# Homework Help: High Power Pulse Propagating Through a Medium

1. May 12, 2015

### Mattman182

1. The problem statement, all variables and given/known data

I have been given this problem but I don't think I'm doing it right as I have just disregarded n0?

Calculate the maximum length of material (nonlinear refractive index n2=2.5×10-19 cm2W-1) that can be traversed if the total accumulated phase difference between the beam centre (Intensity I =1×1011Wcm-2 , wavelength λ=1053nm) and the beam edge (I=0) is to be less than 2 rad.

2. Relevant equations
n = n0 + n2I

2πnL/λ = nkL

Φ(x) = n k L(x)

3. The attempt at a solution

I just combined the equations to get Φ = 2π/λ * (n0 + n2I)L

and put the numbers in but let n0 equal 1

So my answer was L = 3.35x10-7cm

I don't even know if I've used the right equations so help would be much appreciated

2. May 12, 2015

### blue_leaf77

What is the expression for the phase difference between the beam center and beam edge at any distance?

3. May 12, 2015

### Mattman182

I think you mean the B integral?

B = ∫n2I(z)dz

4. May 12, 2015

### blue_leaf77

Not exactly, although you can still get the sense of what I meant out of the B integral.
Just the expression of the difference between phases in two different locations across the beam's cross-section (fixed distance) which is needed to answer your question, so that you indeed are not required to know n0.