Method and apparatus for determining wave characteristics from wave phenomena
U. S. Patent 6,219,142, issued April 17, 2001
The structure of an ultrashort laser pulse has been difficult to quantify. Ideally one wants both the phase and amplitude as a function of time. A smooth amplitude profile and a constant phase are best for achieving the shortest pulses, while pulses with chirped phases or more complex phase and amplitude structures may be desired for producing quantum superposition states. Techniques such as Frequency Resolved Optical Gating ("FROG") map the phase and amplitude onto a time-resolved spectrum. With certain assumptions, one can invert this spectrum to determine the phase and amplitude of the pulse. To date, however, the inversion algorithm has been slow.
The Principal Component Generalized Projection algorithm (PCGP) is a rapid method of computing the phase and amplitude. The algorithm is based on the recognition that the FROG spectrum can be expressed as an outer product of two vectors, corresponding to the gate and the pulse. The phase retrieval problem is reduced to the problem of finding the dominant eigenvector of a matrix. An iterative algorithm projects the guesses and quickly converges on the dominant eigenvectors. Real time updates of the phase and amplitude of ultrafast pulses are possible at video rates (20 Hz or better).
This patent also features an extensive bibliography related to phase retrieval and the measurement of ultrafast pulses.
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