and transmitted beams ${H_y}^{(r)} (x,z)$ and ${H_y}^{(t)} (x,z)$ are given by $$\begin{aligned}
&&{H_y}^{(r)}(x,z) = {1 \over \sqrt{2\pi}} \int_{-\infty}^{\infty}
r(k_x) \tilde{H}(k_x) \exp \left[ i k_x x + i k_z ( z - L )
\right] dk_x ~~(z>L),\nonumber\\
&&{H_y}^{(t)}(x,z) = {1 \over \sqrt{2\pi}} \int_{-\infty}^{\infty}
t(k_x) \tilde{H}(k_x) \exp \left( i k_x x - i k^\prime_z z
\right) dk_x ~~(z<0),\end{aligned}$$ where $k_z$ ($=k_1\cos\theta$) and ${k_z}^\prime$ are the negative $z$ components of the wave vector in the incident ($z>L$) and transmitted ($z<0$) regions respectively.

The GH shifts for the reflected $(\Delta_r)$ and transmitted $(\Delta_t)$ beams, which are also known as the normalized first momenta of the magnetic field [@Shadrivov], are defined by $$\Delta_{r} = \frac{\int_{-\infty}^{\infty} x \left\vert {H_y}^{(r)}(x,L) \right\vert^2 dx} {\int_{-\infty}^{\infty} \left\vert {H_y}^{(r)}(x,L) \right\vert^2 dx},~~~\Delta_{t} = \frac{\int_{-\infty}^{\infty} x \left\vert {H_y}^{(t)}(x,0) \right\vert^2 dx} {\int_{-\infty}^{\infty} \left\vert {H_y}^{(t)}(x,0) \right\vert^2 dx}.$$ The reflected and transmitted beams will be severely deformed when the half-width of the incident beam is small. In order to measure the degree of the deformation of the reflected and transmitted beams, we calculate the normalized second momenta of the magnetic field defined by $$\begin{aligned}
&&\beta_{r} = \frac{4 \int_{-\infty}^{\infty} \left( x - \Delta_{r} \right)^2 \left\vert {H_y}^{(r)}(x,L) \right\vert^2 dx }
 {\int_{-\infty}^{\infty} \left\vert {H_y}^{(r)}(x,L) \right\vert^2 dx},\nonumber\\
&& \beta_{t} = 