Residence time distribution of noise induced hopping in bistable system with delay

This study reports on further experimental and theoretical investigation of a new polarization mode hopping regime. Results show the time traces of polarization resolved output power of a proton-implanted 850 nm VCSEL placed in an external cavity (EC) of about 20 cm (EC roundtrip time t_ext of 1.3 ns). The laser system jumps randomly between two states with linear and orthogonal polarization. However, besides this low frequency polarization mode hopping such system also shows fast oscillations at the EC frequency. The experimentally measured residence-time distribution (RTD) is also shown. In contrast to the case of polarization mode hopping in a solitary VCSEL the residence-time distribution (RTD) shows a discontinuity. The slow mode hopping is responsible for the exponential decay at large time values while the fast oscillations at the EC frequency are responsible for RTD at shorter time-scale. As these fast oscillations always appear during polarization switching (or an attempt to switch) the probability for measuring residence times up to the EC roundtrip time is quite large. Furthermore, due to the stochastic nature of our system, there exists an increased probability to detect the fast oscillations with one, two and more cycles missed, which results in a oscillatory behavior for the RTD.