"""Dielectric interface type components representing physical mirrors."""
import logging
import types
import finesse
import numpy as np
from finesse.parameter import float_parameter, bool_parameter
from finesse.utilities import refractive_index
from finesse.components.general import (
InteractionType,
NoiseType,
LocalDegreeOfFreedom,
)
from finesse.components.surface import Surface
from finesse.components.node import NodeType, NodeDirection
from finesse.tracing import abcd
from finesse.symbols import Constant, Variable, Matrix
LOGGER = logging.getLogger(__name__)
[docs]@float_parameter("R", "Reflectivity", validate="_check_R", post_validate="check_rtl")
@float_parameter("T", "Transmission", validate="_check_T", post_validate="check_rtl")
@float_parameter("L", "Loss", validate="_check_L", post_validate="check_rtl")
@float_parameter(
"phi", "Microscopic tuning (360 degrees = 1 default wavelength)", units="degrees"
)
@float_parameter(
"Rcx",
"Radius of curvature (x)",
units="m",
validate="_check_Rc",
is_geometric=True,
)
@float_parameter(
"Rcy",
"Radius of curvature (y)",
units="m",
validate="_check_Rc",
is_geometric=True,
)
@float_parameter("xbeta", "Yaw misalignment", units="radians")
@float_parameter("ybeta", "Pitch misalignment", units="radians")
@bool_parameter("misaligned", "Misaligns mirror reflection (R=0 when True)")
# IMPORTANT: renaming this class impacts the katscript spec and should be avoided!
class Mirror(Surface):
"""The mirror component represents a thin dielectric surface with associated
properties such as reflectivity, tuning, and radius of curvature. Mirror components
are nominally at normal incidence to the beams. It has two optical ports `p1` and
`p2` which describes the two beams incident on either side of this surface. The
surface normal points out of the mirror on the p1 side. A mirror also has a
mechanical port `mech` which has nodes for longitudinal, yaw, and pitch motions.
These mechanical nodes are purely for exciting small signal oscillations of the
mirror. Static offsets in longitudinal displacements are set by the `phi` parameter
(in units of degrees), yaw by the `xbeta` parameter, and pitch the `ybeta`
parameter.
Parameters
----------
name : str
Name of newly created mirror.
R : float, optional
Reflectivity of the mirror; defaults to 0.5.
T : float, optional
Transmittance of the mirror; defaults to 0.5.
L : float, optional
Loss of the mirror; defaults to 0.0.
phi : float, optional
Tuning of the mirror (in degrees); defaults to 0.0.
Rc : float or container of two floats, optional
The radius of curvature of the mirror (in metres);
defaults to a flat mirror (`Rc=np.inf`).
Astigmatic mirrors can also be set with `Rc=(Rcx, Rcy)`.
A positive value results in a concave mirror on the p1
side of the mirror.
xbeta, ybeta : float, optional
Misalignment of the mirror in yaw and pitch in units of radians
misaligned : bool, optional
When True the mirror will be significantly misaligned and
assumes any reflected beam is dumped. Transmissions will
still occur.
imaginary_transmission : bool, optional
Convention for the transmission and reflection reciprocity relations. 'True'
uses imaginary transmission and equal real reflection from both sides 'False'
uses real transmission, negative reflection from side 1, and positive reflection
from side 2. defaults to True
Attributes
----------
Attributes are set via the Python API and not available via KatScript.
surface_map : :class:`finesse.knm.Map`
Decsribes the surface distortion of this mirror component.
Coordinate system to the map is right-handed with the postive-z
direction as the surface normal on the port 1 side of the mirror.
