  Intrinsic spectrum that results from the coupling of spontaneous emission in
a laser cavity, can determine the energy concentration and coherence of lasers,
which is crucial for the optical high-precision measurement. Up to now, it is
hard to analyze the intrinsic spectrum in the high-speed laser dynamics
process, especially under the condition of fast wavelength sweeping. In this
work, a new method to analyze the laser intrinsic spectrum is proposed with the
laser energy decomposition to a series of chirp-frequency signals, which is
realized by fractional Fourier transform (FRFT) of the coherently reconstructed
laser waveform. The new understanding of the energy distribution of lasers
contributes to the accurate characterization of laser dynamical parameters in
time-frequency domain. In the proof-of-concept experiment, the time-frequency
dynamical process of a commercial wavelength swept laser is tested with
different wavelength-scanning speeds, and the most suitable measurement time
window width required for the FRFT-based narrowest spectrum is also explored.
The proposed analysis method of laser dynamical parameters will promote the
understanding of laser dynamics, and benefit for the optical precision
measurement applications.
