Startseite Sensitive THz sensing based on Fano resonance in all-polymeric Bloch surface wave structure
Artikel Open Access

Sensitive THz sensing based on Fano resonance in all-polymeric Bloch surface wave structure

  • Chi Zhang ORCID logo , Qiang Liu , Xiao Peng , Zhengbiao Ouyang und Suling Shen EMAIL logo
Veröffentlicht/Copyright: 5. Oktober 2021
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

Simultaneous realization of high quality factor (Q), sensitivity, and figure of merit (FOM) play a pivotal role in building the THz sensor. For such purpose, we propose an all-polymeric Bloch surface wave (BSW) structure that supports a bright BSW mode and a dark surface Fano state that is embedded in the continuum, both of which coupled to the same radiation channels. The existence of the sharp dip with a maximum depth of Fano line could be interpreted with the physics of Friedrich–Wintgen bound states in the continuum (FW-BICs), because of the destructive interference between bright BSW and dark surface Fano modes. A strong angular- and frequency-dependent Q was found. Related influential factors to Q value may also include an asymmetric arrangement of top and grating layers, together with the weak coupling provided by photonic crystals. One numerically optimized design shows a quality factor Q of the Fano mode as 23,670, which is almost two orders higher than that in conventional metallic-metamaterial-based designs. The optimized sensitivity can numerically reach 4.34 THz/RIU in the frequency domain, which is one order higher than that reported in all-dielectric metasurfaces. We infer the high sensitivity is related to the phase-matching condition provided by near-subwavelength gratings. The associated FOM can reach 8857/RIU. Besides, the proposed design also numerically demonstrates high sensitivity in the angular domain ∼125.5°/RIU. Considering it poses no specific requirement for materials that own high contrast of permittivity in the THz regime, large interfacing area, the mechanical and chemical robustness offered by polymers and low cost in fabrication, such all-polymeric BSW structure that supports novel Fano resonance in THz window may give access to rich applications in hazardous gas detection and label-free bio-sensing.

1 Introduction

Recently, the terahertz wave has received intensive attention because of its wide applications in communications [1], safety inspections [2], and sensing [3], [4], [5]. Among them, terahertz sensing is a well-worth topic due to the low photon energy and “fingerprints” effect. However, materials in nature show a weak response to terahertz waves. Metamaterial (MM) is one kind of artificially electromagnetic (EM) material, which is generally composed of metallic resonator units with sub-wavelength or deep sub-wavelength scale. They present extraordinary physical properties for manipulating EM waves. More specifically, they are sensitive to the change of the dielectric properties and well suited for sensing applications. For example, Li et al. [6] achieved sensitivity in the wavelength domain of 2290 nm/RIU through graphene-enhanced surface plasmon resonance. Rakhshani et al. [7] proposed a sensing application with a frequency sensitivity of about 6400 nm/RIU and figure of merits (FOM) of 10,000 based on metal-based Fano resonance (FR). It is noted, however, most of the MMs as applied in the field of THz sensing today, are mostly limited to noble materials such as gold [8], silver [9, 10], and graphene [6], which inevitably suffer from high intrinsic loss. In addition, the graphene-based MMs suffer from complex preparation processes, low re-usability, and weak adaptability in aggressively mechanical and chemical environments.

Different from metal-based MM, the Bloch surface wave (BSW) structure [11, 12] employs dielectric materials for significantly reducing the intrinsic loss. Due to the photonic bandgap effect, confinement of EM waves with both s- and p-polarization at the materials interface can be achievable. It is recently reported that BSW structures are suitable for THz sensing applications with a relatively high FOM [11]. However, due to the low permittivity contrast provided by commonly employed THz materials, i.e. all-polymeric materials [13], [14], [15], the bandgap in BSW structure is typically narrow, and therefore the quality factor (Q) is still low, e.g. Q < 1000. Simultaneous realization of high Q, sensitivity, and FOM still poses challenges for more advancements.

The FR is an interesting phenomenon, which is basically involved with the quantum destructive interference in the atomic level [16]. FR has also been reported to be applicable for nonquantum photonic and plasmonic systems [17], [18], [19], [20], [21], [22], [23], [24], [25]. More recently, the FRs in hybrid grating-waveguide structure [26, 27], topological heterostructures [28, 29], and metasurfaces (MSs) [30, 31] have been intensively explored in slow light [26, 27] and strong modal field enhancements [28], [29], [30], [31]. Due to the coherent interaction between a discrete narrow localized photonic state and the incoming radiation with continuum radiation, a sharp asymmetric line shape which represents high quality factor, makes it possible to significantly confine and enhance the EM fields. Particularly, the FR effect [32] based on electromagnetically induced transparency (EIT), has enabled good performance in the THz sensing area. Notably, the simultaneous realization of a Q value ∼54.1, sensitivity ∼231 GHz/RIU, and FOM ∼12.7 have been experimentally achieved in EIT MMs that consisting of silicon split-ring resonators. In such designs, the high sensitivity feature is attractive; however, the limited Q may still require a high concentration of specimen, which may not be well-suited for practical sensing scenarios. A novel technique that employs symmetry-broken FR in MS cavities [25], MM resonators [33, 34] has also been reported, however, the inevitable Ohmic loss would degrade the performance of THz sensors due to the limited Q value, e.g. 58 according to ref. [33]. Other techniques involving FR and toroidal dipole resonance [35], toroidal and magnetic FRs [36], and multi-polar FRs [37] still suffer from a relatively low Q which is less than 100.

An alternative approach for building sensitive THz sensing could be based on bound states in the continuum (BICs) [5, 38, 39], the concept of which was first suggested by Von Neumann and Wigner at the end 1930s [40, 41]. Mathematically, perfectly localized states in the continuum can be supported in a three-dimensional potential, where the energy losses to radiation channel become totally vanished due to the destructive interference. These interesting phenomena have inspired for construction of THz sensing designs that show high performances [3042]. For example, Wang et al. [30] proposed one kind of BICs induced by symmetry-broken-MS that consisting of all-dielectric material, i.e. LiTaO3. Such symmetry-broken among high-index all-dielectric disks simultaneously allows a high Q ∼ 1.2 × 105, sensitivity ∼0.489 THz/RIU, and FOM ∼ 25,352. The BICs induced by the symmetry-broken technique can be also found in ref. [42], where a maximal Q value of 1.2 × 103, sensitivity ∼0.077 THz/RIU, and FOM ∼ 11.1 were experimentally realized. To date, the research in BICs-related THz sensing is somehow incomplete, because most studies are focusing on the symmetry-protected-BICs [5, 30, 38, 39, 42], there have been few reports in another type of BICs namely Friedrich–Wintgen bound states in the continuum (FW-BICs) [40, 43] in THz sensing area.

