Period locking due to delayed feedback in a laser with saturable absorber

Area of Science:

• Nonlinear dynamics
• Laser physics
• Optical engineering

Background:

• Saturable absorbers induce pulsating behavior in lasers.
• Delayed feedback can destabilize laser output.
• Hopf bifurcations are key to understanding transitions to periodic behavior.

Purpose of the Study:

• Investigate the dynamics of a pulsating laser with delayed feedback.
• Analyze the period-locking phenomenon in such laser systems.
• Develop predictive models for laser pulsation states.

Main Methods:

• Mathematical modeling of a laser with a saturable absorber and delayed feedback.
• Derivation of a discrete map to describe periodic pulsations.
• Analysis of bifurcation phenomena and stability.

Main Results:

• Both saturable absorbers and delayed feedback lead to periodic laser output via Hopf bifurcations.
• Delayed feedback induces period-locking of laser pulses to integer fractions of the feedback time.
• Derived equations accurately predict locking states and pump values for state switching.

Conclusions:

• The interplay between saturable absorbers and delayed feedback creates complex but predictable laser dynamics.
• Period-locking is a significant phenomenon in delayed feedback laser systems.
• The developed model provides a tool for controlling and understanding laser pulsation regimes.