Optical Theorem Helps Understand Thresholds of Lasing in Microcavities With Active Regions

Abstract

Within the framework of the recently proposed approach to view the lasing in open microcavities as a linear eigenproblem for the Maxwell equations with exact boundary and radiation conditions, we study the correspondence between the modal thresholds and field overlap coefficients. Macroscopic gain is introduced into the cavity material within the active region via the “active” imaginary part of the refractive index. Each eigenvalue is constituted of two positive numbers, namely, the lasing wavenumber and the threshold value of material gain. This approach yields clear insight into the lasing thresholds of individual modes. The Optical Theorem, if applied to the lasing-mode field, puts the familiar “” condition on firm footing. It rigorously quantifies the role of the spatial overlap of the mode E-field with the active region, whose shape and location are efficient tools of the threshold manipulation. Here, the effective mode volume in open resonator is introduced from first principles. Examples are given for the 1-D cavities equipped with active layers and distributed Bragg reflectors and 2-D cavities with active disks and annular Bragg reflectors.