Guided-mode Resonant Grating Research Articles

Wide spectral range guided-mode resonant grating designed for the wet etching process

We present wideband guided-mode resonant (GMR) gratings made of Si on a SiO2 substrate. Based on the base angle of the grating as the crystal orientation angle (54.74°) of Si, the design process of reflectors suitable for TM-polarized waves is demonstrated in the near-infrared (NIR) and mid-infrared (MIR) wavelengths. Benefiting from the mutual attraction and interaction of the two GMR modes, the bandwidth of reflectivity above 99% for the reflector under the NIR and MIR bands reaches 297 nm (from 1416 nm to 1713 nm) and 657 nm (from 3154 nm to 3811 nm), respectively. In addition, the effects of the incident light source state and the structural parameters on the performance of the reflector are analyzed in detail. The results show that the reflector will maintain good tolerance and stability during fabrication and use. This work will be compatible with the wet etching process in the microelectromechanical system, and the results can be extended to the design of broadband GMR reflectors in other wavelength bands.

Exploiting Thin-Film Properties and Guided-Mode Resonance for Designing Ultrahigh-Figure-of-Merit Refractive Index Sensors

Guided-mode resonance (GMR) gratings have emerged as a promising sensing technology, with a growing number of applications in diverse fields. This study aimed to identify the optimal design parameters of a simple-to-fabricate and high-performance one-dimensional GMR grating. The structural parameters of the GMR grating were optimized, and a high-refractive-index thin film was simulated on the grating surface, resulting in efficient confinement of the electric field energy within the waveguide. Numerical simulations demonstrated that the optimized GMR grating exhibited remarkable sensitivity (252 nm/RIU) and an extremely narrow full width at half maximum (2 × 10−4 nm), resulting in an ultra-high figure of merit (839,666) at an incident angle of 50°. This performance is several orders of magnitude higher than that of conventional GMR sensors. To broaden the scope of the study and to make it more relevant to practical applications, simulations were also conducted at incident angles of 60° and 70°. This holistic approach sought to develop a comprehensive understanding of the performance of the GMR-based sensor under diverse operational conditions.

From coupled plane waves to the coupled-mode theory of guided-mode resonant gratings

We establish the connection between two theoretical approaches widely used for describing resonant optical properties of guided-mode resonant gratings (GMRGs): the coupled plane waves model and the coupled-mode theory (CMT). In the coupled plane waves model (also known as the multiple interference model), the field inside and outside the structure is represented as a small number of propagating plane waves; these waves are coupled at one or several interfaces, which leads to a system of linear equations. In the CMT, the optical properties are described by several coupled differential equations, each corresponding to one of the modes supported by the structure. The approach proposed in the present work provides explicit expressions for the coupling coefficients of the CMT through “local” reflection, transmission, and diffraction coefficients of the coupled plane waves model, which is important for the design and analysis of optical resonators, filters, and sensors based on GMRGs.

Electro-optic symmetry breaking of BIC modes for tunable infrared emissivity

We present an electro-optic pathway to break symmetry to enable dynamic light-matter interaction in guided-mode resonance grating. Breaking of mirror symmetry allows accessing bounds states in the continuum (BIC) that are otherwise inaccessible. We design an electrically tunable GaAs-based guided-mode resonance grating that exhibits infrared absorption peaks in the longwave IR. The grating consists of GaAs dielectric sandwiched between the top gold contacts and the bottom gold reflector. We analyze the dependence of Q-factors on the choice of the design. We show that by careful design of the structure, a substantial radiative coupling can be obtained with broken symmetry. Our simulations predict that due to the electro-optic properties of GaAs, the application of a voltage across the dielectric allows a change in the refractive index to break the symmetry of the structure and turns the emission peak ON. Reversible refractive index tuning restores symmetry and turns the emission OFF. The concept presents a novel route toward tunable directional absorption and emission.

Dual-band tunable filter based on high-Q guided-mode resonance grating

A dual-band tunable filter with a 10.5 nm narrowband based on guided-mode resonance grating is demonstrated. The two filtering working bands around 1200 and 1550 nm can be switched by controlling the TE and TM polarization, respectively. And the Q factor as high as 146.7 at 1550 nm is experimentally realized by optimizing the grating parameters. At TE polarization, an asymmetrical line shape is obtained. In addition, the angle-dependent guided-mode resonance (GMR) effect is well studied in the designed GMR grating filter, in which the tunability and optical bistability based on the thermo-optic effect are first demonstrated.

Topological beaming of light.

