Review on Mathieu (Non-Diffracting) Beams an‎d Their Generation

4/23/2026 12:00:00 AM

Mathieu beams are exact non-diffracting solutions of the scalar Helmholtz equation in elliptic cylindrical coordinates, offering propagation-invariant intensity profiles with continuously tunable ellipticity. This thesis provides a comprehensive review of their theoretical foundations, propagation characteristics, an‎d experimentally validated generation techniques from 2000 to 2025, with special emphasis on the breakthrough role of dielectric metasurfaces since 2020. Four major generation methods — spatial light modulator (SLM) holography, refractive elliptic axicons, diffractive optical elements (DOEs), an‎d metasurfaces are systematically compared in terms of efficiency, fidelity, compactness, power han‎dling, an‎d tunability. Metasurfaces are shown to outperform traditional approaches in most metrics. A novel hybrid SLM–metasurface architecture is proposed for dynamic, high-efficiency control of ellipticity parameter q, mode order m, an‎d orbital angular momentum.Recent nonlinear extensions, such as quasi-multivalue-encoding for second-harmonic generation [58], further expan‎d potential in multi-frequency applications.. Applications in optical trapping of elongated particles, elliptic-mode communications, an‎d structured-light multiplexing are discussed.

پرتوهاي ماتيو , پرتوهاي غيرپراشي , مختصات استوانه‌اي بيضوي

: Mathieu beams , non-diffracting beams , elliptic cylindrical coordinates

Dhurgham Shlash

Homayoon Eshraghi