We demonstrate difference frequency generation of millimeter wave and terahertz (THz) radiation using periodically poled lithium niobate (PPLN). We fabricated PPLN crystals with a 286-μ m period, and with 50.0 and 33.3% duty ratio. Millimeter and THz waves were successfully generated, and higher-order quasi-phase matching (QPM) modes were obtained. We investigated behaviors of the radiation and the influence of the duty cycle on the spectrum using numerical simulation. Higher-order QPM modes could be generated with the proper duty cycle. The conversion efficiency of higher-order modes was controllable by varying the duty cycle of the QPM device.