Transfer Matrix Method
Andrew M. Sarangan · 2020
The transfer matrix method (TMM) can be derived by writing the field expressions and considering their continuity across each boundary. Alternatively, it can also be derived by considering the Fresnel reflections at each boundary, followed by a propagation through each layer. Although both approaches produce identical results, the former approach is taken because it uses the wave equation more systematically rather than via a phenomenological treatment of the interfaces. The reflection and transmission coefficients at normal incidence can be derived by ensuring the continuity of the electric field amplitudes and their derivatives at all interfaces. Complex indices are assumed to have a negative imaginary part for absorption and a positive imaginary part for amplification (though the latter case only occurs in the case of optical amplification). The spatial field distribution inside the film stack can be calculated using the same TMM. This is useful for understanding the optical confinement and resonances taking place in the film stack.