We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.
© 2013 Optical Society of America
Original Manuscript: May 21, 2013
Revised Manuscript: July 6, 2013
Manuscript Accepted: August 12, 2013
Published: September 5, 2013
Gandhi Alagappan, Sajeev John, and Er Ping Li, "Macroscopic response in active nonlinear photonic crystals," Opt. Lett. 38, 3514-3517 (2013)