Mueller Matrix Applied to Detection and Identification of Bio-Medical Materials Possessing Chirality

E. Bahar (USA)


Bio-electromagnetics, Wave Propagation 475-042 207


All sixteen Mueller Matrix elements of Bio-Medical Materials measured by an optical polarimetric scatterometer are examined to develop discrimination algorithms. Special attention was given to the eight quasi off diagonal scattering elements of the Mueller Matrix in order to examine the feasibility of bio-medical identification. Since bio-medical materials possess some degree of chirality, the specific impact of chirality on the Mueller Matrix elements is analyzed extensively. It is shown that (to within first order in chirality) only the eight quasi off diagonal elements of the Mueller Matrix are effected by the chiral property of the bio-medical materials. This reinforces the experimental observations from previous scattering experiments that the quasi off diagonal Mueller Matrix elements could provide a basis for bio-medical detection and identification. The analysis provides the specific relationship between the quasi off diagonal elements and the degree of chirality of the bio medical materials, in order to determine whether the chiral effects are sufficiently large to provide the accuracy necessary to conduct species-level discrimination in the presence of spurious (noise) contributions due to surface roughness, etc. The specific dependence of scattering due to chirality upon frequency and angle of incidence is also determined. 1. Maxwell Equations and the Drude – Born – Fedorov Constitutive Relations Assuming exp( )i tω time excitations Maxwells Equations are 0D∇⋅ = , 0B∇⋅ = , E j B Kω∇× = − − , H j D Jω∇× = + (1) in which D and B are the electric and magnetic flux densities respectively. The electric and magnetic fields are E and H respectively. The electric and the (dual) magnetic sources J and K respectively are assumed here to be z directed and independent of the variable z. Thus the fields are functions of x and y only. The Drude – Born – Fedorov constitutive relations for chiral media are ( )D E Eε β= + ∇× , ( )B H Hµ β= + ∇× (2) in which ε and µ are the permittivity and permeability respectively and β is the chirality parameter. The canonical solutions for chiral media are the right and left circular polarized waves 1Q and 2Q respectively. Thus the magnetic and electric fields can be expressed as follows: 1 2H Q Q= + , ( )1 2E j Q Qη= − − (3) where ( ) 1/2 / 1/η µ ε ζ= = is the characteristic impedance of the achiral host ( ), , 0µ β∈ = . The sources of the canonical solutions 1Q and 2Q are obtained by setting J j Kζ= − and J j Kζ= , respectively. Since the line sources are z directed, the x and y components of 1Q and 2Q can be obtained from their z components that satisfy the following pairs of wave equations for sources that excite right and left circular polarized waves respectively ( ) ( ) 2 2 2 1 1 1 1 2 1 0 2 2 1 2 1 / / , 0 z z z z Q Q j K k j K x x y y k Q Q γ ζγ ζγ δ δ γ ∇ + = = ′− ′− ∇ + = (4) and 2 2 1 1 1 0z z Q Qγ∇ + = , ( ) ( ) 2 2 2 1 2 1 2 2 2 0 / / z Q Q j K k j K x x y y k γ ζγ ζγ δ δ ∇ + = = ′ ′− − 5) in which 1γ and 2γ are the wave numbers for the right and left circular polarized waves

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