Rigorous Coupled-wave Theory Research Articles

Suppression of metal grating to surface plasma radiation

Surface plasmon polaritons (SPP) are widely investigated in many fields because of the surface confinement of their electrocmagnetic field. Grating coupling is one of the methods to achieve the momentum match between light in free space and the surface plasmon to excite SPP. Because of the nature of the grating coupling, its parameters will greatly affect the coupling efficiency. Varying the grating modulation depth but keeping other parameters unchanged, we investigate the reflection spectra of onedimensional rectangle metallic grating by rigorous coupled-wave theory under the irradiation of incident light of 780 and 1500 nm in wavelength, respectively. According to Fano theory, the reflectance of metallic grating is the result of interference of two components, i.e., a directly reflected mode from the metal surface and a resonance radiation mode coupled out by the SPP propagating along the grating surface. We derive the Fano-type expression to describe the reflection spectra, and explain the contributions of directly reflected mode, SPP resonance radiation mode and the interference between these two effects. Near-filed electromagnetic distribution on metallic grating surface proves that the Fano-type expression is accurate enough to reflect the nature of the interference between the direct and radiation modes. Most importantly, our results from the expressions suggest that in some special grating condition, the metallic grating almost completely suppresses the SPP radiation propagating from grating to free space, which means that the energy of light can be completely trapped inside the grating. The phenomenon can be employed in designing light trapping device.

Simulation of nano-grating patterning based on X-ray Talbot effect

High aspect ratio gratings can be made by perpendicularly cutting in the growth direction of multilayers. X-ray exposure technique using a sectioned multilayer grating based on Talbot effect is a new type of nano patterning method. Although 300 nanometer gratings through the experiment are completed, some phenomena in the experiments cannot be satisfactorily explained and the factors influencing the nano pattern quality have not been fully understood yet. Here we use a rigorous coupled-wave theory to discuss several important factors, including grating thickness, the fraction of material thickness and multilayer period, which is the first time as far as we know for Talbot self-imaging in X-ray range. Simulation results show that the grating thickness affects both X-ray transmission efficiency and fringe contrast, while the fraction of material thickness determines the quality of fringes. And the position deviation of the best image plane in near field is related to both the thickness of the grating and the multilayer period. Moreover, the multilayer gratings with smaller periods can achieve higher resolution, indicating that the Talbot effect can be used to fabricate a more detailed structure.

Explaining the success of Kogelnik's coupled-wave theory by means of perturbation analysis: discussion.

The problem of diffraction of an electromagnetic wave by a thick hologram grating can be solved by the famous Kogelnik's coupled-wave theory (CWT) to a very high degree of accuracy. We confirm this finding by comparing the CWT and the exact result for a typical example and propose an explanation in terms of perturbation theory. To this end we formulate the problem of diffraction as a matrix problem following similar well-known approaches, especially rigorous coupled-wave theory (RCWT). We allow for a complex permittivity modulation and a possible phase shift between refractive index and absorption grating and explicitly incorporate appropriate boundary conditions. The problem is solved numerically exact for the specific case of a planar unslanted grating and a set of realistic values of the material's parameters and experimental conditions. Analogously, the same problem is solved for a two-dimensional truncation of the underlying matrix that would correspond to a CWT approximation but without the usual further approximations. We verify a close coincidence of both results even in the off-Bragg region and explain this result by means of a perturbation analysis of the underlying matrix problem. Moreover, the CWT is found not only to coincide with the perturbational approximation in the in-Bragg and the extreme off-Bragg cases, but also to interpolate between these extremal regimes.

Effects of Grating Slant Angle on Surface Plasmon Resonance and its Applications for Sensors

In this study, we emphasized on effects of grating slant angle of tilted dielectric gratings (TG) on surface plasmon resonance (SPR). The momentum conservation for an optical wave exciting an SPR via TG is different from unslant gratings. The coupling condition induces the period along the grating surface (in the direction x) be decided not only by grating period but also by slant angle. The results calculated by rigorous coupled-wave analysis theory (RCWA) indicate that the resonant wavelength and the refractive index sensitivity are strongly dependent on the period in the direction x (noted Λx). And the refractive index sensitivity increases with the rise of the period Λx. The SPR sensor through TG offers high sensitivity about 800nm per refractive index unit and narrow full-width at half maximum (FWHM) about 5nm when monitoring biochemical liquid solutions.

