Stacks and cavities¶

Structures along z, built from expressions of waveguide sections.

class camfr.Stack¶

A stack of waveguides along z.

Stack(wg1(d1) + wg2(d2) + ...). The first and last waveguides are the semi-infinite incidence and exit media (their lengths only matter for field plots). Stack(expression, periods) repeats the expression. The reflection and transmission matrices are computed on demand (calc). Matrix 12 is for light incident from the left (z = 0), 21 from the right (z = length()).

__init__(expression: Expression) -> None

__init__(expression: Expression, periods: int) -> None

__init__(term: Term) -> None

__init__(term: Term, periods: int) -> None

R12()¶

R12() -> ndarray

Reflection matrix for incidence from the left.

R12(i: int, j: int) -> complex

Element (i, j) of R12: reflection from mode j to mode i.

R12_power() → ndarray¶: Reflected power, mode to mode, for incidence from the left. BlochSection stacks only.

R21()¶

R21() -> ndarray

Reflection matrix for incidence from the right.

R21(i: int, j: int) -> complex

Element (i, j) of R21.

T12()¶

T12() -> ndarray

Transmission matrix for incidence from the left.

T12(i: int, j: int) -> complex

Element (i, j) of T12: transmission from mode j to mode i.

T12_power() → ndarray¶: Transmitted power, mode to mode, for incidence from the left. BlochSection stacks only.

T21()¶

T21() -> ndarray

Transmission matrix for incidence from the right.

T21(i: int, j: int) -> complex

Element (i, j) of T21.

animate_field(component, r1, r2, r3=0, filename=0, overlay_n=1, contour=1, ln=0)¶

Animate the time evolution of a complex field component.

As plot_field, but component returns a complex number, e.g. lambda f: f.E2(). filename writes the animation to a GIF file.

calc() → None¶: Calculate the reflection and transmission matrices.

eps(coord: Coord) → complex¶: Permittivity at a Coord.

ext() → Waveguide¶: Exit waveguide.

ext_S_flux(c1_start: float, c1_stop: float, eps: float) → float¶: Power flux along z at z = length() between c1_start and c1_stop, relative precision eps.

field(coord: Coord) → Field¶: Field at a Coord, for the incident field set.

free() → None¶: Free the matrices.

fw_bw()¶

fw_bw(z: float) -> tuple

Return the forward and backward mode amplitudes at z, as a tuple.

fw_bw(z: float, limit: Limit) -> tuple

As fw_bw(z), on the given side (Plus or Min) of an interface at z.

inc() → Waveguide¶: Incidence waveguide.

inc_S_flux(c1_start: float, c1_stop: float, eps: float) → float¶: Power flux along z at z = 0 between c1_start and c1_stop, relative precision eps.

inc_field() → ndarray¶: Incident field from the left (mode amplitudes).

lateral_S_flux()¶

lateral_S_flux(c1: float) -> complex

Power flux across x = c1, integrated from z = 0 to length().

lateral_S_flux(c1: float, k: int) -> complex

Contribution of chunk k to lateral_S_flux(c1).

length() → float¶: Length along z.

mu(coord: Coord) → complex¶: Permeability at a Coord.

n(coord: Coord) → complex¶: Refractive index at a Coord.

plot()¶: Open an interactive (Tk) window with the fields in this structure.

plot_field(component, r1, r2=0, r3=0, filename=0, colormap=0, overlay_n=1, contour=1, arrow=0)¶

Plot a field component.

component maps a Field to a real number, e.g. lambda f: f.E2().real. mode.plot_field(component, r_x) plots a waveguide mode along x; stack.plot_field(component, r_x, r_z) the field in a Stack, Cavity or BlochMode, after an incident field or source has been set (r_x, r_y, r_z for a 3D stack); a SectionMode takes r_x, r_y. overlay_n overlays the index profile, drawn as contours if contour; except for waveguide modes, filename saves the picture instead of showing it.

plot_n(r1, r2=0, r3=0, filename=0, colormap=1)¶

Plot the refractive index profile.

wg.plot_n(r_x) plots a waveguide along x; stack.plot_n(r_x, r_z) a Stack, BlochStack or Cavity in the x-z plane (r_x, r_y, r_z for a 3D stack); plot_n(section, r_x, r_y) a Section. The ranges are arrays such as arange(x0, x1, dx). For stacks and sections, filename saves the picture instead of showing it (format from the suffix: png, gif, jpg, pdf, …).

refl_field() → ndarray¶: Reflected field at the left (mode amplitudes).

scatterer() → MultiScatterer¶: Return the stack as a MultiScatterer.

set_inc_field()¶

set_inc_field(fw: ndarray) -> None

Set the incident field from the left: a vector of N() mode amplitudes.

set_inc_field(fw: ndarray, bw: ndarray) -> None

Set the incident fields from the left (fw) and right (bw).

set_inc_field_function(f: object, eps: float) → None¶: Set the incident field from a function f(x) (E2 for TE, H2 for TM); eps is the precision of the overlap integrals. Slabs only.

set_inc_field_gaussian(amplitude: complex, sigma: complex, x0: complex, eps: float) → None¶: Set a Gaussian incident field amplitude*exp(-((x-x0)/sigma)**2/2); eps is the precision of the overlap integrals. Slabs only.

set_inc_field_plane_wave(amplitude: complex, theta: complex, eps: float) → None¶: Set a plane wave incident at angle theta (radians); eps is the precision of the overlap integrals. Slabs only.

trans_field() → ndarray¶: Transmitted field at the right (mode amplitudes).

width() → float¶: Transverse (c1) size of the incidence waveguide.

class camfr.Expression¶

A sequence of Terms.

