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An all-optical method for generating ultra-intense high-order-mode light pulse is investigated with three-dimensional particle-in-cell simulation. We find that the conversion from a short intense circularly polarized incident Gaussian laser pulse into a transverse magnetic (TM) mode occurs as it propagates into a micro plasma waveguide. The strength of the longitudinal electric field of the excited TM modes can be almost two orders of magnitude higher than that of the original laser. The simulation results show that, for the lower-order modes, the trapped electrons lead to their revolving transverse structures. A linear plasma waveguide model is presented to predict the mode pattern and intensity of the longitudinal electric fields, which are in excellent agreement with those in the simulations. Relativistic-intense high-order-mode light can be useful for many applications, including accelerating charged particles to high energies.