Quickstart¶

This notebook provides a quick start guide to using Anafibre. It covers the basics of:

creating a fibre,
calculating its modes, and
visualising the results.

Imports¶

We will start by importing the necessary libraries and setting up our environment:

import numpy as np
import anafibre as fib

Create A Step-Index Fibre¶

Next, we will create a step-index fibre class instance with a core radius of \(250 \text{ nm}\), a core refractive index of \(2.00\), and a cladding refractive index of \(1.33\):

fibre = fib.StepIndexFibre(
    core_radius=250e-9,
    n_core=2.00,
    n_clad=1.33)

and choose a wavelength of \(\lambda=700 \text{ nm}\) for the mode calculations:

wl = 700e-9

Notice that all the parameters are specified in SI units such as the core radius and wavelength in meters. Refractive indices n_core and n_clad can be specified as functions of wavelength, or as constants like in the example above. If we wanted a function we could pass n_core=lambda x: 2.00+0.01*(x-700e-9) for example, which would give a core refractive index that increases linearly with wavelength. One can also instead specify the relative eps_core and eps_clad parameters, and mu_core and mu_clad if the fibre is magnetic. The fibre object will automatically calculate the missing parameters from the ones that are provided. One can call fibre parameters at any wavelength as shown below:

print(f"Fibre parameters at lambda = {wl*1e9:.0f} nm:")
print(f"  Core radius: {fibre.core_radius*1e9:.0f} nm")
print(f"  n_core:      {fibre.n_core(wl):.2f}")
print(f"  n_clad:      {fibre.n_clad(wl):.2f}")
print(f"\nMaterial properties:")
print(f"  eps_core:    {fibre.eps_core(wl):.2f}")
print(f"  eps_clad:    {fibre.eps_clad(wl):.2f}")
print(f"  mu_core:     {fibre.mu_core(wl):.2f}")
print(f"  mu_clad:     {fibre.mu_clad(wl):.2f}")
print(f"\nV-number at lambda = {wl*1e9:.0f} nm: {fibre.V(wl):.3f}")

Output:

Fibre parameters at lambda = 700 nm:
  Core radius: 250 nm
  n_core:      2.00
  n_clad:      1.33

Material properties:
  eps_core:    4.00
  eps_clad:    1.77
  mu_core:     1.00
  mu_clad:     1.00

V-number at lambda = 700 nm: 3.352

Calculate guided modes¶

The fibre class also contains mode constructor methods which can be used to calculate the guided modes supported by the fibre at a given wavelength. For step-index fibres, these include methods for calculating the \(\text{HE}_{\ell n}\), \(\text{EH}_{\ell n}\), \(\text{TE}_{0n}\), and \(\text{TM}_{0n}\) modes

fibre.HE(ell, n, wl, a_plus=..., a_minus=...)
fibre.EH(...)
fibre.TE(n, wl, a=...)
fibre.TM(...)

Each returns a GuidedMode object. So for instance, to calculate the fundamental \(\text{HE}_{11}\) mode at our chosen wavelength and with linear polarisation along the x-axis, we can do:

HE11x = fibre.HE(ell=1, n=1, wl=wl, a_plus=1/np.sqrt(2), a_minus=1/np.sqrt(2))
HE11x

Output:

Mode	λ [nm]	V	n_eff	S₀	(S₁, S₂, S₃) / S₀
HE₁₁	700.00	3.35	1.7955	1.00	( 1.00, 0.00, 0.00)

The mode class provides methods to calculate the fields at any point in space, for example the electric field at the fibre centre:

E_center = HE11x.E(x=0, y=0)
print("Electric field at the fibre center (0,0,0):")
print(f" Ex = {E_center[0].real:+.2e} {E_center[0].imag:+.2e} i")
print(f" Ey = {E_center[1].real:+.2e} {E_center[1].imag:+.2e} i")
print(f" Ez = {E_center[2].real:+.2e} {E_center[2].imag:+.2e} i")
print(f"\n |E| = {np.abs(E_center).sum():.2e} V/m")

Output:

Electric field at the fibre center (0,0,0):
 Ex = +0.00e+00 +6.68e+07 i
 Ey = +0.00e+00 +0.00e+00 i
 Ez = +0.00e+00 +0.00e+00 i

|E| = 6.68e+07 V/m

We can also list all the guided modes at this wavelength using the mode listing method:

modes = fibre.list_modes_at(wl)
modes

Output:

Mode	λ [nm]	V	n_eff	S₀	(S₁, S₂, S₃) / S₀
HE₁₁	700.00	3.35	1.7955	1.00	( 0.00, 0.00, 1.00)
TM₀₁	700.00	3.35	1.5500	1.00	( 1.00, 0.00, 0.00)
TE₀₁	700.00	3.35	1.4762	1.00	(-1.00, 0.00, 0.00)
HE₂₁	700.00	3.35	1.4571	1.00	( 0.00, 0.00, 1.00)

Where hybrid modes will default to right-handed circular polarisation. It returns a list modes of GuidedMode objects.

Evaluate Fields On A Grid¶

Since \(\vc{E}(\vc{r})\), \(\vc{H}(\vc{r})\), \(\grad\otimes\vc{E}(\vc{r})\), and \(\grad\otimes\vc{H}(\vc{r})\) methods can be calculated at any point in space we can also evaluate them on a grid:

mode = modes[0]
Ngrid = 100
x = np.linspace(-2*fibre.core_radius, 2*fibre.core_radius, Ngrid)
y = np.linspace(-2*fibre.core_radius, 2*fibre.core_radius, Ngrid)
X, Y = np.meshgrid(x, y)

E = mode.E(x=X, y=Y)
H = mode.H(x=X, y=Y)
J_E = mode.gradE(x=X, y=Y)
J_H = mode.gradH(x=X, y=Y)

print(f"Field shapes:\nE:{E.shape}, H:{H.shape}, gradE:{J_E.shape}, gradH:{J_H.shape}")

Output:

Field shapes:
E:(100, 100, 3), H:(100, 100, 3), gradE:(100, 100, 3, 3), gradH:(100, 100, 3, 3)

Visualise Modes¶

anim = fib.animate_fields_xy(modes=modes[0], show=("E",), figsize=(5, 5))
fib.display_anim(anim)

The animation is interactive in Jupyter. In docs, link to the notebook for full rendered widget output: - examples/quick_start.ipynb

To save animation files:

anim.save("mode_animation.mp4", writer="ffmpeg", fps=30)
anim.save("mode_animation.gif", writer="pillow", fps=15)