基于严格耦合波理论的周期性极化铌酸锂晶体的电光衍射性质分析

Using the rigorous coupled wave theory,the electro-optical diffraction properties of periodically poled lithium niobate with different parameters were numerically studied.The analysis show that,the periodic domain structures of a periodically poled lithium niobate act as an index of refraction diffraction grating under the applied electric fields and its diffraction characters have relation to the geometry structures,the period,the applied electric-fields and the incident angles.The periodically poled lithium niobate produces Bragg diffraction under the Bragg condition.In this case,the 0order of diffraction light is periodically converted to-1order of diffraction light with the increase of applying electric field.The maximum conversion efficiency can reach to 100% and the conversion voltage value can be reduced effectively by lengthening crystal.If angle of incidence is the Bragg angle,and the propagation of light in periodically poled lithium niobate does not satisfy the conditions of Bragg diffraction,the power of 0order diffraction light can not transfer to-1order of diffraction light with 100%.Meanwhile,the periodic modulation are damaged.The 0order light is converted to corresponding multiple orders of diffraction lights with high diffraction efficiency when the incident angles are multiple Bragg angles.The maximum conversion efficiency is also reach 100%.The analysis results are helpful for developing the integrated devices of periodically poled lithium niobate.

Design of an integrated polarization band-pass filter

In this study, an integrated polarization band-pass filter was designed; it consists of a bilayer nanowire-grid polarizer and a multilayer dielectric band-pass filter. The grating parameters were optimized by rigorous coupled-wave analysis theory and analyzed by effective medium theory. Transverse magnetic transmission higher than 81% and extinction ratio higher than 1000 were obtained at 400–500 nm, and extremely low transmission in the other spectrum was also realized.

Two Dimensional Photonic Crystal Biosensors

Based on the rigorous coupled wave theory, the narrowband reflect spectral imaging characteristics on two-dimensional photonic crystal are analyzed, and two-dimensional photonic crystal sensor probe biological structure and photonic crystal biosensor system are constructed. The simulation proved that, when the adsorption medium at the surface of two-dimensional photonic crystal are different, the white light narrowband reflection resonance mode peak wavelength would drift, and the drift quantity of the peak wavelength and the refractive index of the adsorptive medium is in a linear relationship. Colored the space imaging spectra of photonic crystal, the changes of the adsorbate refractive index in different area of the photonic crystal surface can be observed , the adsorbate concentration changes can also be got. This conclusion can be applied to biochemical substances, pharmaceutical, biological molecules and environmental pollution detection.

The fabrication of the antireflective periodic nano-arrary structure on Si surface using nanoimprint lithography and the study on its properties

The intrinsic Fresnel reflection of Si surface, which causes more than 30% of the incident light to be reflected back from the surface, seriously influences the photoelectric conversion efficiency of Si-based semiconductor photoelectric device, such as solar cell and infrared detector. Recently, how to find a simple and efficient method, which is also suitable for mass production, aiming to suppress the undesired reflectivity and therefore improving the efficiency of the device, has become a research focus. In this work, we successfully convert a 2D nanopillar array structure into the Si surface via the nanoimprint lithography. The nanopillar has a flat surface and a paraboloid-like side wall profile. The period and the height of the hexagonal array structure are 530 nm and 240 nm, respectively. The cut-paraboloid nanopillar structure generates a relatively smooth gradient of the refractive index in the optical interface, which plays a key role in suppressing the Fresnel reflection in a wide range of wavelength. The reflectivity of the nanopillar arrayed Si surface is tested in a wavelength range from 400 to 2500 nm at an incident angle of 8° during the measurement. Compared with the unstructured Si, the structured Si has a reflectivity that significantly decreases in the test area: in a wavelength range from 400 to 1200 nm, and the reflectivity of the silicon surface is less than 10%. Specifically, the reflectivity is almost zero at a wavelength of about 1360 nm. The results are confirmed with the effective medium and rigorous coupled-wave theory.

Conic hyperspectral dispersion mapping applied to semiconductor plasmonics

The surface plasmon resonance tracking over metal surfaces is a well-established, commercially available, biochemical quantification tool primarily applied in research. The utilization of such a tool is, however, constrained to highly specialized industries, capable of justifying the human and instrumental resource investments required by the characterization method. We have proposed to expand the field of application of this biosensing approach by redesigning this method through the integration and miniaturization within a semiconductor platform. Uncollimated and broadband emission from a light-emitting semiconductor is employed to couple a continuum of surface plasmon modes over a metal–dielectric architecture interfaced with a GaAs–AlGaAs substrate. A tensor version of rigorous coupled wave theory is employed to optimize the various fabrication specifications and to predict the light scatterings over a wide range of variables. We then present a hyperspectral characterization microscope capable of directly mapping the dispersion relation of scattered light, including diffracted surface plasmons, as an intensity distribution versus photon energy and surface wavevectors. Measurements carried out in a buffered solution demonstrate the accurate description of the uncollimated and broadband surface plasmon states. Finally, we introduce a simplified method of dispersion mapping, in which quasi-conic cross-sections of the light's scattering can be acquired directly, thus monitoring surficial responses in as fast as 1.2 s. This is over 300 times faster than required by implementing full dispersion mapping. While compromising on the volume of collected information, this method, combined with the solid-state integration of the platform, shows great promise for the fast detection of biochemical agents. Researchers have miniaturized surface plasmon resonance experiments by using microchips embedded with gallium arsenide ‘quantum wells’. One of the best ways to track biochemical agents is through surface plasmon resonance spectroscopy, a technique that uses vibrations from a thin metal layer to detect specific molecular adsorption events. However, observing surface plasmons for biosensing traditionally requires the use of large, precisely tuned light sources. The scheme developed by Dubowski and co-workers employs hyperspectral imaging—a means of measuring data from hundreds of different spectral bands—to record how the broadband light of quantum well nanostructures scatters after striking a metal film. Advanced algorithms then pick out surface plasmons from the light-scattering data and enable near real-time analysis. Solid-state integration and pre-analysed output make this device ideal for future commercial ventures that could go beyond the application of surface plasmon resonance for biosensing.

