Bragg gratings, based on periodic refractive index modulation, achieve filtering functionality through selective reflection. They are ideal components for high-density photonic integration, high-speed optical communication, and miniature sensing systems. They are particularly important in external-cavity semiconductor lasers, where they can significantly narrow the laser linewidth by increasing the effective cavity length and leveraging the optical injection locking effect. However, fiber Bragg gratings and volume Bragg gratings face challenges such as poor thermal stability, sensitivity to acoustic noise, and difficulty in integration. This makes planar waveguide Bragg gratings a more suitable choice for integration. Among these, cladding-modulated gratings, which have a low coupling coefficient and narrow reflection bandwidth, support long grating designs and demonstrate outstanding potential for realizing ultra-narrow linewidth lasers. In this paper, we use the finite-difference time-domain (FDTD) method to analyze the influence of parameters such as the grating duty cycle and cladding modulation depth on optical properties. This provides essential theoretical support for the design of narrow-linewidth external-cavity lasers.

The cladding-modulated Bragg grating operates in the C-band and employs a single-mode Si₃N₄ waveguide with a width of 1 μm and a thickness of 0.35 μm (Fig. 1). The grating structure consists of periodic Bragg grating pillars. Precise control over the coupling coefficient is achieved by adjusting parameters such as the spacing between the grating pillars and the waveguide, as well as the grating duty cycle. Based on coupled-mode theory, the relationship between the coupling coefficient and structural parameters is derived, and their effects on reflection bandwidth and reflectivity are analyzed. By optimizing these parameters, a long grating structure with a low coupling coefficient can be designed to achieve a narrow-bandwidth Bragg grating. This design can be used to construct external-cavity semiconductor lasers that produce laser outputs with kHz-level narrow linewidths.

In this paper, we systematically investigate how key parameters of cladding-modulated Bragg gratings, including the coupling coefficient, reflection bandwidth, and reflectivity, vary with structural changes. The goal is to provide theoretical guidance for designing waveguide Bragg gratings with low coupling coefficients, narrow bandwidths, and low reflectivity. First, we analyze the effect of the spacing between the grating pillars and the waveguide on the coupling coefficient. When the duty cycle is set to 0.5, increasing the spacing from 600 to 1000 nm reduces the effective refractive index, which leads to a significant decrease in the coupling coefficient from 4.82 to 0.35 cm^-1 (Fig. 3). This indicates that increasing the spacing effectively weakens evanescent field coupling, thus significantly reducing the grating’s coupling coefficient. Furthermore, under the same spacing conditions, increasing the duty cycle enhances the modulation amplitude of the cladding’s refractive index and increases the coupling coefficient. This demonstrates the important role of the duty cycle in controlling the coupling strength. Regarding reflection performance, simulation results show that when the grating length is 30 mm, reducing both the spacing and the duty cycle narrows the reflection bandwidth and lowers reflectivity (Fig. 4). Specifically, as the grating spacing increases from 800 to 1200 nm, the reflectivity decreases from 0.9984 to 0.0870, and the central wavelength blue-shifts from 1550.215 to 1550.162 nm (Fig. 5). Meanwhile, with the grating spacing fixed at 1000 nm, increasing the duty cycle from 0.3 to 0.7 raises the reflectivity from 0.19 to 0.75, and the central wavelength red-shifts from 1550.164 to 1550.188 nm (Fig. 6). Finally, we emphasize the effect of grating length on device performance. Experimental results show that when the grating length reaches 30 mm, the reflectivity can reach 0.63, and the reflection bandwidth is compressed to 42 pm (Fig. 7). These findings demonstrate the feasibility of improving reflection efficiency and achieving narrower bandwidths by extending the grating length.

To meet the requirements for mode selection and linewidth narrowing in hybrid integrated narrow-linewidth lasers, we design a waveguide Bragg grating with cladding refractive index modulation. The grating features a low coupling coefficient and a narrow reflection bandwidth. The periodic refractive index modulation is formed by periodic grating pillars distributed in the cladding. Using the FDTD method, we simulate the influence of grating structure parameters on the Bragg resonance characteristics. The results show that increasing the grating spacing or reducing the duty cycle significantly reduces the coupling coefficient. By optimizing the coupling coefficient, a narrow reflection bandwidth with low reflectivity can be achieved using a grating several centimeters in length. The simulation results reveal an inherent relationship between the coupling coefficient, reflection bandwidth, and reflectivity. Our research provides theoretical guidance for designing cladding-modulated Bragg gratings with low coupling coefficients and demonstrates significant value in the study of narrow linewidth hybrid integrated lasers.