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

Area of Science:

• Coherent control
• Nonlinear optics
• Ultrafast laser science

Background:

• Optimizing phase patterns in multidimensional landscapes is crucial for efficient control.
• Local optima and complex contour lines hinder the speed and ease of finding optimal solutions.
• Wideband second harmonic generation (SHG) is a key process in nonlinear optics.

Purpose of the Study:

• To demonstrate a method for simplifying phase pattern optimization.
• To improve the speed and ease of finding optimal phase patterns by suppressing local optima and tailoring contour lines.
• To apply this method to wideband second harmonic generation for coherent control.

Main Methods:

• Utilizing a linear combination of spectral phase basis functions to shape the phase pattern.
• Employing wideband second harmonic generation as a test case for coherent control.
• Analyzing the resulting phase profiles and their relation to nonlinear shear.

Main Results:

• Achieved suppression of local optima and creation of closed convex contour lines in the solution landscape.
• Demonstrated that spectral phase basis functions lead to separable phase terms, allowing independent optimization.
• Identified suppressed nonlinear shear as the cause for improved contour line shapes and orientation.

Conclusions:

• A linear combination of spectral phase basis functions effectively simplifies phase pattern optimization.
• The method enhances control efficiency in processes like wideband second harmonic generation.
• A first-order approximation reveals a simple input-output phase relationship, beneficial for ultraviolet pulse shaping.