Implementing non-scalar diffraction in Fourier optics via the Braunbek method.

Area of Science:

• Optics and Photonics
• Computational Physics
• Astrophysical Instrumentation

Background:

• Standard Fourier optics, while efficient, neglects crucial 3D structure and material properties of diffracting elements.
• Recent starshade experiments necessitate accounting for these physical properties to explain observed diffraction intensities.
• Existing methods struggle to incorporate detailed physics without sacrificing computational efficiency.

Purpose of the Study:

• To develop an efficient methodology for non-scalar diffraction modeling.
• To integrate detailed physical properties into diffraction calculations for optical systems.
• To validate the new model against experimental data for sub-scale starshades.

Main Methods:

• Adapted Braunbek's methodology by replacing Kirchhoff boundary values with exact edge fields.
• Derived novel diffraction equations to implement non-scalar diffraction.
• Developed a computational framework for solving these equations and simulating diffraction.

Main Results:

• Successfully implemented a non-scalar diffraction model that retains computational efficiency.
• Experimental validation confirmed the model's ability to replicate observed diffraction signatures.
• Model accuracy was validated to better than 10^-10 in relative intensity.

Conclusions:

• The presented methodology offers an efficient approach to incorporate non-scalar diffraction effects.
• This technique is vital for accurate modeling of coronagraphs and starshade external occulters.
• The validated model provides a powerful tool for designing and analyzing advanced optical systems where full electromagnetic solutions are intractable.