Refraction limit of miniaturized optical systems: a ball-lens example

Area of Science:

• Optics and Photonics
• Micro-optics
• Electromagnetism

Background:

• Ball lenses exhibit different optical behaviors based on their diameter, transitioning between ray and wave optics regimes.
• Understanding this transition is key for designing micro-optical systems for imaging and illumination.
• Previous studies have focused on specific regimes, lacking a comprehensive analysis of the transition.

Purpose of the Study:

• To experimentally and theoretically investigate the electromagnetic field behind ball lenses across a wide range of diameters.
• To study the transition between the refraction (ray-optical) and diffraction (wave-optical) regimes.
• To identify the critical diameter that defines the limit between these two optical regimes.

Main Methods:

• Experimental measurements of electromagnetic field amplitude and phase behind ball lenses.
• Theoretical modeling using ray-optical and wave-optical (Mie theory) approaches.
• Analysis of criteria such as focal length, spot size, and cross-polarization to define the refraction limit.

Main Results:

• Observed the transition from ray-optical phenomena (cusp catastrophe, caustics) to wave-optical phenomena (photonic nanojets).
• Identified the vanishing of the cusp catastrophe and emergence of the photonic nanojet as the refraction limit.
• Determined a refraction limit of approximately 10 µm diameter for a glass ball lens at 642 nm wavelength.

Conclusions:

• The study provides a clear understanding of the refraction limit in micro-optical systems.
• Established criteria for distinguishing between refraction and diffraction regimes in ball lenses.
• Offers valuable insights for the design of advanced optical devices for imaging and illumination applications.