Expressions are usually written with + and *, e.g. air(1) + 3*(GaAs(0.1) + AlAs(0.1)). Build one term by term with e = Expression() and e.add(term).

__init__() -> None

__init__(term: Term) -> None

__init__(expression: Expression) -> None

add(expression: Term) → None¶: Append a Term or Expression.

ext() → Waveguide¶: Last waveguide.

flatten() → Expression¶: Return the expression with nested expressions expanded.

inc() → Waveguide¶: First waveguide.

class camfr.Term¶

A building block of expressions.

Examples: material(d), waveguide(d), a Stack or Scatterer, 2*expr.

__init__(scatterer: Scatterer) -> None

__init__(stack: Stack) -> None

__init__(expression: Expression) -> None

ext() → Waveguide¶: Exit waveguide.

inc() → Waveguide¶: Incidence waveguide.

class camfr.Cavity(bottom: Stack, top: Stack)¶

A cavity, cut in two by a plane.

Cavity(bottom, top): the two Stacks are seen from the cavity cut outwards. Lasing modes are found by varying the wavelength and the gain of the material set with set_gain_material.

animate_field(component, r1, r2, r3=0, filename=0, overlay_n=1, contour=1, ln=0)¶

Animate the time evolution of a complex field component.

As plot_field, but component returns a complex number, e.g. lambda f: f.E2(). filename writes the animation to a GIF file.

bot_stack() → Stack¶: The bottom Stack.

field(coord: Coord) → Field¶: Field at a Coord (after find_mode or set_source).

find_all_modes(lambda_start: float, lambda_stop: float, delta_lambda: float, n_imag_start: float = 0.0, n_imag_stop: float = 0.015, passes: int = 1, number: int = 0) → None¶: As find_mode, for all lasing modes in the interval (or the ‘number’ highest ones). Modes closer than delta_lambda are not resolved.

find_mode(lambda_start: float, lambda_stop: float, n_imag_start: float = 0.0, n_imag_stop: float = 0.015, passes: int = 1) → None¶

Find a lasing mode in a wavelength and gain interval.

The wavelength and the imaginary index of the gain material are optimised passes times. The mode is printed, and the cavity field is set to it.

length() → float¶: Total length along z.

n(coord: Coord) → complex¶: Refractive index at a Coord.

plot()¶: Open an interactive (Tk) window with the fields in this structure.

plot_field(component, r1, r2=0, r3=0, filename=0, colormap=0, overlay_n=1, contour=1, arrow=0)¶

Plot a field component.

plot_n(r1, r2=0, r3=0, filename=0, colormap=1)¶

Plot the refractive index profile.

set_source()¶

set_source(pos: Coord, orientation: Coord) -> None

Place a dipole current source in the cavity cut at pos, oriented along the Coord orientation.

set_source(fw: ndarray, bw: ndarray) -> None

Place a source in the cavity cut given by forward and backward mode amplitudes.

sigma() → float¶: Smallest singular value of the cavity at the current wavelength and gain (minimised to find lasing modes).

top_stack() → Stack¶: The top Stack.

width() → float¶: Transverse (c1) size.

class camfr.BlochStack(expression: Expression)¶

An infinite periodic repetition of an expression; its modes are Bloch modes. N() is 2*N(): forward and backward Bloch waves.

beta_vector() → ndarray¶: Propagation constants of all Bloch modes.

length() → float¶: Length of one period along z.

mode(i: int) → BlochMode¶: Return BlochMode i.

plot()¶: Open an interactive (Tk) window with the fields in this structure.

plot_n(r1, r2=0, r3=0, filename=0, colormap=1)¶

Plot the refractive index profile.

width() → float¶: Transverse (c1) size.

class camfr.InfStack(expression: Expression)¶

A semi-infinite periodic repetition of an expression, used to terminate a Stack.

R12() → ndarray¶: Reflection matrix.

class camfr.E_Wall(waveguide: Waveguide)¶: An electric wall terminating a waveguide in z (the default z boundary is open). Not a transverse boundary.

class camfr.H_Wall(waveguide: Waveguide)¶: A magnetic wall terminating a waveguide in z (the default z boundary is open). Not a transverse boundary.

Scatterers¶

class camfr.Scatterer¶

Maps the modes of an incidence waveguide to those of an exit waveguide with reflection and transmission matrices.

calc() → None¶: Calculate the reflection and transmission matrices.

ext() → Waveguide¶: Exit waveguide.

free() → None¶: Free the matrices.

inc() → Waveguide¶: Incidence waveguide.

class camfr.MultiScatterer¶: A Scatterer between MultiWaveguides.

class camfr.DenseScatterer¶: A MultiScatterer with full matrices.

class camfr.DiagScatterer¶: A MultiScatterer with diagonal matrices.

class camfr.MonoScatterer¶: A Scatterer between MonoWaveguides.

class camfr.SquashedScatterer(scatterer: DenseScatterer)¶: A DenseScatterer reduced to a single interface.

class camfr.FlippedScatterer(scatterer: MultiScatterer)¶: A MultiScatterer seen from the other side (inc and ext swapped).