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We design two novel air-hole-array strip waveguides: one with elliptic air holes and the other with sandglass-shaped ones. Simulation results prove that flatband modes with low group velocity and low dispersion can be obtained. Each waveguide has its merits; one can choose waveguides with a low group velocity of 2.52??10-3 c and a narrow bandwidth of 2.71 nm (one with elliptic air holes) or a high group velocity of 1.2??10-2 c and a wide bandwidth of 13.6 nm (one with sandglass-shaped air holes), according to the application. Numerical simulation by finite-difference time domain (FDTD) demonstrates the propagation of the broadband pulse.