Source code for finesse.components.mirror

"""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", setter="set_RTL") @float_parameter("T", "Transmission", validate="_check_T", setter="set_RTL") @float_parameter("L", "Loss", validate="_check_L", setter="set_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. 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, ): super().__init__(name, R, T, L, phi, Rc, xbeta, ybeta) self.misaligned = misaligned self.surface_map = None 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) # 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