Spatiotemporal coupled-mode theory of guided-mode resonant gratings

Narrow-linewidth Fano microcavities with resonant subwavelength grating mirror

We report on the theoretical and experimental investigations of optical microcavities consisting in the plane-plane arrangement of a broadband high-reflectivity mirror and a suspended one-dimensional grating mirror possessing a high-quality factor Fano resonance. By varying the length of these cavities from the millimeter to the few-micron range, we observe at short lengths the reduction of the spectral linewidth predicted to occur for such a Fano cavity as compared to a conventional broadband mirror cavity with the same length and internal losses. Such narrow linewidth and small modevolume microcavities with high-mechanical quality ultrathin mirrors will be attractive for a wide range of applications within optomechanics and sensing.

Spatio-temporal coupled mode theory for nonlocal metasurfaces

Diffractive nonlocal metasurfaces have recently opened a broad range of exciting developments in nanophotonics research and applications, leveraging spatially extended-yet locally patterned-resonant modes to control light with new degrees of freedom. While conventional grating responses are elegantly captured by temporal coupled mode theory, current approaches are not well equipped to capture the arbitrary spatial response observed in the nascent field of nonlocal metasurfaces. Here, we introduce spatio-temporal coupled mode theory (STCMT), capable of elegantly capturing the key features of the resonant response of wavefront-shaping nonlocal metasurfaces. This framework can quantitatively guide nonlocal metasurface design while maintaining compatibility with local metasurface frameworks, making it a powerful tool to rationally design and optimize a broad class of ultrathin optical components. We validate this STCMT framework against full-wave simulations of various nonlocal metasurfaces, demonstrating that this tool offers a powerful semi-analytical framework to understand and model the physics and functionality of these devices, without the need for computationally intense full-wave simulations. We also discuss how this model may shed physical insights into nonlocal phenomena in photonics and the functionality of the resulting devices. As a relevant example, we showcase STCMT's flexibility by applying it to study and rapidly prototype nonlocal metasurfaces that spatially shape thermal emission.

High-speed tunable optical absorber based on a coupled photonic crystal slab and monolayer graphene structure

Reconfigurable metasurfaces have been pursued intensively in recent years for the ability to modulate the light after fabrication. However, the optical performances of these devices are limited by the efficiency, actuation response speed and mechanical control for reconfigurability. In this paper, we propose a fast tunable optical absorber based on the critical coupling of resonance mode to absorptive medium and the plasma dispersion effect of free carriers in semiconductor. The tunable absorber structure includes a single-layer or bi-layer silicon photonic crystal slab (PCS) to induce a high-Q optical resonance, a monolayer graphene as the absorption material, and bottom reflector to remove transmission. By modulating the refractive index of PCS via the plasma dispersion of the free carrier, the critical coupling condition is shifted in spectrum, and the device acquires tuning capability between perfect absorption and total reflection of the incident monochromatic light beam. Simulation results show that, with silicon index change of 0.015, the tunable absorption of light can achieve the reflection/absorption switching, and full range of reflection phase control is feasible in the over coupling region. The proposed reconfigurable structure has potential applications in remote sensing, free-space communications, LiDAR, and imaging.

Polarization-independent optical spatial differentiation with a doubly-resonant one-dimensional guided-mode grating

We report on the design and experimental characterization of a suspended silicon nitride subwavelength grating possessing a polarization-independent guided-mode resonance at oblique incidence. At this resonant wavelength we observe that the transverse intensity profile of the transmitted beam is consistent with a first-order spatial differentiation of the incident beam profile in the direction of the grating periodicity, regardless of the incident light polarization. These observations are corroborated by full numerical simulations. The simple one-dimensional and symmetric design, combined with the thinness and excellent mechanical properties of these essentially loss-free dieletric films, is attractive for applications in optical processing, sensing and optomechanics.

Collimation and finite-size effects in suspended resonant guided-mode gratings

The optical transmission of resonant guided-mode gratings patterned on suspended silicon nitride thin films and illuminated at normal incidence with a Gaussian beam is investigated both experimentally and theoretically. Effects due to the beam focusing and its finite size are accounted for by a phenomenological coupled-mode model whose predictions are found to be in very good agreement with the experimentally measured spectra for various grating structures and beam sizes, and which allow for a detailed analysis of the respective magnitude of these effects. These results are highly relevant for the design and optimization of such suspended structured films that are widely used for photonics, sensing, and optomechanics applications.

Optical spatial differentiation with suspended subwavelength gratings

We investigate first- and second-order spatial differentiation of an optical beam transverse profile using guided-mode resonances in thin, suspended subwavelength gratings. Highly reflective one-dimensional gratings are patterned on freestanding 200 nm-thick silicon nitride membranes using Electron Beam Lithography and plasma etching. The optical transmission of these gratings, designed for illumination with either TM or TE polarized light, are experimentally measured under normal and oblique incidence and found to be in excellent agreement with the predictions of an analytical coupled-mode model as well as Rigorous Coupled Wave Analysis numerical simulations. Intensity profiles consistent with high quality first- and second-order spatial differentiation of a Gaussian beam are observed in transmission at oblique and normal incidence, respectively. Such easy-to-fabricate, ultrathin and loss-free optical components may be attractive for beam shaping and optical information processing and computing.

Large negative and positive optical Goos-Hänchen shift in photonic crystals

Low-loss photonic crystal (PC) mirrors exhibit positive and negative Goos-Hänchen shift (GHS) due to the strong angular and wavelength dependencies of their reflected phase. This Letter demonstrates the existence of large positive and negative GHS in PC mirrors through theoretical, numerical, and experimental approaches. A simple algebraic relation shows that positive effective thickness yields positive (negative) GHS for resonances that blue (red) shift with angle, while the opposite is true for interfaces with negative effective thickness. Spatiotemporal coupled-mode theory demonstrates the above relation for simple systems with one or two resonance modes, and it also shows the existence of both positive and negative GHS. These effects are numerically and experimentally verified in complex PCs with several resonance modes.

Use of aperiodic Fourier modal method for calculating complex-frequency eigenmodes of long-period photonic crystal slabs

We present an iterative method for calculating complex-frequency eigenmodes of photonic crystal slabs with 1D periodicity based on the aperiodic Fourier modal method. By comparison with the known methods, we show that the proposed method is efficient for studying resonant properties of long-period photonic crystal slabs and diffraction gratings. We demonstrate that the method can be used to calculate the eigenmodes of the structures with periods up to at least 500λ. We discuss different aspects of the mode calculation, including convergence of the method, mode field and dispersion analysis. Potential applications of the presented method include investigation of periodic structures with defects and of quasiperiodic and random structures within the super-cell approach.

Coupled-mode theory and Fano resonances in guided-mode resonant gratings: the conical diffraction mounting

We study resonances of guided-mode resonant gratings in conical mounting. By developing 2D time-dependent coupled-mode theory we obtain simple approximations of the transmission and reflection coefficients. Being functions of the incident light's frequency and in-plane wave vector components, the obtained approximations can be considered as multi-variable generalizations of the Fano line shape. We show that the approximations are in good agreement with the rigorously calculated transmission and reflection spectra. We use the developed theory to investigate angular tolerances of the considered structures and to obtain mode excitation conditions. In particular, we obtain the cross-polarization mode excitation conditions in the case of conical mounting.