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# RP Fiber Power – Simulation and Design Software for Fiber Optics, Amplifiers and Fiber Lasers

## Example Case: Nonlinear Self-focusing in a Fiber

### Description of the Model

Here, we investigate details of nonlinear self-focusing in a fiber. First, we calculate how the fundamental mode of a large mode area fiber shrinks as the effect of nonlinear self-focusing.

The mode solver actually ignores nonlinear effects. However, with a few lines of script code we can store the refractive index profile including its nonlinear changes and then recalculate the fiber modes. This is repeated until we get a self-consistent solution:

```dr := 0.05 um
defarray I[0, 200 um, dr]
n_f_nl(r) := n_f(r) + n2 * (if r <= r_max then I~[r])
{ nonlinear refractive index profile }
store_I(P) :=
for r := 0 to 2 * r_co step dr do
I[r] := P * I_lm(0, 1, lambda, r)
{ ignore index changes outside 2 * r_co, where the intensity is small }

CalcNonlinearMode(P) :=
{ Calculate the lowest-order mode with self-focusing for the power P. }
begin
var A, A_l;
A := 0;
repeat
A_l := A;
store_I(P);
set_n_profile("n_f_nl", r_max);
A := A_eff_lm(0, 1, lambda);
until abs(A_l / A - 1) < 1e-6;
end
```

We can also numerically simulate the beam propagation, considering the fiber nonlinearity. For that, we need to define a numerical grid and set various other inputs for the beam propagation:

```x_max := 30 um { maximum x or y value }
N := 2^5 { number of grid points in x and y direction }
dx := 2 * x_max / N { transverse resolution }
z_max := 30 mm { fiber length }
dz := 100 um { longitudinal resolution }
N_z := z_max / dz { number of z steps }
N_s := 100 { number of sub-steps per dz step }

P_11 := 4 MW
A0%(x, y) := sqrt(P_11) * A_lm_xy(1, 1, lambda, x, y)  { initial field }

calc
begin
bp_set_grid(x_max, N, x_max, N, z_max, N_z, N_s);
bp_define_channel(lambda);
bp_set_n('n_f(sqrt(x^2 + y^2))'); { index profile }
bp_set_loss('10e2 * ((x^2 + y^2) / (20 um)^2)^3');  { simulate loss for cladding modes }
bp_set_n2('n2');
bp_set_A0('A0%(x, y)'); { initial amplitude }
end
```

### Results

Figure 1 shows the mode profile for an optical power of 5 MW (not far below the power for catastrophic self-focusing), and the corresponding refractive index profile. Figure 1: Calculated normalized mode intensity profiles with and without self-focusing. The refractive index profiles are also shown. One sees that the index profile is substantially modified by the nonlinear effect.

Figure 2 shows the mode area as a function of the optical power. The mode area shrinks dramatically as the critical power is approached. Figure 2: Mode area versus optical power. The red line indicates the critical power for catastrophic self-focusing.

Figure 3 shows the maximum power as a function of the core radius. For each core radius, one has to calculate the optical power for which the on-axis intensity reaches the damage threshold. Of course, the modes need to be recalculated for each power value.