The discussion revolves around proving the relationship n1 < N < n2 for the effective index N in the context of a symmetric, 3-layer slab waveguide. Participants are exploring the implications of Snell's Law and total internal reflection (TIR) in relation to the effective index.
Some participants have provided insights into the relationships between the effective index and the refractive indices, while others are seeking clarification on definitions and setups. The conversation reflects a mix of interpretations and attempts to reconcile the relationships without reaching a consensus.
Participants note the need for clear definitions of terms such as effective index and the setup of the waveguide, indicating that some foundational knowledge may be assumed but not universally understood.
Yet your "to be shown" has it > n1. Reversing that doesn't help since from Snell's law it should also be less than n2.Alvis said:I know why N is strictly less than n1
Ok.Alvis said:Ah, my mistake. It should be show n2<N<n1.
Effective index is n1sin(theta). This is for the symmetric, 3-layer slab waveguide. The core thickness is d and its index is n1. The clad indices have the same value of n2.
My task is to prove the effective index N of any of the guided modes obeys the relationships n2<N<n1.
I know N<n1 because in(theta) goes from 0 to 1. If it is at 1, theta must be 90 degrees, meaning the light never hit the surface in front of the plane. Therefore, for TIR to actually happen, N must be strictly less than n1.
My apologies!