons in shallow n-type gallium nitride grating. For the grating with a 1 μm depth and an 11 μm period, polariton coherence was observed measuring the reduction of the linewidth and the redshift of the resonance position in both reflection and emission spectra with the increase in the incident angle. Maximum coherence conditions were found at a frequency of 562 cm−1 and an angle of 37°, demonstrating the coherence length value up to 724 μm (41λ).

Optical modes in perovskite nanowire with shallow bi-periodic grating

In this work, we investigate electromagnetic modes supported by a perovskite CsPbBr3 nanowire with a shallow periodic grating on top. By creating a domain-wall geometry, we introduce a topological defect into the nanowire and observe a defect-localized lasing state. By tuning the parameters of the structure we ensure that the frequency of the localized state fits the frequency of exciton resonance in perovskite and perform full-wave numerical simulations of the field distribution for such state.

850 nm GaAs/AlGaAs DFB lasers with shallow surface gratings and oxide aperture.

We present and experimentally demonstrate a novel oxide-confined ridge-waveguide distributed feedback (DFB) laser with the first-order surface grating using only a single growth step. The metal contacts are laterally offset from the ridge waveguide to inject current thus avoiding unwanted light absorption from the electrodes. The oxide aperture is defined by selective wet oxidation of aluminium-rich material, which confines the injection current from the electrodes to the active layer under the ridge waveguide. This allows that a thin ridge layer can be used with relatively higher refractive index compared to the active layer and thus the grating can be shallowly etched but provides a strong coupling effect. The fabricated 150 µm-long DFB laser exhibited a relatively low threshold current of 8 mA and a side mode suppression ratio (SMSR) up to 50 dB at the injected current of 32 mA around 4 times threshold at 20 °C. Stable single mode operation has been observed for the fabricated DFB laser over the temperature range from 10 to 50 °C. The variation of wavelength with temperature Δλ/ΔT was 0.06 nm/°C. The proposed laser may have advantages combined both DFB lasers and vertical-cavity surface-emitting lasers (VCSELs), such as single mode, stabilized polarization, potentially narrow linewidth and low power consumption. In addition, the laser is regrowth free, thus has advantages of low cost and high reliability.

Broadband thermophotovoltaic emitter using magnetic polaritons based on optimized one- and two-dimensional multilayer structures

Thermophotovoltaic (TPV) devices via efficient emitter are used to convert thermal radiation into electricity. We propose new one-and two-dimensional (1D and 2D) nanostructures to reach the broadband highly efficient TPV emitters. The performance of the model is enhanced by more interaction between the excited surface plasmon polaritons and the magnetic polaritons based on the multilayer structure using 1D periodic shallow grating and 2D biperiodic cylindrical deep grating. The highly improved rigorous coupled-wave analysis method is used to predict the emittance with the fewest diffraction orders. It is shown that the proposed wavelength-selective and diffuse-like 1D emitter has high emittance—more than 0.9 and 0.96 in the broadband spectral regions from 0.7 to 1.87 μm and 0.73 to 1.83 μm, respectively, and is silicon-compatible, especially for integrated device technology. Also, for the 2D polarization-insensitive proposed structure, there is high emittance—more than 0.97 from 0.6 to 1.6 μm. The emittance of both structures is below 0.2 at wavelengths longer than 2.55 μm. The strip width of the grating and the emission angle can be set to change the emittance spectrum to improve the conversion efficiency of the photovoltaic cell.

Reflected energy flux anomaly under grazing incidence: the Brewster angle analogy

The paper presents thorough theoretical and numerical analysis of the anomalies accompanying light diffraction on periodical structures (gratings). We have developed appropriate theoretical approach allowing to consider strong anomalous effects. Obtained results are presented in the form of analytical expressions for the quntities of interest, both diffracted field amplitudes and the outgoing waves energy fluxes. It is proved existence of the fluxes extrema at the specific grazing angle of incidenceб or wavelength. Namely, the specular reflection can be suppressed even for rather shallow gratings up to approximately total suppression.This effect is accompanied by essential energy redistribution between all outgoing waves depending on the grating profile. It is of essence that the energy maxima exist in all nonspecular diffraction orders at the same point (angle, wavelength) as the minimal specular reflectivity. For small period gratings, such that there do not exist other outgoing waves except the specular one, the reflectance minimum is attended by approximately total absorption of the incident radiation. Thus, we show that the grazing anomaly (GA) can be accompanied by redirection of the incident wave energy into nonspecular diffraction channels and into absorption. The results are applicable in the wide spectral region, from visible and near-infrared to terahertz and high-frequency regions for metals and semiconductors with high permittivity. The anomaly considered is well expressed for high electromagnetic contrast of the adjacent media, say, air and metal or semiconductor. Then the high contrast is due to the high value of the metal/semiconductor dielectric permittivity  ,  1 , and the anomaly corresponds to incidence of TM polarized wave. It is shown that the grazing anomaly (GA) is of rather general type and can take place if other than the specular diffraction order experiencies grazing propagation also. This property follows from the results obtained by strict application of the optical reciprocity theorem to the geometry under consideration. The specific case of harmonic relief grating is discussed in detail. It is demomstrated existence of the characteristic inclination, cr a , of the relief inclinatuion for the grating period comparable with the incident radiation wavelength, 1 cr a  , where  stays for the surface impedance,  1  . The condition cr a a , or greater, corresponds to highly expressed GA. The theoretical results are illustrated by numerical applications to gratings on Cu\vacuum (air) interface in THz region. The results obtained can be simply transferred to the TE polarized waves. For this we have to consider the adjacent media with high contrast magnetic properties, i.e., high value of the magnetic permeability  ,  1 . This case is of high interest for nowaday applications in nanophotonics and metamaterials development. As compared with other anomalies GA is attributed to the resonance-type behaviour of the energy flux, not wave amplitudes, the latter change monotonically within this anomaly contrary to the well known Rayleigh and resonance anomalies, where the wave amplitude experiences fast nonmonotonous dependence on the angle of incidence and wavelength.