Regarding the property of THz materials, the reported BICs-related THz sensing designs were mostly relevant to a high contrast of permittivity [30, 42] or conductivity [53839]. However, some limitations cannot be neglected. First, the loss tangent of a dielectric material in the THz domain cannot be ignored, for example, silicon demonstrates a large loss tangent over the THz domain. Second, materials that show high contrast of conductivity, e.g. gold, silver, and copper, unavoidably produce obvious Ohmic loss, which results in a low Q despite the appearance of BIC mode [38, 39]. The well-developed polymers, e.g. polyvinylidene fluoride (PVDF) and polycarbonate show low loss in certain parts of the THz domain, they potentially hold promises for the development of THz fiber-optics [13], [14], [15]. However, it is still questionable to deploy all-polymeric materials to produce BICs in the THz sensing area.

In aiming of combining the merits from all-polymeric materials, Fano effect, and BICs, this study proposes a THz sensor based on the surface Fano states embedded in the continuum as provided by an all-polymeric BSW structure. We perform the simulations based on the finite element method in COMSOL (v5.5). It is interesting to find that a bright BSW mode and a dark surface Fano state show the nonorthogonal feature, they are coupled to the same radiation channels with a phase difference of one π. The mechanism may be interpreted with the physics of FW-BICs, due to the destructive interference between such nonorthogonal modes. Detailed investigations show that the Q value associated with the sharp Fano line is k-sensitive, as the Q value is dependent on both incident angle and frequency. The existence of the sharp dip with maximum depth was further studied by changing the asymmetric arrangement of top and grating layers, and the coupling condition provided by the one-dimensional (1D) photonic crystal. To show the performance in THz sensing, we numerically obtained high Q (∼23,670), sensitivity (4.34 THz/RIU and 125.5°/RIU in the frequency and angular domain, respectively), and FOM, e.g. 8857/RIU, all of which were simultaneously achieved in such an all-polymeric BSW structure that owns low contrast in permittivity. In the end, we provide a summary of the state-of-art of THz sensing. The proposed design features as numerically high performance, low contrast in permittivity, large interfacing area, mechanical and chemical robustness, and low fabrication cost, we believe the exploration on utilizing BICs for producing Fano surface wave will facilitate the development of THz sensing.

2 Materials and methods

We show the proposed 2D-BSW-structure in Figure 1(a), in which four parts: top layer, 1D photonics crystals (1D PCs), grating layer, and gratings are included, and the background in Figure 1(a) is filled with the gas analyte. The grating constant, aspect ratio, and thickness of grating are respectively assumed to be Λ = 10 μm, AR = 0.28, and t G  = 10 μm, respectively. Another parameter α is defined to arrange gratings: α = 1 (0) means the gratings do (not) exist; The 1D PCs are formed by overlapping PVDF and Polycarbonate materials with periods N (N = 1, 2, 3,…). The thickness of the two dielectric materials are t PVDF = 7 μm, t Polycarbonate = 5 μm, and the corresponding dielectric properties of PVDF and polycarbonate in the THz domain can be found in Fig. S1, formulas for describing the dispersion of the associated material can be found in ref. [13], note that the dielectric loss of PVDF is small in the frequency regime that closes to 10 THz [11]. Due to the multi-reflections that occur in 1D PCs, the BSW structure is highly sensitive to the thickness of the surface layers, i.e. top and grating layers here. Here, thicknesses of the top and grating layers are denoted by t top and t grl, respectively. Figure 1(b) shows the schematic working mechanism of the suggested design, in which 1D PCs provide weak coupling to BSW and Fano modes.

Figure 1: 
(a) Schematic illustration of the 2D-Bloch surface wave (BSW)-structure that consists of top layer, 1D photonics crystals (1D PCs), grating layer, and gratings. (b) Schematic illustration of the working mechanism, in which two coupled resonators with the corresponding eigenfrequencies f
BSW and f
Fano are involved. (c) Photonic dispersion diagram of the proposed BSW structure, note that red and blue lines are associated with the dispersion of BSW and Fano modes, as mainly confined within grating and top layers, respectively. The white zone represents the stopband, and the gray zone represents nonradiative modes. Note here gratings were added so that α = 1, and t
top = t
grl = 2 μm so that γ = 1.
Figure 1:

(a) Schematic illustration of the 2D-Bloch surface wave (BSW)-structure that consists of top layer, 1D photonics crystals (1D PCs), grating layer, and gratings. (b) Schematic illustration of the working mechanism, in which two coupled resonators with the corresponding eigenfrequencies f BSW and f Fano are involved. (c) Photonic dispersion diagram of the proposed BSW structure, note that red and blue lines are associated with the dispersion of BSW and Fano modes, as mainly confined within grating and top layers, respectively. The white zone represents the stopband, and the gray zone represents nonradiative modes. Note here gratings were added so that α = 1, and t top = t grl = 2 μm so that γ = 1.

As seen from Figure 1(a), the top and grating layers are designed at two opposite edges terminated in the z-direction. Note that the top layer, grating layer, and gratings consist of polycarbonate. We build the model in COMSOL multiphysics, the finite element method is employed for calculating the THz response of the design. All simulations in this paper only consider the polarization as transverse electric (TE) mode. To find the dispersion diagram as depicted in Figure 1(c), the periodic floquet condition is applied to the boundaries that terminated in the x-direction. A large incident angle can potentially increase the gas sensitivity in the angle domain [44], here we select 60° for the following simulations, except for any specific clarification.

The associated dispersion of the fundamental BSW and Fano modes are depicted via red and blue lines, respectively, in Figure 1(b), note here t top = t grl = 2 μm. Since the sharpness of the Fano line is sensitive to the ratio between the t top and t grl, here we introduce the asymmetry factor γ = t top/t grl. Detailed investigation on the mode profiles will be conducted in the following section.

