1.7 Example 7: using functions to define complex structures

In this final example we will illustrate how we can simplify the definition of non-trivial structures by using Python functions, rather than explicitly specifying the refractive index profile.

The following code shows how we automatically generate a staircase approximation of a parabolic refractive index profile.

#!/usr/bin/env python

####################################################################
#
# Parabolic refractive index profile.
#
####################################################################

from camfr import *

set_lambda(1)
set_N(20)
set_polarisation(TE)

w = 5.0  # width of waveguide

set_upper_PML(-0.1)
set_lower_PML(-0.1)

# Define parabolic refractive index profile.

def index(x):
    max_n = 3.5  # max refractive index
    a = 0.1      # slope
    n = max_n - a * pow(w / 2.0 - x, 2)
    if n < 1:
        return 1
    else:
        return n

# Construct a staircase approximation.

expr = Expression()
materials = [] 
steps = 10
for i in range(steps):
    x = i * w / steps
    m = Material(index(x + 0.5 * w / steps))
    materials.append(m)
    d = w / steps 
    expr.add(m(d))

slab = Slab(expr)

# Compare continuous and staircase profile.

outfile = file("tutorial7.out",'w')

steps2 = 100
for i in range(steps2):
    x = i * w / steps2
    print >> outfile, x, index(x), slab.n(Coord(x, 0, 0)).real

outfile.close()

The lines after def index(x): define a function which takes as argument the x coordinate and returns the refractive index at this position in a certain parabolic refractive index profile. This code also illustrates the use of conditionals, and stresses once again the importance of indentation in Python.

The next block of code creates the expression expr, which will describe the staircase approximation of the index profile. The width of the waveguide will be divided in steeps piecewise constant parts.

First, an empty expression is created: expr = Expression(). This expression is gradually filled in a loop while i runs from 0 to steps-1.

A material m is created with the refractive index from the middle of the current step of the index profile. Finally, a term is added to the expression which describes the current step, consisting of material m with thickness d: expr.add(m(d)).

At the end of the loop, this expression is used to define a slab, which can be used in subsequent calculations : slab = Slab(expr).

Very important to notice is that we keep hold of the materials m we create in the loop, by first defining an empty list materials = [], to which we add each material: materials.append(m).

The reason for this lies in Python's garbage collection. Without the list materials to hold on to the materials, Python will see m as just a temporary variable, which it will deallocate and garbage collect after the loop has finished. Since we still need these materials in the subsequent calculations, we have to tell Python not to free them by storing them in a list at the top level in the source code.

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