Dive into the foundational equations behind waveguide light behavior. Starting with Maxwell's equations, we simplify them to arrive at the Helmholtz equation, which is crucial for understanding light propagation in waveguides. We'll explore the key parameters derived from the Helmholtz equation and how they shape the light patterns or modes inside the waveguide. This video provides both a theoretical and practical understanding, bridging fundamental physics with real-world photonics applications.