As the phase-matching mechanism governs the dispersion of both BSW modes, to gain a better understanding, here we provide the related formula:

(1) k BSW = k 0 n 0 sin θ + 2 π m Λ

where k BSW represents the wave vector of BSW which is parallel with x-direction, k 0 = 2π/λ represents the free space wave vector, n 0 is the refractive index of background, i.e. analyte, θ is the incident angle, and m is an integer, here is 1 [45]. The dashed line in Figure 1(b) represents the phase-matching condition as satisfied for an individual and discrete BSW mode at the incident angle θ = 60°, i.e. for BSW mode, it occurs at 14.329 THz and 3.67438 × 105 rad/m; for the nearest Fano mode, it occurs at 14.473 THz and 3.65301 × 105 rad/m.

One unique feature of the THz sensor is the capability to produce an identifiable frequency shift induced by the small change of interested analyte or the weak variation of the environment. Moreover, because the general application scenario is in a noisy environment, the resonance intensity is supposed to be sufficiently large for detection. Because of these restrictions, quality factor Q, sensitivity, and FOM are commonly referred for quantitative evaluation to the performance of a THz sensor. Firstly to evaluate a Q, we introduce the formula given as:

(2) Q = f mid FWHM

in which f mid is the frequency of resonance peak in the transmission spectrum, and FWHM is the full width at half maximum. Besides, sensitivity (S) and FOM are usually employed for evaluating the sensor performance, related formulas are given as:

(3) S f = Δ f Δ n 0 , FOM f = S f FWHM ;

(4) S θ = Δ θ Δ n 0 , FOM θ = S θ FWHM .

where the S f and S θ represent the frequency and angle sensitivity, respectively, and FOM f and FOM θ are the associated FOMs. We will use these parameters to quantify the performance of the THz sensor.

3 Discussions

As shown in Figure 1(a), there are three basic components, namely V 1 component: top layer; V 2 component: 1D PCs; V 3 component: grating layer; and V 4 component: gratings. In the following, we explore the THz response of combination of V i (i = 1, 2, 3, 4), i.e. V 1 + V 2 + V 3, V 1 + V 2 + V 3 + V 4, and V 2 + V 3 + V 4 as presented in Figure 2. To study the fundamental BSW mode, i.e. the number of vertical nodes in the top or grating layer, we select t top = 2 μm and γ = 1 (the arrangement of top and grating layers are symmetric to the 1D PCs). In Figure 2(a), it is found that BSW modes cannot be excited, as the phase-matching condition shown in Eq. (1) cannot be satisfied, note there is no grating here. After adding gratings as shown in Figure 2(b), two critical points can be found in the spectrum. The associated mode profiles show that EM surface wave propagates along the interfaces of the BSW structure [11]. For the wave that traveling along the grating layer, the associated mode profile is mainly concentrated at the grating layer, and it extends to the 1D PCs while decaying along the y-direction, which we termed as BSW mode. This dip may be originated from the relatively strong coupling between the surface wave and BIC mode as shown in Figure 1(a). For the wave that traveling along the top layer, the mode profile shows a similar feature. More importantly, it is obvious to find the associated dip owns an obvious asymmetric profile and much narrower bandwidth, which we termed as the Fano mode. In contrast with the BSW mode, the Fano mode experienced multi-reflections provided by 1D PCs before arriving to the top layer, as a result, it may be originated from the relatively weak coupling between the surface wave and BIC mode as shown in Figure 1(a). It is noted that the individual BSW and Fano modes are discrete. According to Eq. (1), both modes need to satisfy the phase-matching condition. Now consider Figure 2(c) in which the top layer is removed, the Fano mode disappears while the aforementioned BSW mode still exists.

Figure 2: 
Simulated transmission spectra of three scenarios: (a) V
1 + V
2 + V
3, note that there is no grating here, so that α = 0. t
top = t
grl = 2 μm so that γ = 1. (b) V
1 + V
2 + V
3 + V
4, note that α = 1, t
grl = 2 μm, γ = 1. (c) V
2 + V
3 + V
4, here α = 1, t
grl = 2 μm, γ = 0. The number of periodic layers in the photonics crystals (PCs) is N = 8. The distribution of the electric field in z direction is presented next to the resonance peak. The red and blue in the color bar indicate “+” and “-”, respectively.
Figure 2:

Simulated transmission spectra of three scenarios: (a) V 1 + V 2 + V 3, note that there is no grating here, so that α = 0. t top = t grl = 2 μm so that γ = 1. (b) V 1 + V 2 + V 3 + V 4, note that α = 1, t grl = 2 μm, γ = 1. (c) V 2 + V 3 + V 4, here α = 1, t grl = 2 μm, γ = 0. The number of periodic layers in the photonics crystals (PCs) is N = 8. The distribution of the electric field in z direction is presented next to the resonance peak. The red and blue in the color bar indicate “+” and “-”, respectively.

To better understand the origination of BSW and Fano modes, we further investigate the phase difference between them. As shown in Figure 2(b), for the BSW mode, the sequence of nodes in the top (grating) layer is “+/−/+/−” (“−/+/−/+”); for the Fano mode, the sequence of nodes in the top (grating) layer is “−/+/−/+” (“−/+/−/+”). Taking in mind that (1) the resonant frequency and wavenumber in the x-direction k x of BSW and Fano modes are close, note that the arrangement of top and grating layers are symmetric to the 1D PCs because γ = 1; (2) the dip in the spectrum shown in Figure 2(b) represents the destructive interference between the incident and reflected wave, it is evident that BSW and Fano modes show a phase difference of π. As a result, the origination of BSW and Fano modes could be inferred as mode splitting. As also noted, the mode splitting phenomena commonly exists in photonic [46] and plasmonic [47] systems, in which bonding and antibonding modes are involved. According to the phase difference between nodes at the top and grating layer, the antibonding and boding modes could be associated with Fano and BSW modes, respectively. We infer that the operation frequency, incident angle, asymmetric arrangement of top and grating layers, together with tunneling provided by the 1D PCs, play an important role in mediating the coupling between the bonding and antibonding modes shown in Figure 2(b). In the following, for better understanding the principle of designing the sensitive THz sensor in an all-polymeric BSW structure, we will firstly initiate an investigation on modal behaviors by adjusting operation frequency and incident angle.

