In this letter, an energetic and highly efficient dispersive wave (DW) generation at 200 nm has been numerically demonstrated by selectively exciting LP$_{02}$-like mode in a 10 bar Ar-filled hollow-core anti-resonant fiber pumping in the anomalous dispersion regime at 1030 nm with pulses of 30 fs duration and 7 $mu$J energy. Our calculations indicate high conversion efficiency of $>$35% (2.5 $mu$J) after propagating 3.6 cm fiber length which is due to the strong shock effect and plasma induced blue-shifted soliton. It is observed that the efficiency of fundamental LP$_{01}$-mode is about 15% which is much smaller than LP$_{02}$-like mode and also emitted at longer wavelength of 270 nm.
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