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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Employing numerical simulations, we investigate the possibility of using curved guided-mode resonance (GMR) elements to focus light in reflection. We treat GMR reflectors with a parabolic shape and show that they are capable of focusing light effectively across wavelength bands that extend several hundred nanometers. The spatially infinite reflector model is simulated with a finite-element method, whereas the spatially finite reflector is treated with a finite-difference-time-domain method. The numerical results demonstrate that light intensity at the focal point is 8.6 dB stronger than the incident intensity when the GMR reflector's size is on the order of 10 wavelengths. The results indicate potential applicability of wideband-focusing devices in electromagnetics and photonics using compact resonance elements.

Focusing light and electromagnetic waves is important in a host of applications. For instance, parabolic metallic reflectors are widely adopted to focus electromagnetic waves in microwave engineering, and various antenna designs integrate spherical reflectors and paraboloidal/parabolic reflectors [

Guided-mode (or equivalently, leaky-mode) resonance takes advantage of periodic dielectric grating structures to create versatile photonic spectra with associated surface-localized energy states [

The GMR structures treated here are simulated by two numerical methods based on finite-element and finite-difference-time-domain for infinite and finite model dimensions, respectively. The computed results corroborate each other well. The numerical results demonstrate that light intensity at the focal point is 8.6 dB stronger than the incident intensity when the GMR reflector's size is only 10 times the size of the wavelength. Therefore, the curved GMR in this paper offers a means to accomplish local light enhancement, which can be applied, for example, in photo detection. We expect this initial work to serve as the foundation for many other applications where reflective light focusing with low-loss dielectric media is advantageous.

Our curved GMR is based upon a flat GMR design shown in

In

This section presents numerical results to demonstrate light focusing using curved GMR structures. A planar GMR configuration is designed first, providing a reference wideband reflector accommodating a wide range of incident angles. Then this planar GMR reflector is tailored into a parabolic shape. Therefore, light with normal incidence can be focused onto the focal point of the parabolic GMR reflector.

An example planar GMR reflector is illustrated in ^{i}_{0} = ^{jωt}^{r}^{t}

In _{min}, where _{min} is the shortest wavelength of concern. The model GMR structure is assumed to have infinite periodic extension along

In

In summary, by numerical modeling, we demonstrate that parabolic GMR reflectors are capable of focusing light effectively. Specifically, our simulation results show that light intensity at the focal point is 8.6 dB stronger than the incident intensity when the GMR reflector is approximately 10 wavelengths across. Fabrication of the curved GMR structures proposed here is feasible by using electron-beam patterning followed by deep reactive-ion etching, which results in silicon pillars in air that can be tested by illumination with collimated laser beams. Incorporation of the pillars in a lower-index medium that serves additionally as an input-light waveguide is also possible; in this latter case, the refractive-index contrast, and thus the mirror bandwidth, would diminish.

Illustration of

Numerical results for a planar GMR structure:

Numerical results for a curved GMR structure: (

This work was supported in part by the UT System Texas Nanoelectronics Research Superiority Award funded by the State of Texas Emerging Technology Fund. Additional support was provided by the Texas Instruments Distinguished University Chair in Nanoelectronics endowment. The authors would like to acknowledge Texas Advanced Computing Center (TACC) for granting access to its computational facilities.