Optics
A laser lab on an optical table
Lasers, mirrors, lenses, splitters, slits and detectors on a table you can rearrange. The light is computed as real beams with a width, a phase and a polarisation, so interferometers make fringes, slits diffract, and a pair of mirrors around a gain medium lases only if it would in a real lab.
What you are looking at
A top-down view of an optical table, with holes every 25 mm. Each beam is drawn as a ribbon as wide as the beam itself, made a few times wider so you can see it, and as bright as its power on a logarithmic scale: a 1 mW beam and a 1 µW reflection are both visible. The colour is the colour of the wavelength; infrared and ultraviolet beams are drawn in a dim false colour.
Detectors show what reaches them. A screen shows the light falling on it; a camera adds noise and saturation; a power meter reads watts; a spectrometer spreads the light by wavelength. Click one and its reading opens in the Inspect tab. Pin it to keep its card on the table while you work.
The experiments
18 ready-made benches, each with its own guide.
Interference
- Michelson interferometer: Split a beam, send it down two arms and bring it back: fringes that move by nanometres.
- Mach–Zehnder interferometer: Two splitters, two mirrors, two outputs that share the light between them.
- Fabry–Pérot cavity: Two facing mirrors pass light only when it fits between them a whole number of times.
- Beat note between two lasers: Two lasers of slightly different colour make a photodiode flicker at their difference.
Diffraction
- Young’s double slit: Two slits a quarter of a millimetre apart, and fringes on a screen a metre away.
- Single-slit diffraction: A tenth of a millimetre of slit spreads a laser into a row of fading spots.
- Airy disc from a pinhole: A round hole makes a bright disc ringed by faint circles.
Polarisation
- Malus’s law and three polarisers: Crossed polarisers block everything, until a third one goes between them.
- Brewster’s angle: At one angle, glass reflects no light polarised in the plane of incidence.
- Wave plates and circular light: A quarter-wave plate at 45° turns linear light circular.
Rays and beams
- A prism’s spectrum: White light through glass fans out into its colours.
- Imaging with a lens: Rays from an arrow meet again behind a lens, upside down.
- Focusing a laser beam: A lens squeezes a laser to a waist tens of micrometres across, and no smaller.
- Beam expander: Two lenses a focal length apart make a beam four times wider.
- Scattering and fluorescence: A green beam through milky water and a dye: scattered light, and orange glow.
Lasers
- Build a HeNe laser: A discharge tube between two mirrors lases only when they are aligned and stable.
- Passive Q-switching: A saturable absorber turns a continuous Nd:YAG laser into a train of nanosecond pulses.
- Passive mode-locking: A fast saturable absorber locks a laser’s modes into picosecond pulses, c/2L apart.
Using the bench
Open the Parts tab and click a part to pick it up, or drag it onto the table. Select a part to see its settings, move it with the mouse or type its position, and turn it. Real optics sit on kinematic mounts with fine screws, and so do these: “Fine adjustment” tips and tilts a mirror by microradians and moves it by nanometres on a piezo, which is how you walk a beam into a pinhole or scan an interferometer.
Hover over a beam to read its power, width, wavelength and polarisation at that point. The Room tab sets the table’s isolation, air currents and temperature drift, and how the beams are drawn.
Everything you build is saved in your browser. Share copies a link that holds the whole bench, so whoever opens it sees exactly what you see; Save writes it to a file.
| Keys | What they do |
|---|---|
| Click a part in the Parts tab | Pick it up; click the table to put it down |
| Drag a part | Move it, snapping to 5 mm (hold Alt to move freely) |
| Shift-click | Add a part to the selection, or take it out |
| R, Shift+R | Turn the selection 15° anticlockwise or clockwise |
| [ and ] | Turn it by 1° |
| Arrow keys | Move it 1 mm, or 0.1 mm with Shift |
| Ctrl+D | Duplicate |
| Delete | Remove the selection |
| Ctrl+Z, Ctrl+Y | Undo and redo |
| F | Fit the table to the screen |
| Escape | Drop what you are holding, or clear the selection |
How the light is computed
Each beam is a Gaussian beam: a narrow bundle with a width , a wavefront curvature and a direction. Its size and curvature live in one complex number, the beam parameter , and every lens, mirror and stretch of free space changes it by the ABCD rule
A beam carries its polarisation as a Jones vector and its phase as the optical path it has travelled. At a splitter it divides into two beams that remember they came from the same laser. Where beams from one laser meet on a detector, their fields are added, not their powers:
That sum is what makes fringes. Beams from different lasers, or from a lamp, add as powers unless their wavelengths are close enough to beat.
Slits, pinholes, gratings and other apertures need more than beams: the lab replays the light through them by Fresnel propagation on a grid, using the Fourier transform, and the pattern on the screen comes from that calculation, not from a textbook formula.
When mirrors around a gain medium send light back on itself, the lab finds the closed loop, works out the cavity’s mode from its round trip, and balances saturated gain against the losses. If the gain wins it lases and a beam comes out of the output coupler; tilt a mirror by too much and it stops.
What the lab leaves out
- The table is flat: beams stay in its plane. Tip errors push a beam up or down and are counted as misalignment, but nothing is drawn in three dimensions.
- Beams are Gaussian everywhere except behind apertures, where the Fourier engine takes over. Thick lenses and prisms have real surfaces and refraction, but aberrations show only as rays missing their focus.
- Lasers run steadily, or in a steady train of identical pulses when a saturable absorber Q-switches or mode-locks them; the pulses are worked out in closed form, not built up round trip by round trip. There is no dispersion or Kerr effect in a cavity, no nonlinear crystals, and no electronics to drive a Pockels cell, a chopper or a lock-in.
- Photon sources give count rates. Single clicks, coincidences and the correlations between a photon pair’s two arms are not simulated.
References
- E. Hecht (2017), Optics, 5th edition, Pearson.
- B. E. A. Saleh and M. C. Teich (2019), Fundamentals of Photonics, 3rd edition, Wiley.
- A. E. Siegman (1986), Lasers, University Science Books.
- H. Kogelnik and T. Li (1966), Laser beams and resonators, Applied Optics 5, 1550.
- J. W. Goodman (2017), Introduction to Fourier Optics, 4th edition, W. H. Freeman.
