deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 9af96b6..4053b19 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
a) Overlap integral given by \[ \eta=\int_{-\infty}^{\infty} \Psi_{m^{'}} ^{output} \Psi_{m}^{input} dx\] \\  b) Using the mode solver for this part. I wanted to see how modes would look after $LP_{01}$, not single moded. So I went back to the paper and looked at the equation for the diameters that allow for single mode operation, $D< \frac{2.4 \lambda}{\pi \sqrt{n_0^2-n_1^2}}$, where $n_1$ is 1 for air, and $n_0$ is the index of refraction for the medium in use. From the tong paper, the second page of the paper, or pg.817 of the nature journal it was published in, index of refraction for Silica is said to be $n_0=1.46$. This gives $NA=1.063$, using $\lamda=633 $\lambda=633  nm$, the max diameter is then given to be 454.6 nm for single mode operation.