Reconstructing algorithm for frequency-resolved optical gating based on intelligent seeker optimization

Abstract

Frequency-resolved optical gating (FROG) is a common technique of ultrashort pulse measurement. It reconstructs the test pulse by an iterative two-dimensional phase retrieval algorithm from a FROG trace. Now the most widely used FROG algorithm is principal component generalized projection (PCGP), yet its accuracy of pulse retrieval drops obviously under noise condition, and its iterative speed slows down significantly as the size of FROG trace increases. Actually, most of ultrashort pulses delivered from ultrafast oscillators and amplifiers as well as created in most scientific experiments are of smooth spectral phases, so that they can be determined by a few of dispersion coefficients. In this paper, we propose a FROG algorithm based on seeker optimization algorithm (SOA). After recording the spectrum of the test pulse, several main dispersion coefficients of the spectral phase of the pulse are searched directly by the SOA algorithm to fit the corresponding FROG trace. Then the shape of the test pulse can be uniquely reconstructed. Since this algorithm mainly operates in a spectral domain and its routine of iteration is much simpler than PCGP’s, faster speed and higher accuracy of pulse retrieval can be expected. In order to prove the advantages of SOA-FROG algorithm, numeral simulations are performed for test pulses with varying dispersion, in the cases without noise and with 1%, 5%, 10%, 20% noise levels, respectively. The simulation results show that the new algorithm performs much better than PCGP in accuracy and iteration speed. In the case without noise, 97% test pulses reach the condition of rigid convergence (FROG error <i>G</i> ≤ 10<sup>–4</sup>) after 1500 iteration circles by using the SOA, with an average FROG error <i>G</i> < 10<sup>–5</sup>. So the accuracy of pulse reconstruction by SOA is at least three orders of magnitude higher than by PCGP. In cases with different noise levels, the accuracy of pulse reconstruction by SOA is also much higher than by PCGP. By means of background-subtraction and filtering on the FROG traces, the retrieved pulse profiles almost accord with reality. Typically for a 256 × 256 FROG trace, SOA-FROG iterates 100.8 circles per second, about 5 times faster than PCGP. After 300 iteration circles by SOA in about 3 s, most of test pulses can finish their routines of reconstruction and reach high accuracy. Besides SHG-FROG, the SOA-FROG algorithm can also be utilized in other FROG techniques based on the 3<sup>rd</sup> order nonlinear optical effects. In summary, the SOA-FROG is expected to be suitable to the real-time pulse measurement with high accuracy in most of application cases. Yet some measures of improvement should be taken to reconstruct complex pulses with rough spectral phases or/and broken spectra.