Gaussian Beam

Worked optical design

Design a 4F Gaussian beam expander

A 4F or afocal telescope expands a collimated beam by the focal-length ratio. DiffBeam turns that first-order rule into a calculated Gaussian-beam system, checks the actual waist and divergence, and can publish the candidate as a live workspace preview.

Example: expand a 4 mm beam to 12 mm

Assume the stated dimensions are 1/e² beam diameters, so the input radius is 2 mm and the target radius is 6 mm. The required magnification is therefore 3×. A practical stock-like Keplerian pair is 50 mm and 150 mm. For collimated input, the ideal afocal separation is f1 + f2 = 200 mm. The output divergence is approximately one third of the input divergence.

The focal-length ratio is only the start. A useful design must also check the wavelength, the beam's complex q parameter at the first lens, the radius on every optic, and whether the second lens has enough clear aperture. A 12 mm output beam generally calls for a substantially larger optic than a 12.7 mm nominal lens because Gaussian tails extend beyond the 1/e² diameter.

Fast agent workflow

  1. Read the current workspace or create an authored compact system.
  2. Compute the magnification before selecting lenses.
  3. Prefer common focal lengths such as 25, 50, 75, 100, 150, 200, or 250 mm before proposing an oddly precise value.
  4. Use an expression for the separation so the afocal relation stays explicit.
  5. Preview the candidate immediately, then refine only if the solved output misses the target.
{
  "wavelength": {"value": 1064, "unit": "nm", "fixed": true},
  "optical_chain": [
    {"stage": 0, "type": "gaussian_beam", "parameters": {
      "w0": {"value": 2, "unit": "mm", "fixed": true},
      "dz": {"value": 0, "unit": "mm", "fixed": true}}, "resultingBeam": {}},
    {"stage": 1, "type": "lens", "parameters": {
      "f": {"value": 50, "unit": "mm", "fixed": true}}, "resultingBeam": {}},
    {"stage": 2, "type": "lens", "parameters": {
      "f": {"value": 150, "unit": "mm", "fixed": true},
      "dz": {"unit": "mm", "fixed": true, "expr": "l1_f + l2_f"}}, "resultingBeam": {}}
  ]
}

Use the planner to inspect the entire envelope. An MCP-capable client can call validate_optical_system and simulate_optical_system; an internet-capable agent connected to a workspace can use the Direct Agent Bridge. A catalog search is optional and should happen only when the user requests real purchasable components.

DiffBeam does not host or proxy a language model. It supplies deterministic Gaussian beam validation, solving, and visualization, while the user's chosen AI explains the trade-offs.