Electromagnetic Wave MATLAB Library

Effective Propagation Constant for Mie Scatterers Based on QCA

Reference:

Chapter 6 of Scattering of Electromagnetic Waves: Advanced Topics

Chapter 10 of Scattering of Electromagnetic Waves: Numerical Simulations

Main Program

qcamie.m calculates the effective propagation constant in a dense medium consisting of Mie scatterers using the quasi-crystalline approximation in the T-matrix formulation. The Mie scatterers are distributed according to the Percus-Yevick pair distribution function.

• K_eff = qcamie(freq, epsilon_p, f, k0a, n_max)

Input Parameters

• freq: frequency in GHz
• epsilon_p: particle complex relative permittivity
• f: fractional volume of particles
• k0a: size parameter (this can be a vector)
• n_max: maximum spherical multipole used

Input File

• pair.dat contains the pair distribution function. The first column of the file gives the separation normalized by diameter of particle. The second column gives the pair distribution function g(r). The Percus-Yevick pair distribution function can be calculated using pypdf.m.

Output

• K_eff: complex number (per cm) which denote the effective propagation constant at each k0a.

Example

The figures below are generated with the following parameters:

freq=37 GHz, epsilon_p=3.2375+i0.18, f=0.2, ka=linspace(0.01,2.5,40), n_max=4

Note that the (normalized) phase velocity is k/real(K_eff) while the loss tangent is 2*imag(K_eff)/real(K_eff).