"""
[docs] def __init__(
self,
name,
R=None,
T=None,
L=None,
phi=0,
Rc=np.inf,
xbeta=0,
ybeta=0,
misaligned=False,
imaginary_transmission=True,
):
super().__init__(name, R, T, L, phi, Rc, xbeta, ybeta)
self.misaligned = misaligned
self.surface_map = None
self.imaginary_transmission = imaginary_transmission
self._add_port("p1", NodeType.OPTICAL)
self.p1._add_node("i", NodeDirection.INPUT)
self.p1._add_node("o", NodeDirection.OUTPUT)
self._add_port("p2", NodeType.OPTICAL)
self.p2._add_node("i", NodeDirection.INPUT)
self.p2._add_node("o", NodeDirection.OUTPUT)
# Optic to optic couplings
self._register_node_coupling(
"P1i_P1o",
self.p1.i,
self.p1.o,
interaction_type=InteractionType.REFLECTION,
# enabled_check=lambda: self.R > 0 and not self.R.is_changing
)
self._register_node_coupling(
"P2i_P2o",
self.p2.i,
self.p2.o,
interaction_type=InteractionType.REFLECTION,
# enabled_check=lambda: self.R > 0 and not self.R.is_changing
)
self._register_node_coupling(
"P1i_P2o",
self.p1.i,
self.p2.o,
interaction_type=InteractionType.TRANSMISSION,
# enabled_check=lambda: self.T > 0 and not self.T.is_changing
)
self._register_node_coupling(
"P2i_P1o",
self.p2.i,
self.p1.o,
interaction_type=InteractionType.TRANSMISSION,
# enabled_check=lambda: self.T > 0 and not self.T.is_changing
)
# Mirror motion couplings
self._add_port("mech", NodeType.MECHANICAL)
self.mech._add_node("z", NodeDirection.BIDIRECTIONAL)
self.mech._add_node("yaw", NodeDirection.BIDIRECTIONAL)
self.mech._add_node("pitch", NodeDirection.BIDIRECTIONAL)
self.mech._add_node("F_z", NodeDirection.BIDIRECTIONAL)
self.mech._add_node("F_yaw", NodeDirection.BIDIRECTIONAL)
self.mech._add_node("F_pitch", NodeDirection.BIDIRECTIONAL)
# Optic to motion couplings
self._register_node_coupling("P1i_Fz", self.p1.i, self.mech.F_z)
self._register_node_coupling("P2i_Fz", self.p2.i, self.mech.F_z)
self._register_node_coupling("P1o_Fz", self.p1.o, self.mech.F_z)
self._register_node_coupling("P2o_Fz", self.p2.o, self.mech.F_z)
self._register_node_coupling("P1i_Fyaw", self.p1.i, self.mech.F_yaw)
self._register_node_coupling("P2i_Fyaw", self.p2.i, self.mech.F_yaw)
self._register_node_coupling("P1o_Fyaw", self.p1.o, self.mech.F_yaw)
self._register_node_coupling("P2o_Fyaw", self.p2.o, self.mech.F_yaw)
self._register_node_coupling("P1i_Fpitch", self.p1.i, self.mech.F_pitch)
self._register_node_coupling("P2i_Fpitch", self.p2.i, self.mech.F_pitch)
self._register_node_coupling("P1o_Fpitch", self.p1.o, self.mech.F_pitch)
self._register_node_coupling("P2o_Fpitch", self.p2.o, self.mech.F_pitch)
# motion to optic coupling: phase coupling on reflection
self._register_node_coupling("Z_P1o", self.mech.z, self.p1.o)
self._register_node_coupling("Z_P2o", self.mech.z, self.p2.o)
self._register_node_coupling("yaw_P1o", self.mech.yaw, self.p1.o)
self._register_node_coupling("yaw_P2o", self.mech.yaw, self.p2.o)
self._register_node_coupling("pitch_P1o", self.mech.pitch, self.p1.o)
self._register_node_coupling("pitch_P2o", self.mech.pitch, self.p2.o)
# Define typical degrees of freedom for this component
self.dofs = types.SimpleNamespace()
self.dofs.z = LocalDegreeOfFreedom(
f"{self.name}.dofs.z", self.phi, self.mech.z, None
)
self.dofs.yaw = LocalDegreeOfFreedom(
f"{self.name}.dofs.yaw", self.xbeta, self.mech.yaw, 1
)
self.dofs.pitch = LocalDegreeOfFreedom(
f"{self.name}.dofs.pitch", self.ybeta, self.mech.pitch, 1
)
self.dofs.F_z = LocalDegreeOfFreedom(
f"{self.name}.dofs.F_z", self.phi, self.mech.F_z, None, AC_OUT=self.mech.z
)
self.dofs.F_yaw = LocalDegreeOfFreedom(
f"{self.name}.dofs.F_yaw",
self.xbeta,
self.mech.F_yaw,
None,
AC_OUT=self.mech.yaw,
)
self.dofs.F_pitch = LocalDegreeOfFreedom(
