prysm.thinfilm#

Tools for performing thin film calculations.

prysm.thinfilm.brewsters_angle(n0, n1, deg=True)#

Compute the Brewster’s angle at a given interface.

Parameters:

  • n0 (float) – refractive index on the “left” of the boundary

  • n1 (float) – refractive index on the “right” of the boundary

  • deg (bool, optional) – if True, convert output to degrees

prysm.thinfilm.critical_angle(n0, n1, deg=True)#

Minimum angle for total internal reflection at an interface.

Parameters:

  • n0 (float) – index of refraction of the “left” material

  • n1 (float) – index of refraction of the “right” material

  • deg (bool, optional) – if true, returns degrees, else radians

Returns:

the angle in degrees at which TIR begins to occur

Return type:

float

prysm.thinfilm.snell_aor(n0, n1, theta, deg=True)#

Compute the angle of refraction using Snell’s law.

Parameters:

  • n0 (float) – index of refraction of the “left” material

  • n1 (float) – index of refraction of the “right” material

  • theta (float) – angle of incidence, in degrees if deg=True

  • deg (bool, optional) – if True, theta is interpreted as an angle in degrees

Returns:

angle of refraction

Return type:

float

prysm.thinfilm.fresnel_rs(n0, n1, theta0, theta1)#

Compute the “r sub s” fresnel coefficient.

This is associated with reflection of the s-polarized electric field.

Parameters:

  • n0 (float) – refractive index of the “left” material

  • n1 (float) – refractive index of the “right” material

  • theta0 (float) – angle of incidence, radians

  • theta1 (float) – angle of reflection, radians

Returns:

the fresnel coefficient “r sub s”

Return type:

float

prysm.thinfilm.fresnel_ts(n0, n1, theta0, theta1)#

Compute the “t sub s” fresnel coefficient.

This is associated with transmission of the s-polarized electric field.

Parameters:

  • n0 (float) – refractive index of the “left” material

  • n1 (float) – refractive index of the “right” material

  • theta0 (float) – angle of incidence, radians

  • theta1 (float) – angle of refraction, radians

Returns:

the fresnel coefficient “t sub s”

Return type:

float

prysm.thinfilm.fresnel_rp(n0, n1, theta0, theta1)#

Compute the “r sub p” fresnel coefficient.

This is associated with reflection of the p-polarized electric field.

Parameters:

  • n0 (float) – refractive index of the “left” material

  • n1 (float) – refractive index of the “right” material

  • theta0 (float) – angle of incidence, radians

  • theta1 (float) – angle of reflection, radians

Returns:

the fresnel coefficient “r sub p”

Return type:

float

prysm.thinfilm.fresnel_tp(n0, n1, theta0, theta1)#

Compute the “t sub p” fresnel coefficient.

This is associated with transmission of the p-polarized electric field.

Parameters:

  • n0 (float) – refractive index of the “left” material

  • n1 (float) – refractive index of the “right” material

  • theta0 (float) – angle of incidence, radians

  • theta1 (float) – angle of refraction, radians

Returns:

the fresnel coefficient “t sub p”

Return type:

float

prysm.thinfilm.characteristic_matrix_p(lambda_, d, n, theta)#

Compute the characteristic matrix M_j^p for a layer of a material stack and p-polarized light.

Uses (4.49) to compute (4.55) from BYU optics book, edition 2015

Parameters:

  • lambda (float) – wavelength of light, microns

  • d (float) – thickness of the layer, microns

  • n (float or complex) – refractive index of the layer

  • theta (float) – angle of incidence, radians

Returns:

a 2x2 matrix

Return type:

numpy.array

prysm.thinfilm.characteristic_matrix_s(lambda_, d, n, theta)#

Compute the characteristic matrix M_j^p for a layer of a material stack and s-polarized light.

Uses (4.49) to compute (4.55) from BYU optics book, edition 2015

Parameters:

  • lambda (float) – wavelength of light, microns

  • d (float) – thickness of the layer, microns

  • n (float or complex) – refractive index of the layer

  • theta (float) – angle of incidence, radians

Returns:

a 2x2 matrix

Return type:

numpy.array

prysm.thinfilm.multilayer_matrix_p(n0, theta0, characteristic_matrices, nnp1, theta_np1)#

Reduce a multilayer problem to give the 2x2 matrix A^p.

Computes (4.58) from BYU optics book.

Parameters:

  • n0 (float or complex) – refractive index of the first medium

  • theta0 (float) – angle of incidence on the first medium, radians

  • characteristic_matrices (iterable of ndarray each of which of shape 2x2) – the characteristic matrices of each layer

  • nnp1 (float or complex) – refractive index of the final medium

  • theta_np1 (float) – angle of incidence on final medium, radians

Returns:

2x2 matrix A^s

Return type:

ndarray

prysm.thinfilm.multilayer_matrix_s(n0, theta0, characteristic_matrices, nnp1, theta_np1)#

Reduce a multilayer problem to give the 2x2 matrix A^s.

Computes (4.62) from BYU optics book.

Parameters:

  • n0 (float or complex) – refractive index of the first medium

  • theta0 (float) – angle of incidence on the first medium, radians

  • characteristic_matrices (iterable of ndarray each of which of shape 2x2) – the characteristic matrices of each layer

  • nnp1 (float or complex) – refractive index of the final medium

  • theta_np1 (float) – angle of incidence on final medium, radians

Returns:

2x2 matrix A^s

Return type:

ndarray

prysm.thinfilm.rtot(Amat)#

Compute rtot, the equivalent total fresnel coefficient for a multilayer stack.

Parameters:

Amat (ndarray) – 2x2 array

Returns:

the value of rtot, either s or p.

Return type:

float or complex

prysm.thinfilm.ttot(Amat)#

Compute ttot, the equivalent total fresnel coefficient for a multilayer stack.

Parameters:

Amat (ndarray) – 2x2 array

Returns:

the value of rtot, either s or p.

Return type:

float or complex

prysm.thinfilm.multilayer_stack_rt(indices, thicknesses, wavelength, polarization, substrate_index, aoi=0, ambient_index=1)#

Compute r and t for a given stack of materials.

Parameters:

  • indices (ndarray) – refractive index for each film layer. The first axis is the layer axis; any trailing axes are vectorized calculation dimensions.

  • thicknesses (ndarray) – thickness of each film layer, microns. Must be broadcastable to the same shape as indices.

  • wavelength (float) – wavelength of light, microns

  • polarization (str, {'p', 's'}) – the polarization state

  • substrate_index (float or ndarray) – refractive index of the medium after the final film layer. May be a scalar, or broadcastable to the trailing dimensions of indices and thicknesses.

  • aoi (float, optional) – angle of incidence, degrees

  • ambient_index (float, optional) – The refractive index the film is immersed in, defaults to 1 (vacuum)

Returns:

r, t coefficients

Return type:

(float, float)