Subwavelength Grating Structures Research Articles

Design and Analysis of High-Index-Contrast Gratings Using Coupled Mode Theory

We analyze high-refractive-index-contrast subwavelength grating structures using truncated coupled mode theory (CMT). CMT not only provides physical insight into the role of each mode in the overall response but also allows for improved design. An analytic expression is derived for the design of broadband reflectors, providing a near-optimal design that is within 0.08% of the maximum broadband reflectivity calculated by the finite-difference time-domain method. Furthermore, the CMT is used to design a high-quality narrow-band reflector with 28% improved quality factor over previously reported results, as quantified by rigorous coupled wave analysis.

Effect of etching parameters on antireflection properties of Si subwavelength grating structures for solar cell applications

Silicon (Si) subwavelength grating (SWG) structures were fabricated on Si substrates by holographic lithography and subsequent inductively coupled plasma (ICP) etching process using SiCl4 with or without Ar addition for solar cell applications. To ensure a good nanosized pattern transfer into the underlying Si layer, the etch selectivity of Si over the photoresist mask is optimized by varying the etching parameters, thus improving antireflection characteristics. For antireflection analysis of Si SWG surfaces, the optical reflectivity is measured experimentally and it is also calculated theoretically by a rigorous coupled-wave analysis. The reflectance depends on the height, period, and shape of two-dimensional periodic Si subwavelength structures, correlated with ICP etching parameters. The optimized Si SWG structure exhibits a dramatic decrease in optical reflection of the Si surface over a wide angle of incident light (θi), i.e. less than 5% at wavelengths of 300–1100 nm, leading to good wide-angle antireflection characteristics (i.e. solar-weighted reflection of 1.7–4.9% at θi<50°) of Si solar cells.

Subwavelength grating structures with magnetic resonances at visible frequencies fabricated by nanoimprint lithography for large area applications

Transmission of TM-polarized light through a subwavelength metal-dielectric grating structure exhibits strong resonance in the visible range. Simulations by finite-difference time-domain and finite-element methods show that the resonance can be attributed to the magnetic response. Further simulation shows that the grating structure can be optimized by adding an index matching dielectric layer to produce negative refractive index response in the visible band. Easily fabricated using nanoimprint lithography and conveniently able to be excited by incident light normal to the fabrication plane, such metal-dielectric grating structure could find potential use in large area negative refractive index applications.

Influence of polarization on absorbance modulated subwavelength grating structures

The feasibility of using absorbance modulated structures as subwavelength optical transmission gratings was studied using both analytical techniques and finite element method simulations. Particular note was taken of the relevance of this work to absorbance modulation optical lithography (AMOL) and the understanding of the authors of how to control and improve the transmission of light through the photochromic layer. It was found that absorbance gratings share many characteristics with similar-sized metal gratings, in particular, transmitting transverse magnetic (TM) polarized light better than transverse electric polarized light. For both polarizations the transmission through an absorbance grating produces lower contrast intensity profiles compared to both metal and dielectric gratings; however, there was reasonable contrast to a depth of approximately 40 nm beneath the grating in the TM case for gratings with half-pitch as small as 20 nm. Full vector-field AMOL simulations demonstrate similar trends in which there was improved propagation and confinement of TM polarized light at the short resist-exposing wavelength.

Sub-wavelength grating mode transformers in silicon slab waveguides

We report on several new types of sub-wavelength grating (SWG) gradient index structures for efficient mode coupling in high index contrast slab waveguides. Using a SWG, an adiabatic transition is achieved at the interface between silicon-on-insulator waveguides of different geometries. The SWG transition region minimizes both fundamental mode mismatch loss and coupling to higher order modes. By creating the gradient effective index region in the direction of propagation, we demonstrate that efficient vertical mode transformation can be achieved between slab waveguides of different core thickness. The structures which we propose can be fabricated by a single etch step. Using 3D finite-difference time-domain simulations we study the loss, polarization dependence and the higher order mode excitation for two types (triangular and triangular-transverse) of SWG transition regions between silicon-on-insulator slab waveguides of different core thicknesses. We demonstrate two solutions to reduce the polarization dependent loss of these structures. Finally, we propose an implementation of SWG structures to reduce loss and higher order mode excitation between a slab waveguide and a phase array of an array waveguide grating (AWG). Compared to a conventional AWG, the loss is reduced from -1.4 dB to < -0.2 dB at the slab-array interface.

