Optical fiber directional coupler can realize beam coupling and splitting, which is one of the most important passive devices in the optical fiber communication system after the optical connector. In recent years, with the wide application of various high-capacity wavelength division multiplexing (WDM) communication networks, the bandwidth characteristics of optical fiber directional couplers are facing great challenges. As a practical product, the fabrication technology of optical fiber couplers based on the melt-drawing cone process is very mature and has the advantages of good directionality, high-temperature stability, and low cost. However, due to the strong dependence of the beam-splitting ratio on the operating wavelength, most of the current optical fiber directional couplers operate at specific wavelengths and have narrow bandwidths. The advent of photonic crystal fibers (PCFs) makes it possible to design fiber couplers with higher performance. Compared with traditional fiber couplers, PCF-based couplers have the advantages of low wavelength dependence, short coupling length, and low insertion loss, and they have become a hot spot in related research fields. Among them, the dual-core PCF-based directional coupler has been reported in many experimental and theoretical studies. However, most researchers usually give the structure and parameters of the designed coupler directly and do not make a more detailed summary and generalization of the specific rules of parameter design. If the specific rules of PCF parameter design are summarized in detail, it can provide a meaningful reference for the efficient design of broadband optical fiber directional couplers.

In a dual-core fiber, each core region can be considered as an independent optical waveguide, and the optical field energy conducted within each core is affected by the other core and changes periodically with the length of the coupling region. According to the coupling theory, it can be seen that for two parallel lossless optical waveguides, the internal optical field energy can be expressed by Eqs. (1) and (2), respectively. Eq. (3) indicates that when the two waveguides and their nearby spatial structure and material are consistent, the effective coupling coefficient is equal to the coupling coefficient. When the two waveguides and their nearby spatial structure or material are inconsistent, the effective coupling coefficient will be greater than the coupling coefficient, in which case there will be no specific interaction length so that the incident light field energy can be completely into the coupling arm. At this point, by changing the fiber structure parameters, the effective coupling coefficient can be adjusted without changing the interaction length, and then the desired coupling ratio can be obtained near the center of the target wavelength range with a shorter interaction length. In this paper, the coupling characteristics of the coupler structure under different fiber structure parameters are simulated by using the beam transmission method to obtain the variation of the optical field energy in the structure with the transmission distance. For the determined fiber structure, the variation curves of the optical field energy in the straight through arm and the coupling arm satisfy Eqs. (1) and (2), respectively. Specifically, I₁ and I₂ are functions of the variable L and the unknown constants κ and δ, which exactly satisfy the applicable conditions for estimating the constants using the least squares method. Since the beam transmission method can provide a sufficiently large number of simulation data points, Eq. (5) is overdetermined, and the equations can be solved by curve fitting using the trust-domain reflection algorithm. After κ and δ are obtained using the least squares method, the difference in transmission constants between the cores of the dual-core PCF fibers at this point can also be obtained from Eq. (3).

The influence of structural parameters on the inter-core coupling efficiency in dual-core PCF fibers is discussed in detail. According to the analysis results of Fig. 6, it can be seen that changing the hole spacing and air hole symmetry can realize the coarse adjustment of the coupling region length; changing the air hole symmetry can realize the coarse adjustment of the maximum coupling ratio; changing the core refractive index difference, the central air hole diameter ratio, and the core diameter ratio can realize the fine adjustment of the coupling region length and the maximum coupling ratio. To verify the above theory, we design a broadband 50∶50 coupler containing 1310 nm and 1550 nm with ±5% coupling ratio. We find that the designed structure has the largest bandwidth value of 240 nm while satisfying the design requirements when L=3000 μm, d₂=1.8 μm, and d₀=0.51 μm. It can be seen from Fig. 8(a) that the coupling ratios of the two arms for wavelengths from 1310 nm to 1550 nm can all fall between 45% and 55%. The additional loss of the structure and the insertion loss of the straight through arm and the coupling arm with wavelength are shown in Fig. 8(b). The insertion loss of the designed structure is not higher than 0.2 dB, and the insertion loss of both arms is around 3 dB.

In this paper, the influence of various parameters on the coupling efficiency between cores of a dual-core PCF is analyzed by using the beam transmission method, and the coupling coefficient and other parameters between waveguides are estimated by using the least squares method according to the principle of dual-core coupling. It makes clear that in a dual-core PCF, each structural parameter regulates the coupling ratio and the length of the coupling region. By summarizing the specific rules of parameter design in detail, the coarse and fine-tuning design methods for the coupling performance of dual-core PCFs are proposed. Then, an asymmetric dual-core PCF broadband directional coupler is designed according to the proposed design method, and the coupling ratio and coupling zone length of the designed coupling structure are coarse-tuned and fine-tuned by adjusting the symmetry of the air holes and the diameter of the central air holes, respectively, enabling the coupler to achieve a coupling ratio of 50%±5% in the interval of 1. 31-1.55 μm, a bandwidth of 240 nm, and an ultra-short coupling length of 3 mm. The research results can provide a meaningful reference for the efficient design of broadband optical fiber directional couplers.