An efficient bent waveguide and an optical power splitter with a resonator constructed by a metal-dielectric-metal plasmonic waveguide have been analyzed. The method of solution is the finite difference time domain (FD-TD) method with the piecewise linear recursive convolution (PLRC) method. The resonator can be realized by utilizing impedance mismatch at the connection between a narrow waveguide and an input/output waveguide. Numerical results for the bent waveguide show that transmission bands can be controlled by adjusting the length of the narrow waveguide. We have also shown that the optical power of the power splitter is entirely distributed into the output waveguide at the resonant wavelength and its distribution ratio can be controlled.