## 2 NBDSs
The peak frequency of the Bragg defect state is 0.462 THz, and that of NBDS is 0.695 THz. As comparedwith the Bragg defect state, the width of the transmission peak for the NBDS is much narrower. This indicates that the characteristics of the NBDS are completely different from those of the Bragg defect state (it is well-known that a non-Bragg gap is created by the involvement of high-order modes). As demonstrated in Figure 1b,c, the magnetic field distributions (\(H_{\varphi}\)) of the Bragg gap state and NBDS show that each defect state is caused by a local resonance, with its origin in the energy concentrations of the THz waves in the inserted tube. This type of local resonance will, hence, induce a longitudinal accumulation of each defect state. However, the radial distribution is different, which is caused by the involvement of high-order transverse modes in the NBDS. Due to the rotation symmetry with respect to the \(z\)-axis, Figure 1b,c denotes any shaft sections. The magnetic field distributions of the defect states were also investigated (as can be seen in Figure 2b). The underlying reason was to study the effect of different transverse modes on the NBDSs. The longitudinal location of a specific radius, \(r\), was selected at the maximum (absolute) value of the amplitude in the waveguide. There is one radius of this kind in the Bragg defect state, but two in the NBDS. To quantitatively identify the mode components of the defect states, a least-square fit to the radial distributions was utilized:  
\[H_{\varphi}(r)=\sum_{m=1}^{4}a_{m}\mathrm{J}_{1}\Big{(}k_{r}^{(m)}r\Big{)} \tag{2}\]  
where \(r\) represents the radius (normalized by its own maximum), \(a_{m}\) denotes the coefficients of the different transverse modes, and \(\mathrm{J}_{1}(\cdot)\) is the first-order Bessel function. The best fitting curves for the Bragg and non-Bragg defect states are shown in blue vs. red in Figure 2b. The optimal coefficients for the Bragg defect state are \(a_{1}=1.1810\), \(a_{2}=0.0232\), \(a_{3}=-0.0012\), and \(a_{4}=0.0001\), while these are \(a_{1}=0.1369\), \(a_{2}=1.0960\), \(a_{3}=-0.0145\), and \(a_{4}=0.0148\) for the NBDS. Thus, it is obvious that the first mode plays a major role for the Bragg defect state, while the other modes are all sufficiently small. It is the other way around for the NBDS, for which the second mode dominates (as compared with the others). In fact, this second mode is essential for the major characteristics of the NBDS. Figure 1: (**a**) Configurations of the proposed waveguide. The middle straight pipe contains the defect structure, where \(L\) and \(R\) are the length and the radius of the defect, respectively. (**b**) The magnetic field distribution at the peak frequency (0.462 THz) of the Bragg defect state. (**c**) The magnetic field distribution (\(H_{\varphi}\)) at the peak frequency (0.695 THz) of the non-Bragg defect state (NBDS). In short, by introducing a straight tube into a periodically corrugated waveguide, longitudinal accumulation with local resonances was the result. This is quite different from the Bragg defect state and is a very promising way to achieve a sensor with much higher sensitivity. The use of NBDS is thus very promising and can be applied in various types of THz sensing systems, such as ambient temperature monitoring.