Nanophotonic light emitters are key components in numerous application areas because of their compactness and versatility. Here, we propose a topological beam emitter structure that takes advantage of submicrometer footprint size, small divergence angle, high efficiency, and adaptable beam shaping capability. The proposed structure consists of a topological junction of two guided-mode resonance gratings inducing a leaky Jackiw-Rebbi state resonance. The leaky Jackiw-Rebbi state leads to in-plane optical confinement with funnel-like energy flow and enhanced emission probability, resulting in highly efficient optical beam emission. In addition, the structure allows adaptable beam shaping for any desired positive definite profiles by means of Dirac mass distribution control, which can be directly encoded in lattice geometry parameters. Therefore, the proposed approach provides highly desirable properties for efficient micro-light emitters and detectors in various applications including display, solid-state light detection and ranging, laser machining, label-free sensors, optical interconnects, and telecommunications.

Optical properties of guided-mode resonant gratings with linearly varying period

Guided-mode resonant gratings with spatially varying parameters are widely used as linear variable optical filters, and their behavior is often described using the so-called local periodic approximation, in which the structure is locally replaced by a strictly periodic grating with the period coinciding with the ``local'' period at the considered point. In this work, we investigate the optical properties of guided-mode resonant gratings with the period linearly varying along the periodicity direction. Using full-wave numerical simulations, we show that when the period change rate is relatively high (about 0.5--1 $\ensuremath{\mu}\mathrm{m}/\mathrm{mm}$ for the considered structures), the local periodic approximation becomes inapplicable, and the linewidth and the line shape of the resonances depend significantly on the period change rate. We qualitatively explain the appearance of an asymmetric non-Fano line shape with secondary maxima by analyzing the local photonic band structure of the studied varying-period gratings. For a more accurate description of such gratings, we develop a spatiotemporal coupled-mode theory, the predictions of which are in good agreement with the rigorous numerical simulation results. The validity of the derived theoretical model is additionally confirmed by a proof-of-concept experiment with a varying-period guided-mode resonant grating. The obtained results may find application in the design of compact linear variable filters based on resonant gratings with spatially varying parameters.

Low-threshold lasing behavior based on quasi-bound states in the continuum in a slanted guided-mode resonance nanocavity.

In this study, hybrid resonance modes are obtained when symmetry-breaking is introduced into a guided-mode resonance (GMR) grating, which transforms bound states in the continuum (BICs) into quasi-BICs with a high-quality factor while retaining the intrinsic GMR mode. The structural parameters are modified such that GMR and quasi-BICs resonance occur at the pump and emission wavelengths of the gain medium, respectively. Resonant optical pumping and high-quality nanocavities are utilized simultaneously, and a low-threshold laser is realized. We theoretically demonstrate that the threshold can be reduced to 24.6 µJ/cm2, which is approximately 4 times lower than that of the laser based on GMR alone. The lasing action can be modulated by optimizing the asymmetry parameter and the electric field, and the threshold can be further reduced.

Two-dimensional guided-mode resonance gratings with an etch-stop layer and high tolerance to fabrication errors.

Guided-mode resonance (GMR) bandpass filters have many important applications. The tolerance of fabrication errors that easily cause the transmission wavelength to shift has been well studied for one-dimensional (1D) anisotropic GMR gratings. However, the tolerance of two-dimensional (2D) GMR gratings, especially for different design architectures, has rarely been explored, which prevents the achievement of a high-tolerance unpolarized design. Here, GMR filters with common 2D zero-contrast gratings (ZCGs) were first investigated to reveal their differences from 1D gratings in fabrication tolerance. We demonstrated that 2D ZCGs are highly sensitive to errors in the grating linewidth against the case of 1D gratings, and the linewidth orthogonal to a certain polarization direction has much more influence than that parallel to the polarization. By analyzing the electromagnetic fields, we found that there was an obvious field enhancement inside the gratings, which could have a strong effect on the modes in the waveguide layer through the field overlap. Therefore, we proposed the introduction of an etch-stop (ES) layer between the gratings and the waveguide-layer, which can effectively suppress the interaction between the gratings and modal evanescent fields, resulting in 4-fold increased tolerance to the errors in the grating linewidth. Finally, the proposed etch-stop ZCGs (ES-ZCGs) GMR filters were experimentally fabricated to verify the error robustness.

Flat-top filter using slanted guided-mode resonance gratings with bound states in the continuum

The attribute of bound states in the continuum (BICs) for highly efficient flat-top filter by using a slanted guided-mode resonance (GMR) grating is developed in this work. By introducing a slanted angle θ, the fully symmetric grating is broken to transform the dark BICs into bright quasi-BICs mode. Theoretical analysis based on the finite-different time-domain method is applied to evaluate the filtering performances. It is found that the GMR and quasi-BICs peaks combine at θ=31.4°, and the flat-top filtering response is realized at the central wavelength of 1550 nm under normal incidence. Moreover, the linewidth-tunable and central wavelength-tunable spectral response can be varied according to the change in the coupling strength of the GMR grating by changing the structural parameters such as period, fill factor and refractive index of the grating. It is the first report of a flat-top filter designed by combining GMR and quasi-BICs. The proposed structure shows promise for application in high-performance optical communication systems.

