# SPDX-FileCopyrightText: 2025 PairInteraction Developers
# SPDX-License-Identifier: LGPL-3.0-or-later
from __future__ import annotations
from typing import TYPE_CHECKING
import numpy as np
import scipy.constants as const
from typing_extensions import override
from pairinteraction.green_tensor.dynamic_green_tensor import (
dynamic_green_tensor_homogeneous,
dynamic_green_tensor_scattered,
)
from pairinteraction.green_tensor.green_tensor_base import GreenTensorBase
from pairinteraction.green_tensor.utils import (
evaluate_relative_permittivity,
get_lab_to_local_rotation_matrix,
rotate_tensor_to_lab,
rotate_vector_to_local,
)
from pairinteraction.units import QuantityScalar, ureg
if TYPE_CHECKING:
from typing_extensions import Self
from pairinteraction.green_tensor.utils import PermittivityLike
from pairinteraction.units import ArrayLike, NDArray, PintArrayLike
[docs]
class GreenTensorSurface(GreenTensorBase):
"""Green tensor for two atoms near a single infinite surface.
Examples:
>>> from pairinteraction.green_tensor import GreenTensorSurface
>>> gt = GreenTensorSurface(
... [0, 0, 0], [10, 0, 0], point_on_plane=[0, 0, -5], surface_normal=[0, 0, 1], unit="micrometer"
... )
>>> transition_energy = 2 # h * GHz
>>> gt_dipole_dipole = gt.get(1, 1, transition_energy, "planck_constant * GHz")
>>> print(f"{gt_dipole_dipole[0, 0]:.2f}")
-4.37 / bohr
"""
[docs]
def __init__(
self,
pos1: ArrayLike | PintArrayLike,
pos2: ArrayLike | PintArrayLike,
point_on_plane: ArrayLike | PintArrayLike,
surface_normal: ArrayLike,
unit: str | None = None,
static_limit: bool = True,
interaction_order: int = 3,
*,
without_vacuum_contribution: bool = False,
) -> None:
"""Create a Green tensor for two atoms near a single infinite surface.
The surface is an infinite plane specified by a point on the plane and its normal vector.
If not specified otherwise (see `set_relative_permittivities`), the surface is treated as a perfect mirror.
Args:
pos1: Position of the first atom in the given unit.
pos2: Position of the second atom in the given unit.
point_on_plane: A point on the surface plane in the given unit.
surface_normal: The surface normal vector.
unit: The unit of the distance, e.g. "micrometer".
Default None expects a `pint.Quantity`.
static_limit: If True, the static limit is used.
Default True.
interaction_order: The order of interaction, e.g., 3 for dipole-dipole.
Defaults to 3.
without_vacuum_contribution: If True, return only the scattered contribution and
omit the homogeneous vacuum term. Defaults to False.
"""
super().__init__(
pos1, pos2, unit, static_limit, interaction_order, without_vacuum_contribution=without_vacuum_contribution
)
self.point_on_plane_au = np.array(
[QuantityScalar.convert_user_to_au(v, unit, "distance") for v in point_on_plane]
)
if np.isclose(np.linalg.norm(surface_normal), 0):
raise ValueError("Normal vector cannot be zero.")
self.surface_normal = np.array(surface_normal, dtype=float)
# Almost perfect mirror # TODO make utils be able to handle inf
self.surface_epsilon: PermittivityLike = 1e9
[docs]
def set_relative_permittivities(self, epsilon: PermittivityLike, surface_epsilon: PermittivityLike) -> Self:
"""Set the relative permittivities of the system.
Args:
epsilon: The relative permittivity (dimensionless) of the medium inside the cavity.
surface_epsilon: The relative permittivity (dimensionless) of the surface.
"""
if self.without_vacuum_contribution and epsilon != 1.0: # NOSONAR
raise ValueError(
"If the Green tensor is provided without the vacuum contribution, "
"the relative permittivity of the medium needs to be set to 1."
)
self.epsilon = epsilon
self.surface_epsilon = surface_epsilon
return self
@override
def _get_scaled_au(self, kappa1: int, kappa2: int, transition_energy_au: float) -> NDArray:
if kappa1 == 1 and kappa2 == 1:
return self._get_scaled_dipole_dipole_au(transition_energy_au)
raise NotImplementedError("Only dipole-dipole Green tensors are currently implemented.")
def _get_scaled_dipole_dipole_au(self, transition_energy_au: float) -> NDArray:
"""Calculate the dipole dipole Green tensor in cartesian coordinates for a single surface in atomic units.
Args:
transition_energy_au: The transition energy in atomic units at which to evaluate the Green tensor.
Returns:
The dipole dipole Green tensor in cartesian coordinates as a 3x3 array in atomic units (i.e. 1/bohr).
"""
au_to_meter: float = ureg.Quantity(1, "atomic_unit_of_length").to("meter").magnitude
lab_to_local_rotation = get_lab_to_local_rotation_matrix(self.surface_normal)
pos1_local_m = rotate_vector_to_local(self.pos1_au * au_to_meter, lab_to_local_rotation)
pos2_local_m = rotate_vector_to_local(self.pos2_au * au_to_meter, lab_to_local_rotation)
point_on_plane_local_m = rotate_vector_to_local(self.point_on_plane_au * au_to_meter, lab_to_local_rotation)
z1_m = point_on_plane_local_m[2]
# Assume two surfaces, where the further apart atom is located in the center
# but the second surface has the same permittivity as the inbetween medium
height = 2 * max(abs(pos1_local_m[2] - z1_m), abs(pos2_local_m[2] - z1_m))
if pos1_local_m[2] < z1_m and pos2_local_m[2] < z1_m:
z2_m = z1_m - height
elif pos1_local_m[2] > z1_m and pos2_local_m[2] > z1_m:
z2_m = z1_m + height
else:
raise ValueError("Both atoms must be located either above or below the surface.")
omega_hz = ureg.Quantity(transition_energy_au, "hartree").to("hbar Hz").magnitude
epsilon = evaluate_relative_permittivity(self.epsilon, transition_energy_au, "hartree")
epsilon1 = evaluate_relative_permittivity(self.surface_epsilon, transition_energy_au, "hartree")
epsilon2 = epsilon
# unit: # m^(-3) [hbar]^(-1) [epsilon_0]^(-1)
gt = dynamic_green_tensor_scattered(
pos1_local_m, pos2_local_m, z1_m, z2_m, omega_hz, epsilon, epsilon1, epsilon2, only_real_part=True
)
if not self.without_vacuum_contribution:
gt += dynamic_green_tensor_homogeneous(pos1_local_m, pos2_local_m, omega_hz, epsilon, only_real_part=True)
gt = rotate_tensor_to_lab(gt, lab_to_local_rotation)
to_au = au_to_meter ** (-3) * ((4 * np.pi) ** (-1)) / (const.epsilon_0 * const.hbar)
# hbar * epsilon_0 = (4*np.pi)**(-1) in atomic units
return np.real(gt) / to_au