Light propagation in composite materials with gain layers

Light propagation through a single gain layer and a multilayer system with gain layers is studied. Results from the Fresnel formulas, Airys series summation and the numerical solution of the nonlinear MaxwellBloch equations by the finite difference time domain (FDTD) method are analyzed and compared. Normal and oblique propagation of a wave through a gain layer and a slab of a photonic crystal are examined. For the latter problem, the gain line may be situated in either the pass or stop band of the photonic crystal. It is shown that the monochromatic plane wave approximation is generally inapplicable for active media because it leads to results that violate causality. However, the problem becomes physically meaningful and correct results can be obtained for all three approaches once the structure of the wavefront and the finite aperture of the beam are taken into account.