Data fields: 

length: the cavity length. Units: metres
wavelength: The resonant wavelength: Units: metres
mirror_radius: The radius (i.e. half-diameter) of the non-planar mirror. Units: metres


surface_x: radial coordinates at which the surfaces are sampled. Ranges from 0 to the mirror radius. Units: metres
spherical_protrusion: The protrusion of the best spherical mirror at the points of surface_x. Units: metres
surface_protrusion: The protrusion of the retroreflective optimised surface at radial coordinates of surface_x. Units: metres
surface_residuals: Residuals of the retroreflective optimised surface from the best spherical surface (i.e. surface_resduals = surface_protrusion-spherical_protrusion). Units: metres

length_deltas: Changes in length from the nominal used for the length scan. Units: metres
length_scan_cint: C_{int}^{0} for the retroreflective optimised cavity for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless
length_scan_spherical_cint: C_{int}^{0} for the cavity with the best spherical radius of curvature (from inline equation just preceding Eq. (9) in the manuscript) for the length changes from nominal in length_deltas. At each length, the mode with the best C_{int}^{0} is chosen. Units: dimensionless

emitter_intensity_x: The radial coordinates at which intensity samples were taken over the emitter plane. Units: metres
spherical_emitter_intensities: The mode intensity in the emitter plane for the cavity with the best spherical radius of curvature (from inline equation just preceding Eq. (9) in the manuscript). Units: inverse metres squared
retroreflective_optimised_emitter_intensities: The mode intensity in the emitter plane for the retroreflective optimised cavity. Units: inverse metres squared
mirror_intensity_x: The radial coordinates at which intensity samples were taken over the mirror plane. Units: metres
spherical_mirror_intensities: The mode intensity in the mirror plane for the cavity with the best spherical radius of curvature (from inline equation just preceding Eq. (9) in the manuscript). Units: inverse metres squared
retroreflective_optimised_mirror_intensities: The mode intensity in the mirror plane for the retroreflective optimised cavity. Units: inverse metres squared

density_z: The axial coordinate of samples in the mode density plot. A 2D array indexed in order (y_index, x_index). Units: metres
density_x: The transverse (for example 'x', but the cavity is radially symmetric) coordinate of samples in the mode density plot. A 2D array indexed in order (y_index, x_index). Units: metres
density_spherical: The mode intensity at the corresponding axial and transverse coordinates of density_z and density_x for the mode of the cavity with the best spherical radius of curvature (from inline equation just preceding Eq. (9) in the manuscript). A 2D array indexed in order (y_index, x_index). Units: inverse metres squared
density_optimised: The mode intensity at the corresponding axial and transverse coordinates of density_z and density_x for the mode of the retroreflective optimised cavity. A 2D array indexed in order (y_index, x_index). Units: inverse metres squared

 

Figure plots:

Panel a:
Black line: surface_x vs spherical_protrusion (identical data plotted for negative r)
Blue line: surface_x vs surface_protrusion (identical data plotted for negative r)
Red line: surface_x vs surface_residuals (identical data plotted for negative r)

Panel b:
Blue line: length_deltas vs length_scan_cint
Black line: length_deltas vs length_scan_spherical_cint

Panel c:
i:
Blue line: emitter_intensity_x vs retroreflective_optimised_emitter_intensities (identical data plotted for negative r)
Black line: emitter_intensity_x vs spherical_emitter_intensities (identical data plotted for negative r)
ii:
Blue line: mirror_intensity_x vs retroreflective_optimised_mirror_intensities (identical data plotted for negative r)
Black line: mirror_intensity_x vs spherical_mirror_intensities (identical data plotted for negative r)
Black vertical line: mirror_radius (identical data plotted for negative r)

Panel d:
i:
Heat map: density_spherical on the coordinate grid laid out by density_z vs density_x. i.e. for all x and y indices in the arrays, the value density_spherical[y_index, x_index] is placed at density_z[y_index, x_index] on the horizontal axis and density_x[y_index, x_index] on the vertical axis. 
Left white line: perfectly vertical
Right white line: surface_x vs spherical_protrusion (titled vertical, and with identical data plotted for negative x)
ii:
Heat map: density_optimised on the coordinate grid laid out by density_z vs density_x. i.e. for all x and y indices in the arrays, the value density_optimised[y_index, x_index] is placed at density_z[y_index, x_index] on the horizontal axis and density_x[y_index, x_index] on the vertical axis. 
Left white line: perfectly vertical
Right white line: surface_x vs surface_protrusion (titled vertical, and with identical data plotted for negative x)


