# Exceptional Points in Non-Hermitian Photonic Crystals Incorporated With a Defect
## 4 Applications and Giant GH Shift
The maximum positive and negative GH shifts were \(10^{5}\lambda\) and \(-10^{4}\lambda\), respectively, indicating that the GH shift of the reflected light from the right was smaller than that of the reflected light from the left. Therefore, the GH shift of the reflected beam was dependent on the direction incident from the left and right. The lateral shift also existed in the transmitted light. Figure 6d shows the GH shift of the transmitted light beam near CPA-LP. The region was divided into two parts by the dotted line. The GH shift in part I was positive, while the GH shift in part II was negative. The positive and negative GH shifts were \(2\times 10^{4}\lambda\) and \(-6.5\times 10^{4}\lambda\), respectively. CPA-LP was the singular point for the GH shift and the GH shift was infinite at CPA-LP. The GH shift along the dotted line was 0. Even though the CPA laser state was not stable enough, the incident light and transmitted light were located at the two sides of the PCs, respectively. Therefore, the spatial discrimination of sensors based on the GH shift of the transmitted beam was better than that of sensors based on the GH shift of the reflected beam. Based on the GH shift, the PCs can be utilized for highly sensitive sensors in probing the gain or loss factor of materials. Here, we take the normalized frequency \((\omega-\omega_{0})/\omega_{\text{gap}}=0.065\), for example, to demonstrate the application. To make the phenomenon more obvious, the given normalized frequency was near \(\omega_{\text{LP}}\) and \(\omega_{\text{EP}}\). Figure 7a shows the lateral GH shift. One can see that the GH shift changed with the gain-loss coefficient of the defect and there were positive and negative GH shifts around the EPs and LP. The positive and negative maxima could reach as high as the magnitude of \(10^{3}\lambda\). Figure 7b gives the sensitivity coefficient of sensors based on the GH shift in defecting gain or loss coefficient of materials. The maximum sensitivity coefficient (SC) was \(6.65\times 10^{4}\), since the frequency of incident wave was fixed. The SC can be further improved if the chosen frequency is closer to \(\omega_{\text{LP}}\) and \(\omega_{\text{EP}}\). Different from our one-dimensional PC of the multilayer type, PC fibers can also utilized for highly sensitive sensors for temperature sensing application via a Sagnac interferometer [53] or for detection of high refractive index liquid analytes via surface plasmon resonance [54]. The incident angle was selected as \(20^{\circ}\) and the purpose was to take a specific incident angle as an example to demonstrate that EPs and CPA-LP can be induced in the parameter space when a TM wave is obliquely incident into the non-Hermitian PCs. EPs and the CPA-LP can also be derived as the incident angle is chosen as some other values. The positions of EPs and the CPA-LP changed with the incident angle in the parameter space. If the incident wave was transverse electromagnetic (TE) wave instead, EPs and CPA-LP could also obtained, while the lateral shift of the reflected beam was defined as the Imb  
Figure 7: (**a**) Lateral GH shift varying with the gain-loss coefficient. (**b**) Sensitivity coefficient (SC) of sensors used for detecting the gain-loss coefficient of material based on the GH shift. The normalized frequency is \((\omega-\omega_{0})/\omega_{\text{gap}}=0.065\) for (**a**,**b**).