High-aperture diffraction of a scalar, off-axis Gaussian beam

Area of Science:

• Optics and Photonics
• Microscopy
• Electromagnetism

Background:

• Gaussian beams are fundamental in optics, but their behavior when offset from the optic axis and focused by high-NA lenses requires detailed theoretical treatment.
• Doppler microscopes often utilize multiple offset beams for simultaneous measurements, necessitating an understanding of their focal characteristics.

Purpose of the Study:

• To develop a scalar theory for Gaussian beams offset from the optic axis and focused by high-numerical-aperture (NA) lenses.
• To derive analytic expressions for focal intensity and analyze the effects of beam size, offset, and NA on the focal distribution.

Main Methods:

• Development of a scalar diffraction theory for offset Gaussian beams.
• Derivation of analytic expressions for the intensity distribution in the focal region.
• Numerical calculation and analysis of focal intensity variations based on key parameters.

Main Results:

• The Strehl ratio can increase above unity for small-diameter Gaussian beams offset from the optic axis due to an increased effective NA.
• Focal intensity distribution exhibits rotation for small beam sizes.
• Increasing beam diameter leads to rotation and shearing (distortion) of the focal distribution.
• The distortion of the focal distribution intensifies with increasing numerical aperture.

Conclusions:

• The presented scalar theory accurately describes the focal behavior of offset Gaussian beams.
• Beam offset and lens parameters significantly influence focal intensity and distribution, offering insights for optimizing optical systems.
• Understanding these distortions is critical for applications like Doppler microscopy where precise focal characteristics are paramount.