Abstract

The existence of a nonlinear resonance (NLR) in optical parametric oscillators was appreciated since the first derivations of order parameter equations for both the degenerate (DOPO) and nondegenerate (OPO) optical parametric oscillators [1]. These equations read: Eqs. (1) and (2) are have been derived for close to threshold operation and small signal detuning Δ₁. A is the signal field [which is real for DOPOs, Eq.(1), and complex for OPOs, Eq.(2)], r is the pump over threshold parameter (for Δ₁< 0 patterns exist for r ≥ 0), and Δ₀ is the pump detuning. When Δ₀ = 0 (resonant pump) the order parameter equations (1) and (2) become the real and complex Swift-Hohenberg equations, respectively. A detuned pump induces a NLR (governed by the terms Δ₀A² or Δ₀|A|²) and, in the OPO case, an additional nonlinear nonlocal phase modulation [last term in Eq.(2)]. We have investigated the role of these new terms on the stability and competition of the basic patterns of optical parametric oscillators: standing (SWs) and traveling (TWs) waves. When almost resonant patterns are studied, a single control parameter μ = rΔ₀²/2 can be defined.

© 1998 IEEE