Figure 3(a) shows the spectra response when the incident angle and operation frequency are changed. It is noted there exists a broad shaded region that is associated with a bright BSW mode and a narrow line region associated with dark Fano mode. The FR can thus be understood in terms of a bright, broad mode (see the symmetric transmission line associated with bonding mode in Figure 2(b)) and a dark, narrow mode (see the antisymmetric transmission line associated with the antibonding mode in Figure 2(b)) [48]. It is noted, both BSW and Fano modes can be considered as nonorthogonal surface states [43] which share the same radiation channels, see the background above the top layer and below the gratings. Incidentally, there exits destructive or constructive interference at some accidental frequency and incident angle, that characteristically results in a dip or peak shown in the spectra. Moreover, the dark mode becomes narrower at a region colored with a dashed blue dot and the destructive interference becomes maximum, leading to the appearance of an eigen-state that is embedded in a continuum, namely super-mode. Because of the destructive interference, the leaky Fano surface wave transformed into a super mode, which may be associated with a Fano surface state. Further simulation shows the Q of dark Fano mode is tunable because it is sensitive to the wave-vector k. The maximum of Q can be found at an incident angle of 58°, seen in Figure 3(b). We notice that the behavior of such surface Fano mode is quite similar with quasi-Friedrich–Wintgen bound states in the continuum (quasi-FW-BICs). For a better understanding, we provide the coupled-mode theory [49] shown in Supplementary material for potential explanations on the destructive interference that occurred in the shared radiation channels.

Figure 3: 
(a) Transmission spectrum as a function of the incident angle of the Bloch surface wave (BSW) structure. The quasi-bound states in the continuum (BIC) mode are highlighted by dotted circles colored with blue, it is related to the eigenstate that is embedded in a continuum, see the bright yellow region. Notice bright BSW and dark Fano modes are respectively highlighted by dotted circles colored with white and green. Besides, there exists a parasitic mode that is embedded in photonics crystal (PC) layers. (b) The relationship between Q value of dark Fano mode and incident angle, with an operation frequency as 14.58 THz. Note the parasitic mode in PC is caused by destructive interference that occurred in the PC layers, it may also belong to quasi-FW-BICs. However, since the electric field is mainly extended within PC layers, such mode is useless for sensing applications.
Figure 3:

(a) Transmission spectrum as a function of the incident angle of the Bloch surface wave (BSW) structure. The quasi-bound states in the continuum (BIC) mode are highlighted by dotted circles colored with blue, it is related to the eigenstate that is embedded in a continuum, see the bright yellow region. Notice bright BSW and dark Fano modes are respectively highlighted by dotted circles colored with white and green. Besides, there exists a parasitic mode that is embedded in photonics crystal (PC) layers. (b) The relationship between Q value of dark Fano mode and incident angle, with an operation frequency as 14.58 THz. Note the parasitic mode in PC is caused by destructive interference that occurred in the PC layers, it may also belong to quasi-FW-BICs. However, since the electric field is mainly extended within PC layers, such mode is useless for sensing applications.

The asymmetric arrangement of top and grating layers could be another factor for determining the Q value of the Fano mode. By tuning the asymmetric factor γ, the transmissive responses of BSW and Fano modes can be adjusted, as shown in Figure 4(a–e). With the increment of γ, the asymmetry gradually becomes severe, it results in (i) the appearance of higher order of Fano modes, note that the number of nodes along the y-direction in the top layer from Figure 4(a–d) are respectively 1, 2, 3, and 3; (ii) the change of the sharpness of the spectral profile that associated with Fano mode; (iii) the Fano mode behaves a redshift. More detailed investigations on (ii) and (iii) could be found in Fig. S1 contained in Supplementary material. Interestingly, when γ = 11.5, a phenomenon related to electromagnetically induced transparency [50] could be numerically observed, as shown in Figure 4(d). More importantly, when γ = 100, the thickness of the top layer is at a millimeter scale, which is comparable to the thickness of a substrate, see Figure 4(e). Based on the numerical fact that the thickness of the top layer could be as sufficiently large as that of a substrate, and the associated Fano dip shows with maximum depth, it may make the design experimentally feasible and applicable for building a physical THz sensor. We notice that the versatile technologies for fabricating layer-by-layer-polymer thin films [51], substrate-free polymer thin films [52], and optical-fiber-gratings [53] may become truly useful for the future fabrication of such BSW design.

Figure 4: 
The transmissions response of different scenarios by adjusting the asymmetry factor (a) γ = 1, (b) γ = 6, (c) γ = 11, (d) γ = 11.5 and (e) γ = 100, note here N = 8 and t
grl = 2 μm. The transmissions response of different scenarios by adjusting the number of periodic layers (f) N = 2, (g) N = 4, (h) N = 8, (i) N = 12 and (j) N = 16, note here γ = 1 and t
grl = 2 μm. The distribution of the electric field in z direction is presented next to the resonance peak.
Figure 4:

The transmissions response of different scenarios by adjusting the asymmetry factor (a) γ = 1, (b) γ = 6, (c) γ = 11, (d) γ = 11.5 and (e) γ = 100, note here N = 8 and t grl = 2 μm. The transmissions response of different scenarios by adjusting the number of periodic layers (f) N = 2, (g) N = 4, (h) N = 8, (i) N = 12 and (j) N = 16, note here γ = 1 and t grl = 2 μm. The distribution of the electric field in z direction is presented next to the resonance peak.

To understand the weak coupling that governs the profile of the Fano line shown in the spectra, we also examine the transmissive responses which are tuned by the number of periodic layers consisted of 1D PCs, as shown in Figure 4(f–i). From Figure 4(f) in which N is small, due to the fact that the photonic bandgap is not well-formed, there is no dark mode. As it is well-known, 1D PCs are important in the sensor structure, a dark mode is formed because of the discrete and defective state that is confined within the bandgap (see the blue and red dots in Figure 1(b)). When N keeps increasing, e.g. N = 4 as shown in Figure 4(g), two BSW modes that feature asymmetric and broad profiles in the spectrum can be found. Relatively large N could induce much sharper Fano lines, as presented in Figure 4(c) and (d). We attributed such phenomena to the evanescent tunneling that was well depicted in ref. [54]. Due to the fact that 1D PCs provide multi-reflections to the incident wave, only a small proportion of EM energy could be tunneling through the 1D PCs channel when N becomes larger. The coupling becomes weaker, and consequently, much sharper Fano line can be observed in the simulations. It is noted, however, if the N keeps rising to a large number, e.g. N = 12 or 16, the evanescent wave is strongly suppressed, and the resonance depth of Fano mode becomes low and finally disappears, see Figure 4(h) and (i). An appropriate N is thus of vital importance for designing sensitive THz sensors. It is noted, compared with the air layer that was used for providing evanescent tunneling [26], 1D PCs are more suitable for THz sensing.

