Disclosed is a mode-filtering and mode-selecting method in a multi-mode waveguide, and a waveguide amplifier, a semiconductor laser, and a VCSEL using the method. These optical elements include a cladding region that has a periodically changed refractive-index structure, thereby obtaining a mode-filtering or mode-selecting function, which in turn allows only a single mode in the transverse direction to propagate along the waveguide. By forming the periodic index-variation structure, the EDF, the semiconductor laser, and the VCSEL achieve a single mode operation although the cross-sectional area is much larger than that of the prior art, consequently realizing a high-performance or high-power single-mode amplifier and laser.