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  • 3 votes cast
Jul
6
awarded  Commentator
May
29
awarded  Supporter
May
29
accepted Problem with an integration
May
29
comment Problem with an integration
Ok, now I understand what do you do.
May
29
comment Problem with an integration
@joriki Otherwise, is there any way to move this question to physics.se?
May
29
comment Problem with an integration
@joriki I asked here because my biggest problem was mathematical, not physical. I didnt understand what property had been used to manipulate the integral. So, I thought that here was the best place to show my doubt.
May
29
comment Problem with an integration
@joriki sorry about this misunderstood... I just thought that here would be more constructive.
May
29
comment Problem with an integration
don't you forget a piece of the argument of the exponential? The complete argument is: $i\left(k_{x}x+k_{y}y+z\left(k−\dfrac{k^{2}_{x}+k^{2}_{y}}{2k}\right)\right)$. Then the last term will not vanish.
May
29
comment Problem with an integration
@PatrickDaSilva and, as you could note, the exponential term does not represent a plane wave... Its because I used the paraxial approximation, which says that: $ k_{x}^{2}+k_{y}^{2} \ll k^{2} $.
May
29
awarded  Editor
May
29
revised Problem with an integration
added 13 characters in body
May
29
comment Problem with an integration
@PatrickDaSilva well, the l.h.s of the first equation its the spread of the field intensity in a plane normal to the direction of the propagation ($\vec{z}$) of electric field $E(x,y)$. This field could be regarded as a infinitesimal superposition of plane waves.
May
29
comment Problem with an integration
@LubošMotl $A$ is a general function, as you pointed. Could you please show me the "simplest explicit way" that you said above? I just can't see this step.
May
29
asked Problem with an integration
May
29
awarded  Scholar
May
29
accepted Problem with an integral
Mar
21
awarded  Student
Mar
21
comment Problem with an integral
@Approximist Yes, but I don't know any trigonometric relation that give me $\arctan$ by manipulation of $\text{Ei}$. Is there any?
Mar
21
asked Problem with an integral