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SCATMECH > Classes and Functions >
Polarization >
JonesMatrix
class JonesMatrix
The class JonesMatrix represents a Jones matrix in a
Jones representation of polarization states. Arithmetic
operations between Jones matrices and Jones vectors,
various properties of a Jones matrix, and transformation
operations are defined.
Include file:
#include "mueller.h"
Source code:
jmatrix.cpp
See also:
SCATMECH Home,
Conventions, MuellerMatrix, JonesVector, StokesVector
C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).
H.C. van de Hulst, Light Scattering by Small Particles, (Dover, New York, 1981).
R.A. Chipman, "Polarimetry." in Handbook of Optics, (McGraw-Hill, New York, 1995).
Definition of public
elements:
class JonesMatrix {
public:
JonesMatrix();
JonesMatrix(const JonesMatrix& x);
JonesMatrix(const COMPLEX& pp,const COMPLEX& ss,const COMPLEX& ps,const COMPLEX& sp);
explicit JonesMatrix(const MuellerMatrix& x);
JonesMatrix& operator=(const JonesMatrix& x);
JonesMatrix operator*(const JonesMatrix& matrix) const;
JonesMatrix operator*(const COMPLEX& x) const;
friend JonesMatrix operator*(const COMPLEX& x,const JonesMatrix& y);
JonesMatrix operator/(const COMPLEX& x) const;
JonesMatrix& operator*=(const JonesMatrix& a);
JonesMatrix& operator*=(const COMPLEX& a);
JonesMatrix& operator/=(const COMPLEX& a);
JonesVector operator*(const JonesVector& a) const;
JonesMatrix operator+(const JonesMatrix& a) const;
JonesMatrix operator-(const JonesMatrix& a) const;
JonesMatrix operator+=(const JonesMatrix& a);
JonesMatrix operator-=(const JonesMatrix& a);
JonesMatrix operator-() const;
COMPLEX& operator[](int i);
const COMPLEX& operator[](int i) const;
JonesMatrix rotate(double angle) const;
JonesMatrix transpose() const;
COMPLEX& PP();
COMPLEX PP() const ;
COMPLEX& SS();
COMPLEX SS() const ;
COMPLEX& PS();
COMPLEX PS() const ;
COMPLEX& SP();
COMPLEX SP() const ;
};
ostream& operator<<(ostream& os,const JonesMatrix& j);
istream& operator>>(istream& is, JonesMatrix& j);
JonesMatrix()
Null constructor.
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JonesMatrix(const JonesMatrix& x)
Copy constructor.
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JonesMatrix(const COMPLEX& pp,const COMPLEX& ss,const COMPLEX& ps,const COMPLEX& sp)
Explicit constructor with COMPLEX elements. Note
that the order of the parameters is important. ps
is the p to s matrix element, while sp is the s to
p matrix element.
Example:
JonesMatrix a(COMPLEX(1,0),COMPLEX(1,0),0.,0.);
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explicit JonesMatrix(const MuellerMatrix& x)
Explicit constructor that converts a MuellerMatrix to a
JonesMatrix. This conversion is "improper" since a
MuellerMatrix does not
maintain phase information and allows for depolarization.
The result is the JonesMatrix that corresponds to
the part of the MuellerMatrix that is
polarization preserving.
Example:
MuellerMatrix m;
JonesMatrix j(m);
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JonesMatrix& operator=(const JonesMatrix& x)
The assignment operator.
Example:
JonesMatrix j1,j2;
j1=j2;
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JonesMatrix operator*(const JonesMatrix& matrix) const
Multiplication of one JonesMatrix by another.
Example:
JonesMatrix j1,j2,j3;
j3=j1*j2;
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Multiplication and division of a JonesMatrix by a
scalar.
Example:
COMPLEX scalar;
JonesMatrix matrix;
matrix = matrix * scalar;
matrix = scalar * matrix;
matrix *= scalar;
matrix = matrix / scalar;
matrix = scalar / matrix; // Not allowed.
matrix /= scalar;
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JonesVector operator*(const JonesVector& a) const
Left multiplication of a JonesVector by a
JonesMatrix.
Example:
JonesMatrix matrix;
JonesVector vector;
vector = matrix*vector;
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Addition and subtraction of two JonesMatrix
objects.
Example:
JonesMatrix matrix1,matrix2,matrix3;
matrix3=matrix1+matrix2;
matrix3=matrix1-matrix2;
matrix1+=matrix2;
matrix1-=matrix2;
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JonesMatrix operator-() const
Negation of a JonesMatrix.
Example:
JonesMatrix matrix;
matrix= -matrix;
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COMPLEX& operator[](int i)
const COMPLEX& operator[](int i) const
Element referencing operator. The elements are defined in
the example.
Example:
JonesMatrix a;
COMPLEX pp,ss,ps,sp;
a[0]=pp;
a[1]=ss;
a[2]=ps;
a[3]=sp;
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JonesMatrix rotate(const double angle) const
Function that returns a JonesMatrix rotated by
angle clockwise about the direction of
propagation.
Example:
JonesMatrix a,b;
a = b.rotate(45.*PI/180.);
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JonesMatrix transpose() const
Function that returns the transpose of a
JonesMatrix.
Example:
JonesMatrix a,b;
a = b.transpose();
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COMPLEX& PP()
const COMPLEX& PP() const
COMPLEX& SS()
const COMPLEX& SS() const
COMPLEX& PS()
const COMPLEX& PS() const
COMPLEX& SP()
const COMPLEX& SP() const
Element referencing by name. PS() corresponds to the p-in/s-out configuration, and SP() corresponds to the s-in/p-out configuration.
Example:
JonesMatrix a;
a.PP() = COMPLEX(1.,0.);
cout << a.SS() << " " << a.PS() << endl
<< a.SP() << " " << a.PP() << endl;
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ostream& operator<<(ostream& os,const JonesMatrix& j)
Operator to output a JonesMatrix to an output
stream. The result is four complex numbers, separated by commas, and surrounded by parentheses, e.g., ((1,2),(3,4),(5,6),(7,8)).
The order of the values is: P to P, S to S, P to S, S to P.
Example:
JonesMatrix J;
cout << "J = " << J << endl;
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istream& operator>>(istream& is, JonesMatrix& j)
Operator to input a JonesMatrix from an input
stream. The stream should contain four complex numbers, separated by commas, and surrounded by parentheses, e.g., ((1,2),(3,4),(5,6),(7,8)).
The order of the values is: P to P, S to S, P to S, S to P.
Example:
JonesMatrix J;
cin >> J;
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Current SCATMECH version: 7.22 (April 2021)
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