Phase-shifted gratings are often used in the fields of biosensing, narrow-band filtering, laser, ultra-high-speed optical signal processing, and optical computing and has received widespread attention. Compared with the traditional ring resonator, the phase-shifted grating has a larger working wavelength range and can meet the requirement of narrow-band filtering of a large-bandwidth input signal. In addition, the slightly larger size also brings a larger sample contact area, which can effectively improve the sensing sensitivity. The Q value is often an important indicator for device performance evaluation. For example, in narrow-band filtering, the larger the Q value, the better the wavelength selection performance of the filter, and the purer the filtered signal frequency. In the on-chip biomedical sensors, the larger the Q value, the lower the detection limit of the sensors. Therefore, the study of high-Q phase-shifted gratings has great practical application value. Although the existing π phase-shifted grating schemes have the advantages of a simple process, a high Q value, a narrow bandwidth, and flexible adjustment, they are all reflective schemes. The reflected signals of the gratings will be output through the original input port, and an optical ring needs to be added in practical applications. A magneto-optical device such as a detector separates the reflected signal from the input signal. Adding magneto-optical devices will increase the complexity of the system, and it is difficult to integrate magneto-optic materials with silicon-based devices on a large scale, so the application scenarios of π phase-shifted gratings will also be limited. Therefore, it is of great practical significance to study the contra-directional coupling type of π phase-shifted gratings.

To reduce the use of magneto-optical devices such as optical circulators and improve integration, the Moire grating structure is adopted to achieve a high Q value and an ultra-narrow bandwidth performance. According to the refractive index distribution function of a single grating, the refractive index distribution function of the system consisting of two gratings with slightly different periods is deduced, and the refractive index distribution is a rapidly changing structure with a slowly changing envelope. From the distribution of the refractive index, it can be concluded that the π phase shift can be realized at a special position. Therefore, the numerical analysis of the structure is carried out. Since the coupling coefficient of the structure is a function of the change in the position, its spectral characteristics are calculated according to the transmission matrix method. By optimizing different parameters, it is found that the Q value and the bandwidth of the structure have obvious advantages. Therefore, the Moire grating structure is adopted to solve the problem of low Q value in the phase shift gratings.

It is assumed that the grating period Λ₁ is 312 nm, the number of gratings P₁ is 521, the grating period Λ₂ is 312.6 nm and the number of gratings P₂ is 520. Through calculation, the 3 dB bandwidth of the contra-directional coupled phase shift grating is 0.1 nm, the extinction ratio (ER) is 19.08 dB, and the Q value is 15771, but the sidelobe suppression ratio is only 0.4 dB (Fig. 4). To further improve the sidelobe suppression ratio, the grating is optimized for apodization (Fig. 5). At this time, the sidelobe suppression of the spectral line at long wavelengths is more obvious (Fig. 6), which is caused by the uneven refractive index change (Fig. 5). At this time, the phase shift wavelength is 1547.18 nm, the Q value is 12893, the 3 dB notch bandwidth is 0.12 nm, the ER is 18.81 dB, and the sidelobe suppression ratio is 10.4 dB (Fig. 8), which are close to the performance parameters calculated by theory. After apodization optimization, the resonance wavelength is blue-shifted from the original 1577.10 nm to 1547.18 nm. To reduce the influence of apodization on wavelength shift, the part of the grating without any apodization is designed as a semi-concave and semi-convex structure (Fig. 9). At this time, the resonance wavelength is 1546.04 nm, and the resonance wavelength shifts only 1.14 nm (Fig. 10). It is proved that the designed structure can effectively reduce the influence of apodization on the wavelength shift.

A contra-directional coupling phase-shift grating with a high-Q value and an ultra-narrow bandwidth based on the Moire effect is presented. Firstly, the distribution function of the refractive index of the designed structure is analyzed. From the distribution function, it can be concluded that the refractive index has π phase shift characteristic at a special position. The transmission matrix method is used to prove that the combination of two gratings with slightly different periods can produce a π phase shift. Then, the proposed structure is optimized, and the contra-directional coupling phase-shift spectral line witha Q value of 12893, 3 dB notch bandwidth of 0.12 nm, ER of 18.81 dB, and sidelobe suppression ratio of 10.4 dB can be obtained. The part of the grating without any apodization is designed as a semi-concave and semi-convex structure, which can effectively reduce the influence of apodization on the wavelength shift. The contra-directional coupling phase-shift grating has the advantages of small size, light weight, high Q value, ultra-narrow notch bandwidth, and high sidelobe suppression ratio, and can be widely used in the fields of biosensing, lasers, and wavelength filtering.