The FM response of vertical-cavity surface-emitting lasers (VCSELs), i.e., the dynamic wavelength tuning behavior, is scrutinized. The FM amplitude and phase shift are measured up to 80 MHz for GaAs-, InP-, and GaSb-based VCSELs from 763 to 2300 nm. From measurements, it is found that the FM response consists of three components: intrinsic thermal tuning (dominating to several megahertz) with characteristic 1/ √ if behavior, the plasma effect (dominating from several megahertz), and a small

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... ct (10-100 Hz) caused by the interaction of laser chip and submount. All effects are modeled and the measurement data are fitted to obtain effective thermal diffusivities, strength of the plasma effect, and time constant of the laser chip submount interaction. Comparing thermal models with different asymptotic behaviors, an approximation of the heat source in the laser with a nonzero thickness turned out to be necessary. Due to the plasma effect, with influence starting at 100 kHz, VCSELs cannot be considered a minimum phase system, which makes separate amplitude and phase measurements essential for device characterization. The "N time constants model" is the proper choice for empirical description of the intrinsic thermal tuning component. The best fit coefficients to a rational frequency response are given for use in time-domain simulation programs. Index Terms-FM phase shift, FM response, Hilbert transform, plasma effect, thermal time constant, thermal tuning, verticalcavity surface-emitting laser (VCSEL). K NOWLEDGE of the dynamics of the laser tuning coefficient is important in all applications where tunable lasers are employed. In tunable diode laser spectroscopy, the laser is tuned to record absorption spectra and knowledge of the wavelength response at specific current modulation of the used tunable lasers is very important. Since the wavelength tuning is predominantly a thermal effect and heat conduction is a "slow" process, the wavelength response does not instantaneously follow the modulation current. The small signal dynamics are fully described by the FM response or the frequency-dependent cur-Manuscript