Guided-Mode-Resonance Reflectors for Performance Enhancement of Sapphire Based Fabry-Perot Sensors in Harsh Environment

This paper presents a guided-mode resonance (GMR) reflector for sapphire based Fabry-Perot (F-P) sensors that enables tunable or wideband high reflectance with high temperature resistance,which is expected to effectively regulate the performance of F-P sensors and offer a novel approach for designing F-P sensors in harsh environments. Intrinsic and extrinsic GMR gratings are proposed, and their optical and thermal properties are investigated and compared through numerical simulations, such as rigorous coupled-wave analysis and finite element analysis methods. The quantitative results indicate high feasibility for harsh environment applications and the potential for adopting different demodulation methods. Significant enhancement in the F-P sensor performance is obtained through analysis based on the F-P interference model, and the spectrum fineness and sensor sensitivity can be enhanced by at least one order of magnitude. The GMR reflector can be extended to other types of F-P sensors, demonstrating significant potential in high-temperature applications.

Broadband and Ultra-Low Threshold Optical Bistability in Guided-Mode Resonance Grating Nanostructures of Quasi-Bound States in the Continuum.

We model optical bistability in all-dielectric guide-mode resonance grating (GMR) nanostructures working at quasi-bound states in the continuum (BICs). The complementary metal-oxide-semiconductor (CMOS) compatible material silicon nitride (SiN) is used for the design of nanostructures and simulations. The ultra-low threshold of input intensity in the feasible nanostructure for nanofabrication is obtained at the level of ~100 W/cm2 driven by quasi-BICs. Additionally, the resonance wavelength in the GMR nanostructure can be widely tuned by incident angles with the slightly changed Q-factor that enables the optical bistable devices to work efficiently over a wide spectrum. The impact of the defects of grating that may be introduced in the fabrication process on the optical properties is discussed, and the tolerance of the defects to the optical performance of the device is confirmed. The results indicate that the GMR nanostructures of broadband and ultra-low threshold optical bistability driven by quasi-BICs are promising in the application of all-optical devices.

Ultimate conversion efficiency of second harmonic generation in all-dielectric resonators of quasi-BICs in consideration of nonlinear refraction of dielectrics

We investigate second harmonic generation (SHG) in all-dielectric resonance nanostructures of high-Q factors assisted by quasi-bound states in the continuum (quasi-BICs). The typical resonators, e.g., guided-mode resonance gratings and asymmetric metasurfaces, fabricated by AlGaAs were numerically studied with the consideration of nonlinear refraction of AlGaAs. The resonance peak and line-shape of linear transmission and SHG spectra in the resonators can be dramatically changed under intense pump intensities. The SHG conversion efficiency in the nanostructures working at quasi-BICs is much lower than the traditionally expected values without considering the nonlinear refraction of dielectrics. The ultimate SHG conversion efficiency is finally obtained. The investigation has the significance for the design and understanding of efficient nonlinear metasurfaces of high-Q factors.

THz guided-mode resonance notch filter with variable filtering strength

In this paper, we propose a terahertz (THz) guided-mode resonance (GMR) notch filter made of a monolithic polyethylene terephthalate (PET) film, which has a monolayer grating structure. The proposed configuration shows both polarization-dependent and polarization-independent notch filter characteristics for the incident THz wave depending on the rotation angle of the second grating film. When the rotation angle is 0°, the filtering strength (transmittance) at resonance frequency changes from 0.4 (0.996) to 99.0% (0.010) according to the incident polarization. The transmittance continuously decreases with increasing rotation angle until 90°. When the rotation angle is 90°, the transmittance converges to 0.065 (± 0.015) independent of the incident wave polarization. When the incident polarization angle ranges from 90° to 180°, paradoxically, the transmittance through the two GMR grating films is greater than the transmittance through only the first GMR grating film due to the enhancement of the vertical component of the THz wave. These results agree well with a calculation using a polar coordinate system.

Double Electromagnetically Induced Transparency and Its Slow Light Application Based On a Guided-Mode Resonance Grating Cascade Structure.

In recent years, the achievement of the electromagnetically induced transparency (EIT) effect based on the guided-mode resonance (GMR) effect has attracted extensive attention. However, few works have achieved a double EIT-like effect using this method. In this paper, we numerically achieve a double EIT-like effect in a GMR system with a three-layer silicon nitride waveguide grating structure (WGS), using the multi-level atomic system model for theoretical explanation. In terms of slow light performance, the corresponding two delay times reach 22.59 ps and 8.43 ps, respectively. We also investigate the influence of wavelength detuning of different GMR modes on the transparent window and slow light performance. Furthermore, a wide-band flat-top transparent window was also achieved by appropriately adjusting the wavelength detuning between GMR modes. These results indicate that the EIT-like effect in the WGS has potential application prospects in low-loss slow optical devices, optical sensing, and optical communications.

