add type hints to Medium class and other improvements and fixes to docs

doc/docs/Build_From_Source.md

@@ -93,7 +93,7 @@ If you are not the system administrator of your machine, and/or want to install
 
 ### Python
 
-If you have Python on your system, then the Meep compilation scripts automatically build and install the `meep` Python module, which works with both the serial and parallel (MPI) versions of Meep. Note: Meep's [visualization module](Python_User_Interface.md#data-visualization) includes animation routines which require [matplotlib](https://matplotlib.org/) version `3.1`+ and the [adjoint solver](Python_Tutorials/Adjoint_Solver.md) requires [autograd](https://github.com/HIPS/autograd).
+If you have Python on your system, then the Meep compilation scripts automatically build and install the `meep` Python module, which works with both the serial and parallel (MPI) versions of Meep. Note: Meep's [visualization module](Python_User_Interface.md#data-visualization) includes animation routines which require [matplotlib](https://matplotlib.org/) version `3.1`+ and the [adjoint solver](Python_Tutorials/Adjoint_Solver.md) requires [autograd](https://github.com/HIPS/autograd) version 1.5 or newer.
 
 By default, Meep's Python module is installed for the program `python` on your system.  If you want to install using a different Python program, e.g. `python3`, pass `PYTHON=python3` (or similar) to the Meep `configure` script. An Anaconda (`conda`) [package for Meep](Installation.md#conda-packages) is also available on some systems.
 

doc/docs/FAQ.md

@@ -201,9 +201,9 @@ Usage: Fields
 
 ### Why are the fields blowing up in my simulation?
 
-Instability in the fields is likely due to one of five causes: (1) [PML](Python_User_Interface.md#pml) overlapping dispersive materials based on a [Drude-Lorentzian susceptibility](Python_User_Interface.md#lorentziansusceptibility) in the presence of [backward-wave modes](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.79.065601) (fix: replace the PML with an [Absorber](Python_User_Interface.md#absorber)), (2) the frequency of a Lorentzian susceptibility term is *too high* relative to the grid discretization (fix: increase the `resolution` and/or reduce the `Courant` factor), (3) a material with a [wavelength-independent negative real permittivity](#why-does-my-simulation-diverge-if-0) (fix: [fit the permittivity to a broadband Drude-Lorentzian susceptibility](#how-do-i-import-n-and-k-values-into-meep)), (4) a grid voxel contains *more than one* dielectric interface (fix: turn off subpixel averaging), or (5) a material with a *wavelength-independent* refractive index between 0 and 1 (fix: reduce the `Courant` factor; alternatively, [fit the permittivity to a broadband Drude-Lorentzian susceptibility](#how-do-i-import-n-and-k-values-into-meep)).
+Instability in the fields is likely due to one of five causes: (1) [PML](Python_User_Interface.md#pml) overlapping dispersive materials based on a [Drude-Lorentzian susceptibility](Python_User_Interface.md#lorentziansusceptibility) in the presence of [backward-wave modes](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.79.065601) (fix: replace the PML with an [Absorber](Python_User_Interface.md#absorber)), (2) the frequency of a Lorentzian susceptibility term is *too high* relative to the grid discretization (fix: increase the `resolution` and/or reduce the `Courant` factor), (3) a material with a [wavelength-independent negative real permittivity](#why-does-my-simulation-diverge-if-the-permittivity-is-less-than-0) (fix: [fit the permittivity to a broadband Drude-Lorentzian susceptibility](Materials.md#how-do-i-import-n-and-k-values-into-meep)), (4) a grid voxel contains *more than one* dielectric interface (fix: turn off subpixel averaging), or (5) a material with a *wavelength-independent* refractive index between 0 and 1 (fix: reduce the `Courant` factor; alternatively, [fit the permittivity to a broadband Drude-Lorentzian susceptibility](Materials.md#how-do-i-import-n-and-k-values-into-meep)).
 
-Note: when the fields blow up, the CPU *slows down* due to [floating-point exceptions in IEEE 754](https://en.wikipedia.org/wiki/IEEE_754#Exception_handling). Also, Meep automatically checks the fields at the cell origin after every timestep and [aborts the simulation if the electric energy density has diverged](https://github.com/NanoComp/meep/blob/master/src/step.cpp#L97-L98).
+Note: when the fields blow up, the CPU *slows down* due to [floating-point exceptions in IEEE 754](https://en.wikipedia.org/wiki/IEEE_754#Exception_handling). Also, Meep automatically checks the fields at the cell origin after every timestep and aborts the simulation if the electric energy density has diverged.
 
