Theory of the linewidth-power product of photonic-crystal surface-emitting lasers

A general theory for the intrinsic (Lorentzian) linewidth of photonic--crystal surface--emitting lasers (PCSELs) is presented. The effect of spontaneous emission is modeled by a classical Langevin force entering the equation for the slowly varying waves. The solution of the coupled--wave equations, describing the propagation of four basic waves within the plane of the photonic crystal, is expanded in terms of the solutions of the associated spectral problem, i.e. the laser modes. Expressions are given for photon number, rate of spontaneous emission into the laser mode, Petermann factor and effective Henry factor entering the general formula for the linewidth. The theoretical framework is applied to the calculation of the linewidth--power product of air--hole and all--semiconductor PCSELs. For output powers in the Watt range, intrinsic linewidths in the kHz range are obtained in agreement with recent experimental results.