Screen

Free space "type": "screen"

A screen records what arrives on its face: the rays and the diffracted field. Its panel reads them out as a spot and a profile, a point spread function and MTF, aberrations across the field, the pulse that arrives, and an optical trap at its focus.

The model

A screen is a line across the bench, flat or curved, facing the light it records. By default it stops the light it records. Untick Stop the rays it records and it samples the light without stopping it, so a screen can sit in the middle of a system. A curved screen’s centre of curvature can be on either side. A negative radius puts it on the side the light comes from, like a retina.

Rays

Each ray that lands is recorded with where it lands, its power, its direction, its optical path and its polarisation. From the rays the screen gives:

• the spot’s power, its centroid \(\bar y\) and its RMS radius about the centroid, weighted by power:

  \[\sigma_y = \sqrt{\frac{\sum_k P_k\,(y_k - \bar y)^2}{\sum_k P_k}};\]
• the binned intensity, rays of one launch added as fields bin by bin, which shows interference fringes;
• the wavefront: each ray’s optical path to a reference sphere centred on the centroid, as an RMS and peak-to-valley error.

With interpolation on (the default, binInterp), each beam of rays is laid onto the bins as a sampled wavefront before the fields are added, which stops fringes aliasing against the ray spacing.

The diffracted field

The Diffraction tab shows the field that arrives from every Gaussian beam and every ray fan:

• Gaussian beams, from the field engine;
• Ray fans, taken as uniform pupils of their width and curvature.

Light from separate lasers counts for each one’s power: the map and figures are per unit power of the strongest arrival’s laser, the others in proportion. From the strongest arrival it gives the irradiance map, the point spread function, the MTF (quoted at a spatial frequency you set), enclosed energy, and the Strehl ratio. Strehl is the peak against the peak a perfect wave from the same amplitude at the last surface would reach, which makes defocus against the screen count.

Near a steep focus the vector focal field is used (Vector focus: auto, on or off), so a screen at the focus of a high-NA objective shows the field along the axis too (see Free-space optics: steep foci).

The map is placed where the light lands on the face, above or below its centre too, and on a screen tipped or rolled out of the plane it is the pattern on the face itself, stretched up it where the light meets it at a slope.

Phase shows the phase of the field across the screen, from −π to π as hue, its brightness the field’s amplitude. It is taken along the polarisation of the brightest point, whose phase is zero there. A beam meeting the screen at an angle shows tilt fringes, a diverging or converging one rings of its curvature, and a vortex turns once round its dark core for each unit of its charge. With several lasers, only the strongest one’s light has a phase.

Polarisation shows the polarisation point by point: the colour is how circular it is (S3/S0, red right-handed, blue left-handed, white linear), its brightness the irradiance, and an ellipse every few pixels traces the field there, its long axis along the polarisation (across the map is in the bench plane, p; up it, out of the plane, s). Separate lasers add as Stokes parameters, so where they overlap the light is partly polarised and the ellipses shrink with its degree of polarisation. The overall Stokes parameters and degree of polarisation are listed under the map.

Show its diffraction pattern on its face (3D view) paints the map onto the screen’s face in the 3D view, where the light lands, in the same colours and scale as the tab (linear or log). It updates as the field is worked out again.

Aberrations

The Aberrations tab sweeps a fan source across the field:

• a collimated source by a field angle;
• a diverging source (a point object) by an object height.

The fan is traced again at each field. Where an aperture stop lies further along, each field’s chief ray is aimed through the stop’s centre. At each field the screen gives the chief ray (so the distortion), the spot, the best focus along the screen’s normal (the tangential field curvature), and the wavefront, carried back to a sphere about where the chief ray lands. The wavefront is fitted with Zernike polynomials along the meridian, and across the fields with Seidel’s terms \(W_{040}, W_{131}, W_{222}, W_{311}\).

The bench is two-dimensional, so this is the tangential (meridional) section only: astigmatism shows as a focus that moves with the field.

Pulses

For a pulsed source, the Pulse tab shows the pulse that arrives: its duration, group delay, GDD and TOD, from a polynomial fit to its spectral phase, with its spatial chirp and pulse-front tilt. Branches of one laser add as fields, separate lasers and the two polarisations as powers.

Optical traps

The Trap tab reads an optical trap near the screen, for an atom (rubidium, caesium, potassium or sodium) or a dielectric sphere. Every beam through the screen’s region is taken as its full vector field near the focus. Beams of one laser add as fields, so two counter-propagating beams make a standing-wave trap.

For an atom, the polarisability comes from its D lines, with the counter-rotating terms that matter far from resonance:

with the scattering rate \(\operatorname{Im}(\alpha)\,I/(\hbar\varepsilon_0 c)\), plus the ion core’s own polarisability.

For a sphere smaller than the wavelength, the polarisability is the Clausius–Mossotti one with radiation reaction. With \(m = n_p/n_m\) and \(k = 2\pi n_m/\lambda\), the force is \(\mathbf F = \tfrac12\operatorname{Re}\!\left(\alpha \sum_j E_j \nabla E_j^*\right)\), where

From the brightest point, Newton’s method on the force finds where it is zero. The stiffness there gives the trap frequencies each way. The tab also gives the depth (in kelvin, and in units of \(kT\)), the scattering rate and recoil heating, and for a sphere the damping by the gas around it.

Settings

From the tool's own tables, file format version 1: the names are those in a .jekray file.

Assumptions

Related

• Source, for what launches the light.
• Photodetector, for an electrical signal from the light.