In the following, we propose a THz gas sensor based on the platform shown in Figure 1(a) and consequently conduct an analysis to the performance of it. As discussed before, a high value of t top (the thickness of the top layer) is necessary for practically building the THz sensor, however, the time cost in simulations would be high, which is inefficient and not necessary. To catch the physical essentials while efficiently demonstrate the numerical performance of the proposed THz sensor, here we respectively select the thicknesses of the top and grating layers as t top = 14 μm and t grl = 35 μm. In addition, the air is selected as the reference analyte. The refractive index of the tested gas can be varied by tuning the concentration or pressure, as according to ref. [43]. We assumed the refractive index n 0 is increased from 1 to 1.009 while the incidence angle is assumed to be 60°. The spectra responses in Figure 5(a) demonstrate an obvious frequency shift. Alternatively, by tuning the incident angle while fixing the operation frequency, i.e. 14 THz here, we could obtain the angular response, as depicted in Figure 5(b), it could be found that a sharp dip in the angular domain also exists. To quantify the sensitivity in frequency and angular domains respectively, Eqs. (2)(3) are employed. The resulted (S f , FOM f ) and (S θ , FOM θ ) are presented in Figure 5(c) and (d), respectively. Among them, it is observed that S f decreases as n 0 increases, for the optimal value of n 0 that is close to 1, S f and FOMf can reach 4.34 THz/RIU and 8857/RIU, respectively. Of note, the sensitivity ∼4.34 THz/RIU is almost one order higher than that reported in all-dielectric MSs [30]. We attribute it to the phase-matching condition [55] provided by the near-subwavelength gratings [56] that work with an incident angle of 60°, detailed mathematical derivation regarding the sensitivity in our design can be found in Supplementary material.

Figure 5: 
Numerical performance of THz sensor in the frequency and angle domains. (a) and (b) show the variation of transmittance in frequency and angular spectra, respectively, for a varied refractive index of the gaseous analyte: n
0 = 1.000, 1.003, 1.006, and 1.009. (c) and (d) reveal the sensitivity and figure of merit (FOM) of the Fano mode, respectively, with different refractive indexes arising from 1.00 to 1.01.
Figure 5:

Numerical performance of THz sensor in the frequency and angle domains. (a) and (b) show the variation of transmittance in frequency and angular spectra, respectively, for a varied refractive index of the gaseous analyte: n 0 = 1.000, 1.003, 1.006, and 1.009. (c) and (d) reveal the sensitivity and figure of merit (FOM) of the Fano mode, respectively, with different refractive indexes arising from 1.00 to 1.01.

We additionally notice that the optimal S θ and FOM θ can reach up to 125.5°/RIU and 7335/RIU, respectively. In the interested n 0 region, the proposed THz sensor shows relatively stable performance, as the change of an individual parameter, e.g. FOM f , is within the same order of magnitude.

Considering that the proposed design could simultaneously provide high Q, sensitivity, and FOM in both the frequency and the angular domains, it is believed that such designs could potentially be utilized for sensing applications. We also point out that, since this THz sensor is consisted of all-polymer materials, by incorporating a microporous structure at the interface of the top layer which owns a large surface, a large number of gas molecules can be filled in microporous structures, which would change the effective refractive index at the top layer, the performance of it could be potentially improved.

Last but not the least, we provide a summary of the state-of-art sensing designs as built upon MMs and BSW structures [5, 11, 30, 32, 38, 39, 42] as shown in Table 1. Till now, BSW designs have demonstrated high Q factor, e.g. >5000 [57], high sensitivity, e.g. 9650 nm/RIU [57], and high FOM, e.g. 48,250 [57], which are meaningful for sensing. However, the operation wavelength is mostly focused on the visible regime, and there are quite a few things that are involved in the infrared and THz domains. Since hazardous gas such as N2O, HCN, H2, and CO2, demonstrates their specific “fingerprint” in the THz range, the application of these well-developed MMs and BSW designs may be limited.

The proposed BSW design has the potential to be applied as a THz refractive index sensor, as the optimized quality factor Q of the Fano mode is 23,670, which is at least two orders higher than that in conventional metallic-MMs-based designs. The optimized sensitivity can numerically reach 4.34 THz/RIU and 125.5°/RIU in the frequency and angular domain, respectively, and the associated FOM can reach 8857/RIU and 7335/RIU, respectively. In terms of simultaneous realization of high Q, sensitivity, and FOM, we believe that such FR that mediated by BICs [58] may potentially improve the performance of the THz sensor as built upon all-polymer BSW structure.

Table 1:

Parametric comparison of the recently proposed resonators in the THz sensing area.

Type/mechanisms Main materials Sensitivity Q FOM (/RIU) Years
MMs/EIT-based Fano Silicon 231 GHz/RIU 54.1 12.7 2019 [32]
MS/quais-BICs induced by symmetry broken + Fano Silicon 77 GHz/RIU <1200 11.1 2020 [42]
MMs/quasi-BICs induced by symmetry broken + Fano Copper 160 GHz/RIU 5.67 0.91 2020 [5]
MMs/Friedrich–Wintgen BICs Copper N/A 27 N/A 2020 [38]
Double slit arrays/quasi-BICs induced by symmetry broken Copper N/A <230 N/A 2021 [39]
MS/toroidal resonance + BICs LiTaO3 0.489 THz/RIU 120,000 25,353 2021 [30]
BSW/general Fano Polymers 4.7 THz/RIU <1000 147.3 and 301.3 2020 [11]
BSW/quasi-Friedrich–Wintgen BICs + Fano Polymers 4.34 THz/RIU

