Describing and measuring the time-frequency parameters of low-power bright picosecond optical pulses using the interferometric technique

We present a theoretic approach to the characterization of low-power bright picosecond optical pulses with an internal frequency modulation simultaneously in both time and frequency domains. This approach exploits the joint Wigner time-frequency distribution, which can be determined and developed for these bright optical pulses by using a novel interferometric technique under our proposal. Either power or spectral densities inherent in such pulses can be obtained through integrating the Wigner distribution with respect to the corresponding conjugate variable. At first, the analysis and computer simulations are applied to studying the capability of Wigner distribution to characterize solitary pulses or train-average values for pulse string in practically much used case of the Gaussian shape, when the Wigner distribution is positive. In the context of this analysis, the relation between the spectrum density and the auto-correlation function is followed. Then, the simplest two-beam scanning Michelson interferometer is selected for shaping the field-strength auto-correlation function of low-power picosecond pulse trains. We are proposing and considering in principle the key features of a new interferometric experimental technique for accurate and reliable measurements of the train-average width as well as the value and sign of the frequency chirp of pulses in high-repetition-rate trains. This technique is founded on an ingenious algorithm for the advanced metrology, assumes using a specially designed supplementary semiconductor cell, and suggests carrying out a pair of additional measures with exploiting this semiconductor cell. Such a procedure makes it possible to construct the Wigner distribution and to describe the above-listed time-frequency parameters of low-power bright picosecond optical pulses. In the appendix, we follow the avenue of deriving the joint Wigner time-frequency distribution via choosing the Weil's correspondence between classical functions and operators.