Integrated optical intensity or phase modulators capable of very low modulation voltage, broad modulation bandwidth, low optical power loss for device insertion, and very small device size are of interest. Such modulators can be of electro-optic or electro-absorption type made of an appropriate electro-optic or electro-absorption material in particular or referred to as an active material in general. An efficient optical waveguide structure for achieving high overlapping between the optical beam mode and the active electro-active region leads to reduced modulation voltage. In an embodiment, ultra-low modulation voltage, high-frequency response, and very compact device size are enabled by a semiconductor modulator device structure, together with an active semiconductor material that is an electro-optic or electro-absorption material, that are appropriately doped with carriers to substantially lower the modulator voltage and still maintain the high frequency response. In another embodiment, an efficient optical coupling structure further enables low optical loss. Various embodiments combined enable the modulator to reach lower voltage, higher frequency, low optical loss, and more compact size than previously possible in the prior arts.