Data fields: 

example_inverse_curvatures: The inverse curvatures of the spherical mirror investigated for the example geometry. Units: inverse metres
example_spherical_cints: The C_{int}^{min} of the cavities with spherical mirrors in the example geometry. Units: dimensionless
expected_spherical_performance: The expected maximum C_{int}^{min} achievable in the example geometry with a spherical mirror
expected_spherical_inverse_curvature: The inverse radius of curvature of the spherical mirror at this expected maximum achievable C_{int}^{min}. Units: inverse metres
example_optimised_cint: The C_{int}^{min} achievable through retroreflective optimisation in the example geometry. Units: dimensionless

spherical_r: Radial coordinate values to plot the spherical surface that maximises C_{int}^{min}. Units: metres
spherical_protrusion : The protrusion of the spherical surface that maximises C_{int}^{min}. Units: metres
surface_r: Radial coordinate values to plot the retroreflective optimised surface. Units: metres
surface_protrusion: The protrusion of the retroreflective optimised surface. Units: metres
surface_residuals: The residuals of the retroreflective optimised surface from the spherical surface that maximises C_{int}^{min} (i.e. surface_residuals = surface_protrusion - spherical_protrusion). Units: metres
centre_radius_fit_protrusion: The protrusion of the fit to the centre radius of curvature. Units: metres
outer_radius_fit_protrusion: The protrusion of the fit to the outer radius of curvature. Units: metres
fit_r_centre: The fit value of the radius of curvature of the central portion of the two-curvature fit. Units: metres
fit_r_outer: The fit value of the radius of curvature of the outer portion of the two-curvature fit. Units: metres
fit_critical_radius: The fit value of the radius at which the central curvature transforms to the outer curvature. Units: metres

emitter_r_array: Radial coordinate values at which the intensity of the modes are calculated in the emitter plane. Units: metres
emitter_intensities_spherical_mirror: Intensities of the mode in the emitter plane for the cavity with the spherical mirror. Units: inverse metres squared
emitter_intensities_optimised_mirror': Intensities of the mode in the emitter plane for the cavity with the optimised mirror. Units: inverse metres squared
mirror_r_array: Radial coordinate values at which the intensity of the modes are calculated in the mirror plane. Units: metres
mirror_intensities_spherical_mirror: Intensities of the mode in the mirror plane for the cavity with the spherical mirror. Units: inverse metres squared
mirror_intensities_optimised_mirror: Intensities of the mode in the mirror plane for the cavity with the optimised mirror. Units: inverse metres squared
mirror_clipping_radius: physical radius (i.e. half the diameter) of the mirror. Units: metres

density_zz: Axial coordinates of the intensity values for the density plot. Units: metres
density_xx: Transverse x coordinates of the intensity values for the density plot. Units: metres
spherical_mirror_mode_density: Intensities of the mode with the spherical mirror that maximises C_{int}^{min} for the density plot. Units: inverse metres squared
optimised_mirror_mode_density: Intensities of the mode with the optimised for the density plot. Units: inverse metres squared 
surface_r_reduced: Radial coordinate values to plot the retroreflective optimised surface in the density plot. Units: metres
surface_protrusion_reduced: The protrusion of the retroreflective optimised surface in the density plot. Units: metres
example_emitter_separation: The distance along the cavity axis separating the emitters in the example case. Units: metres
example_length: The length of the cavity in the example case

scan_lengths: The lengths over which the cavity geometry was scanned. Units: metres
scan_emitter_separation_to_length_ratio: The ratios of emitter separation to length over which the cavity geometry was scanned. Units: dimensionless
scan_spherical_cints: The values of C_{int}^{min} for the best spherical mirrors over the scan of geometry. Units: dimensionless
scan_optimised_cints: The values of C_{int}^{min} for the optimised mirrors over the scan of geometry. Units: dimensionless
s_over_l_crits: The emitter separation to length ratios that correspond to s_crit. Units: dimensionless
l_for_d_crit: The length at which the cavity mirror diameter is D_crit (a single value for the dataset). Units: metres
example_emitter_separation_to_length_ratio: The ratio of emitter separation to length in the example case. Units: dimensionless
cint_improvement_factor: The factor by which C_{int}^{min} is improved over the best spherical case by performing retroreflective optimisation. i.e. cint_improvement_factor = scan_optimised_cints / scan_spherical_cints
 