125.5°/RIU
23,670 8857

7335
Proposed

4 Conclusions

In this article, an all-polymeric THz sensor based on a novel FR in BSW structure is proposed. We demonstrate and investigate the performance by the finite element method. The sensor shows relatively high sensitivity ∼4.34 THz/RIU, which is one order higher than that reported in all-dielectric MSs. The sensitivity in the angular domain is numerically found to be 125.5°/RIU, and the FOM values in frequency and angular domains are 8857/RIU and 7335/RIU, respectively. The Q factor of the Fano mode that is confined in the 1D PCs and top layer, can be as high as 23,670, which is about two orders higher than that of the conventional MM THz-sensors. The mechanism was interpreted with the physics of Friedrich–Wintgen BICs due to the destructive interference between two nonorthogonal surface waves that share the same radiation channels. The existence of the sharp dip with maximum depth was inferred to be the results of k-sensitive-feature, the asymmetric arrangement of top and grating layers, and weak coupling provided by the 1D photonics crystal. As the thickness of the top layer could be sufficiently high that is comparable to a substrate, and the associated Fano dip shows with maximum depth, it may make the design experimentally feasible and applicable for building sensitive THz sensors. Because it is completely composed of polymeric materials, it will not cause the propagation wave to produce high intrinsic losses. Combined with the merit as no specific requirement for high contrast of permittivity, the mechanical and chemical robustness offered by polymers, large interfacing area, design convenience, and low cost in fabrication, we believe the proposed all-polymeric BSW structure that working in the THz regime may become a good candidate for the hazardous gas sensing and bio-sensing applications.


Corresponding author: Suling Shen, College of Physics & Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China; and National-Regional Key Technology Engineering Laboratory for Medical Ultrasound, Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, School of Biomedical Engineering, Health Science Center, Shenzhen University, Shenzhen 518060, China, E-mail:
Chi Zhang and Qiang Liu have contributed equally to this work.

Funding source: Basic and Applied Basic Research Foundation of Guangdong Province

Award Identifier / Grant number: 2019A1515111007

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors gratefully acknowledge the financial support for this work provided by the Basic and Applied Basic Research Foundation of Guangdong Province (grant number: 2019A1515111007).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] I. F. Akyildiz, J. M. Jornet, and C. Han, “Terahertz band: next Frontier for wireless communications,” Phys. Commun., vol. 12, pp. 16–32, 2014, https://doi.org/10.1016/j.phycom.2014.01.006.Suche in Google Scholar

[2] J. Chen, Y. Q. Chen, H. W. Zhao, G. J. Bastiaans, and X. C. Zhang, “Absorption coefficients of selected explosives and related compounds in the range of 0.1–2.8 THz,” Opt. Express, vol. 15, pp. 12060–12067, 2007, https://doi.org/10.1364/oe.15.012060.Suche in Google Scholar PubMed

[3] S. J. Park, J. T. Hong, S. J. Choi, et al.., “Detection of microorganisms using terahertz metamaterials,” Sci. Rep., vol. 4, p. 4988, 2014, https://doi.org/10.1038/srep04988.Suche in Google Scholar PubMed PubMed Central

[4] B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Phys. Med. Biol., vol. 47, pp. 3807–3814, 2002, https://doi.org/10.1088/0031-9155/47/21/319.Suche in Google Scholar PubMed

[5] R. J. Cheng, L. Xu, X. Yu, L. E. Zou, Y. Shen, and X. H. Deng, “High-sensitivity biosensor for identification of protein based on terahertz Fano resonance metasurfaces,” Opt. Commun., vol. 473, p. 125850, 2020, https://doi.org/10.1016/j.optcom.2020.125850.Suche in Google Scholar

[6] B. Li, T. L. Cheng, J. X. Chen, and X. Yan, “Graphene-enhanced surface plasmon resonance liquid refractive index sensor based on photonic crystal fiber,” Sensors, vol. 19, p. 3666, 2019, https://doi.org/10.3390/s19173666.Suche in Google Scholar PubMed PubMed Central

[7] M. R. Rakhshani, “Fano resonances based on plasmonic square resonator with high figure of merits and its application in glucose concentrations sensing,” Opt. Quant. Electron., vol. 51, p. 287, 2019, https://doi.org/10.1007/s11082-019-2007-5.Suche in Google Scholar

[8] A. Sathukarn, C. Jia yi, S. Boonruang, et al.., “The simulation of a surface plasmon resonance metallic grating for maximizing THz sensitivity in refractive index sensor application,” Int. J. Opt., vol. 2020, p. 3138725, 2020, https://doi.org/10.1155/2020/3138725.Suche in Google Scholar

[9] J. T. Hong, S. W. Jun, S. H. Cha, et al.., “Enhanced sensitivity in THz plasmonic sensors with silver nanowires,” Sci. Rep., vol. 8, p. 15536, 2018, https://doi.org/10.1038/s41598-018-33617-2.Suche in Google Scholar PubMed PubMed Central

[10] M. Janneh, A. De Marcellis, E. Palange, A. T. Tenggara, and D. Byun, “Design of a metasurface-based dual-band terahertz perfect absorber with very high Q-factors for sensing applications,” Opt. Commun., vol. 416, pp. 152–159, 2018, https://doi.org/10.1016/j.optcom.2018.02.013.Suche in Google Scholar

[11] C. Zhang, S. L. Shen, Q. Wang, M. Lin, Z. B. Ouyang, and Q. Liu, “Highly sensitive THz gas-sensor based on the guided Bloch surface wave resonance in polymeric photonic crystals,” Materials, vol. 13, p. 1217, 2020, https://doi.org/10.3390/ma13051217.Suche in Google Scholar PubMed PubMed Central

[12] J. X. Chen, D. G. Zhang, P. Wang, and H. Ming, “Strong polarization transformation of Bloch surface waves,” Phys. Rev. Appl., vol. 9, p. 024008, 2018, https://doi.org/10.1103/physrevapplied.9.024008.Suche in Google Scholar

[13] M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett., vol. 90, p. 113514, 2007, https://doi.org/10.1063/1.2713137.Suche in Google Scholar

[14] D. R. Chen and H. B. Chen, “A novel low-loss terahertz waveguide: polymer tube,” Opt. Express, vol. 18, pp. 3762–3767, 2010, https://doi.org/10.1364/oe.18.003762.Suche in Google Scholar PubMed

[15] P. D. Cunningham, N. N. Valdes, F. A. Vallejo, et al.., “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys., vol. 109, p. 043505, 2011, https://doi.org/10.1063/1.3549120.Suche in Google Scholar

[16] K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett., vol. 66, pp. 2593–2596, 1991, https://doi.org/10.1103/physrevlett.66.2593.Suche in Google Scholar

