טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGil Ilan Haham
Subjectmultiplexed FROG (Frequency Resolve Optical Gating)
DepartmentDepartment of Physics
Supervisor Professor Cohen Oren
Full Thesis textFull thesis text - English Version


Abstract

In this work, I explore the ability to characterize several pulses from a single, multiplexed Frequency Resolved Optical Gating (FROG) spectrogram.

Laser pulses were first produced in the 1960s, and have since been a prominent subject of study. Pulse characterization poses an interesting problem because laser pulses are the basic and most common tool used to explore fast phenomena, as they are some of the shortest events that are controllably produced. Characterizing laser pulses has allowed us to better our understanding in a vast range of scientific fields, including biology, chemistry, physics, and engineering.

Invented in 1993, FROG is the most popular method for full laser pulse characterization (i.e. measuring both the amplitude and phase of the complex envelope of the electric field of a pulse with femtosecond scale duration). It operates by optically gating the pulse with a delayed replica of itself in nonlinear process, and spectrally resolving the obtained signal. By measuring this result for a set of certain delays between the original pulse and its replica, a spectrogram (which is also called a FROG trace) is recorded. A FROG trace contains many redundant measurements - as was shown recently, a pulse can be fully characterized using only several measured spectra from its full FROG spectrogram.

FROG shares many common traits with Ptychography, an imaging technique whereby an object is scanned using a probe in overlapping steps, and reconstructed from the far-field measurements of the propagated field. It was recently shown that ptychographic multi-state reconstructions are possible, enabling reconstruction of several states from their incoherent sum.

Inspired by the similarities between ptychography and FROG, a FROG reconstruction algorithm was recently developed based on a ptychographic reconstruction approach. By modifying this approach to pulse characterization from FROG spectrograms to accommodate multi-state reconstruction, I propose in this work reconstruction of several pulses from a multiplexed FROG trace, which is the sum of their FROG traces. I show numerically that reconstruction of up to three pulses is possible from such a trace reliably even when noise is added, without any other constraints. Up to five pulses are reconstructed from such a trace, if their power spectra are known and used as an additional constraint. I also demonstrate this experimentally, by reconstructing two pulses from their measured multiplexed FROG trace.

Reconstructing multiple pulses from a single trace in this approach enables reconstruction of isolated (i.e. non-repeating) pulse bursts, which today isn’t possible. This can be done by using a single-shot FROG device to record their multiplexed FROG trace and reconstructing it using the approach proposed here. Multiplexed FROG reconstruction also enables reconstruction of repetitive pulse bursts using a delay range much smaller than needed today, which is an experimental advantage.

I also propose and demonstrate a slight variation on this concept, called Multiplexed Blind FROG, which can enable reconstruction of pulse bursts with precise delay and order, but requires a-priori knowledge of their power spectra, and a rough knowledge of the inter-pulse interval.