In the optical fiber transmission system, an optical amplifier emerges to compensate for the device loss and attenuation caused by long-distance optical fiber transmission. Traditional erbium-doped fiber amplifiers (EDFAs) often require tens of meters of fiber, and the larger footprint is increasingly unable to meet the trend of integrated and miniaturized communication systems. Thus, erbium-doped optical waveguide amplifiers (EDWAs) with smaller volume and lower energy consumption have been proposed by researchers. However, EDWA also faces many challenges. For a mature chip foundry, the waveguide design is particularly critical, and second, when the chip is employed in a communication system, the coupling problem between the fiber and the chip should be solved. Thus, we propose an accurate design model for the waveguide width of EDWA based on a 400 nm silicon nitride platform. This model takes into account the fiber-chip coupling problem and obtains the waveguide parameters with the best gain effect based on the interaction between signal light and pump light. We hope our research can help design a high-gain EDWA and provide ideas for implementing EDWA on different platforms.

The waveguide cutoff condition and single mode condition of signal light are obtained by the semi-vector finite difference method, with the range of waveguide width determined. Considering the coupling between the optical fiber and the waveguide, and different excitation effects of the pump light by the edge coupler in different modes, the double-layer edge coupler of 980 nm pump light is simulated. By analyzing the power distribution coefficients corresponding to different waveguide widths, the model of the pump optical mode field is built accurately. Finally, considering the interaction between 1550 nm signal light and 980 nm pump light, the rate-transfer equation of EDWA is optimized. The effects of different waveguide widths, lengths, and distances between waveguides on EDWA gain are systematically analyzed. With the interaction between signal light and pump light considered, the waveguide width, length, and distance between waveguides with the best gain effect are selected and compared with the simulation without the interaction between signal light and pump light.

A model optimization of on-chip EDWA is proposed. First, based on the recent excellent results of ultra-low insertion loss of silicon nitride waveguide, silicon nitride becomes the preferred material for waveguide. Second, previous studies on EDWA tend to treat EDWA as a single entity on the chip, and then obtain information about the effect of various EDWA design parameters on the gain effect. By taking EDWA as a part of the optical signal transmitting and receiving system and considering the connection between EDWA and optical fiber, we design and simulate an edge coupler suitable for 980 nm pump light (Fig. 2), whose coupling efficiency is greater than 80%. The excitation of the pump optical mode field after the light from the fiber enters the waveguide is precisely solved (Table 1). Then, we modify the overlap factor term of the transmission equation, add the influence of the interaction between the pump light and signal light to the rate-transmission equation, and compare with the situation without considering the interaction between the pump light and signal light (Fig. 5). It is found that considering the overlapping effect of signal light and pump light will decrease gain and the optimal waveguide width is selected to be 0.8 μm. Finally, in the actual design of an optical waveguide amplifier, we often design it into a spiral shape to minimize the optical waveguide amplifier’s chip area. However, the spiral optical waveguide amplifier requires us to obtain two parameters, including the length of the waveguide and the distance between waveguides. The influence of these two parameters on the gain effect of the optical waveguide amplifier is analyzed in Fig. 6, which indicates that there is an optimal waveguide length of 20 cm. If the length is greater or less than this value, the gain effect will decrease. Additionally, the distance between waveguides should be greater than 4 μm, and then the waveguides will not interact with each other.

We propose an accurate model of EDWA on the chip, which not only can be employed based on the silicon nitride platform but also is compatible with other platforms. Meanwhile, we take the 400 nm silicon nitride platform as an example, design a 980 nm edge coupler with coupling efficiency greater than 80%, and accurately model the pump optical mode field. Additionally, we correct the overlap factor term in the rate-transfer equation and compare the gain simulation results before. After correction, it is found that this correction will decrease the gain effect. The effects of waveguide width, length, and distance between waveguides on gain are analyzed, and selected waveguide width of 0.8 μm, waveguide length of 20 cm, and distance between waveguides of 4 μm are the optimal parameter. As a result, the calculation model lays a foundation for the design of an EDWA waveguide with a high gain coefficient in the future and provides a new idea for further improving the EDWA gain effect.