Normal-incidence operation, based on TE electron intersub-band transitions in n-type unipolar optoelectronic devices, would have a wide range of applications. However, TE intersub-band transitions are generally accepted to be (nearly) forbidden in direct gap conduction-band quantum wells. The paper describes 14-band k.p effective mass theory calculations of TE electron intersub-band matrix elements in n-type, direct-gap systems, to determine the extent to which TE intersub-band transition strengths can be enhanced by choice of quantum well shape and composition. The possibility of enhanced TE:TM transition strength ratios, owing to remote-band contributions to the matrix elements, is described but no significant enhancement of matrix elements over predictions of the single-band model is calculated for conventional quantum wells. A mechanism is presented for nonsquare wells which is suggested to enhance TE:TM transition strength ratio based on remote-band coupling effects through bulk momentum matrix elements P/sub 1/ and Q.