f"{self.name}.dofs.F_pitch",
self.ybeta,
self.mech.F_pitch,
None,
AC_OUT=self.mech.pitch,
)
[docs] def optical_equations(self):
with finesse.symbols.simplification():
_f_ = Variable("_f_")
_f0_ = Variable("_f0_")
r = (self.R.ref) ** 0.5
t = (self.T.ref) ** 0.5
phi = self.phi.ref * (1 + _f_ / _f0_) * np.pi / 180
nr1 = self.ports[0].refractive_index
nr2 = self.ports[1].refractive_index
if self._model._settings.phase_config.v2_transmission_phase or nr1 == nr2:
# old v2 phase on transmission
# The usual i on transmission and reflections
# are opposite phase on each side, ignores refractive index
phi_r1 = 2 * phi
r1 = r * np.exp(1j * phi_r1)
r2 = r * np.exp(-1j * phi_r1)
t12 = t21 = 1j * t
else:
# Uses N=-1, Eq.2.25 in Living Reviews in Relativity (2016)
# 19:3 DOI 10.1007/s41114-016-0002-8
# beamsplitter transmission phase depends on the reflectivity
# refractive indices and angle of incidence
phi_r1 = +2 * phi * nr1
phi_r2 = -2 * phi * nr2
phi_t = np.pi / 2 + 0.5 * (phi_r1 + phi_r2)
r1 = r * np.exp(1j * phi_r1)
r2 = r * np.exp(1j * phi_r2)
t12 = t * np.exp(1j * phi_t)
t21 = t * np.exp(-1j * phi_t)
if self._model._settings.is_modal:
return {
f"{self.name}.P1i_P1o": r1
* (1 - self.misaligned.ref)
* Matrix(f"{self.name}.K11"),
f"{self.name}.P2i_P2o": r2
* (1 - self.misaligned.ref)
* Matrix(f"{self.name}.K22"),
f"{self.name}.P1i_P2o": t12 * Matrix(f"{self.name}.K12"),
f"{self.name}.P2i_P1o": t21 * Matrix(f"{self.name}.K21"),
}
else:
return {
f"{self.name}.P1i_P1o": r1 * (1 - self.misaligned.ref),
f"{self.name}.P2i_P2o": r2 * (1 - self.misaligned.ref),
f"{self.name}.P1i_P2o": t12,
f"{self.name}.P2i_P1o": t21,
}
def _resymbolise_ABCDs(self):
# -> reflections
self.__symbolise_ABCD(self.p1.i, self.p1.o, "x")
self.__symbolise_ABCD(self.p1.i, self.p1.o, "y")
self.__symbolise_ABCD(self.p2.i, self.p2.o, "x")
self.__symbolise_ABCD(self.p2.i, self.p2.o, "y")
# -> transmissions
self.__symbolise_ABCD(self.p1.i, self.p2.o, "x")
self.__symbolise_ABCD(self.p1.i, self.p2.o, "y")
self.__symbolise_ABCD(self.p2.i, self.p1.o, "x")
self.__symbolise_ABCD(self.p2.i, self.p1.o, "y")
@property
def refractive_index_1(self):
"""Refractive index on size 1 (port 1)"""
if self.p1.attached_to:
return self.p1.refractive_index
else:
return Constant(1)
@property
def refractive_index_2(self):
"""Refractive index on size 2 (port 2)"""
if self.p2.attached_to:
return self.p2.refractive_index
else:
return Constant(1)
def __symbolise_ABCD(self, from_node, to_node, direction):
if self.interaction_type(from_node, to_node) == InteractionType.REFLECTION:
# reflection
nr = refractive_index(from_node, symbolic=True)
if direction == "x":
Rc = self.Rcx.ref
ABCD = abcd.mirror_refl_t
else:
Rc = self.Rcy.ref
ABCD = abcd.mirror_refl_s
# Opposite side of mirror looks inversely curved
if from_node.port is self.p1:
M_sym = ABCD(Rc, nr=nr)
else:
M_sym = ABCD(-Rc, nr=nr)
else: # transmission
nr1 = self.refractive_index_1
nr2 = self.refractive_index_2
if direction == "x":
Rc = self.Rcx.ref
else:
Rc = self.Rcy.ref
if from_node.port is self.p1:
M_sym = abcd.mirror_trans(Rc, nr1=nr1, nr2=nr2)
else:
M_sym = abcd.mirror_trans(-Rc, nr1=nr2, nr2=nr1)
key = (from_node, to_node, direction)
# For mirrors the symbol nr can change when connected up to spaces
# in a model so here we update the ABCD matrix entry
if key in self._abcd_matrices:
self._abcd_matrices[key] = M_sym, np.array(M_sym, dtype=np.float64)
# Otherwise just register the new ABCD matrix as usual
else:
self.register_abcd_matrix(M_sym, (from_node, to_node, direction))
@property
def abcd11x(self):
"""Numeric ABCD matrix from port 1 to port 1 in the tangential plane.