[17] S. Wang, T. G. Zhao, S. L. Yu, and W. Y. Ma, “High-performance nano-sensing and slow-light applications based on tunable multiple Fano resonances and EIT-like effects in coupled plasmonic resonator system,” IEEE Access, vol. 8, pp. 40599–40611, 2020, https://doi.org/10.1109/access.2020.2974491.Suche in Google Scholar

[18] U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev., vol. 124, pp. 1866–1878, 1961, https://doi.org/10.1103/physrev.124.1866.Suche in Google Scholar

[19] C. Ott, A. Kaldun, P. Raith, et al.., “Lorentz meets Fano in spectral line shapes: a universal phase and its laser control,” Science, vol. 340, pp. 716–720, 2013, https://doi.org/10.1126/science.1234407.Suche in Google Scholar PubMed

[20] M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics, vol. 11, pp. 543–554, 2017, https://doi.org/10.1038/nphoton.2017.142.Suche in Google Scholar

[21] F. Jiang, C. S. Deng, Q. Lin, and L. L. Wang, “Simulation study on active control of electromagnetically induced transparency analogue in coupled photonic crystal nanobeam cavity-waveguide systems integrated with graphene,” Opt. Express, vol. 27, pp. 32122–32134, 2019, https://doi.org/10.1364/oe.27.032122.Suche in Google Scholar

[22] M. Sahrai and M. Abbasabadi, “All-optical switch based on doped graphene quantum dots in a defect layer of a one-dimensional photonic crystal,” Appl. Opt., vol. 57, pp. 521–526, 2018, https://doi.org/10.1364/ao.57.000521.Suche in Google Scholar PubMed

[23] C. Shu and J. S. Mei, “Realizations of electromagnetically induced transparency effect in microwave frequency based on metamaterials,” Integr. Ferroelectr., vol. 210, pp. 188–196, 2020, https://doi.org/10.1080/10584587.2020.1728859.Suche in Google Scholar

[24] A. Nagarajan, K. van Erve, and G. Gerini, “Ultra-narrowband polarization insensitive transmission filter using a coupled dielectric-metal metasurface,” Opt. Express, vol. 28, pp. 773–787, 2020, https://doi.org/10.1364/oe.383781.Suche in Google Scholar PubMed

[25] M. Gupta and R. Singh, “Terahertz sensing with optimized Q/Veff metasurface cavities,” Adv. Opt. Mater., vol. 8, p. 1902025, 2020, https://doi.org/10.1002/adom.201902025.Suche in Google Scholar

[26] S. G. Lee, S. Y. Jung, H. S. Kim, S. Lee, and J. M. Park, “Electromagnetically induced transparency based on guided-mode resonances,” Opt. Lett., vol. 40, pp. 4241–4244, 2015, https://doi.org/10.1364/ol.40.004241.Suche in Google Scholar PubMed

[27] Q. Wang, L. Yu, H. X. Gao, S. W. Chu, and W. Peng, “Electromagnetically induced transparency in an all-dielectric nano-metamaterial for slow light application,” Opt. Express, vol. 27, p. 375975, 2019, https://doi.org/10.1364/OE.27.035012.Suche in Google Scholar PubMed

[28] W. Gao, X. Hu, C. Li, et al.., “Fano-resonance in one-dimensional topological photonic crystal heterostructure,” Opt. Express, vol. 26, pp. 8634–8644, 2018, https://doi.org/10.1364/oe.26.008634.Suche in Google Scholar PubMed

[29] Z.-N. Farzad and F. Romain, “Topological Fano resonances,” Phys. Rev. Lett., vol. 122, p. 014301, 2019.10.1103/PhysRevLett.122.014301Suche in Google Scholar PubMed

[30] Y. Wang, Z. Han, Y. Du, and J. Qin, “Ultrasensitive terahertz sensing with high-Q toroidal dipole resonance governed by bound states in the continuum in all-dielectric metasurface,” Nanophotonics, vol. 10, pp. 1295–1307, 2021, https://doi.org/10.1515/nanoph-2020-0582.Suche in Google Scholar

[31] C. Salvatore, S. Liu, L. I. Basilio, et al.., “Broken symmetry dielectric resonators for high quality factor Fano metasurfaces,” ACS Photonics, vol. 3, pp. 2362–2367, 2016.10.1021/acsphotonics.6b00556Suche in Google Scholar

[32] T. Ma, Q. Huang, H. C. He, Y. Zhao, X. X. Lin, and Y. L. Lu, “All-dielectric metamaterial analogue of electromagnetically induced transparency and its sensing application in terahertz range,” Opt. Express, vol. 27, pp. 16624–16634, 2019, https://doi.org/10.1364/oe.27.016624.Suche in Google Scholar

[33] Q. Xie, G. X. Dong, B. X. Wang, and W. Q. Huang, “High-Q Fano resonance in terahertz frequency based on an asymmetric metamaterial resonator,” Nanoscale Res. Lett., vol. 13, p. 294, 2018, https://doi.org/10.1186/s11671-018-2677-0.Suche in Google Scholar PubMed PubMed Central

[34] X. P. Zhu, S. Zhang, Y. Q. Chen, et al.., “Near-field coupling derived plasmon-induced transparency and Fano dip in symmetry-broken terahertz metamaterials by the “sketch and peel” lithography process,” Microelectron. Eng., vol. 220, p. 111155, 2020, https://doi.org/10.1016/j.mee.2019.111155.Suche in Google Scholar

[35] S. Y. Duan, J. B. Wu, Z. Shen, et al.., “Tunable and high quality factor Fano and toroidal dipole resonances in terahertz superconducting metamaterials,” Mater. Res. Express, vol. 7, p. 046001, 2020, https://doi.org/10.1088/2053-1591/ab85fa.Suche in Google Scholar

[36] S. Han, M. Gupta, L. Q. Cong, et al.., “Toroidal and magnetic Fano resonances in planar THz metamaterials,” J. Appl. Phys., vol. 122, p. 113105, 2017, https://doi.org/10.1063/1.5001246.Suche in Google Scholar

[37] L. Chen, N. N. Xu, L. Sigh, et al.., “Defect-induced Fano resonances in corrugated plasmonic metamaterials,” Adv. Opt. Mater., vol. 5, p. 1600960, 2017, https://doi.org/10.1002/adom.201600960.Suche in Google Scholar

