minor fixes and tweaks to docs (#1454)

* minor tweaks

* replace imshow with plot2D

* Update Subpixel_Smoothing.md

Co-authored-by: Steven G. Johnson <stevenj@mit.edu>

doc/docs/Python_Tutorials/Eigenmode_Source.md

@@ -272,15 +272,16 @@ sim = mp.Simulation(cell_size=cell_size,
 sim.run(until=100)
 
 nonpml_vol = mp.Volume(center=mp.Vector3(), size=mp.Vector3(10,10,0))
-ez_data = sim.get_array(vol=nonpml_vol, component=mp.Ez)
 
-plt.figure()
-plt.imshow(np.flipud(np.transpose(np.real(ez_data))), interpolation='spline36', cmap='RdBu')
-plt.axis('off')
-plt.show()
+sim.plot2D(fields=mp.Ez,
+           output_plane=nonpml_vol)
+
+if mp.am_master():
+    plt.axis('off')
+    plt.savefig('pw.png',bbox_inches='tight')
 ```
 
-Note that the line source spans the *entire* length of the cell. (Planewave sources extending into the PML region must include `is_integrated=True`.) This example involves a continuous-wave (CW) time profile. For a pulse profile, the oblique planewave is incident at a given angle for only a *single* frequency component of the source; see [Tutorial/Basics/Angular Reflectance Spectrum of a Planar Interface](../Python_Tutorials/Basics.md#angular-reflectance-spectrum-of-a-planar-interface). This is a fundamental feature of FDTD simulations and not of Meep per se. To simulate an incident planewave at multiple angles for a given frequency $\omega$, you will need to do separate simulations involving different values of $\vec{k}$ (`k_point`) since each set of ($\vec{k}$,ω) specifying the Bloch-periodic boundaries and the frequency of the source will produce a different angle of the planewave. For more details, refer to Section 4.5 ("Efficient Frequency-Angle Coverage") in [Chapter 4](https://arxiv.org/abs/1301.5366) ("Electromagnetic Wave Source Conditions") of [Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology](https://www.amazon.com/Advances-FDTD-Computational-Electrodynamics-Nanotechnology/dp/1608071707).
+Note that the line source spans the *entire* length of the cell. (Planewave sources extending into the PML region must include `is_integrated=True`.) This example involves a continuous-wave (CW) time profile. For a pulse profile, the oblique planewave is incident at a given angle for only a *single* frequency component of the source as described in [Tutorial/Basics/Angular Reflectance Spectrum of a Planar Interface](../Python_Tutorials/Basics.md#angular-reflectance-spectrum-of-a-planar-interface). This is a fundamental feature of FDTD simulations and not of Meep per se. To simulate an incident planewave at multiple angles for a given frequency $\omega$, you will need to do separate simulations involving different values of $\vec{k}$ (`k_point`) since each set of $(\vec{k},\omega)$ specifying the Bloch-periodic boundaries and the frequency of the source will produce a different angle of the planewave. For more details, refer to Section 4.5 ("Efficient Frequency-Angle Coverage") in [Chapter 4](https://arxiv.org/abs/1301.5366) ("Electromagnetic Wave Source Conditions") of [Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology](https://www.amazon.com/Advances-FDTD-Computational-Electrodynamics-Nanotechnology/dp/1608071707).
 
 Shown below are the steady-state field profiles generated by the planewave for the three rotation angles. Residues of the backward-propagating waves due to the discretization are slightly visible.
 

doc/docs/Python_Tutorials/GDSII_Import.md

@@ -143,7 +143,7 @@ if __name__ == '__main__':
     main(args)
 ```
 
