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This paper describes the application of a time-domain modeling approach for a laterally coupled distributed feedback (LC-DFB) semiconductor laser for the first time. We numerically study the effect of the radiation modes on LC-DFB laser properties. We integrate the Streifer's coefficients, which represent the effects of radiation and evanescent modes into the time-domain coupled-wave equations. High-order corrugated gratings with λ/4 phase-shift are analyzed, where the degree of longitudinal spatial hole burning can be effectively reduced by means of fine tuning of the grating duty cycle. Additionally, we show a remarkably enhanced side-mode suppression ratio (SMSR). For example, for the third-order gratings with a 50% duty cycle, an SMSR as high as 45 dB can be predicted.