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} of the cavities with spherical mirrors in the example geometry. Units: dimensionless
example_ansatz_cints = The C_{int} of the cavities designed through the retroreflective ansatz method. This is a 2D array, where the first index corresponds to the inverse curvature, and the second index corresponds to the number of states used in the retroreflective ansatz. A second index of 0 corresponds to 2 states in the retroreflective ansatz, with the number of states incrementing by one per index from there. Units: dimensionles
example_optimised_cint: The C_{int} 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
residuals_protrusion: 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

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_length: The length of the cavity in the example case

scan_lengths: The lengths over which the cavity geometry was scanned. Units: metres
scan_mirror_diameter_to_length_ratio: The ratios of mirror_diameter 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
d_over_l_crits: The mirror diameter to length ratios that correspond to D_crit. Units: dimensionless
example_mirror_diameter: The cavity mirror diameter in the example case. Units: metres
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
under_critical_diameter_mask: Boolean mask which is true when the configuration of the scan corresponds to a mirror diameter below D_crit. Units: boolean
 



Figure plots:

Panel a:
Black line: example_inverse_curvatures vs example_spherical_cints
Black horizontal dashed line: The maximum value of example_spherical_cints
Blue horizontal line: example_optimised_cint
Purple dashed lines: example_inverse_curvatures vs example_ansatz_cints[:,n-2], where n is the number of states used in the retroreflective ansatz (labelled on each line)

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 residuals_protrusion (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. 
Left white line: perfectly vertical
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
both:
Cyan crosses: crosses at the origin

Panel e:
i: 
Heat map: scan_spherical_cints (data) vs scan_lengths (x) and scan_mirror_diameter_to_length_ratio (y)
ii:
Heat map: scan_optimised_cints (data) vs scan_lengths (x) and scan_mirror_diameter_to_length_ratio (y)
both:
Diagonal white line: scan_lengths vs d_over_l_crits. This represents the critical diameter
Green cross: example_length vs example_mirror_diameter / example_length

Panel f:
Heat map: Heat map: cint_improvement_factor (data) vs scan_lengths (x) and scan_mirror_diameter_to_length_ratio (y). Data only shown when under_critical_diameter_mask is False 
Green cross: example_length vs example_mirror_diameter / example_length





