A general eigen equation has been deduced that can handle ideal and non-ideal quarter-wavelength cases of Bragg-reflection waveguide structure for nonlinear interaction with matching layers on each side of the active region. In particular, this equation allows for solving the cases when the Bragg reflectors are non-ideal quarter-wavelength thick. With this equation, we propose a Bragg-reflection waveguide structure based on the AlxGa1-xAs/GaAs material system with high figure-of-merit |ξdeff| total nonlinearity and checked the influence if the thickness of the quarter-wavelength Bragg reflectors is off by 10%.