Equivalent to ``mirror.ABCD(1, 1, "x")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(1, 1, "x")
@property
def abcd11y(self):
"""Numeric ABCD matrix from port 1 to port 1 in the sagittal plane.
Equivalent to ``mirror.ABCD(1, 1, "y")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(1, 1, "y")
@property
def abcd22x(self):
"""Numeric ABCD matrix from port 2 to port 2 in the tangential plane.
Equivalent to ``mirror.ABCD(2, 2, "x")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(2, 2, "x")
@property
def abcd22y(self):
"""Numeric ABCD matrix from port 2 to port 2 in the sagittal plane.
Equivalent to ``mirror.ABCD(2, 2, "y")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(2, 2, "y")
@property
def abcd12x(self):
"""Numeric ABCD matrix from port 1 to port 2 in the tangential plane.
Equivalent to ``mirror.ABCD(1, 2, "x")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(1, 2, "x")
@property
def abcd12y(self):
"""Numeric ABCD matrix from port 1 to port 2 in the sagittal plane.
Equivalent to ``mirror.ABCD(1, 2, "y")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(1, 2, "y")
@property
def abcd21x(self):
"""Numeric ABCD matrix from port 2 to port 1 in the tangential plane.
Equivalent to ``mirror.ABCD(2, 1, "x")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(2, 1, "x")
@property
def abcd21y(self):
"""Numeric ABCD matrix from port 2 to port 1 in the sagittal plane.
Equivalent to ``mirror.ABCD(2, 1, "y")``.
:`getter`: Returns a copy of the (numeric) ABCD matrix for this coupling
(read-only).
"""
return self.ABCD(2, 1, "y")
[docs] def ABCD(
self,
from_node,
to_node,
direction="x",
symbolic=False,
copy=True,
retboth=False,
allow_reverse=False,
):
r"""Returns the ABCD matrix of the mirror for the specified coupling.
In both cases below, the sign of the radius is defined such that :math:`R_c`
is negative if the centre of the sphere is located in the direction of propagation.
.. rubric:: Transmission
.. _fig_abcd_mirror_transmission:
.. figure:: ../images/abcd_mi.*
:align: center
For transmission this is given by,
.. math::
M_{t} = \begin{pmatrix}
1 & 0 \\
\frac{n_2 - n_1}{R_c} & 1
\end{pmatrix},
where :math:`n_2` and :math:`n_1` are the indices of refraction of the spaces
connected to the mirror and :math:`R_c` is the radius of curvature of the mirror.
The matrix for transmission in the opposite direction of propagation is identical.
.. rubric:: Reflection
.. _fig_abcd_mirror_reflection:
.. figure:: ../images/abcd_mr.*
:align: center
In the case of reflection the matrix is,
.. math::
M_{r} = \begin{pmatrix}
1 & 0 \\
-\frac{2n_1}{R_c} & 1
\end{pmatrix}.
Reflection at the back surface can be described by the same type of matrix by setting
the :math:`C` element to :math:`C = 2n_2/R_c`.
See :meth:`.Connector.ABCD` for descriptions of parameters, return values and possible
exceptions.
