Recently

there has been an increasing interest in nonlinear optical properties of semiconductor quantum well structures

because of their relevance for studying practical applications and as a probe for the electronic structure of mesoscopic media. In this paper

the nonlinear electro-optic effects in special asymmetric quantum wells are studied. Because of this kind of quantum well is more approximate a practical quantum well between the conduction band and valence band

and it can be realized very easily in experiment. The analytical expressions of electro-optic coefficient have been derived by compact density-matrix approach and the numerical results were presented for GaAs/AlGaAs asymmetric quantum wells. The shape of the quantum well varying with the parameter

a

and the parameter V

0

were plotted. It is found that the asymmetry of the quantum wells enhances with the increase of parameter

a

. On the contrary

the asymmetry of the quantum wells decreases with the increase of the parameter V

0

. The maximum values of the electro-optic coefficient varying with the parameter

a

and the parameter V

0

were plotted. The numerical results show the electro-optic coefficient enhances with the increases of the parameter

a

and the decrease of the parameter V

0

. Therefore

it is found that the electro-optic coefficient increases with the enhancement of the quantum wells’ asymmetry. The electro-optic coefficient as a function of the photon energy with different values of parameter

a

and different values of parameter V

0

were also plotted. It can be observed that there are three peak values in the figures

respectively. And it is obvious that the larger the asymmetry of quantum wells is

the bigger the peak value is. It can be seen that with the increase of the asymmetry of quantum well

the peaks move to the low energy side. Moreover

the electro-optic coefficient obtained in this special quantum well is as large as 10

-6

m/V. With the advances of nanofabrication technology recently

it is possible to fabricate such semiconductor quantum wells and it is possible for us to get better nonlinear materials in experiments.