B4x4

B4x4 is a module for optical simulation of cholesteric liquid crystals based on Berreman 4x4 matrix method. It sits on top of Berreman4x4 created by Olivier Castany. While Berreman4x4 is flexible and fully capable of complex simulations of stratified anisotropic media, it tends to lack user-friendliness. B4x4 aims to provide a straightforward interface by focusing its scope to simple cholesteric liquid crystals.

Setup

B4x4 has been tested with Python 2.7. If you don't have Python installed, Anaconda2 is recommended because it includes all the required modules.

Initialisation

B4x4.py and Berreman4x4.py have to be in the Python search path, see here for instructions if you don't know what that means. From a Python interactive session, (e.g. in terminal, iPython notebook, etc.) run the following commands.

import B4x4
sim = B4x4.Simulator()

Simulating the reflectance of a cholesteric liquid crystal

To run simulations,

result_left = sim.calculateL()
result_left.plot() #plotting result_left.spectrum against B4x4.wavelength(result_left.settings).

This figure shows the reflection spectrum of the simulated cholesteric liquid crystal, with left circularly polarized light (LCP) illumination and detection. This simulation assumes a left handed helix of the cholesteric structure, therefore a prominent peak is found in the reflectance of LCP. To simulate right circularly polarized light,

result_right = sim.calculateR()
result_right.plot()

In this case, there is very little light reflected and fringes are present instead of a prominent peak.

Changing parameters

The default parameters can be displayed by

sim.settings

In [4]: sim.settings
Out[4]: 
{'angle': 0,
 'lbda_max': 800,
 'lbda_min': 400,
 'nSubstrate': 1.59,
 'nSuperstrate': 1,
 'ne': 1.586,
 'no': 1.524,
 'pitch': 190,
 'points': 101,
 'slices': 23,
 'stack': 10}

The parameters are described in the docstring. iPython allows easy access to the docstring, simply put a question mark after the object and press enter.

sim?
# for plain python, use dir(sim)

In [5]: sim?
Type:        Simulator
String form: <B4x4.Simulator object at 0x10fcd6f50>
File:        ~/Documents/Scripts/Python/Berreman4x4/B4x4.py
Docstring:
Performes simulations using properties stored in class instances.
The default parameteres are based on Dumanli et. al.ACS Appl. Mater. Interfaces 2014, 6, 12302,
which is suitable for simulating dry wood pulp CNC films.

Methods
  calculateL: Returns instance of Spectrum containing LCP reflectance.
  calculateR: Same as calculateL but for RCP reflectance.
  matrix: Under construction.

Properties
  pitch:        pitch in nm (180 degree twist)
  no:           refractive index of ordinary ray
  ne:           refractive index of extraordinary ray
  nSuperstrate: refractive index of superstrate (air: n = 1)
  nSubstrate:   refractive index of suberstrate (PS: n = 1.59, SiO2: n=1.55)
  stack:        number of pitches (180 degree twist) in the structure
  angle:        angle of incidence in degrees
  lbda_min:     wavelength min (in meters)
  lbda_max:     wavelength max (in meters)
  points:       number of data points in simulation
  slices:       number of discrete anisotropic layers per 180 twist

Attribute
  settings:     All the above properties are stored here.

To change the parameters of the simulation,

sim.pitch = 230
sim.stack = 20
result_another = sim.calculateL()
result_another.plot()

It can be seen that modifying the pitch and stack has changed the reflection spectrum, especially the peak wavelength and the peak reflectance, which have increased.

Batch simulation

To run simulations in a batch, use the matrix method.

sim.pitch = 190
sim.stack = 10
result_matrix = sim.matrix('angle',0,90,1)
#vary angle of incidence between 0 to 90 degrees, 1 degree per step
result_matrix.image()

Saving results

To save the spectra,

result_left.save('left_reflection.txt')
result_right.save('right_reflection.txt')
result_another.save('another_reflection.txt')
result_matrix.save('matrix.txt')

which will produce txt files that contains the spectra and other information in the current folder.

Related publications

This package was used for the simulation in the following publications.

Dumanli, Ahu Gumrah, et al. "Controlled, Bio‐inspired Self‐Assembly of Cellulose‐Based Chiral Reflectors." Advanced optical materials 2.7 (2014): 646-650.
Dumanli, Ahu Gümrah, et al. "Digital color in cellulose nanocrystal films." ACS applied materials & interfaces 6.15 (2014): 12302-12306.

gkamita/B4x4