Green's Tensors

GreenTensors is a module aimed to compute the renormalized (dimensionless) electric and magnetic Green's tensors. To learn more about the renormalization and the expressions that are used, please see the Theory pdf.

Functions Documentation

Renormalized Green's Tensors

Main.CoupledElectricMagneticDipoles.GreenTensors.G_e_renorm — Function

G_e_renorm(kr1,kr2)

Computes the renormalized (dimensionless) electric Green's tensor between two positions r1 and r2, where the inputs are the positions multiplied by the host medium wave number kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.G_m_renorm — Function

G_m_renorm(kr1,kr2)

Computes the renormalized (dimensionless) magnetic Green's tensor between two position r1 and r2, where the inputs are the positions multiplied by the host medium wave number kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.G_em_renorm — Function

G_em_renorm(kr1,kr2)

Computes the renormalized (dimensionless) electric and magnetic Green's tensors between two positions r1 and r2, where the inputs are the positions multiplied by the host medium wave number kr1 and kr2. The outputs are two dimensionless 3x3 complex matrix (electric and magnetic Green's tensor respectively).

Main.CoupledElectricMagneticDipoles.GreenTensors.G_em_far_field_renorm — Function

G_em_far_field_renorm(kr1,kr2)

Computes the renormalized (dimensionless) electric and magnetic Green's in the far field approximation tensors between two positions r1 and r2, where the inputs are the positions multiplied by the host medium wave number kr1 and kr2.Note that is is only valid for $kr_1>>kr_2$ and $kr_1>>1$. The outputs are two dimensionless 3x3 complex matrix (electric and magnetic Green's tensor respectively).

Derivatives of the Renormalized Green's Tensors

Main.CoupledElectricMagneticDipoles.GreenTensors.dxG_e_renorm — Function

dxG_e_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) electric Green's tensor with respect to the kx component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.dyG_e_renorm — Function

dyG_e_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) electric Green's tensor with respect to the ky component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.dzG_e_renorm — Function

dzG_e_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) electric Green's tensor with respect to the kz component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.dxG_m_renorm — Function

dxG_m_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) magnetic Green's tensor with respect to the kx component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.dyG_m_renorm — Function

dyG_m_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) magnetic Green's tensor with respect to the ky component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.dzG_m_renorm — Function

dzG_m_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) magnetic Green's tensor with respect to the kz component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix.

Main.CoupledElectricMagneticDipoles.GreenTensors.dxG_em_renorm — Function

dxG_em_renorm(kr1,kr2)
Computes the derivative of the renormalized (dimensionless) electric and magnetic Green's tensors with respect to the `kx` component of `kr1` between two positions (multiplied by the host medium wavenumber)  `kr1` and `kr2`.
The output is a dimensionless 3x3 complex matrix (electric and magnetic Green's tensor respectively).

Main.CoupledElectricMagneticDipoles.GreenTensors.dyG_em_renorm — Function

dyG_em_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) electric and magnetic Green's tensors with respect to the ky component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix (electric and magnetic Green's tensor respectively).

Main.CoupledElectricMagneticDipoles.GreenTensors.dzG_em_renorm — Function

dzG_em_renorm(kr1,kr2)

Computes the derivative of the renormalized (dimensionless) electric and magnetic Green's tensors with respect to the kz component of kr1 between two positions (multiplied by the host medium wavenumber) kr1 and kr2. The output is a dimensionless 3x3 complex matrix (electric and magnetic Green's tensor respectively).

Utility Functions

Main.CoupledElectricMagneticDipoles.GreenTensors.denormalize_G_e — Function

denormalize_G_e(Ge,knorm)

Passes from a dimensionless electric Green's tensor Ge to a Green's tensor with units of length⁻¹ by multiplying by a factor $k/(4\pi)$. knorm is the wavenumber in the host medium $k$.

Main.CoupledElectricMagneticDipoles.GreenTensors.denormalize_G_m — Function

denormalize_G_m(Gm,knorm)

Passes from a dimensionless magnetic Green's tensor Gm to a Green's tensor with units of length⁻² by multiplying by a factor $k^2/(4\pi)$. knorm is the wavenumber in the host medium $k$.