Introduction

JEKray is an optical bench simulator that runs in the browser. You lay out sources, optics, fibres, electronics and chips on a 2D bench, and it works out what the light does: rays, beams, interference, cavities, and the signals your detectors would read.

These pages explain how it works. The free-space, fibre, electronics and chip pages set out the physics and the approximations behind each kind of model. Each element then has a page of its own, with its model, its equations, and the settings you can give it.

What it models

JEKray brings four kinds of model together on one bench, joined where light and signals pass from one to another:

• Free-space opticsExact ray tracing, Gaussian beams, the diffracted field, interference, cavities and pulses.
• Fibre opticsSingle-mode networks solved path by path, with phase, delay, polarisation and coherence.
• ElectronicsSteady-state signals as tones and noise, through amplifiers, filters, mixers and instruments.
• Photonic chipsCompact scattering-matrix models of couplers, rings and phase shifters, solved as one linear system.

What it does not model

Every free-space part is placed freely in space: its x and y on the bench, its z (height above it, 0 to 2 m), and its facing, tip and roll, all six degrees of freedom. The light is followed in three dimensions through all of it, and the 3D view shows it (see Free-space optics: heights). What is left out:

• Fibre, electronic and chip parts lie in the plane: the 3D view leaves them out.
• Aberrations across a field of view are worked out in the tangential section.
• There are no mechanics and no heating: mounts, forces on optics and thermal lensing are not modelled. Optical forces on atoms and small particles in a trap are the exception.

Each modelling page ends with the limits of its own models, and each element page lists the assumptions its model makes.

How the models fit together

1. The tracer follows rays through the free-space optics, with exact geometry, real glass, polarisation and optical path. Along the way it builds the beam tree: every branch a Gaussian beam takes at splitters, surfaces and round trips in cavities.
2. The field engine propagates each source’s diffracted field along that tree, adds the branches of one laser as fields, and solves cavities in their steady state.
3. The fibre network takes in the light that reaches fibre tips by mode overlap, follows every path through couplers, circulators and amplifiers, and sends light back out of tips into free space.
4. The chip solver treats each photonic chip as one part of the fibre network, with a scattering matrix found by solving its circuit at each wavelength.
5. The electronics read photodiodes and drive lasers and modulators. Light is worked out quasi-statically against the slow electrical signals.

Conventions in these pages

Lengths are in millimetres unless a unit is given, angles in degrees, wavelengths in nanometres. The bench’s x is to the right and y is up. s polarisation is out of the bench plane and p is in it. Fields go as \(e^{-ikz}\) (Siegman’s convention), so a Gaussian beam is \(\exp(-ikr^2/2q)\) with \(q = z + i z_R\). The Concepts page sets these out in full.

Checking the models

The validation page compares JEKray with analytic results and published data, case by case, and runs in your browser. Element pages link to the cases that test them.