In this paper we numerically demonstrate that an optical memory can be based on a two-mode laser diode with
optical feedback and injection in the short external cavity regime. For modelling this system we use a two-mode
extension of the Lang-Kobayashi rate equations with gain saturation and optical injection. The parameters
chosen are consistent with the simultaneous oscillation of the two modes in the free running laser, which is
possible for frequency spacings greater than approximately 500 GHz at optical frequencies around 200 THz. For
certain values of the system parameters, we have found a hysteresis loop between single-mode equilibrium states
for increasing and decreasing feedback strength. Our simulations show that injected optical pulses can switch the
system between single mode equilibrium states when the feedback parameters are fixed in this bistable region,
demonstrating the function of the optical memory. This system has attractive features such as the absence of a
holding beam and the symmetry between the two states of the memory element. These properties along with
the external cavity length of 1 cm make the system an interesting candidate for optical integration.
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