Analytical theory of phase-locked arrays of antiguided diode lasers

A general theory of periodic diode laser arrays is developed in the approximation of an effective complex refractive index described by a step periodic function. Rigorous expressions are derived for the elements of a translation matrix. Explicit expressions are obtained for the near-field and far-field patterns of finite array modes. The concept of 2-dimensional Gamma-factor and the explicit expression for it are presented. Accurate analytical expressions for key parameters characterizing the resonant and adjacent array modes are obtained for the resonant structure. By using an expansion, the radiation loss versus index-step curve is well approximated near resonance by a parabola, which gives curve half-width at half intensity only 10 to 15% less than numerically calculated values. The analogy between the resonant arrays of antiguides and DFB lasers is discussed, and differential equations for the slowly varying envelope are derived.