Starting from the Maxwell equations, a set of coupled planewave equations of frequency doubling in the refractiveindex modulated medium is derived, and a solution to the equations is given under the smallsignal approximation. The smallsignal solution, a form composed of Fresnel functions presents a special dephasing structure which is different from the typical sinc function. Analysis shows that the refractiveindex modulated crystal has a larger phase matching bandwidth than that in a normal nonlinear crystal, so possesses larger temperature, phase matching ange and spectral bandwidths; however the total conversion efficiency has to make sacrifice to pay for this enhancement of bandwidths. It should be noted that the dephasing function can be flattened with a suitable modulating parameter, which will lower the sensitivities of the frequency doubling crystal to erratic shifts of working points out of any thermal and mechanical reasons. It is found by a simulation in the high conversion efficiency case, the characteristics of dephasing function are still in accordance with the result from the smallsignal approximation, except rendering a magnitude difference which depends on coupling strength.