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The limits of applicability of the Lang-Kobayashi (LK) model for asemiconductor laser with optical feedback are analyzed. The model equations,equipped with realistic values of the parameters, are investigated belowsolitary laser threshold where Low Frequency Fluctuations (LFF) are usuallyobserved. The numerical findings are compared with experimental data obtainedfor the selected polarization mode from a Vertical Cavity Surface Laser (VCSEL)subject to polarization selective external feedback. The comparison reveals thebounds within which the dynamics of the LK can be considered as realistic. Inparticular, it clearly demonstrates that the deterministic LK, for realisticvalues of the linewidth enhancement factor $\alpha$, reproduces the LFF only asa transient dynamics towards one of the stationary modes with maximal gain. Areasonable reproduction of real data from VCSEL can be obtained only byconsidering noisy LK or alternatively deterministic LK for extremely high$\alpha$-values.Comment: 18 pages, 28 figures, submitted to Physical Review

Low-frequency fluctuations in vertical cavity lasers: Experiments versus Lang-Kobayashi dynamics