Waveguide laser mode patterns in the near and far field.

Area of Science:

• Optics and Photonics
• Electromagnetism
• Waveguide Theory

Background:

• Discrepancies exist in mathematical notations between dielectric waveguide researchers and those focused on waveguide lasers.
• Standardizing notation is crucial for clear communication and accurate modeling in optical engineering.

Purpose of the Study:

• To reconcile differing notations used in the fields of dielectric waveguides and waveguide lasers.
• To rederive equations for field components of modes in large radius hollow dielectric waveguides using a more common notation.
• To analyze the free-space field distributions resulting from specific mode combinations at waveguide terminations.

Main Methods:

• Re-derivation of electromagnetic field component equations for dielectric waveguide modes.
• Mathematical analysis of linear combinations of modes to achieve linearly polarized fields.
• Calculation of Fresnel and Fraunhofer diffraction patterns for launched waveguide modes.

Main Results:

• Unified notation for dielectric waveguide mode equations is presented.
• Linear combinations of modes producing linearly polarized fields are identified.
• Formulas for Fresnel and Fraunhofer field distributions are derived for mode identification and mirror aperture selection.

Conclusions:

• The derived equations and field distributions aid in identifying oscillation modes within dielectric waveguides.
• This work provides a basis for selecting appropriate mirror apertures to ensure fundamental waveguide mode oscillation.
• Standardized notation enhances the understanding and application of dielectric waveguide theory in laser systems.