Abstract

Otsuka observed chaotic burst generation in a cw LNP laser coupled to an optical fiber (multimode as well as single mode fibers).¹ This chaotic burst generation is closely related to the optical frustration phenomenon predicted by Ikeda and Mizuno which is based on a generalized model of compound cavity passive resonator.² It is known that the competition between two time delayed feedback may causes “frustration” in selecting an oscillating mode, when there exist many potential modes with subtly different stabilities.³ Thus, a slight change in cavity length enables an oscillation in a quite different mode. The mechanism is similar to the frustration phenomenon in thermal equilibrium systems. Here, we employ a diode-pumped microchip Nd:YVO₄ laser with multimode fiber feedback which forms a compound cavity. Different fiber lengths (1 m, 3 m, and 5 m) have been utilized. Meanwhile, with the attenuator, the feedback strength is adjustable. The lasing eigenmode frequency of the compound cavity is determined from the frequency arrangement of the Nd:YVO₄ laser cavity mode and the external cavity (fiber) modes for which the number of modes is very large. It is expected that the state of frustration can occur due to the small mode spacing of external cavity modes. On the other hand, multimode oscillation and intrinsic mode-partition noise as well as frequency dependent nonlinear refractive index are the dynamical origins to cause the chaotic bursts in the presence of the fiber.² It is because that a random intensity fluctuation in each mode results in the mode-dependent random fluctuation in phase shift.² To the contrary, we report an experimental result of single-mode laser in which mode-partition noise is not essential, but the intrinsic noise fluctuation in intensity is dominant for the frustration. As shown in Fig. 1, the rf-spectrum for the microchip Nd: YVO₄ laser is shown. The single mode oscillation with harmonics can be seen. The wavelength is identified by a multiwavelength meter as 1064.245 nm. With fiber feedback, as shown in Fig. 2, the rf-spectrum is broadened. We note that the polarization is still not changed. We investigate the statistical behavior based on the method of probability association.⁴ As time series is measured, we calculate the probability distribution of the data with fixed time step difference. The association of two probability distributions with different time difference can be evaluated based on a common ^χ2 statistics. If there is no correlation for any two data with fixed time difference in time series, the corresponding probability distributions should be the same and this results in a zero degree of probability association. As shown in Fig. 3, the degree of probability association never decreasing to zero suggests that the frustration phenomena has a strong correlation even it has the signature of chaos. However, as the feedback strength is increased, the frustration disappears but a locking to external cavity mode takes place instead.

© 1999 Optical Society of America