• Cylindrical GaAs waveguides enable efficient conversion of laser energy into multi-millijoule THz pulses.
• An eigenvalue equation derived from Hertz potentials describes guided modes, providing a theoretical framework for optimizing THz generation.
• The effective mode index and laser pulse power significantly influence the electric field components of TE and TM modes.
• GaAs waveguides offer a pathway to compact, portable THz systems with enhanced generation efficiency and broad practical applications.