Investigation of geometrical effects of antireflective subwavelength grating structures for optical device applications

We calculated diffraction efficiencies of subwavelength grating (SWG) structures for various optical device applications by using a rigorous coupled-wave analysis method. The geometrical effects, such as grating shape, height, and period, were investigated in order to obtain better antireflection performance. Cone shaped SWG structures with a taller height provide lower reflectance over a broadband wavelength range compared to that of flat surface and nanorod. It was found that the low reflection regions are quite related with the grating period and the refractive index of substrate materials. From the comparison between external and internal reflection of SWG structures, we also showed that the internal reflection requires shorter grating period than the case of external reflection to acquire broadband antireflection properties.

Closely packed and aspect-ratio-controlled antireflection subwavelength gratings on GaAs using a lenslike shape transfer

We report a simple and low-cost fabrication of antireflection subwavelength grating (SWG) structures on GaAs using the lenslike shape transfer by a holographic lithography and a reflowed photoresist mask. The use of an additional thermal reflow process enhances the close packing of two-dimensional SWGs with a conical shape. The aspect ratio of conical SWG was also controlled easily by adjusting the rf power during the dry etch process. The fabricated SWGs exhibited low reflection properties over a wide spectral range, in agreement with the calculated values using by a rigorous coupled-wave analysis simulation.

Sub-wavelength surface structuring of NiTi alloy by femtosecond laser pulses

Generation of self-organized sub-wavelength surface structures on a nickel–titanium alloy plate by femtosecond laser pulses is investigated experimentally through line-scribing experiments in air. It is found that Bragg-like relief gratings, with the orientation perpendicular to the laser polarization, are formed over the entire laser-scribed regions. The average period is measured as 630±30 nm. Distinctive features of these novel surface structures include nanoparticle-covered grating ridges and the maintainable spatial period regardless of incidence angles. With different laser parameters and sample scan speeds, sub-wavelength grating structures can evolve into cellular-like nanotextures. Optimal conditions for forming these surface structures are determined in terms of laser energy and scan speed. Elementary analyses of the structured surfaces by X-ray diffraction and photoelectron spectroscopy reveal that both the crystal structures and the chemical elements can remain in their original states, but the surface grains are refined and the atomic percentages are varied after femtosecond laser treatments.

Numerical Investigation of Surface Plasmons AssociatedSubwavelength Optical Single-Pass Effect

Surface plasmons (SPs) associated optical single-pass effect has beeninvestigated in novel subwavelength metallic structures, includingsingle slit and grating structures. With influence of SPs, thesemetallic structures can enhance transmission in incident direction andsuppress it in the opposite direction, exhibiting a single-pass effect.The finite difference time domain method is employed to study theinfluences of structure parameters on far-field transmission,near-field electric field distribution and extinction ratio of thesingle-pass transmission effect. A maximal extinction ratio of 47.83 dBis achieved in the grating structure.

Wafer-based diffractive polarizer design for low-reflectivity applications

We present designs of a diffractive polarizer having low zeroth-order reflectivity that is compact, potentially mass-producible and cost-effective, and compatible for high-power applications. It consists of subwavelength grating structures superimposed over a diffraction grating. Using rigorous coupled wave analysis, we optimized the parameters of multilevel grating structures to achieve antireflection for both incident TE and TM polarization states with one polarization passing in the zeroth order and the other into the first and higher orders. We focused on polarizer designs for the 1.31-µm wavelength range, and the theoretical values for zeroth-order reflection were calculated to be 0.01% for TE and 0.29% for TM modes. The zeroth-order transmission efficiencies were 97.2% for TE and 0.01% for TM modes. A prototype of one design was fabricated and tested to verify the functionality of the device, and the zeroth-order reflection was determined to be 1.2% and 3.5% for the two modes.

