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.


Slab.png
Download Sample Configuration 1 (Slab)


Slab.png
Download Sample Configuration 2 (Bragg mirror cavity)

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

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:
* 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