Abstract
A semi-analytic tool is developed for investigating pulse dynamics in mode-locked lasers. It provides a set of rate equations for pulse energy, width, and chirp, whose solutions predict how these pulse parameters evolve from one round trip to the next and how they approach their final steady-state values. An actively mode-locked laser is investigated using this technique and the results are in excellent agreement with numerical simulations and previous analytical studies.
Highlights
Mode-locked lasers are routinely used for a wide variety of applications since they can provide optical pulses ranging in widths from a few femtoseconds to hundreds of picoseconds
One is able to retain a high degree of accuracy in the pulse parameters if a judicious choice is made for the pulse shape
In an effort to study the pulse evolution process under the influence of Eq (1), without resorting to full numerical simulations, we have employed the moment method [2,3,4]. This approach allows us to develop ordinary differential equations that govern the evolution of the pulse parameters
Summary
Mode-locked lasers are routinely used for a wide variety of applications since they can provide optical pulses ranging in widths from a few femtoseconds to hundreds of picoseconds. We develop a new tool for investigating mode-locked lasers by essentially treating the mode-locked pulses as particles with a fixed analytic shape This approach allows us to simplify the governing nonlinear partial differential equation, often called the master equation. The resulting equations are similar to the rate equations commonly used to describe continuously operating lasers They can be solved quickly using standard techniques and have the added benefit that under steady-state conditions they reduce to algebraic equations describing pulse energy, width, and chirp. Pulse shape is invariably close to Gaussian or hyperbolic secant, depending on the type of mode-locking employed, the cavity dispersion (normal vs anomalous), and the strength of nonlinearities This observation is at the root of our approach since the moment method requires a knowledge of the pulse shape. One is able to retain a high degree of accuracy in the pulse parameters if a judicious choice is made for the pulse shape
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