Imprinted Polymer-Based Guided Mode Resonance Grating Strain Sensors.

Optical sensors based on guided mode resonance (GMR) realized in polymers are promising candidates for sensitive and cost effective strain sensors. The benefit of GMR grating sensors is the non-contact, easy optical read-out with large working distance, avoiding costly alignment and packaging procedures. The GMR gratings with resonance around 850–900 nm are fabricated using electron beam lithography and replicated using a soft stamp based imprinting technique on 175 m-thick foils to make them suitable for optical strain sensing. For the strain measurements, foils are realized with both GMR gratings and waveguides with Bragg gratings. The latter are used as reference sensors and allow extracting the absolute strain sensitivity of the GMR sensor foils. Following this method, it is shown that GMR gratings have an absolute strain sensitivity of 1.02 ± 0.05 at 870 nm.

Cross-stacking of guided-mode resonance gratings for polarization-independent flat-top filtering

A guided-mode resonance filter (GMRF) consists of a subwavelength grating on a thin-film waveguide and can provide narrowband filtering with fewer layers in contrast to a multilayer dielectric mirror. A GMRF normally shows a peaky reflection spectrum and polarization dependency. In this Letter, two GMRFs are orthogonally stacked to give polarization-independent narrowband flat-top filtering. The GMRFs are designed by numerical methods and then fabricated and stacked. Each GMRF is formed by corrugation of a T i O 2 grating layer on a SiN guiding core layer on a S i O 2 substrate. A narrowband flat-top filter is demonstrated with a 7 nm full-width at half-maximum.

Analytical design of flat-top transmission filters composed of several resonant structures.

Resonant properties of composite structures consisting of several identical resonant structures (e.g. multilayer thin-film structures or guided-mode resonance gratings) separated by phase-shift layers are investigated theoretically. Using the scattering matrix formalism, we analytically demonstrate that, at properly chosen thicknesses of the phase-shift layers, the composite structures comprising two or four resonant diffractive structures with a Lorentzian transmittance profile optically implement the Butterworth filters of the order two or three, respectively, and enable achieving flat-top transmission spectra with steep slopes and low sidebands. In addition, we show that the composite structures consisting of three or four second-order Butterworth filters can accurately approximate the fourth- or fifth-order Butterworth filters, respectively. The presented theoretical results are confirmed by rigorous numerical simulations of composite structures consisting of the so-called W-structures (simple three-layer resonant structures comprising a high-index core layer and two low-index cladding layers in a high-index dielectric environment). The simulation results confirm the formation of flat-top transmittance peaks, the shape of which fully agrees with the derived theoretical description. Moreover, we demonstrate an exceptionally simple mechanism of controlling the transmittance peak width, which consists in changing the thicknesses of the cladding layers of the initial W-structure and enables generating flat-top transmission peaks with a significantly subnanometer width.

Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings

We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in 1D-periodic guided-mode resonant gratings (GMRGs) consisting of a slab waveguide layer with a binary grating attached to one or both of its interfaces. Using these models, we obtain simple closed-form expressions predicting the locations of the BICs and quasi-BICs in the $\omega$-$k_x$ parameter space. We study two mechanisms of the BIC formation: coupling between two counter-propagating guided modes and coupling between a guided mode and a Fabry-P\'erot mode. The BIC conditions for the two considered mechanisms are formulated in terms of the scattering coefficients of the binary grating. The predictions of the presented models are in excellent agreement with the results of rigorous numerical simulations obtained using the Fourier modal method.

High performance refractive index sensor with stacked two-layer resonant waveguide gratings

Abstract A refractive index (RI) sensor which contains a dielectric cavity composed of two parallel planar waveguide gratings (WGGs) is proposed. Reflection and transmittance through stacked gratings are studied after converting the diffraction problem into the two coupled resonances. The method of analysis is applied to estimate the performance when used as a biosensor. The sensor achieves its high-sensitive detection by tracking a narrow resonant reflection peak via a tunable wavelength light source, and the desired RI can be determined from the resonant wavelength shift. It will be shown that, in comparison with conventional single grating guided mode resonance (GMR) sensor with equal available area, extremely narrow resonance linewidth can be obtained by using stacked gratings. The sensitivity of the sensor can reach to 497.83 nm/RIU, and the value of the figure of merit (FOM) can reach up to 551. Because of its advantages such as high-sensitivity, label-free, small size and non-destructive, the sensor has an extremely broad application prospect in the field of biomedicine detection.