# Power of higher order mode beam

1. Apr 14, 2012

### semc

1. The problem statement, all variables and given/known data
Evaluate the ratio of the power contained within a circle of radius W(z) in the transverse plane to the total power in the Hermite-Gaussian beams of order (1,0)

2. Relevant equations
P=$\int$IdA

3. The attempt at a solution
I have determined the ratio for the Gaussian beam but the higher order modes have a extra 'x' or 'y' in the integral but I am integrating w.r.t r (r2=x2+y2). So how can I evaluate the integral?

2. Apr 14, 2012

### ivanis

Why don't you integrate in Decartes coordinates x and y? Because, if I understood correctly, then the integral is can be represented as
$\int^{W(z)}_{0} x*e^{-x^2}dx \int^{\sqrt{W(z)^2-x^2}}_{0}y*e^{-y^2}dy$
this is only a quarter of the full energy of course.

Last edited: Apr 15, 2012
3. Apr 15, 2012

### semc

I don't understand what is Decartes coordinates but I managed to solve it. Its simply x=rcos$\vartheta$. Have no idea why I didn't think of that when I posted this. Thanks