k ue8a0 u03bb ue89e l ue89e u03bbcos ue89e ue89e u03b8 u2032 i ue89e u03b1 k ue8a0 u03bb ue89e l 2 ue89e cos ue89e ue89e u03b8 u2032 1 where u03bb is the wavelength l is the thickness of the active layer 78 u03b8 u2032 is the angle between the direction of propagation and the surface normal u03b7 k is the wavelength dependent k th fourier coefficient of the refractive index grating and u03b1 k is the k th fourier coefficient of the absorption grating in the device where k u00b1 1 0 are the grating vectors of interest in two wave mixing this complex phase shift modulates the amplitude and phase of the reference wave 20 causing it to partially diffract in the direction of the signal beam 32 the copropagating partially diffracted wave 20 u2032 and the partially transmitted signal beam 32 u2032 together comprise the beam 40 that reaches the photodetector 46 homodyne detection occurs because there is a phase relationship between the partially diffracted reference beam 20 u2032 and the partially transmitted signal beam 32 u2032 the superposed beam 40 is given by e 40 e 32 ue89e exp ue89e ue89e i ue89e ue89e u03b4 o 1 2 ue89e u03b4 1 ue89e e 20 ue89e exp ue89e ue89e i ue8a0 u03b4 o u03c6 o 4 ue89e u03c0 u03bb ue89e d ue8a0 t u03c0 2 2 where e 40 is the amplitude of the combined beam after.