RSE for spherically symmetric inhomogeneous systems - Version 1.0

Usage Instructions

• Option 1 - Executable
• Installation:
  
• Install MATLAB Runtime compiler version R2019b
• Download the compressed executable
• Unpack the executable
• Usage
  
• Run RSE.exe
• Enter the parameters of the basis system (homogeneous sphere)
• The number of modes N determine the spectral range of coverage and the accuracy. For increasing N the accuracy of a given mode increases, and the maximum value of wavenumber that is calculated also increases.
  
• Enter the parameters of the perturbed system
  
• The permittivity and permeability of the perturbed system is given by a power law function:
  permittivity = sum_n b_(n-1) r^(n-1)
  permeability = sum_n b_(n-1) r^(n-1)
  where n is row number, and the coefficients a_(n-1) are entered in the table.
  
• The start and end coordinate of the perturbation is given as ratio with respect to the radius (R) of the basis sphere. For example, setting start=0 and end=1 means that the perturbation is across the whole sphere. Setting start=0.5 and end=1 means that the perturbation is limited to the outer shell (of thickness 0.5R) of the basis sphere.
  
• The 'scaling' options scales all Bessel and Hankel functions by an exponential factor (see MATLAB documentation). This is needed for 80<L as otherwise numerical inaccuracies occur due to Bessel function values growing. The wavenumber values are independent of the scaling factor. The normalisation coefficient of the field (see output) is affected by the scaling, and scaled by the exponential factor.
  
• The output is a '.mat' MATLAB data file which contains the following data:
• k_n: basis eigenvalues (eigenwavenumbers)
  
• A_n: normalisation constant of basis eigenmodes
• k_rse: perturbed eigenvalues (eigenwavenumbers)
• a_n: expansion coefficient of resonant-state fields
• b_n: expansion coefficient of static mode fields
• k_n_s: basis eigenvalue of static modes
• A_n_s: normalisation constant of basis static modes
• In addition, it also contains some of the input data for reference
• The '.mat' file can be opened in MATLAB, or with the free software GNU Octave
• The perturbed eigenvalues 'k_rse'  are also saved in a '.txt' file for easier access
  
• Option 2 - MATLAB code
• Download the MATLAB code
• Unpack the compressed files
• The main RSE function ('Frse') is contained in the matlab file 'Frse.m'
  
• The 'run_Frse.m' contains examples on how to call the function 'Frse'
• Additionally, based on the output from 'run_Frse.m' the matlab file 'PerturbedField.m' can be used to plot the field of the perturbed modes