TM-Mode in Inhomogeneous Slab Wave-guide as an Exactly Solvable Oscillator-like Hamiltonian

In all practical wave-guides, the index of refraction made by diffusion process (e.g. ion exchange) is inhomogeneous. For determining the optical characteristics, the numerical approach is suitable in general case. In this paperwe will obtain a mathematical analogy between quantum mechanical Harmonic oscillator-like Hamiltonian and Helmholtz equation for TM-Mode electromagnetic field propagated in the slab wave-guide. Using this approach, the oscillator-like index of refraction profiles for exact solution of Helmholtz equation are proposed.

Keywords:

Oscillator like index of Refraction , Inhomogeneous Media , Helmholtz Optics , Slab Wave-guides