Volume Holograms in Photopolymers: Comparison between Analytical and Rigorous Theories

There is no doubt that the concept of volume holography has led to an incredibly great amount of scientific research and technological applications. One of these applications is the use of volume holograms as optical memories, and in particular, the use of a photosensitive medium like a photopolymeric material to record information in all its volume. In this work we analyze the applicability of Kogelnik’s Coupled Wave theory to the study of volume holograms recorded in photopolymers. Some of the theoretical models in the literature describing the mechanism of hologram formation in photopolymer materials use Kogelnik’s theory to analyze the gratings recorded in photopolymeric materials. If Kogelnik’s theory cannot be applied is necessary to use a more general Coupled Wave theory (CW) or the Rigorous Coupled Wave theory (RCW). The RCW does not incorporate any approximation and thus, since it is rigorous, permits judging the accurateness of the approximations included in Kogelnik’s and CW theories. In this article, a comparison between the predictions of the three theories for phase transmission diffraction gratings is carried out. We have demonstrated the agreement in the prediction of CW and RCW and the validity of Kogelnik’s theory only for gratings with spatial frequencies higher than 500 lines/mm for the usual values of the refractive index modulations obtained in photopolymers.

Formulation of rigorous coupled-wave theory for gratings in bianisotropic media

A formulation of rigorous coupled-wave theory for diffraction gratings in bianisotropic media that exhibit linear birefringence and/or optical activity is presented. The symmetric constitutive relations for bianisotropic materials are adopted. All of the incident, exiting, and grating materials can be isotropic, uniaxial, or biaxial, with or without optical activity. The principal values of the electric permittivity tensor, the magnetic permeability tensor, and the gyrotropic tensor of the media can take arbitrary values, and the principal axes may be arbitrarily and independently oriented. Procedures for Fourier expansion of Maxwell's equations are described. Distinctive polarization coupling effects due to optical activity are observed in sample calculations.

The influence of the conical incidence on the waveguide-type colour-separating backlight for liquid crystal display

The lightguide assisted by diffraction gratings is used to implement colour-separating backlight for Liquid Crystal Display (LCD). In the configuration, the light incidence angle is required to be a precise designed one. However, the light incidence is conical always. In this paper, by rigorous coupled wave theory, the influence of conical input on the colour-separating backlight is investigated. It shows that, when the azimuthal angle of the light increases, the diffraction efficiency could be enhanced by a factor of 2, which means that the conical input will benefit the diffraction efficiency of the lightguide. However, it also leads to a larger output spot area at the same time, which could result in the mixing of RGB pix. When the azimuthal angle is smaller than 12°, the maximum diffraction angles of RGB light can be completely separated, which means that, with a designed distance or with an assisted micro-lens layer between the grating and the pix layer, the RGB light can reach their corresponding pix. The influence of the conical input on the polarized light is also investigated. The conical input will result in the output with composite polarization, which, in principle, disables the use of polarized light source in LCD.

Design of a highly efficient light-trapping structure for amorphous silicon solar cell

A highly efficient light-trapping structure consisting of a diffractive grating, a MgF2 film, a ZnS film and Ag reflector, is used for a-Si:H solar cell. Using the rigorous coupled wave theory, the weighted absorptance photon number (AM1.5) of a 1 m thick a-Si:H solar cell is calculated in a wavelength range from 400 to 1000 nm for the AM1.5 solar spectrum at 25 ℃. It is used to design the optimal parameters of the light-trapping structure. Results indicate that AM1.5 of the solar cell can reach 74.3%, if the period, the depth and the duty cycle of the diffractive grating, and the height of the MgF2 film and the ZnS film are 800 nm, 160 nm, 0.6125, 90 nm and 55 nm, respectively. If a ZnS/Ag film is fabricated on the rear surface of the solar cell, a larger AM1.5 (76.95%) can be obtained. It is demonstrated that the trapping structure is useful for elevating the efficiency of the solar cell.