"""
return super().ABCD(
from_node, to_node, direction, symbolic, copy, retboth, allow_reverse
)
def _get_workspace(self, sim):
"""Returns a workspace to use in a simulation."""
from finesse.simulations.sparse.simulation import SparseMatrixSimulation
if isinstance(sim, SparseMatrixSimulation):
from finesse.components.modal.mirror import (
mirror_carrier_fill,
mirror_signal_opt_fill,
mirror_signal_mech_fill,
mirror_fill_qnoise,
MirrorWorkspace,
)
_, is_changing = self._eval_parameters()
carrier_refill = (
sim.is_component_in_mismatch_couplings(self)
or self in sim.trace_forest
or sim.carrier.any_frequencies_changing
or len(is_changing)
)
ws = MirrorWorkspace(self, sim)
ws.imaginary_transmission = self.imaginary_transmission
# This assumes that nr1/nr2 cannot change during a simulation
ws.nr1 = refractive_index(self.p1)
ws.nr2 = refractive_index(self.p2)
ws.carrier.add_fill_function(mirror_carrier_fill, carrier_refill)
if sim.signal:
signal_refill = carrier_refill or (
sim.model.fsig.f.is_changing
and not (self.phi.value == 0 and self.phi.is_changing)
)
ws.signal.add_fill_function(mirror_signal_opt_fill, signal_refill)
signal_refill = carrier_refill or (sim.model.fsig.f.is_changing)
ws.signal.add_fill_function(mirror_signal_mech_fill, signal_refill)
# Initialise the ABCD matrix memory-views
if sim.is_modal:
ws.abcd_p1p1_x = self.ABCD(self.p1.i, self.p1.o, "x", copy=False)
ws.abcd_p1p1_y = self.ABCD(self.p1.i, self.p1.o, "y", copy=False)
ws.abcd_p2p2_x = self.ABCD(self.p2.i, self.p2.o, "x", copy=False)
ws.abcd_p2p2_y = self.ABCD(self.p2.i, self.p2.o, "y", copy=False)
ws.abcd_p1p2_x = self.ABCD(self.p1.i, self.p2.o, "x", copy=False)
ws.abcd_p1p2_y = self.ABCD(self.p1.i, self.p2.o, "y", copy=False)
ws.abcd_p2p1_x = self.ABCD(self.p2.i, self.p1.o, "x", copy=False)
ws.abcd_p2p1_y = self.ABCD(self.p2.i, self.p1.o, "y", copy=False)
ws.set_knm_info(
"P1i_P1o",
abcd_x=ws.abcd_p1p1_x,
abcd_y=ws.abcd_p1p1_y,
nr_from=ws.nr1,
nr_to=ws.nr1,
is_transmission=False,
beta_x=self.xbeta,
beta_x_factor=2,
beta_y=self.ybeta,
beta_y_factor=-2,
apply_map=self.surface_map,
map_phase_factor=-2 * ws.nr1,
map_fliplr=False,
)
ws.set_knm_info(
"P2i_P2o",
abcd_x=ws.abcd_p2p2_x,
abcd_y=ws.abcd_p2p2_y,
nr_from=ws.nr2,
nr_to=ws.nr2,
is_transmission=False,
beta_x=self.xbeta,
beta_x_factor=2,
beta_y=self.ybeta,
beta_y_factor=2,
apply_map=self.surface_map,
map_phase_factor=2 * ws.nr2,
map_fliplr=True,
)
ws.set_knm_info(
"P1i_P2o",
abcd_x=ws.abcd_p1p2_x,
abcd_y=ws.abcd_p1p2_y,
nr_from=ws.nr1,
nr_to=ws.nr2,
is_transmission=True,
beta_x=self.xbeta,
beta_x_factor=-(1 - ws.nr1 / ws.nr2),
beta_y=self.ybeta,
beta_y_factor=(1 - ws.nr1 / ws.nr2),
apply_map=self.surface_map,
map_phase_factor=(ws.nr2 - ws.nr1),
map_fliplr=False,
)
ws.set_knm_info(
"P2i_P1o",
abcd_x=ws.abcd_p2p1_x,
abcd_y=ws.abcd_p2p1_y,
nr_from=ws.nr2,
nr_to=ws.nr1,
is_transmission=True,
beta_x=self.xbeta,
beta_x_factor=-(1 - ws.nr2 / ws.nr1),
beta_y=self.ybeta,
beta_y_factor=-(1 - ws.nr2 / ws.nr1),
apply_map=self.surface_map,
map_phase_factor=-(ws.nr1 - ws.nr2),
map_fliplr=True,
)
if sim.signal:
ws.signal.set_fill_noise_function(NoiseType.QUANTUM, mirror_fill_qnoise)
return ws