-For a given waveguide separation distance (`d`), the simulation computes the transmittance of Ports 2, 3, and 4. The transmittance is the square of the [S-parameter](https://en.wikipedia.org/wiki/Scattering_parameters) which itself is equivalent to the [mode coefficient](Mode_Decomposition.md). There is an additional mode monitor at Port 1 to compute the input power from the adjacent eigenmode source; this is used for normalization when computing the transmittance. The eight layers of the GDSII file are each converted to a `Simulation` object: the upper and lower branches of the coupler are defined as a collection of [`Prism`](../Python_User_Interface.md#prism)s, the rectilinear regions of the source and flux monitor as a [`Volume`](../Python_User_Interface.md#volume) and [`FluxRegion`](../Python_User_Interface.md#fluxregion). The size of the cell in the $y$ direction is dependent on `d`. The default dimensionality is 2d. (Note that for a 2d cell the `Prism` objects returned by `get_GDSII_prisms` must have a finite height. The finite height of `Volume` objects returned by `GDSII_vol` are ignored in 2d.) An optional input parameter (`three_d`) converts the geometry to 3d by extruding the coupler geometry in the $z$ direction and adding an oxide layer beneath similar to a [silicon on insulator](https://en.wikipedia.org/wiki/Silicon_on_insulator) (SOI) substrate. A schematic of the coupler design in 3d generated using MayaVi is shown below.
+For a given waveguide separation distance ($d$), the simulation computes the transmittance of Ports 2, 3, and 4. The transmittance is the square of the [S-parameter](https://en.wikipedia.org/wiki/Scattering_parameters) which itself is equivalent to the [mode coefficient](Mode_Decomposition.md). There is an additional mode monitor at Port 1 to compute the input power from the adjacent eigenmode source; this is used for normalization when computing the transmittance. The eight layers of the GDSII file are each converted to a `Simulation` object: the upper and lower branches of the coupler are defined as a collection of [`Prism`](../Python_User_Interface.md#prism)s, the rectilinear regions of the source and flux monitor as a [`Volume`](../Python_User_Interface.md#volume) and [`FluxRegion`](../Python_User_Interface.md#fluxregion). The size of the cell in the $y$ direction is dependent on $d$. The default dimensionality is 2d. (Note that for a 2d cell the `Prism` objects returned by `get_GDSII_prisms` must have a finite height. The finite height of `Volume` objects returned by `GDSII_vol` are ignored in 2d.) An optional input parameter (`three_d`) converts the geometry to 3d by extruding the coupler geometry in the $z$ direction and adding an oxide layer beneath similar to a [silicon on insulator](https://en.wikipedia.org/wiki/Silicon_on_insulator) (SOI) substrate. A schematic of the coupler design in 3d generated using MayaVi is shown below.
 
