We show that silicon-based metagratings capable of large-angle, multifunctional performance can be realized using inverse freeform design. These devices consist of nonintuitive nanoscale patterns and support a large number of spatially overlapping optical modes per unit area. The quantity of modes, in combination with their optimized responses, provides the degrees of freedom required to produce high-efficiency devices. To demonstrate the power and versatility of our approach, we fabricate metagratings that can efficiently deflect light to 75° angles and multifunctional devices that can steer beams to different diffraction orders based on wavelength. A theoretical analysis of the Bloch modes supported by these devices elucidates the spatial mode profiles and coupling dynamics that make high-performance beam deflection possible. This approach represents a new paradigm in nano-optical mode engineering and utilizes different physics from the current state-of-the-art, which is based on the stitching of nonint...

Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries

Diffractive optical structures for increasing the efficiency of crystalline silicon solar cells are discussed. As a consequence of the indirect band gap, light absorption becomes very ineffective near the band edge. This can be remedied by use of optimized diffraction gratings that lead to light trapping. We present blazed gratings that increase the optically effective cell thickness by approximately a factor of 5. In addition we present a wideband antireflection structure for glass that consists of a diffraction grating with a dielectric overcoat, which leads to an average reflection of less than 0.6% in the wavelength range between 300 and 2100 nm.

Submicrometer gratings for solar energy applications.

The existing theories which aim to explain the extraordinary optical transmission of a metallic film pierced by a two-dimensional subwavelength hole array [T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, Natural (London) 391, 667 (1998)] all have in common the following feature: instead of studying the two-dimensional crossed grating resulting from the hole array, they consider a one-dimensional grating with infinite slits. We show that such a simplification introduces an efficient channel for light transmission in lamellar gratings, which does not exist for hole arrays. Therefore in order to explain the relatively high transmission observed by Ebbesen et al., it is necessary to take into account the existence of the holes in the array. In this paper we develop a two-dimensional analysis of the experiment performed by Ebbesen et al. No simplification is introduced. This allows us to obtain theoretically the long-wavelength peak reported by Ebbesen et al. with the same grating thickness as the one used by these authors. We also review and study in detail the various contributions devoted to this very surprising effect.

/pdf/theory-of-light-transmission-through-subwavelength-periodic-2kaxlsw2or.pdf

Theory of light transmission through subwavelength periodic hole arrays

A numerically stable method is presented for the analysis of diffraction gratings of arbitrary profile, depth, and in conical mountings. It is based on the classical modal method and uses a stack of lamellar gratpermittivity to approximate an arbitrary profile. A numerical procedure known as the R-matrix propagation aling layers gorithm is used to propagate the modal fields through the layers. This procedure renders the implementation of this new method completely immune to the numerical instability that is associated with the conventional algorithm. Numerical examples including diffraction efficiencies of both dielectric and metallic propagation gratings of depths that range from subwavelength to hundreds of wavelengths are presented. Information about the convergence and the computation time of the method is also included.

Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity : addendum

Numerical evidence is presented that shows that, for metallic lamellar gratings in TM polarization, the coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am. A3, 1780 ( 1986)] converges slowly. (In some cases, for achieving a relative error of less than 1% in diffraction efficiencies, the number of spatial harmonics retained in the computation must be much greater than 100.) By classification of the modal methods for analyzing diffraction gratings into two distinct categories, the cause for the slow convergence is analyzed and attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region. The eigenvalues and the eigenfunctions of the modal fields in the grating region, whose accurate determination is crucial to the success of the coupled-wave method, are shown to converge slowly as a result of the use of these Fourier expansions. Despite its versatility and simplicity, the coupled-wave method should be used with caution for metallic surface-relief gratings in TM polarization.

Convergence of the coupled-wave method for metallic lamellar diffraction gratings

A rigorous modal theory describing the diffraction properties of a dielectric lamellar grating is presented. The numerical implementation is shown to be suited to modelling the behaviour of high refractive index gratings. This suggests that an approach of this type may be successfully applied to the problem of lossy metallic lamellar gratings.

I.C. Botten

Papers

The Dielectric Lamellar Diffraction Grating