高损伤阈值矩形石英闪耀光栅的设计分析

The design of fused silica transmission blazed grating based on modal method is presented under Littrow mounting. A -1st transmitted order blazed grating is designed at the wavelength of 1.06 μm. The first two modes (i.e. mode 0 and mode 1) propagate through the grating with different effective indices and couple out at the grating-substrate interface. And a high diffraction efficiency of -1st transmitted order can be achieved if the first two modes have a phase difference of odd multiple of π. The diffraction performance of the blazed grating is analyzed by the rigorous coupled-wave analysis theory. The design of blazed grating based on modal method matches the analysis perfectly.

Microscope system for Blu-ray disc samples

We introduce a microscope system using a solid immersion lens (SIL) to image Blu-ray disc samples without removing the protective cover layer. The aberration caused by the cover layer is minimized with a truncated SIL. A subsurface imaging simulation is achieved by using the rigorous coupled wave theory, partial coherence, vector diffraction, and the Babinet principle. Simulated results are compared with experimental images and atomic force microscopy measurements.

Illumination artifacts in hyper-NA vector imaging

Off-axis polarized monopole illumination is applied to a hyper-numerical-aperture (NA) (NA>1) microscopic system. Illumination artifacts due to vector effects are observed, which are asymmetric and depend on illumination conditions. A model based on rigorous coupled wave theory is used to simulate image profiles for dielectric, semiconductor, and metal gratings with different monopole locations and polarization states. A solid immersion lens microscope is used to image different types of samples including MoSi photomask, patterned silicon wafer, and chrome photomask. The experimental images are in good agreement with simulation results.

Rigorous interference and diffraction analysis of diffractive optic elements using the finite-difference time-domain method

The Finite-Difference Time-Domain (FDTD) method has proven to be a useful tool to analyze electromagnetic scattering phenomena. In this work, the FDTD method is applied at optical wavelengths. More precisely, we present the results obtained using the FDTD algorithm to simulate the performance of optical devices such as volume diffraction gratings. The Perfectly Matched Layers (PML), Total-Field Scattered-Field formulation (TF/SF) and Near-Field to Far-Field transformation (NF/FF) are some add-ons included in order to correctly calculate the far field distribution obtained from the numerical near-field values computed in the simulation region. These values in the near-field region are computed by illuminating the grating with of a plane wave at the Bragg angle of incidence. In addition, we compare the results obtained by the FDTD method to those obtained using the Rigorous Coupled Wave Theory (RCWT) applied to diffraction gratings. As will be seen in this paper there is good agreement between the two approaches, thus validating our FDTD implementation.

Generation of double femtosecond pulses by using two transmissive gratings

Double femtosecond laser pulses are usually generated by using a Michelson structure. We propose a novel and simple device by using two high-density transmissive gratings for generation of double pulses and conversion between single and double laser pulses by shifting one of the two gratings by a quarter period. The apparatus has the advantages of compact volume, simple structure, and convenience in manipulation. Experimental outputs of the double laser pulses are well verified in experiment, which can be properly explained by numerical simulation with the rigorous coupled-wave theory. This structure provides an interesting approach for generation of double pulses and conversion between single and double laser pulses for practical applications of the femtosecond laser.

High-numerical-aperture image simulation using Babinet’s principle

Simulation techniques are developed for high-numerical-aperture (NA) polarized microscopy with Babinet's principle, including partial coherence and vector diffraction for non-periodic geometries. The model includes vector illumination and diffraction in high-NA (up to NA=3.5) object space that is imaged into low-NA image space and recorded on an image sensor. A mathematical model for the Babinet approach is developed and interpreted that includes partial coherence using expanded mutual intensity, where object reflective characteristics modify the coherence functions. Simulation results of the Babinet's principle approach are compared with those of rigorous coupled wave theory (RCWT) for periodic structures to investigate the accuracy of this approach and its limitations.

Ordered amorphous silicon nanoisland arrays and reflection spectral dependence on nanoisland geometrical parameters

We report an anodic porous alumina mask technique for fabricating orderly hemispherical silicon nanoisland arrays with island diameters of 30–120 nm. Reflection spectral measurements show that the phase transition of incident light can periodically be transferred with changes in geometrical parameters of the ordered arrays. Thus the redshift of the reflection peak with decreasing both sizes of the nanoislands and incident angle of light wave can be explained well on the basis of a modified rigorous vector coupled-wave theory. The simple fabrication technique and reflection spectral redshift of the ordered arrays have potential applications in optical devices and solar cells.