Coherence length for second-harmonic generation in nonlinear, one-dimensional, finite, multilayered structures

Abstract

We find an analytic expression for second-harmonic conversion efficiency (both forward and backward) in generic, 1D, finite, multilayered structures, where the respective roles of effective phase-matching conditions and field overlap are clearly identified. Our approach places the notions of effective index and effective phase-matching conditions on a more solid theoretical ground and clarifies the meaning and the limits of applicability of these concepts. We also define a coherence length for the process in an unambiguous way and point out similarities and differences with the coherence length that is usually defined for bulk materials. Finally, we address the role played by absorption and provide numerical examples that confirm the analytical results found.