Photonic crystals (PCFs) are artificial microstructures characterised by a periodic refractive index distribution. The concept of photonic crystals was first proposed by Eli Yablonovitch in 1987

and subsequently introduced to the field of fibre optics by Philip Russell in 1992. The formation of a photonic bandgap is achieved by the introduction of structural defects within the core

thereby exerting control the propagation of light. In contrast to conventional optical fibres

PCFs employ photonic band gaps or total internal reflection to guide light

thereby ensuring low loss

high confinement and exceptional propagation performance. PCFs have a plethora of applications in the domain of optical communications and integrated photonic devices.However

extant photonic crystal structure designs principally rely on numerical calculation methods

including finite difference methods and transmission matrix methods

which incur high computational costs and protracted design cycles. This complicates the optimization process for complex structures. The proposed methodology integrates physical constraints with a neural network framework to facilitate rapid prediction and design evaluation. Initially

a data set is constructed through the utilization of numerical simulations

thereby facilitating the establishment of a correlation between structural parameters and bandgap properties. Subsequently

a feed-forward neural network is trained using these data to fit the nonlinear mapping between geometric parameters and intrinsic frequency response. Of particular significance is the incorporation of physical constraints into the design criteria

a process informed by the fundamental physical principle that "the working frequency of the waveguide must be within the photonic bandgap." This principle is integrated into the model

thereby ensuring the integrity and efficacy of the method. This approach enables a direct mapping between structural parameters and device usability.The findings of the study demonstrate that the proposed method exhibits a high degree of accuracy in prediction (R² > 0.97)

thereby significantly reducing the computational expense when compared to conventional simulation methods. Additionally

the model effectively captures the non-linear relationship between structural parameters and electrical characteristics

facilitating efficient design of waveguides. This approach enhances the interpretive capabilities and practical applications of the model

providing a streamlined solution for the rapid design of complex photonic crystal components.