Resonant State Expansion applied to planar open optical systems

M.B. Doost, W. Langbein, and E.A. Muljarov

School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, United Kingdom

This page provides and implementation of the Resonant State Expansion applied to planar open optical systems [2], which is based on the origibnal application [1]. Recently, we have applied the theory also to two-dimenesional systems [3], like optical fibres

Program

We provide here an executable program RSE.exe (for microsoft windows 32 bit) implementing the RSE for one-dimensional (planar) systems. Two sample configurations are available, a slab and a Bragg Microcavity.

Download Sample Configuration 1 (Slab)

Download Sample Configuration 2 (Bragg mirror cavity)

RSE.exe requires two text files from the command line arguments.

The first command line argument is a text file which contains a table of the thickness of each layer of the slab and it's refractive index. We have called this text file 'Pslab.text' in the sample configurations although it can take any name.The refractive index of each layer is equal to n+ik, where i is the unit imaginary number. Accordingly we have labelled the columns of the table thickness, n, and k. The sequence in the table corresponds to their sequence in real space
The second command line argument is a text file with parameters for the RSE. We have called this text file 'Parameters.text' in the sample configurations although it can take any name. There are three parameters that must be labelled as in the sample configurations. These parameters are, in order:

The number of layers making up the planar system
The basis size N, defined in our paper. According to our definition N must be an odd number.
The refractive index of the unperturbed homogeneous slab which must be a real number. Only as many layers as have been specified in the first command line argument text file will be read into RSE.exe. If more or less layers are specified in the second command line argument text file than are contained in the first command line argument text file RSE.exe will behave erratically. If the parameters are miss labelled or place in the wrong order the program will not proceed.

The external boundaries of the perturbed and unperturbed slab are chosen to coincide. The perturbed and unperturbed slabs are surrounded by vacuum. In our sample configurations, the calculation is started from the command line using "RSE.exe Pslab.txt Parameters.txt"

RSE.exe produces two output files:

*_All_poles.dat

*_Accepted_poles.dat

* is the name of the first command line argument to RSE.exe, without it's file type extension.

Output file *_All_poles.dat gives information about all perturbed poles produced by RSE.exe.

Re(a*Chi)	Im(a*Chi)	M	AR(1)	alpha	a*error	F	AR(2)
6.102122e-17	-2.344420e-01	2.293706e-07	1	-4.981052e-01	3.458102e-08	2.548814e+00	0
....

The columns are

Re(a*Chi)	Extrapolated or perturbed Real part of the perturbed wave number* and multiplied by the unperturbed slab half width
Im(a*Chi)	Extrapolated or perturbed Imaginary part of the perturbed wave number* and multiplied by the unperturbed slab half width
M	Absolute error M given by (21) in our paper
AR(1)	True=1, False=0 that state has been accepted by selection criteria (SC) 2 of our paper
alpha	Power law exponent for the given state as defined by (11) of our paper
a*error	Absolute value of the extrapolation of our perturbed wave number to the exact perturbed wave number estimated using the convergence and extrapolation algorithm as defined in (17) and multiplied by the unperturbed slab half width
F	Relative extrapolation error as defined by (18) in our paper
AR(2)	True=1, False=0 that state has been accept by SC 1 of our paper

* Whenever the extrapolation conditions set out in the paper are met we extrapolate the wave number.

Output file *_Accepted_poles.dat only gives information about perturbed poles produced by RSE.exe which are accepted by the at least one of the two SC stated in the paper. The column headers of output file 2 are the same as for output file 1.

When it is impossible to calculate a parameter we assign it the value 10^19 in our tables of results.

References

[1] Brillouin-Wigner perturbation theory in open electromagnetic systems, E. A. Muljarov, W. Langbein and R. Zimmermann, Eurphys. Lett. 92,50010 (2010) DOI: 10.1209/0295-5075/92/50010

[2] Resonant-state expansion applied to planar open optical systems M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 85, 023835 (2012) DOI: 10.1103/PhysRevA.85.023835

[3] Resonant state expansion applied to two-dimensional open optical systems M. B. Doost, W. Langbein, and E. A. Muljarov, submitted to Phys. Rev. A (2013), arXiv:1302.0245v1 [physics.optics] 1 Feb 2013

W. Langbein, Mark Doost, Egor Muljarov, last changes 26/02/2013