 ### How do I compute the steady-state fields?
 

mkdocs.yml

@@ -17,7 +17,7 @@ markdown_extensions:
     - wikilinks
     - toc:
         title: Table of Contents
-        permalink: []
+        permalink: "#"
     - attr_list
     - fenced_code
     - md_in_html

python/geom.py

@@ -1,12 +1,18 @@
-from typing import Union, Tuple
+"""
+A collection of geometry- and material-related objects and helper routines.
+"""
+
+from __future__ import annotations
+
+from collections import namedtuple
+from copy import deepcopy
 import functools
 import math
-import numbers
+from numbers import Number
 import operator
+from typing import List, NamedTuple, Optional, Type, Tuple, Union
 import warnings
-from collections import namedtuple
-from copy import deepcopy
-from numbers import Number
+
 import numpy as np
 import meep as mp
 
@@ -311,78 +317,78 @@ class Medium:
 
     def __init__(
         self,
-        epsilon_diag=Vector3(1, 1, 1),
-        epsilon_offdiag=Vector3(),
-        mu_diag=Vector3(1, 1, 1),
-        mu_offdiag=Vector3(),
-        E_susceptibilities=None,
-        H_susceptibilities=None,
-        E_chi2_diag=Vector3(),
-        E_chi3_diag=Vector3(),
-        H_chi2_diag=Vector3(),
-        H_chi3_diag=Vector3(),
-        D_conductivity_diag=Vector3(),
-        D_conductivity_offdiag=Vector3(),
-        B_conductivity_diag=Vector3(),
-        B_conductivity_offdiag=Vector3(),
-        epsilon=None,
-        index=None,
-        mu=None,
-        chi2=None,
-        chi3=None,
-        D_conductivity=None,
-        B_conductivity=None,
-        E_chi2=None,
-        E_chi3=None,
-        H_chi2=None,
-        H_chi3=None,
-        valid_freq_range=FreqRange(min=-mp.inf, max=mp.inf),
+        epsilon_diag: Vector3 = Vector3(1.0, 1.0, 1.0),
+        epsilon_offdiag: Vector3 = Vector3(),
+        mu_diag: Vector3 = Vector3(1.0, 1.0, 1.0),
+        mu_offdiag: Vector3 = Vector3(),
+        E_susceptibilities: Optional[List[Type[Susceptibility]]] = None,
+        H_susceptibilities: Optional[List[Type[Susceptibility]]] = None,
+        E_chi2_diag: Vector3 = Vector3(),
+        E_chi3_diag: Vector3 = Vector3(),
+        H_chi2_diag: Vector3 = Vector3(),
+        H_chi3_diag: Vector3 = Vector3(),
+        D_conductivity_diag: Vector3 = Vector3(),
+        D_conductivity_offdiag: Vector3 = Vector3(),
+        B_conductivity_diag: Vector3 = Vector3(),
+        B_conductivity_offdiag: Vector3 = Vector3(),
+        epsilon: Optional[float] = None,
+        index: Optional[float] = None,
+        mu: Optional[float] = None,
+        chi2: Optional[float] = None,
+        chi3: Optional[float] = None,
+        D_conductivity: Optional[float] = None,
+        B_conductivity: Optional[float] = None,
+        E_chi2: Optional[float] = None,
+        E_chi3: Optional[float] = None,
+        H_chi2: Optional[float] = None,
+        H_chi3: Optional[float] = None,
+        valid_freq_range: NamedTuple = FreqRange(min=-mp.inf, max=mp.inf),
     ):
         """
         Creates a `Medium` object.
 
-        + **`epsilon` [`number`]** The frequency-independent isotropic relative
+        + **`epsilon` [ `number` ]** The frequency-independent isotropic relative
           permittivity or dielectric constant. Default is 1. You can also use `index=n` as
           a synonym for `epsilon=n*n`; note that this is not really the refractive index
-          if you also specify μ, since the true index is $\\sqrt{\\mu\\varepsilon}$. Using
+          if you also specify $\\mu$, since the true index is $\\sqrt{\\mu\\varepsilon}$. Using
           `epsilon=ep` is actually a synonym for `epsilon_diag=mp.Vector3(ep, ep, ep)`.
 
-        + **`epsilon_diag` and `epsilon_offdiag` [`Vector3`]** — These properties allow
+        + **`epsilon_diag` and `epsilon_offdiag` [ `Vector3` ]** — These properties allow
           you to specify ε as an arbitrary real-symmetric tensor by giving the diagonal
           and offdiagonal parts. Specifying `epsilon_diag=Vector3(a, b, c)` and/or
-          `epsilon_offdiag=Vector3(u, v, w)` corresponds to a relative permittivity ε
+          `epsilon_offdiag=Vector3(u, v, w)` corresponds to a relative permittivity $\\varepsilon$
           tensor \\begin{pmatrix} a & u & v \\\\ u & b & w \\\\ v & w & c \\end{pmatrix}
           Default is the identity matrix ($a = b = c = 1$ and $u = v = w = 0$).
 
