Robust orthogonal parameterization of evolution strategy for adaptive laser pulse shaping

Abstract

Many spectroscopic applications of femtosecond laser pulses require properly-shaped spectral phase profiles. The optimal phase profile can be programmed on the pulse by adaptive pulse shaping. A promising optimization algorithm for such adaptive experiments is evolution strategy (ES). Here, we report a four fold increase in the rate of convergence and ten percent increase in the final yield of the optimization, compared to the direct parameterization approach, by using a new version of ES in combination with Legendre polynomials and frequency-resolved detection. Such a fast learning rate is of paramount importance in spectroscopy for reducing the artifacts of laser drift, optical degradation, and precipitation. shaper with common-path spectral interferometry and application to coherent control with a covariance matrix adaptation evolutionary strategy," Rev. Sci. Instrum. 79(3), 033103 (2008).

Tailoring pulses for coherent Raman microscopy

“…The patterns associated with similar-parity orders feature a reduced symmetry, compared to quasi-symmetric patterns of oppositeparity orders. These symmetries are very similar to the 2D polynomial landscapes of second harmonic generation [68,71].…”

“…Replacing the spectral phase basis of a coherent control experiment with appropriate linear combinations of the basis functions can result in a new landscape with more convex contours, less shear, and even separable phase terms [68,71]. This technique can also be used successfully in the case of a CARS experiment.…”

“…The optimization is performed using Legendre polynomials, which are normalized between −2Δω and 2Δω, where Δω is the half-width at half maximum (HWHM) bandwidth of the pump pulse. These Legendre polynomials form an orthogonal basis set and show good performance for laser pulse compression [71]. The phase profile that is applied is described using the first eight Legendre polynomials (L 0 -L 7 ).…”

Tailoring a coherent control solution landscape by linear transforms of spectral phase basis

“…At low levels of signal to noise ratio, the learning process does not start in the first place, as small improvements of the fitness function are comparable or negligible compared to noise level. We studied this effect previously and proposed to use orthogonal functions for robust implementations [18]. Here, we consider a different type of noise, which is more common in coherent control experiments, and study its effect on original and modified φ 2 -φ 4 landscapes of the SHG process.…”

“…Previously, Roslund et al reported a comprehensive study of the reduced landscape of the SHG process with three degrees of freedom [17] and also a statistical steepest-ascent technique to probe the local structure of the landscape [13]. We reported the changes of a solution landscape in the context of robust and orthogonal parameterization of an evolutionary algorithm [18]. In this work, we study the properties of 1D, 2D, and 3D landscapes of the SHG process by including up to the sixth order phase term.…”