The discussion focuses on proving the relationship n2 < N < n1 for the effective index N in a symmetric, 3-layer slab waveguide. The effective index is defined as N = n1sin(theta), where n1 is the refractive index of the core and n2 is the refractive index of the cladding. The participants clarify that for total internal reflection (TIR) to occur, N must be strictly less than n1, and they seek to establish the upper bound of N in relation to n2. The conclusion emphasizes that the effective index must satisfy the inequality n2 < N < n1 for guided modes.
PREREQUISITESOptical engineers, physicists, and students studying waveguide theory or working on optical communication systems will benefit from this discussion.
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!