Normal vector method for convergence improvement using the RCWA for crossed gratings

Schuster, Thomas; Ruoff, Johannes; Kerwien, Norbert; Rafler, Stephan; Osten, Wolfgang

doi:10.1364/josaa.24.002880

Cited by 140 publications

(99 citation statements)

References 10 publications

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“…9 One of the simplest ways to calculate the scattering distribution in a periodic structure such as one comparable to Figure 1, is through the application of the rigorous coupled wave analysis (RCWA) proposed by Glytsis and Gaylord 10 and later optimized by many authors. 11,12 In this method, all the diffraction orders are characterized by a pair of forward and backward flux transfer coefficients, much like the classical Fresnel coefficients for reflection and transmission. This method is relatively uncomplicated, robust, can account for arbitrary grating geometries and is capable of providing exact solutions for specific shapes.…”

Section: Theoretical Analysismentioning

confidence: 99%

Conic hyperspectral dispersion mapping applied to semiconductor plasmonics

et al. 2012

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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. Keywords: biosensors; light scattering; optical devices; semiconductors; surface plasmon resonance INTRODUCTION Surface plasmon resonance (SPR) is a well-established and easy-toinduce phenomenon enabling the study of surficial optical properties, such as those related to the alterations of the local dielectric constants. The resonance tracking of the surface plasmon (SP) coupling has already found a wide range of applications, especially in the field of biochemical analysis, where SPR systems are employed to determine the concentration of molecules and kinetics of intermolecular interactions.1 Using proper stabilization and correction procedures, it has been demonstrated that the SPR technique can be used to detect biochemical fluctuations inducing refractive index changes lower than 10 28 refractive index unit. 2 The same approach can also be employed for the spatial imaging of binding events.3 However, the SPR technology has remained in the realm of trained professionals, in academic laboratories and within specialized industries, requiring relatively large space, capital investment and the support of qualified personnel.

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Section: Theoretical Analysismentioning

confidence: 99%

Conic hyperspectral dispersion mapping applied to semiconductor plasmonics

et al. 2012

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“…The offset of the computed solution with respect to the reference solution visible in Table 1 and the plateau on Figure 5 (error remains constant for N > 50) are due to staircasing. This effect is well known for the FMM [19] and can be reduced by a normal vector field approach [20].…”

Section: Numerical Resultsmentioning

confidence: 89%

Modified S-matrix algorithm for the aperiodic Fourier modal method in contrast-field formulation

et al. 2011

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“…In the case of DM, the implementation of the Fourier factorization rules [6] was obtained through the introduction of a normal-vector field inside the unit cells, such that the appropriate factorization rules could be applied to the normal and tangential field components separately. This same technique was then applied to the footprint of 2D-periodic gratings in RCWA [7] and made the staircase approximation in the periodic directions superfluous. Nevertheless, the staircase approximation in the aperiodic direction, which is inherent to RCWA, can still introduce scattering that is not present in the smooth structure that is approximated [6].…”

Section: Introductionmentioning

confidence: 99%

A Spectral Volume Integral Method Using Geometrically Conforming Normal-Vector Fields

Coenen¹,

Beurden²

2013

PIER

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Abstract-Scattering characteristics of periodic dielectric gratings can be accurately and efficiently computed via a spectral volume integral equation combined with normal-vector fields defined on the grating geometry. We study the impact of the geometrical discretization on the convergence rate of the scattering characteristics for two-dimensional gratings in both T E and T M polarization and compare these with an independent semi-analytical reference for circular cylinders. We demonstrate that geometrically conforming normal vector fields lead to substantially faster convergence and shorter computation times, as opposed to the commonly applied staircasing or slicing.

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Normal vector method for convergence improvement using the RCWA for crossed gratings

Cited by 140 publications

References 10 publications

Conic hyperspectral dispersion mapping applied to semiconductor plasmonics

Conic hyperspectral dispersion mapping applied to semiconductor plasmonics

Modified S-matrix algorithm for the aperiodic Fourier modal method in contrast-field formulation

A Spectral Volume Integral Method Using Geometrically Conforming Normal-Vector Fields

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