• Propagation in lens-like and guiding media, developing approximate methods for beam width, phase, and ray trajectories, while addressing off-axis aberrations and Gaussian-beam stability in quadratic-variation refractive-index systems [1], [2], [6], [12], [9].

• Mode structure and resonance in optical cavities and interferometers, including off-axis paths, plane-parallel end reflectors, and loss/selection analyses in curved-mirror geometries, with turbulence-related phase perturbations as a testing context [15], [16], [13], [17].

• Integrated optics and active beam control approaches, including miniature laser-beam circuitry, traveling-wave electro-optic modulators, and grating-couplers on thin films, enabling multi-position beam deflection and digital deflection strategies [5], [14], [4], [10], [8].

• Material properties and loss mechanisms shaping guided-wave performance, including tubular gas lenses, gas-gradient focusing, refractive-index data for semiconductors, and attenuation in clad/bulk glasses [3], [11], [18], [20].