Many applications across the whole EM spectrum rely on the interactions between EM waves and matters, which are however not strong enough in many regions of the EM spectrum, especially when the sources are less developed. One typical example is the terahertz (THz) technology, which has attracted broad research interests in recent years in both fundamental disciplines like physics, chemistry and astronomy as well as in applied sciences including security checking, bio-medical diagnosis, gas detection, environmental monitoring and semiconductor industry, etc. [1], [2], due to the unique properties of spectral resolving capability, high transmission in many optically opaque dielectrics and low photon radiation energy. In particular, many chemicals have unique absorption spectral features arising from the molecular vibration or rotations, and these spectral fingerprints can be used for the detection and identification of unknown samples, including the typical examples of toxic gases [3] and drugs. Compared to electromagnetic waves in the visible and infrared frequencies, THz waves have much longer wavelengths, which suggests the requirement of correspondingly larger optical path to get a similar level of drop in the transmission spectrum. On the other hand, most samples have generally a high-level of absorption resulting from the spectral overlap of multiple absorption resonances in the THz band. This situation is more significant for biological samples where water is always present. As a result, a thin level of sample thickness is preferred to be used. The fact that most terahertz sources, especially those based on the optical generation method, have relatively weak output powers, further aggravates this situation from the point of view of signal-to-noise ratios.
In the optical frequencies, it has long been investigated by using artificial structures to enhance light-matter interaction so that many exotic phenomena can be observed even when the optical input is weak. Nanoscale optical elements in the form of surface plasmon based metallic nanoantennas [4] or all-dielectric nanostructures [5] have been mainly explored, with demonstrated success in a large variety of applications ranging from enhanced spontaneous emission [6], nonlinear optics with alleviated phase matching condition [7], and photodetection [8], to name just a few. Following the same methodology, one can also use artificial structures to have enhanced interactions between THz waves and matters so that many applications of the THz technology can come true even with the current THz sources. Unfortunately, in the THz band the electromagnetic characteristics of most metals are quite different from the optical frequencies, e.g. the conductivities are extremely high (~ 107 S/m), leading to a near-zero skin depth of the THz waves in metals and a loosely confined surface mode. That’s why most metal-based metamaterials in the terahertz band or even lower frequencies have extremely low quality factors at the order of only 10, although the material loss is relatively low for metals in these frequencies. To this end, the concept of spoof surface plasmon (SSP) has been introduced into THz optics [9], and THz stripe antennas have been proposed to have a confined mode with large local field enhancement [10]. However, the requirement of metal corrugations to support the SSP mode has limited the versatile applications in many circumstances.
One of the main attributes used in characterizing a resonating structure is its quality (Q) factor, which measures the damping rate of the resonance mode. While the Q factor can be straightforwardly quantified by the spectral width of the resonance, it is also related with other characteristics of the resonator, e.g. the maximum field enhancement [11]. As a result, to achieve an optimal THz-matter interaction, one aims at designing a resonating structure with finite yet ultra-high quality factors. For instance, Ranjan Singh et al. studies a Fano-type resonance in a two-gap split ring resonator composed of two asymmetric metal arcs, and demonstrated a Q factors of 50 in the THz band [12]. Generally speaking, the overall damping rate of the energy inside a resonator consists of two parts, one due to the non-radiative losses e.g. Ohmic loss, and the other is due to the radiation of energy to the external environment. The total Q factor, defined as the ratio between the resonance wavelength λ0 and its full width at half maximum ∆λ, consists of two contributions from the absorption Q factor and radiation Q factor by the following equations:
$${Q_{{\text{tot}}}}={\lambda _0}/\Delta \lambda$$
1
$$1/{Q_{{\text{tot}}}}=1/{Q_{abs}}+1/{Q_{rad}}$$
2
For metal-based THz metamaterials, although the metals have particularly high conductivity and the ohmic loss is relatively low, i.e. Qabs is quite large, the electromagnetic mode is not tightly confined on the metallic structures and the radiative loss is still quite considerable. As a result, the Qrad factors with metallic THz metamaterials are generally small, leading to a final low Qtot, even when some novel physics like the Fano resonance is employed.
In order to achieve metamaterials with high Q factors in the THz band, the main barrier is the radiative loss which should be reduced so as to increase the Qrad. One effective method to achieve this goal in the optical frequencies is the exploration of the concept of bound states in the continuum (BICs), which was first proposed in quantum mechanics [13] and then intensively investigated in nanophotonics only in recent years to achieve ultra-high Q resonances [14]–[17]. Optical BICs by employing the grating structures on a slab have also been investigated in the literature [18], [19]. However, the reported results either use asymmetric gratings on the opposite side of the slab [18] or use multiple layers of gratings [19], which both pose significant challenges in the fabrication. The BIC effect is mainly realized on the all-dielectric platform in the optical frequencies where even the noble metals exhibit high absorption losses. Some efforts to explore the use of BIC in the THz band have also been made quite recently. Different from the scenario in the optical band, most metals exhibit negligible losses in the THz frequencies, so the BIC phenomenon can also be observed in metal-based THz metamaterials [20], [21] as well as in all-dielectric structures [22].
In this paper, we present a simple structure, which is lithographically more practical and feasible to realize the quasi-BIC effect in the THz band by making use of the guide-mode resonance (GMR) supported by a lossless silicon slab. The GMR is a well-investigated phenomenon where a grating structure helps provide the momentum matching between free space excitation and the guided mode in the slab structure [23]–[32]. When the grating extends infinitely along the direction of the slab, the guided mode can also be coupled back to free space, manifesting itself as a leaky mode. The coupling efficiency of the leaky mode to free space can be manipulated to realize the quasi-BIC effect. Although a simple ridge grating structure on a slab can also support the ideal BIC at normal incidence and the quasi-BIC effect at oblique incidence respectively [33], we should note that the quasi-BIC resonances with ultra-high yet finite Q factors are of more interest and the resonances achieved with normal incidence are preferred for practical applications. We propose to use an new type of composite grating composed of two alternatingly aligned ridge gratings with the same pitch but different ridge width on a silicon slab. Compared to a regular ridge grating, this type of structure supports the quasi-BIC resonance at normal incidence. Quasi-BIC phenomena can be steady observed in this kind of structure at normal incidence. The quasi-BIC resonance exhibits a Q factor more than 105 and huge local field enhancement which is even higher than that provided by optical nanoantennas in the optical frequencies. The electromagnetic characteristics of these quasi-BIC resonances in the THz band is comprehensively investigated, laying out the foundation to manipulate and enhance the interactions between THz waves and matters and opening the horizon for novel THz applications in real life.