ab,\]</div>
<div class="math notranslate nohighlight">
\[\nabla\vec {E} =\displaystyle\frac {4I (a + b)} {\pi (a + b) ab} =\displaystyle\frac {4I} {\pi ab} = 4\pi\rho.\]</div>
<p>Since the fields are linear, they are added to the fields of the focusing lens. Substitute <span class="math notranslate nohighlight">\(\displaystyle a =\sqrt\epsilon_x w_x, b =\sqrt\epsilon_y w_y:\)</span> in the envelope equation</p>
<div class="math notranslate nohighlight">
\[a '' + k_ {xt} a -\frac {\epsilon_x ^ 2} {a ^ 3} = 0