Gaussian Beam

Worked optical design

Design a fiber collimator from MFD

A single-mode fiber supplies a Gaussian waist at its facet. DiffBeam uses the mode-field diameter, wavelength, focal length, and spacing to calculate the emerging beam rather than treating the collimator as a geometric ray source.

Example: 5 µm MFD at 689 nm

A 5 µm mode-field diameter corresponds to a 2.5 µm Gaussian radius. In the paraxial approximation, the free-space divergence half-angle is about λ/(πw0) = 0.0877 rad. Placing a 15.3 mm effective-focal-length collimator one focal length from the facet gives a first estimate of roughly fλ/(πw0) = 1.34 mm beam radius, or about 2.68 mm diameter.

That estimate is useful, but the final design should be solved. Real fiber collimators often use characteristic effective focal lengths such as 4.6, 6.2, 9.6, 11, 15.3, or 18.4 mm rather than the round focal-length ladder used for ordinary telescope lenses. Those values are engineering priors, not product or availability claims. DiffBeam should never invent a part number.

Compact authored system

{
  "wavelength": {"value": 689, "unit": "nm", "fixed": true},
  "optical_chain": [
    {"stage": 0, "type": "fiber_end", "parameters": {
      "mfd": {"value": 5, "unit": "µm", "fixed": true},
      "dz": {"value": 0, "unit": "mm", "fixed": true}}, "resultingBeam": {}},
    {"stage": 1, "type": "lens", "parameters": {
      "f": {"value": 15.3, "unit": "mm", "fixed": true},
      "dz": {"unit": "mm", "fixed": true, "expr": "l1_f"}}, "resultingBeam": {}}
  ]
}

What the agent should check

  • MFD is a diameter while the propagated Gaussian quantity w0 is a radius.
  • The lens is positioned from the fiber facet, not from an unrelated global origin.
  • The requested wavelength lies within the intended optical coating range when real hardware is requested.
  • The calculated beam fits the clear aperture with margin for Gaussian tails.
  • If an exact downstream diameter is required, keep the collimator realistic and let a following telescope provide the exact ratio.

An AI can publish this candidate quickly through the Direct Agent Bridge or validate and simulate it through the DiffBeam MCP server. Catalog lookup should be deferred unless the user asks for purchasable parts. DiffBeam does not host or proxy a language model; it supplies deterministic optics calculations and a live planner preview.