Bound states in the continuum (BICs) [[1], [2], [3]], characterized by infinite quality (Q) factors, have gained increasing attention in recent years compared to traditional discrete spectral bound states. Optical BIC can be stimulated by perturbation of in-plane or out-of-plane symmetry [4], leading to the formation of symmetry-protected BIC [5,6]. The ideal BIC exhibits no radiation leakage and is considered a dark mode [7] with infinite lifetime, which makes it difficult to detect. In practical applications, a quasi-BIC (Q-BIC) [[8], [9], [10]] with a high Q factor can be created by introducing asymmetric structure and material parameters, manifesting as a sharp Fano resonance [11], which is easier to observe. Furthermore, BICs can effectively suppress the light radiation, localize the light within the micro-nano optical cavity, and enhance the electromagnetic field due to the infinite Q factor resonance properties. This interaction between light and matter is prolonged, significantly improving the performance of photonic devices. In recent years, compound grating structures designed to realize dual quasi-BICs has been applied in various fields. For instance, in 2021, I. Al-Ani et al. [12] achieved enhanced coupling between the transition-metal dichalcogenides (TMDC) monolayer exciton and cavity resonance based on a symmetry-protected BIC and electric toroidal dipole (TD) BIC. In 2022, I. Al-Ani et al. [13] demonstrated ultra-strong coupling between the exciton of WSe2 monolayer and cavity resonance based on BICs. In 2023, R. Jin et al. [14] demonstrated perfect absorption by integrating a monolayer graphene on top of a silicon compound grating supporting BICs in the near-infrared region. In 2024, S. Zhang et al. [15] proved that the two quasi-BICs could be manipulated independently by either an adjustable grating or an asymmetry in the air gap. These compound grating structures that can realize BICs provide valuable design insights ideas for our subsequent work.

In our work, we primarily focus on enhancing the Goos-Hänchen (GH) shift effect enhancement based on quasi-BICs. When a beam is incident at the interface between two different media, the reflected light undergoes a lateral shift in space relative to the incident light: the GH shift. These shifts can be either negative or positive. On the one hand, positive GH shifts can be applied in optical sensing [[16], [17], [18]] and communication due to their separation characteristics. On the other hand, the negative GH shift can be used for optical storage [19] to realize a closed optical path. Therefore, in addition to achieving giant positive GH shifts, researchers are also highly interested in achieving large negative GH shifts. The symbolic transformation of the GH shift can be achieved by adjusting optical and structural parameters, which can be applied in optical switches [20]. In recent years, numerous studies have focused on enhancing GH shifts based on mechanisms except for BICs using grating structures. For example, in 2014, Yang et al. [21] realized a large negative and positive GH shift caused by guided mode resonance on a designed dielectric grating, which can reach 5000 times of the operating wavelength. In 2020, Petrov NI et al. [22] designed a subwavelength metal grating, demonstrating that the structure generates large positive and negative GH shifts under the influence of surface plasmonic resonance (SPR) effects, up to 95 times of the operating wavelength. In 2023, Du et al. [23] achieved large GH shifts with high transmittance, up to 40 times of the operating wavelength in a double-layer coupled grating structure. With the rise of BIC research, enhanced GH shift effects based on the BIC mechanism have been reported. As early as 2019, Wu et al. [24] achieved a giant GH shift in a compound grating waveguide system with the assistance of a Q-BIC, enhancing it by approximately 1674 times of the operating wavelength. In 2021, Zheng et al. [25] achieved GH shift enhancement based on magnetic dipole Q-BIC in all-dielectric metasurface, with the shift reaching about 1654 times of the operating wavelength. In 2024, Wu et al. [26] achieved a huge GH shift based on Fabry-Perot Q-BIC [27] by designing double-layer gratings, with a shift of approximately 2050 times of the operating wavelength. Clearly, achieving an enhanced GH shift reaching three orders of magnitude in wavelength is already impressive, let alone achieving such an effect across dual bands. Based on the above, in this paper, we design a compound waveguide grating system that generates giant negative (up to −2253.38 times of the operating wavelength) and positive GH shifts (up to 5615.81 times of the operating wavelength), capable of meeting diverse application requirements.

Currently, dynamic control [[28], [29], [30], [31]] of BICs is an emerging trend. Graphene [32] is frequently used as a dynamically regulated material due to its unique electro-optical properties. In 2019, Zhou et al. [33] regulated the GH shifts through the Fermi energy of graphene layer at the resonance wavelength λ0 = 1550 nm, with shift amplitudes varying from −100λ0 to 100λ0. In 2020, Li et al. [34] achieved enhanced GH shift at λ0 = 632.8 nm for a hybrid structure composed of one-dimensional dielectric grating layers. The shifts vary from 500λ0 to 1000λ0 under the regulation of graphene Fermi level. In 2023, Zhou et al. [35] achieved adjustable GH shifts in a metal dielectric grating system containing a single layer of graphene. For a polarized wave incident at λ0 = 783 nm, the shifts vary from 1655λ0 to 8589λ0. In our study, the grating structure was designed based on existing graphene-containing structures. However, instead of using a conventional full-layer graphene coating, our design incorporates spaced-strip graphene. Furthermore, to the best of our knowledge, none of the studies mentioned above have employed the quasi-BIC mechanism to achieve dynamically adjustable GH shift enhancement. Near-infrared light offers several benefits for industrial applications. The wavelength range between 1260 and 1625 nm is optimal for waveguides because of their low transmission losses in silicon photonics and fiber optics. This makes them ideal for industrial applications related to communications, computing and sensing. We successfully achieve dynamic regulation of GH shifts at both 1306.08558 nm (λ01) and 1310.09494 nm (λ02) wavelengths based on the effective enhancement mechanism of quasi-BICs, with the regulated shifts ranging from −0.30λ01 to −2253.38λ01 and 40.372λ02 to 5615.81λ02, respectively. Compared with these examples of dynamic control, we have the obvious advantage that we can simultaneously achieve a large range of dynamic control of positive and negative shifts in the near-infrared band. Due to the GH shift enhancement in this structure, we further study its sensing application performance. Through the simulation calculation, we verify the great angular sensitivity of the structure in a wide range of angles, which has practical significance for the design of excellent multi-band sensors.

We propose and realize dynamically adjustable and giant GH shifts based on dual quasi-BICs by changing the Fermi level of the graphene layer. Directly adjusting the applied voltage without changing the structural parameters greatly reduces the time and cost associated with creating different structures, and holds considerable practical significance. Moreover, this grating structure based on quasi-BIC mechanism enables dynamic control of positive and negative shifts in two bands, meeting the needs of multiband systems and offering improved practical sensing value and advantages.