Optimization-free customization of optical tightly focused fields: uniform needles and hotspot chains

Area of Science:

• Optics and Photonics
• Nanotechnology

Background:

• Designing optical elements to precisely control light is crucial for advanced applications.
• Traditional methods for designing diffractive optical elements often rely on complex optimization algorithms.

Purpose of the Study:

• To develop an optimization-free method for designing binary phase diffraction optical elements (BPDOEs).
• To enable the customization of axisymmetric focal fields for high-numerical-aperture (NA) objective lenses.

Main Methods:

• An inverse problem approach based on nonlinear equations was used for BPDOE design.
• The method avoids iterative optimization, simplifying the design process.
• Finite-difference time-domain (FDTD) simulations were employed for verification.

Main Results:

• Successfully designed a 27-belt BPDOE to generate a 43λ-long longitudinally polarized needle beyond the diffraction limit.
• Achieved a record-low cost (belt number to needle length ratio) compared to other methods.
• Created a 10-belt BPDOE generating a longitudinal field with multiple hotspots.
• FDTD simulations confirmed the generated focal fields, validating the Richards-Wolf vector diffraction theory.

Conclusions:

• The optimization-free method is effective for designing complex BPDOEs.
• This approach facilitates the generation of tailored focal fields for diverse applications.
• Potential applications include optical trapping, super-resolution imaging, and lithography.