Figure plots:

Panel a:
Black line: example_inverse_curvatures vs example_spherical_cints
Black crosshair: x value: expected_spherical_inverse_curvature, y value: expected_spherical_inverse_curvature
Blue horizontal line: example_optimised_cint

Panel b:
Black line: spherical_r vs spherical protrusion (identical data plotted for negative r)
Blue line: surface_r vs surface_protrusion (identical data plotted for negative r)
Red line: surface_r vs surface_residuals (identical data plotted for negative r)
Green dotted curve: surface_r vs centre_radius_fit_protrusion (identical data plotted for negative r)
Green dashed curve: surface_r vs outer_radius_fit_protrusion (identical data plotted for negative r)
Thin green vertical dashed line: fit_critical_radius (identical data plotted for negative r)

Panel c:
i:
Black line: emitter_r_array vs emitter_intensities_spherical_mirror (identical data plotted for negative r)
Blue line: emitter_r_array vs emitter_intensities_optimised_mirror (identical data plotted for negative r)
ii:
Black line: mirror_r_array vs mirror_intensities_spherical_mirror (identical data plotted for negative r)
Blue line: mirror_r_array vs mirror_intensities_optimised_mirror (identical data plotted for negative r)
Black vertical line: mirror_clipping_radius (identical data plotted for negative r)

Panel d:
i:
Heat map: spherical_mirror_mode_density on the coordinate grid laid out by density_zz vs density_xx. i.e. for all x and y indices in the arrays, the value spherical_mirror_mode_density[y_index, x_index] is placed at density_zz[y_index, x_index] on the horizontal axis and density_xx[y_index, x_index] on the vertical axis. 
Right white line: spherical_r vs spherical_protrusion (titled vertical, placed at plus 0.5 * example_length, and with identical data plotted for negative x)
Left white line: The right white line reflected
ii:
Heat map: optimised_mirror_mode_density on the coordinate grid laid out by density_zz vs density_xx. i.e. for all x and y indices in the arrays, the value optimised_mirror_mode_density[y_index, x_index] is placed at density_zz[y_index, x_index] on the horizontal axis and density_xx[y_index, x_index] on the vertical axis. 
Right white line: surface_r_reduced vs surface_protrusion_reduced (titled vertical, placed at plus 0.5 * example_length, and with identical data plotted for negative x)
Left white line: The right white line reflected
Green diagonal guide lines: 8 individual line segments. The following details the 4 lines at positive transverse coordinate (the y axis of the graph), and the other 4 lines are the reflection to negative transverse coordinate. Lines expressed as (z_start, x_start) -> (z_end, x_end)
	1) (-0.5 * example_length, fit_critical_radius) -> (-0.5 * example_length + fit_r_centre, 0.0)
	2) (-0.5 * example_length, mirror_clipping_radius) -> (-0.5 * example_length + fit_r_outer, 0.0)
	3) (0.5 * example_length, fit_critical_radius) -> (0.5 * example_length - fit_r_centre, 0.0)
	4) (0.5 * example_length, mirror_clipping_radius) -> (0.5 * example_length - fit_r_outer, 0.0)
Green vertical dashed lines: positioned at z coordinates 0.5 * example_length - fit_r_centre and 0.5 * example_length - fit_r_outer 

both:
Cyan crosses: crosses at zero transverse coordinate and axial coordinates of plus/minus 0.5 * example_emitter_separation

Panel e:
i: 
Heat map: scan_spherical_cints (data) vs scan_lengths (x) and scan_emitter_separation_to_length_ratio (y)
ii:
Heat map: scan_optimised_cints (data) vs scan_lengths (x) and scan_emitter_separation_to_length_ratio (y)
both:
Vertical white line: l_for_d_crit
Diagonal white line: scan_lengths vs s_over_l_crits. This represents the critical separation
Green cross: example_length vs example_emitter_separation_to_length_ratio

Panel f:
Heat map: Heat map: cint_improvement_factor (data) vs scan_lengths (x) and scan_emitter_separation_to_length_ratio (y). Data only shown for length (x value) greater than l_for_d_crit
Green cross: example_length vs example_emitter_separation_to_length_ratio