[38] X. G. Zhao, C. X. Chen, K. Kaj, et al.., “Terahertz investigation of bound states in the continuum of metallic metasurfaces,” Optica, vol. 7, pp. 1548–1554, 2020, https://doi.org/10.1364/optica.404754.Suche in Google Scholar

[39] D. J. Liu, X. Yu, F. Wu, S. Y. Xiao, F. Itoigawa, and S. Ono, “Terahertz high-Q quasi-bound states in the continuum in laser-fabricated metallic double-slit arrays,” Opt. Express, vol. 29, pp. 24779–24791, 2021, https://doi.org/10.1364/oe.432108.Suche in Google Scholar PubMed

[40] C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater., vol. 1, p. 16048, 2016, https://doi.org/10.1038/natrevmats.2016.48.Suche in Google Scholar

[41] J. V. Neumann and E. P. Wigner, Über Merkwürdige Diskrete Eigenwerte, Berlin Heidelberg, Springer-Verlag, 1993.10.1007/978-3-662-02781-3_19Suche in Google Scholar

[42] Y. J. Zhong, L. H. Du, Q. Liu, et al.., “Ultrasensitive specific sensor based on all-dielectric metasurfaces in the terahertz range,” RSC Adv., vol. 10, pp. 33018–33025, 2020, https://doi.org/10.1039/d0ra06463g.Suche in Google Scholar PubMed PubMed Central

[43] S. G. Lee, S. H. Kim, and C. S. Kee, “Bound states in the continuum (BIC) accompanied by avoided crossings in leaky-mode photonic lattices,” Nanophotonics, vol. 9, pp. 4373–4380, 2020, https://doi.org/10.1515/nanoph-2020-0346.Suche in Google Scholar

[44] X. B. Kang, L. W. Wen, and Z. G. Wang, “Design of guided Bloch surface waves resonance bio-sensors with high sensitivity,” Opt. Commun., vol. 383, pp. 531–536, 2017, https://doi.org/10.1016/j.optcom.2016.10.004.Suche in Google Scholar

[45] S. T. Koev, A. Agrawal, H. J. Lezec, and V. A. Aksyuk, “An efficient large-area grating coupler for surface plasmon polaritons,” Plasmonics, vol. 7, pp. 269–277, 2012, https://doi.org/10.1007/s11468-011-9303-7.Suche in Google Scholar

[46] Q. Liu, Z. B. Ouyang, and S. Albin, “Coupled photonic crystal micro-cavities with ultra-low threshold power for stimulated Raman scattering,” Opt. Express, vol. 19, pp. 4795–4804, 2011, https://doi.org/10.1364/oe.19.004795.Suche in Google Scholar PubMed

[47] Q. S. Li and Z. L. Zhang, “Bonding and anti-bonding modes of plasmon coupling effects in TiO2–Ag core–shell dimers,” Sci. Rep., vol. 6, p. 19433, 2016, https://doi.org/10.1038/srep19433.Suche in Google Scholar PubMed PubMed Central

[48] M. C. Schaafsma, A. Bhattacharya, and J. G. Rivas, “Diffraction enhanced transparency and slow THz light in periodic arrays of detuned and displaced dipoles,” ACS Photonics, vol. 3, pp. 1596–1603, 2016, https://doi.org/10.1021/acsphotonics.6b00121.Suche in Google Scholar

[49] W. Suh, Z. Wang, and S. H. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quant. Electron., vol. 40, pp. 1511–1518, 2004, https://doi.org/10.1109/jqe.2004.834773.Suche in Google Scholar

[50] H. L. Zhao, Y. Ren, L. Fang, and H. Lin, “Electromagnetic induced transparency in graphene waveguide 304 structure for terahertz application,” Results Phys., vol. 16, p. 102971, 2020, https://doi.org/10.1016/j.rinp.2020.102971.Suche in Google Scholar

[51] X. L. Yu, W. Ma, and S. F. Zhang, “Hydrophobic polymer-incorporated hybrid 1D photonic crystals with brilliant structural colors via aqueous-based layer-by-layer dip-coating,” Dyes Pigments, vol. 186, p. 108961, 2021, https://doi.org/10.1016/j.dyepig.2020.108961.Suche in Google Scholar

[52] S. Jun, B. K. Ju, and J. W. Kim, “Fabrication of substrate-free double-side emitting flexible device based on silver nanowire-polymer composite electrode,” Curr. Appl. Phys., vol. 17, pp. 6–10, 2017, https://doi.org/10.1016/j.cap.2016.10.016.Suche in Google Scholar

[53] R. Min, B. Ortega, and C. Marques, “Latest achievements in polymer optical fiber gratings: fabrication and applications,” Photonics, vol. 6, p. 36, 2019, https://doi.org/10.3390/photonics6020036.Suche in Google Scholar

[54] W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys., vol. 98, p. 033102, 2005, https://doi.org/10.1063/1.1999031.Suche in Google Scholar

[55] J. J. Cao, Y. Sun, Y. Kong, and W. Y. Qian, “The sensitivity of gratings-based SPR sensors with wavelength interrogation,” Sensors, vol. 19, p. 405, 2019, https://doi.org/10.3390/s19020405.Suche in Google Scholar PubMed PubMed Central

[56] B. Zeng, A. Majumdar, and F. Wang, “Tunable dark modes in one-dimensional “diatomic” dielectric gratings,” Opt. Express, vol. 23, pp. 12478–12487, 2015, https://doi.org/10.1364/oe.23.012478.Suche in Google Scholar PubMed

[57] A. K. Goyal and J. Saini, “Performance analysis of Bloch surface wave-based sensor using transition metal dichalcogenides,” Appl. Nanosci., vol. 10, pp. 4307–4313, 2020, https://doi.org/10.1007/s13204-020-01538-0.Suche in Google Scholar

[58] C. W. Hsu, B. Zhen, J. Lee, et al.., “Observation of trapped light within the radiation continuum,” Nature, vol. 499, pp. 188–191, 2013, https://doi.org/10.1038/nature12289.Suche in Google Scholar PubMed


Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/nanoph-2021-0339).


Received: 2021-07-03
Accepted: 2021-09-16
Published Online: 2021-10-05

© 2021 Chi Zhang et al., published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

Heruntergeladen am 1.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/nanoph-2021-0339/html
Button zum nach oben scrollen