 <center>
 ![](../images/coupler3D.png)
@@ -159,13 +159,13 @@ done
 grep trans: directional_coupler.out |cut -d , -f2- > directional_coupler.dat;
 ```
 
-The transmittance results converted into [insertion loss](https://en.wikipedia.org/wiki/Insertion_loss) for Ports 3 and 4 are shown in the figure below. (There is essentially no flux into Port 2 and thus $|S_{12}|^2$ is not shown in the figure.) When the two waveguide branches are sufficiently separated (`d` > 0.2 μm), practically all of the input power remains in the top branch and is transferred to Port 3. A small amount of the input power is lost due to scattering into radiative modes within the light cone in the tapered sections where the translational symmetry of the waveguide is broken. This is why the power in Port 3 never reaches exactly 100%. For separation distances of less than approximately 0.2 μm, evanescent coupling of the modes from the top to the lower branch begins to transfer some of the input power to Port 4. For `d` of 0.13 μm, the input signal is split evenly into Ports 3 and 4. For `d` of 0.06 μm, the input power is transferred completely to Port 4. Finally, for `d` of less than 0.06 μm, the evanescent coupling becomes rapidly ineffective and the signal again remains mostly in Port 3.
+The transmittance results converted into [insertion loss](https://en.wikipedia.org/wiki/Insertion_loss) for Ports 3 and 4 are shown in the figure below. (There is essentially no flux into Port 2 and thus $|S_{12}|^2$ is not shown in the figure.) When the two waveguide branches are sufficiently separated ($d$ > 0.2 μm), practically all of the input power remains in the top branch and is transferred to Port 3. A small amount of the input power is lost due to scattering into radiative modes within the light cone in the tapered sections where the translational symmetry of the waveguide is broken. This is why the power in Port 3 never reaches exactly 100%. For separation distances of less than approximately 0.2 μm, evanescent coupling of the modes from the top to the lower branch begins to transfer some of the input power to Port 4. For $d$ of 0.13 μm, the input signal is split evenly into Ports 3 and 4. For $d$ of 0.06 μm, the input power is transferred completely to Port 4. Finally, for $d$ of less than 0.06 μm, the evanescent coupling becomes rapidly ineffective and the signal again remains mostly in Port 3.
 
 <center>
 ![](../images/directional_coupler_flux.png)
 </center>
 
-These quantitative results can also be verified qualitatively using the field profiles shown below for `d` of 0.06, 0.13, and 0.30 μm. To generate these images, the pulse source is replaced with a [continuous wave](../Python_User_Interface.md#continuoussource) (CW) and the fields are time stepped for a sufficiently long run time until they have reached steady state. The [array slicing](../Python_User_Interface.md#array-slices) routines `get_epsilon` and `get_efield_z` are then used to obtain the dielectric and field data over the entire cell.
+These quantitative results can also be verified qualitatively using the field profiles shown below for $d$ of 0.06, 0.13, and 0.30 μm. To generate these images, the pulse source is replaced with a [continuous wave](../Python_User_Interface.md#continuoussource) (CW) and the fields are time stepped for a sufficiently long run time until they have reached steady state. The [array slicing](../Python_User_Interface.md#array-slices) routines `get_epsilon` and `get_efield_z` are then used to obtain the dielectric and field data over the entire cell.
 
 ```py
 sources = [mp.EigenModeSource(src=mp.ContinuousSource(fcen,fwidth=df),
@@ -200,7 +200,7 @@ plt.show()
 ![](../images/directional_coupler_field_profiles.png)
 </center>
 
-The field profiles confirm that for `d` of 0.06 μm (Figure 1), the input signal in Port 1 of the top branch is almost completely transferred to Port 4 of the bottom branch. For `d` of 0.13 μm (Figure 2), the input signal is split evenly between the two branches. Finally, for `d` of 0.30 μm (Figure 3), there is no longer any evanescent coupling and the signal remains completely in the top branch. The waveguide regions with no fields in Ports 3 and 4 are PML.
+The field profiles confirm that for $d$ of 0.06 μm (Figure 1), the input signal in Port 1 of the top branch is almost completely transferred to Port 4 of the bottom branch. For $d$ of 0.13 μm (Figure 2), the input signal is split evenly between the two branches. Finally, for $d$ of 0.30 μm (Figure 3), there is no longer any evanescent coupling and the signal remains completely in the top branch. The waveguide regions with no fields in Ports 3 and 4 are PML.
 
 ### When computing the reflection coefficient |S<sub>11</sub>|<sup>2</sup>, is it necessary to perform a separate normalization run to obtain the incident fields?
 

doc/docs/Subpixel_Smoothing.md

@@ -23,7 +23,7 @@ $$ \tilde{\varepsilon}^{-1} = \textbf{P}\langle\varepsilon^{-1}\rangle + \big(1-
 
