Input Fields

plane_wave_e(krf;khat=[0,0,1],e0=[1,0,0])

Computes the electric field of a monochromatic plane wave evaluated at a set of dimensionless positions krf. khat is the direction of propagation and e0 is the polarization. The user is responsible for using physical inputs. krf is a $N\times 3$ float array. The output is a $N\times 3$ complex array representing the electric field at each of the positions in the krf array.

plane_wave_e_m(krf;khat=[0,0,1],e0=[1,0,0])

Computes the electric and magnetic fields of a monochromatic plane wave evaluated at a set of dimensionless positions krf. khat is the direction of propagation and e0 is the polarization. The user is responsible for using physical inputs. krf is a $N\times 3$ float array. The output is a $N\times 6$ complex array representing the electric and magnetic fields at each of the positions in the krf array.

point_dipole_e(krf, krd, dip, e0_const=1)

Computes the electric field emitted by an electric point dipole.

Arguments

• krf: 2D float array of size $N\times 3$ containing the dimensionless positions $k\mathbf{r}$ where the field is computed.
• krd: 1D float array of size 3 containing the dimensionless position $k\mathbf{r_d}$ where the source is located.
• dip: integer defining the dipole moment (dip = 1,2,3 is an electric dipole along x,y,z respectively)

or complex array of size 3 with the components for the electric dipole moment.

• e0: float with the modulus of dip.

Outputs

• e_dipole: 2D $N\times 3$ complex array with the electromagnetic field.

point_dipole_e_m(krf, krd, dip, e0=1)

Computes the electric and magnetic fields emitted by an electric and/or magnetic point dipole.

Arguments

• krf: 2D float array of size $N\times 3$ containing the dimensionless positions $k\mathbf{r}$ where the field is computed.
• krd: 1D float array of size 3 containing the dimensionless position $k\mathbf{r_d}$ where the source is located.
• dip: integer defining the dipole moment (dip = 1,2,3 is an electric dipole along x,y,z respectively and dip = 4,5,6 is a magnetic dipole along x,y,z respectively)

or complex array of size 6 with the first 3 components for the electric dipole moment and the last 3 components for the magnetic dipole moment.

• e0: float with the modulus of dip.

Outputs

• phi_dipole: 2D $N\times 6$complex array with the electromagnetic fields at each position.

gaussian_beam_e(krf, kbw0,n,m; n = 0, m = 0, kind = "hermite", e0 = 1, kmax = nothing, maxe=Int(5e3))

Computes the electric field distribution of a Gaussian, Hermite-Gaussian and Laguerre-Gaussian beam that propagates along the z-axis and where the electric field is polarized along the x-axis (polarized electric). By default, the Gaussian beam profile is calculated. For another polarization just rotate the field in the xy-plane. Also, for a polarized magnetic field, exchange E with ZH and H with -E.

Arguments

• krf: 2D float array of size $N\times 3$ containing the dimensionless positions $k\mathbf{r}$ where the field is computed.
• kbw0: float with the dimensionless beam waist radius ($k\omega_0$, where $\omega_0$ is the beam waist radius).
• n: int with the order of the beam.
• m: int with the degree of the beam.
• kind: string with the kind of beam ("hermite" or "laguerre").
• e0: float with the modulus of the electric field at the origin of coordinates of the theoretical field (including evanescent waves).
• kmax: float setting the limit of the radial integration (it should be kmax < 1).
• maxe: maximum number of evaluations in the adaptive integral (see Cubature.jl for more details).

Outputs

• e_gauss: 2D complex array of size $N\times 3$ with the value of the electric field at each positions.

gaussian_beam_e_m(krf, kbw0,n,m; n = 0, m = 0, kind = "hermite", e0 = 1, kmax = nothing, maxe=Int(5e3))

Computes the electromagnetic field distribution of a Gaussian, Hermite-Gaussian and Laguerre-Gaussian beam that propagates along the z-axis and where the electric field is polarized along the x-axis (polarized electric). By default, the Gaussian beam profile is calculated. For another polarization just rotate the field in the xy-plane. Also, for a polarized magnetic field, exchange E with ZH and H with -E.

Arguments

• krf: 2D float array of size $N\times 3$ containing the dimensionless positions $k\mathbf{r}$ where the field is computed.
• kbw0: float with the dimensionless beam waist radius ($k\omega_0$, where $\omega_0$ is the beam waist radius).
• n: int with the order of the beam.
• m: int with the degree of the beam.
• kind: string with the kind of beam ("hermite" or "laguerre").
• e0: float with the modulus of the electric field at the origin of coordinates of the theoretical field (including evanescent waves).
• kmax: float setting the limit of the radial integration (it should be kmax < 1).
• maxe: maximum number of evaluations in the adaptive integral (see Cubature.jl for more details).

Outputs

• phi_gauss: 2D complex array of size $N\times 6$ with the value of the electric and magnetic fields at each positions.

d_plane_wave_e(kr;khat=[0,0,1],e0=[1,0,0])

Computes the spatial derivatives of an electric field generated with plane_wave_e (the arguments are the same as for plane_wave_e). Outputs three 2D arrays of size $N\times 3$ containing the electric field derivatives with respect k*x, k*y and k*z.

d_plane_wave_e_m(kr;khat=[0,0,1],e0=[1,0,0])

Computes the spatial derivatives of an electromagnetic field generated with plane_wave_e_m (the arguments are the same as for plane_wave_e_m). Outputs three 2D arrays of size $N\times 6$ containing the electric and magnetic fields derivatives with respect of k*x, k*y and k*z.

d_point_dipole_e(krf, krd, dip, e0=1)

Computes the spatial derivatives of an electric field generated with point_dipole_e (the arguments are the same as for point_dipole_e). Outputs three 2D arrays of size $N\times 3$ containing the electric field derivatives with respect k*x, k*y and k*z.

d_point_dipole_e_m(krf, krd, dip, e0=1)

Computes the spatial derivatives of an electromagnetic field generated with point_dipole_e_m (the arguments are the same as for point_dipole_e_m). Outputs three 2D arrays of size $N\times 6$ containing the electric and magnetic fields derivatives with respect of k*x, k*y and k*z.

d_gaussian_beam_e(krf, kbw0; n = 0, m = 0, kind = "hermite", e0 = 1, kmax = nothing, maxe=Int(5e3))

Computes the spatial derivatives of an electric field generated with gaussian_beam_e (the arguments are the same as for gaussian_beam_e_m). Outputs three 2D arrays of size $N\times 3$ containing the electric field derivatives with respect k*x, k*y and k*z.

d_gaussian_beam_e_m(krf, kbw0; n = 0, m = 0, kind = "hermite", e0 = 1, kmax = nothing, maxe=Int(5e3))

Computes the spatial derivatives of an electromagnetic field generated with gaussian_beam_e_m (the arguments are the same as for gaussian_beam_e_m). Outputs three 2D arrays of size $N\times 6$ containing the electric and magnetic field derivatives with respect of k*x, k*y and k*z.