##
Electromagnetic Wave MATLAB Library

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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*

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#### 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).

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