We numerically studied the chaotic dynamics of a laser diode (LD) system with optical injection, where a pseudorandom signal is applied to the drive current of the master LD, and compared two different methods of quantifying the orbital instability of the LD system, i.e., calculating the orbital expansion exponent (OEE) and the Lyapunov exponent. We found that both exponents are increased and the orbital instability is enhanced by applying a pseudorandom signal when the inherent system without the applied signal is a “window”. On the other hand, when the inherent system is chaotic, the OEE is increased and the Lyapunov exponent is decreased with increasing standard deviation of the applied signal. Although the two exponents have a different tendency, it is suggested that the variation of the standard deviation of the applied signal can be identified using both exponents. We then investigated the response of the orbital instability to the frequency range of the applied signal and showed that the orbital instability is efficiently enhanced by using the inherent system is a window and by applying a broad signal that does not have a frequency near the spectral peak of the inherent system and has lower-frequency components than this frequency.
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