Time-frequency representation measurement based on temporal Fourier transformation

• A new scheme to physically realize the short-time Fourier transform of chirped optical pulse using time lens array.
• The core advantage of the phase measurement scheme is real-time representation and high efficiency.
• Theoretical analysis of optimal measurement.
• The scheme is another application of time-lens and space-time duality.

We propose a new scheme to physically realize the short-time Fourier transform (STFT) of chirped optical pulse using time-lens array that enables us to get time-frequency representation without using FFT algorithm. The time-lens based upon the four-wave mixing is used to perform the process of temporal Fourier transformation. Pump pulse is used for both providing the quadratic phase and being the window function of STFT. The idea of STFT is physically realized in our scheme. Simulations have been done to investigate performance of the time-frequency representation scheme (TFRS) in comparison with STFT using FFT algorithm. Optimal measurement of resolution in time and frequency has been discussed.