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Domain inversion (DI) is applied to traveling-wave integrated electrooptic (EO) LiNbO3 modulators to achieve predefined EO frequency response and improved performance with respect to standard single-domain (not domain-inverted) counterparts, including lower driving voltages and larger modulation bandwidths. In particular, when an appropriate poling (DI) is performed along the interaction length, two novel configurations are envisaged. 1) An apodised longitudinal poling profile is used in non-velocity-matched (NVM) modulators to achieve a desired EO response, such as amplitude modulation with intrinsic third-order Bessel-type optical filtering for duobinary transmission. 2) Two- section longitudinal poling is used to counteract the detrimental microwave loss effect in VM modulators and to increase the bandwidth to driving voltage ratio, achieving a value up to 50% larger than that of single-domain (unpoled) structure.