设双曲线\( \dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} =1(a > 0 , b > 0)\)的右焦点为\(F\)，右顶点为\(A\)，过\(F\)作\(AF\)的垂线与双曲线交于\(B\)、\(C\)两点，过\(B\)、\(C\)分别作\(AC\)、\(AB\)的垂线，两垂线交于点\(D.\)若\(D\)到直线\(BC\)的距离等于\(a+ \sqrt {a^{2}+b^{2}}\)，则该双曲线的离心率\(e= (\:\:\:\:)\)