טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentZohar Avnat
SubjectSuper Resolution in Frequency Resovled Optical
Gating (FROG)
DepartmentDepartment of Physics
Supervisor Professor Cohen Oren
Full Thesis textFull thesis text - English Version


Abstract

Invented in 1993, Frequency Resolved Optical Gating (FROG) is the most popular method for full characterization of ultrashort laser pulses (i.e. measuring the amplitude and phase of the electric field complex envelop of laser pulses with femtosecond scale pulse duration).  It operates by optically gating the pulse with a delayed replica of itself in a nonlinear process, and spectrally resolving the obtained signal. The result of a FROG measurement is a spectrogram, which is a non-negative function of frequency and time delay. FROG reconstruction algorithms are designed to extract the original pulse from the measured spectrogram. However, the non-linear process that generates the measured spectrogram has a limited bandwidth (which is typically determined by the phase matching window of the nonlinear crystal). When the bandwidth of the laser pulse is broader than the bandwidth of the nonlinear process, the measured spectrogram is incomplete.  Current FROG reconstruction algorithms do not succeed in retrieving the original pulses from such incomplete spectrograms. While one can increase the bandwidth of the FROG nonlinear process (by using a narrower nonlinear crystal), it results in a decreased signal to noise ratio (SNR). Thus, the pulses that current FROG devices can characterize depend on an interplay between the pulses intensity and bandwidth: very weak and ultrashort laser pulses cannot be measured by FROG.  

We propose two new approaches for reconstructing the original pulse from FROG measurements, even when current FROG reconstruction algorithms fail because the measured spectrograms are incomplete and/or very lossy. We compensate for the information loss by using two types of additional information. First, we measure the power spectrum of the original pulse and add it as a constraint to the measurements. Second, we assume that the pulse can be described well by a low order polynomial function, and use it as an additional constraint. We propose and test two algorithms that utilize the additional information. We find that the new algorithms can handle comparably large information loss in frequency with respect to a classical algorithm. The second algorithm can also handle large information loss in time delay, achieving good results even for fixed delay time, enabling “single shot” measurements.

The new FROG reconstruction approaches that are proposed in this thesis may allow measurement of very weak laser pulses with very broad bandwidth. In addition, it may be extended to FROG-CRAB which is a technique for characterizing pulses with attosecond pulse duration. This extension may be critical since the bandwidths of pulses with several attosecond pulse duration are broader than all nonlinear processes that were so far used for measuring ultrashort pulses.