High Power Pulse Propagating Through a Medium

[Mattman182]

Homework Statement

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.

Homework Equations

n = n₀ + n₂I

2πnL/λ = nkL

Φ(x) = n k L(x)

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

 

[blue_leaf77]

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

 

[Mattman182]

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

I think you mean the B integral?

B = ∫n₂I(z)dz

 

[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.