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

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 (<inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula>) is smaller than the dominant mode frequency of the free-running laser (<inline-formula> <tex-math notation="LaTeX">$v_{e}$ </tex-math></inline-formula>). For type-I SB, which occurs through fixing <inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula> and scanning injection power (<inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>) 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 <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>, and the hysteresis loop width increases sharply for increasing <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$\Delta v = v_{\textrm {inj}}- v_{e}$ </tex-math></inline-formula>) with relatively strong <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> whereas the loop width increases slowly for relatively weak <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>, in agreement with our recent experimental report. Furthermore, type-II SB is also investigated through fixing <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> and scanning <inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>, the hysteresis loop width located at lower <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula> increases sharply and then decreases after reaching a maximum. However, for the hysteresis loop located at higher <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula>, the loop width gradually increases with the increase of <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>.