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Solve an ideal Gaussian laser beam: Rayleigh range, divergence, radius at a distance, and the waist behind a focusing lens.

gaussianBeam

Solve an ideal Gaussian laser beam: Rayleigh range, divergence, radius at a distance, and the waist behind a focusing lens.

The identical function behind the worked examples on /lab/gaussian-beam-calculator, built from the same q-propagation the calculator runs. Give a wavelength and a 1/e^2 waist radius to get the Rayleigh range, the far-field half-angle divergence and the depth of focus. Add distance (metres from the waist) for the beam radius and phase-front curvature there. Add focal (millimetres) to put a thin lens at the waist and get the focused waist radius, its distance behind the lens and its Rayleigh range.

Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
focalNoFocal length in millimetres of a thin lens placed at the waist. When given, the result includes the focused waist.
waistYes1/e^2 waist RADIUS in millimetres (not the diameter). At least one wavelength: the model is paraxial.
distanceNoDistance in metres, from the waist (or, when `focal` is given, from the lens, after it). Negative is upstream. When given, the result includes the beam radius and phase-front curvature there.
wavelengthYesVacuum wavelength in nanometres (632.8 for HeNe, 1064 for Nd:YAG).

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
inputsYesThe parsed inputs, echoed back with defaults filled in.
resultYesThe solved analysis. Shape is per-tool.
licenseYes
provenanceYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A4.4/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the behavioral burden and does so well by explaining the q-propagation model, conditional result fields, and the provenance.canonicalUrl included in every result. It could add more about failure modes or input constraints, but the core calculation behavior is disclosed.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is front-loaded with the core purpose and then proceeds through optional inputs and provenance in a logical order. The opening sentence repeats the title, but the rest is efficient and informative.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the output schema exists, the description does not need to detail return fields, and it instead supplies the missing behavioral and conditional-input context. It is complete enough for an agent to invoke the tool correctly with or without the optional parameters.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is already 100%, so the baseline is 3, but the description adds relational meaning by explaining that `distance` is from the waist unless `focal` places it from the lens, and that `focal` creates a focused-waist result. This goes beyond the individual parameter descriptions in the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific verb and resource: solving an ideal Gaussian laser beam, with named outputs including Rayleigh range, divergence, radius at a distance, and focused waist. It is clearly distinct from the listed sibling tools, which are unrelated calculators except for the broader opticsResonator.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description gives clear context for use by explaining what the two required inputs return and how adding `distance` or `focal` changes the output. It does not name an alternative tool or explicitly state when not to use this one, but no close alternative is present among the siblings.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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