 </center>
 
-where $\textbf{P}$ is the projection matrix $P_{ij}=n_{i}n_{j}$ onto the normal $\vec{n}$. The $\langle\cdots\rangle$ denotes an average over the voxel $sΔx\times sΔy\times sΔz$ surrounding the grid point in question where $s$ is a smoothing diameter in grid units equal to 1/`resolution`. If the initial materials are anisotropic (via `epsilon_diag` and `epsilon_offdiag`), a more complicated formula is used. They key point is that, even if the structure consists entirely of isotropic materials, the discretized structure will use anisotropic materials. For interface pixels, Meep computes the effective permittivity tensor automatically at the start of the simulation prior to time stepping via analytic expressions for the filling fraction and local normal vector. For details involving derivation of the effective permittivity tensor and its implementation in Meep/FDTD, see [Optics Letters, Vol. 36, pp. 2972-4, 2006](https://www.osapublishing.org/ol/abstract.cfm?uri=ol-31-20-2972) and [Optics Letters, Vol. 35, pp. 2778-80, 2009](https://www.osapublishing.org/abstract.cfm?uri=ol-34-18-2778).
+where $\textbf{P}$ is the projection matrix $P_{ij}=n_{i}n_{j}$ onto the normal $\vec{n}$. The $\langle\cdots\rangle$ denotes an average over the voxel $sΔx\times sΔy\times sΔz$ surrounding the grid point in question where $s$ is a smoothing diameter in grid units equal to 1/`resolution`. (This analysis assumes that interface is approximately planar throughout the voxel, which will hold in the regime where the voxels are small compared to the geometric feature sizes.) If the initial materials are anisotropic (via `epsilon_diag` and `epsilon_offdiag`), a more complicated formula is used. They key point is that, even if the structure consists entirely of isotropic materials, the discretized structure will use anisotropic materials. For interface pixels, Meep computes the effective permittivity tensor automatically at the start of the simulation prior to time stepping via analytic expressions for the filling fraction and local normal vector. For details involving derivation of the effective permittivity tensor and its implementation in Meep/FDTD, see [Optics Letters, Vol. 36, pp. 2972-4, 2006](https://www.osapublishing.org/ol/abstract.cfm?uri=ol-31-20-2972) and [Optics Letters, Vol. 35, pp. 2778-80, 2009](https://www.osapublishing.org/abstract.cfm?uri=ol-34-18-2778).
 
 In [parallel simulations](Parallel_Meep.md), each [chunk](Chunks_and_Symmetry.md) computes the effective permittivity separately for its owned voxels. This means that the time required for the grid initialization (`set_epsilon` in the output) should typically scale [linearly with the number of processors](FAQ.md#should-i-expect-linear-speedup-from-the-parallel-meep). The same is true even when subpixel smoothing is disabled.
 
@@ -256,4 +256,4 @@ The plot of the resonant mode frequency with resolution is shown in the figure b
 
 Finally, it is worth mentioning that a Gaussian blur (which provides only first-order accuracy) would probably be slower than doing the second-order accurate anisotropic smoothing using a [level set](https://en.wikipedia.org/wiki/Level_set) since the smoothing (e.g., via a Sigmoid function) as well as the normal vector can be computed analytically for the level set (see [\#1229](https://github.com/NanoComp/meep/issues/1229)).
 
-In the future, Meep may provide built-in interpolation methods for material functions (see [\#1199](https://github.com/NanoComp/meep/issues/1199)).
+In the future, Meep may provide built-in interpolation methods for material functions (see [\#1199](https://github.com/NanoComp/meep/issues/1199)).

python/examples/oblique-planewave.py

@@ -38,9 +38,10 @@
 sim.run(until=100)
 
 nonpml_vol = mp.Volume(center=mp.Vector3(), size=mp.Vector3(10,10,0))
-ez_data = sim.get_array(vol=nonpml_vol, component=mp.Ez)
 
-plt.figure()
-plt.imshow(np.flipud(np.transpose(np.real(ez_data))), interpolation='spline36', cmap='RdBu')
-plt.axis('off')
-plt.show()
+sim.plot2D(fields=mp.Ez,
+           output_plane=nonpml_vol)
+
+if mp.am_master():
+    plt.axis('off')
+    plt.savefig('pw.png',bbox_inches='tight')