1.2.1. Implemented propagation constants

This example shows the group-velocity and group-velocity dispersion profiles of several propagation constants implemnted in module propagation_constant.

We first start by importing the functionality of numpy and fmas into the current namespace. Specifically, we import the module propagation_constant that contains the convenience class PropConst as well as the implemented propagation constant. A function that allows to plot the group-velocity and group-velocity dispersion profiles is imported from module tools.

import numpy as np
import fmas
import fmas.propagation_constant as prop_const
from fmas.tools import plot_details_prop_const

Below we show a list of the basic properties of several propatgation constants implemented in fmas.

1.2.1.1. NLPM750

pc = prop_const.PropConst(prop_const.define_beta_fun_NLPM750())
w  = np.linspace(1.3, 3.2, 200)
plot_details_prop_const(w, pc.vg(w), pc.beta2(w))

with zero-dispersion points

w_Z1 = pc.find_root_beta2(1.4, 1.7)
w_Z2 = pc.find_root_beta2(2.2, 2.5)

print('w_Z1 = ', w_Z1)
print('w_Z2 = ', w_Z2)

Out:

w_Z1 =  1.4907331965874615
w_Z2 =  2.385682823499155

1.2.1.2. ESM

pc = prop_const.PropConst(prop_const.define_beta_fun_ESM())
w  = np.linspace(1., 3.5, 200)
plot_details_prop_const(w, pc.vg(w), pc.beta2(w))

# sphinx_gallery_thumbnail_number = 2

with zero-dispersion point

w_Z1 = pc.find_root_beta2(1.5, 2.0)

print('w_Z1 = ', w_Z1)

Out:

w_Z1 =  1.7408233167097933

1.2.1.3. ZBLAN

pc = prop_const.PropConst(prop_const.define_beta_fun_ZBLAN())
w  = np.linspace(0.5, 5., 200)
plot_details_prop_const(w, pc.vg(w), pc.beta2(w))

with zero-dispersion point

w_Z1 = pc.find_root_beta2(1., 1.3)

print('w_Z1 = ', w_Z1)

Out:

w_Z1 =  1.1756242446612304

1.2.1.4. Silicon slot waveguide

pc = prop_const.PropConst(prop_const.define_beta_fun_slot_waveguide_Zhang2012())
w  = np.linspace(0.86, 1.37, 200)
plot_details_prop_const(w, pc.vg(w), pc.beta2(w))

with four zero-dispersion points

w_Z1 = pc.find_root_beta2(0.9, 0.95)
w_Z2 = pc.find_root_beta2(0.95, 1.05)
w_Z3 = pc.find_root_beta2(1.1, 1.2)
w_Z4 = pc.find_root_beta2(1.25, 1.3)

print('w_Z1 = ', w_Z1)
print('w_Z2 = ', w_Z2)
print('w_Z3 = ', w_Z3)
print('w_Z4 = ', w_Z4)

Out:

w_Z1 =  0.9080704496314868
w_Z2 =  0.9972144603743801
w_Z3 =  1.1596715570267406
w_Z4 =  1.2904820787647622