-        + **`mu` [`number`]** — The frequency-independent isotropic relative permeability
-          μ. Default is 1. Using `mu=pm` is actually a synonym for `mu_diag=mp.Vector3(pm,
+        + **`mu` [ `number` ]** — The frequency-independent isotropic relative permeability
+          $\\mu$. Default is 1. Using `mu=pm` is actually a synonym for `mu_diag=mp.Vector3(pm,
           pm, pm)`.
 
-        + **`mu_diag` and `mu_offdiag` [`Vector3`]** — These properties allow you to
-          specify μ as an arbitrary real-symmetric tensor by giving the diagonal and
-          offdiagonal parts exactly as for ε above. Default is the identity matrix.
+        + **`mu_diag` and `mu_offdiag` [ `Vector3` ]** — These properties allow you to
+          specify $\\mu$ as an arbitrary real-symmetric tensor by giving the diagonal and
+          offdiagonal parts exactly as for $\\varepsilon$ above. Default is the identity matrix.
 
-        + **`D_conductivity` [`number`]** — The frequency-independent electric
+        + **`D_conductivity` [ `number` ]** — The frequency-independent electric
           conductivity $\\sigma_D$. Default is 0. You can also specify a diagonal
           anisotropic conductivity tensor by using the property `D_conductivity_diag`
           which takes a `Vector3` to give the $\\sigma_D$ tensor diagonal. See also
           [Conductivity](Materials.md#conductivity-and-complex).
 
-        + **`B_conductivity` [`number`]** — The frequency-independent magnetic
+        + **`B_conductivity` [ `number` ]** — The frequency-independent magnetic
           conductivity $\\sigma_B$. Default is 0. You can also specify a diagonal
           anisotropic conductivity tensor by using the property `B_conductivity_diag`
           which takes a `Vector3` to give the $\\sigma_B$ tensor diagonal. See also
           [Conductivity](Materials.md#conductivity-and-complex).
 
-        + **`chi2` [`number`]** — The nonlinear electric
+        + **`chi2` [ `number` ]** — The nonlinear electric
           [Pockels](https://en.wikipedia.org/wiki/Pockels_effect) susceptibility
           $\\chi^{(2)}$ (quadratic nonlinearity). Default is 0. See also [Nonlinearity](Materials.md#nonlinearity).
           This is equivalent to setting `E_chi2`; alternatively, an analogous magnetic
           nonlinearity can be specified using `H_chi2`. These are isotropic nonlinearities,
           but *diagonal* anisotropic polarizations of the form $\\chi_i^{(2)} E_i^2$ can
           be specified with `E_chi2_diag` (which defaults to `[E_chi2,E_chi2,E_chi2]`).
 
-        + **`chi3` [`number`]** — The nonlinear electric
+        + **`chi3` [ `number` ]** — The nonlinear electric
           [Kerr](https://en.wikipedia.org/wiki/Kerr_effect) susceptibility $\\chi^{(3)}$
           (cubic nonlinearity). Default is 0. See also [Nonlinearity](Materials.md#nonlinearity).
           This is equivalent to setting `E_chi3`; alternatively, an analogous magnetic nonlinearity
@@ -391,12 +397,12 @@ def __init__(
           `E_chi3_diag` (which defaults to `[E_chi3,E_chi3,E_chi3]`).
 
         + **`E_susceptibilities` [ list of `Susceptibility` class ]** — List of dispersive
-          susceptibilities (see below) added to the dielectric constant ε in order to
+          susceptibilities (see below) added to the dielectric constant $\\varepsilon$ in order to
           model material dispersion. Defaults to none (empty list). See also [Material
           Dispersion](Materials.md#material-dispersion).
 
         + **`H_susceptibilities` [ list of `Susceptibility` class ]** — List of dispersive
-          susceptibilities (see below) added to the permeability μ in order to model
+          susceptibilities (see below) added to the permeability $\\mu$ in order to model
           material dispersion. Defaults to none (empty list). See also [Material
           Dispersion](Materials.md#material-dispersion).
         """
@@ -1688,7 +1694,7 @@ def find_root_deriv(f, tol, x_min, x_max, x_guess=None):
     f_memo = memoize(f)
 
     def lazy(x):
-        return x if isinstance(x, numbers.Number) else x()
+        return x if isinstance(x, Number) else x()
 
     def pick_bound(which):
         def _pb():
@@ -1730,7 +1736,7 @@ def newton(x, a, b, dx):
         ):
             raise ValueError("failed to bracket the root in find_root_deriv")
 
-        if isinstance(a, numbers.Number) and isinstance(b, numbers.Number):
+        if isinstance(a, Number) and isinstance(b, Number):
             is_in_bounds = in_bounds(x, f, df, a, b)
         else:
             is_in_bounds = in_bounds(x, f, df, x_min, x_max)