Lattice#

class nannos.Lattice(basis_vectors, discretization=(256, 256), truncation='circular', harmonics_array=None)[source]#

A lattice object defining the unit cell.

Parameters:

basis_vectors (tuple) – The lattice vectors \(((u_x,u_y),(v_x,v_y))\). For mono-periodic gratings, specify the x-periodicity with a float a.
discretization (int or tuple of length 2) – Spatial discretization of the lattice. If given an integer N, the discretization will be (N, N).
truncation (str) – The truncation method, available values are “circular” and “parallelogrammic” (the default is “circular”). This has no effect for mono-periodic gratings.
harmonics_array (array of shape (2, nh)) – Array of harmonics. If specified, this is used instead of harmonics generated by the lattice object and nh is deduced from it.

Layer(name='layer', thickness=0, epsilon=1, mu=1, lattice=None, tangent_field=None, tangent_field_type='opt')[source]#

Return a new Layer object.

Parameters:

name (str, optional) – Name of the layer. The default is “layer”.
thickness (float, optional) – Thickness of the layer. The default is 0.
epsilon (complex or array_like, optional) – Relative permittivity. The default is 1.
mu (complex or array_like, optional) – Relative permeability. The default is 1.
lattice (nannos.Lattice, optional) – The lattice object. The default is None.
tangent_field (array_like, optional) – The tangent field. The default is None.
tangent_field_type (str, optional) – Type of tangent field (‘opt’ or ‘fft’). The default is “opt”.

Returns:

The new layer object.

Return type:

nannos.Layer

circle(center, radius)[source]#

Return a boolean mask for a circle.

Parameters:

center (tuple of float) – The center of the circle.
radius (float) – The radius of the circle.

Returns:

The shape mask.

Return type:

array of bool

constant(value)[source]#

Return a new array filled with value.

Returns:: A uniform complex 2D array with shape self.discretization.
Return type:: array like

ellipse(center, radii, rotate=0)[source]#

Return a boolean mask for an ellipse.

Parameters:

center (tuple of float) – The center of the ellipse.
radii (tuple of float) – The radii of the ellipse.
rotate (float) – The rotation of the ellipse in degrees.

Returns:

The shape mask.

Return type:

array of bool

geometry_mask(geom)[source]#

Return a geametry boolean mask discretized on the lattice grid.

Parameters:: geom (Shapely object) – The geometry.
Returns:: The shape mask.
Return type:: array of bool

get_harmonics(nh, sort=False)[source]#

Get the harmonics with a given truncation method.

Parameters:

nh (int) – Number of harmonics.

Returns:

G (list of tuple of integers of length 2) – Harmonics (i1, i2).
nh (int) – The number of harmonics after truncation.

property grid#

Grid in lattice vectors basis.

Returns:: The grid of size equal to the attribute discretization.
Return type:: array like

property matrix#

Basis matrix.

Returns:: Matrix containing the lattice vectors (L1,L2).
Return type:: array like

ones()[source]#

Return a new array filled with ones.

Returns:: A uniform complex 2D array with shape self.discretization.
Return type:: array like

polygon(vertices)[source]#

Return a boolean mask for a polygon.

Parameters:: vertices (array like) – The vertices of the polygon.
Returns:: The shape mask.
Return type:: array of bool

property reciprocal#

Reciprocal matrix.

Returns:: Matrix containing the lattice vectors (K1,K2) in reciprocal space.
Return type:: array like

rectangle(center, widths, rotate=0)[source]#

Return a boolean mask for a rectangle.

Parameters:

center (tuple of float) – The center of the rectangle.
widths (tuple of float) – The widths of the rectangle.

Returns:

The shape mask.

Return type:

array of bool

square(center, width, rotate=0)[source]#

Return a boolean mask for a square.

Parameters:

center (tuple of float) – The center of the square.
width (float) – The width of the square.
rotate (float, optional) – The rotation angle in degrees. Defaults to 0.

Returns:

The shape mask.

Return type:

array of bool

stripe(center, width)[source]#

Return a boolean mask for a stripe along the x-axis.

Parameters:

center (float) – The center of the stripe.
width (float) – The width of the stripe.

Returns:

A boolean mask of the stripe.

Return type:

array of bool

transform(grid)[source]#

Transform from cartesian to lattice coordinates.

Parameters:: grid (tuple of array like) – Input grid, typically obtained by meshgrid.
Returns:: Transformed grid in lattice vectors basis.
Return type:: array like