Dirac-like cones in photonic crystals typically arise from accidental degeneracies, yet the connection between their emergence and the scattering properties of the constituent particles remains unclear. Here, we establish a Mie scattering—band structure correspondence, demonstrating that such Dirac-like cones are fundamentally related to the Mie scattering properties of an individual particle. Specifically, when the Mie coefficients of an isolated particle satisfy either dipolar duality ($a_1=b_1$) or quadrupolar duality ($a_2=b_2$) at a certain frequency, a photonic crystal composed of such particles with a suitable lattice constant exhibits balanced global electric and magnetic responses. This balance induces the formation of a Dirac-like cone from dipolar or quadrupolar modes at that frequency. This scattering-band correspondence enables a two-step design strategy: first engineering the Mie coefficients of a single particle and then tuning the lattice constant, thereby avoiding computationally costly global optimization. Using this approach, we demonstrate configurable semi-Dirac cones that support unique wave-transport phenomena. Our work directly bridges single-particle scattering behavior and photonic mode degeneracy, providing a powerful route for photonic band engineering.

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• Mie scattering
• Photonic crystals
• Nanoparticles
• Band structure methods