(a) The reflection process from a quarter-wave film with low losses (k₂ ≪ n₂) on a perfectly reflecting substrate at normal incidence, showing the partial waves. Many multiple reflections are involved because of the small losses. (b) Phasor addition diagram (the reflected partial waves are represented in the complex plane) demonstrating that a properly engineered quarter wave film on a reflecting substrate can result in zero reflection via destructive interference, corresponding to complete absorption. This occurs for a particular value of k₂, which is relatively small, leading to a small imaginary part of r₀, and corresponding to critical coupling. The phase of the first partial wave r₀ is ≃ π with respect to the incident wave, but the phase of all of the other partial waves is ≃ 0. (c) Reflection process from a highly absorbing (k₂ ∼ n₂), ultra-thin film in a reflecting substrate. (d) Phasor diagram demonstrating that a zero-reflection (and hence perfect absorption) condition is achievable if the complex refractive index of the film has a large imaginary component. In this case, the phase of r₀ deviates significantly from π (the phasor is not along the horizontal axis) and a small number of reflections is sufficient to cancel r₀ and maximize absorption.