Theoretical Investigation of State Bistability Between Pure- and Mixed-Mode States in a 1550-nm VCSEL Under Parallel Optical Injection

Abstract

Based on the spin-flip model, state bistability (SB) between pure- and mixed-mode states in a 1550-nm vertical-cavity surface-emitting laser under parallel optical injection is theoretically investigated. The simulated results show that two types of SB can be observed when the injection light frequency ( $v_{\textrm {inj}}$ ) is smaller than the dominant mode frequency of the free-running laser ( $v_{e}$ ). For type-I SB, which occurs through fixing $v_{\textrm {inj}}$ and scanning injection power ( $P_{\textrm {inj}}$ ) along different routes, there exist two hysteresis loops in which the laser operates at pure- or mixed-mode state, depending on the variation route of $P_{\textrm {inj}}$ , and the hysteresis loop width increases sharply for increasing $\vert \Delta \nu \vert $ ( $\Delta v = v_{\textrm {inj}}- v_{e}$ ) with relatively strong $P_{\textrm {inj}}$ whereas the loop width increases slowly for relatively weak $P_{\textrm {inj}}$ , in agreement with our recent experimental report. Furthermore, type-II SB is also investigated through fixing $P_{\textrm {inj}}$ and scanning $v_{\textrm {inj}}$ along different routes. There also exist two hysteresis loops in which the laser may operate at a pure- or mixed-mode state. With an increase of $P_{\textrm {inj}}$ , the hysteresis loop width located at lower $\vert \Delta \nu \vert $ increases sharply and then decreases after reaching a maximum. However, for the hysteresis loop located at higher $\vert \Delta \nu \vert $ , the loop width gradually increases with the increase of $P_{\textrm {inj}}$ .