Subwavelength waveguide grating for mode conversion and light coupling in integrated optics

We propose a new method for mode conversion and coupling between an optical fiber and a sub-micrometer waveguide using a subwavelength grating (SWG) with a period less than the 1st order Bragg period. The coupler principle is based on gradual modification of the waveguide mode effective index by the SWG effect that at the same time frustrates diffraction and minimizes reflection loss. We demonstrate the proposed principle by two-dimensional Finite Difference Time Domain (FDTD) calculations of various SWG structures designed for the silicon-on-insulator (SOI) platform with a Si core thickness of 0.3 microm. We found a coupling loss as small as 0.9 dB for a 50 microm-long SWG device and low excess loss due to fiber misalignment, namely 0.07 dB for a transverse misalignment of +/-1 microm, and 0.24 dB for an angular misalignment of +/-2 degrees. Scaling of the SWG coupler length down to 10 microm is also reported on an example of a 2D slab waveguide coupling structure including aspect ratio dependent etching and micro-loading effects. Finally, advantages of the proposed coupling principle for fabricating 3D coupling structures are discussed.

Enhanced phase shift in a zeroth-order beam from subwavelength grating structures formed in uniaxial birefringent materials

A subwavelength grating structure made in an isotropic medium induces form birefringence effects, and the artificially produced optical axis is parallel to the grating vector. The phase shift between the two orthogonal electric-field components exiting this grating varies linearly with the thickness of the grating. When a grating with subwavelength period is formed on a uniaxial birefringent material with the grating vector aligned parallel to its natural optical axis, the total effect enhances the birefringence of the material. As a result, the thickness of the material can be reduced and still produce the same phase shift. If the natural optical axis and the induced optical axis lie within the surface plane and have an angular separation between them, the phase shift varies nonlinearly with the thickness of the grating.

Comparison between continuous and discrete subwavelength grating structures for antireflection surfaces

Both continuously tapered and discrete multilevel subwavelength grating structures are examined to determine the optimum method of designing antireflection surfaces. Continuously tapered gratings are designed with use of the optimal Klopfenstein graded index technique, while discrete multilevel stair-step gratings are designed with use of the Tschebyscheff quarter-wave synthesis technique. It is shown that a continuous design is always deeper than a discrete design. It is determined that since a subwavelength grating structure produces a bandpass surface, the high-pass (short-wave) performance of the continuous taper design cannot be realized. Therefore the discrete method of designing antireflection subwavelength gratings will always produce a shallower spatial profile or a smaller aspect ratio for any specified maximum reflection threshold level over a given passband.

Optimal design for antireflective tapered two-dimensional subwavelength grating structures

Techniques for the design of continuously tapered two-dimensional (2D) subwavelength surface-relief grating structures for broadband antireflection surfaces are investigated. It has been determined that the Klopfenstein taper [ Proc. IRE44, 31 ( 1956)] produces the optimum graded-index profile with the smallest depth for any specified minimum reflectance. A technique is developed to design the equivalent tapered subwavelength surface-relief grating structure by use of 2D effective-medium theory. An optimal Klopfenstein tapered 2D subwavelength grating is designed to reduce the Fresnel reflections by 20 dB over a broad band from an air–substrate (ns = 3.0) interface. The performance is verified by use of both a 2D effective-medium-theory simulation algorithm and rigorous coupled-wave analysis. These structures are also shown to achieve this low reflectance over a wide field of view (θFOV &gt; 110°). The pyramidal spatial profile, which has generally been assumed to produce the optimal broadband antireflection grating structure, is shown to require a significantly larger depth to achieve the same performance as a Klopfenstein-designed tapered antireflection grating structure.