Soliton area theorems express the pulse energy as a function of the pulse shape and the system parameters. From an analytical solution to the cubic-quintic complex Ginzburg–Landau equation, we derive an area theorem for dissipative optical solitons. In contrast to area theorems for conservative optical solitons, the energy does not scale inversely with the pulse duration, and in addition there is an upper limit to the energy. Energy quantization explains the existence of, and conditions for, multiple-pulse solutions. The theoretical predictions are confirmed with numerical simulations and experiments in the context of dissipative soliton fiber lasers.
© 2010 Optical Society of America
Original Manuscript: May 19, 2010
Manuscript Accepted: July 6, 2010
Published: September 9, 2010
William H. Renninger, Andy Chong, and Frank W. Wise, "Area theorem and energy quantization for dissipative optical solitons," J. Opt. Soc. Am. B 27, 1978-1982 (2010)