Gaussian beam calculator

optics

Rayleigh range, divergence and beam radius w(z) from waist and wavelength.

For a Gaussian beam of waist \(w_0\) and wavelength \(\lambda\), the Rayleigh range is \(z_R = \dfrac{\pi w_0^2}{\lambda}\) and the radius grows as \(w(z) = w_0\sqrt{1 + (z/z_R)^2}\).

viewof w0 = Inputs.range([1, 500], {value: 50, step: 1, label: "Waist w₀ (µm)"})
viewof lambda_um = Inputs.range([0.4, 1.6], {value: 1.064, step: 0.001, label: "Wavelength λ (µm)"})
zR = Math.PI * (w0 * 1e-6) ** 2 / (lambda_um * 1e-6)
theta_mrad = (lambda_um * 1e-6) / (Math.PI * (w0 * 1e-6)) * 1e3
html`<p style="font-size:1.15rem;margin:.4rem 0 1rem">Rayleigh range&nbsp; <b>z<sub>R</sub> = ${(zR * 1e3).toLocaleString("en", {maximumFractionDigits: 2})} mm</b> &nbsp;·&nbsp; half-divergence&nbsp; <b>θ = ${theta_mrad.toFixed(2)} mrad</b></p>`

Plot.plot({
  width: 660, height: 280,
  marginLeft: 55,
  x: { label: "z (mm)" },
  y: { label: "beam radius w (µm)", grid: true },
  marks: [
    Plot.line(
      d3.range(-4, 4.02, 0.05).map(k => k * zR).map(z => ({ z: z * 1e3, w: w0 * Math.sqrt(1 + (z / zR) ** 2) })),
      { x: "z", y: "w", stroke: "#0E4D64", strokeWidth: 2 }
    ),
    Plot.line(
      d3.range(-4, 4.02, 0.05).map(k => k * zR).map(z => ({ z: z * 1e3, w: -w0 * Math.sqrt(1 + (z / zR) ** 2) })),
      { x: "z", y: "w", stroke: "#0E4D64", strokeWidth: 2, opacity: 0.4 }
    ),
    Plot.ruleX([-zR * 1e3, zR * 1e3], { stroke: "#6C4AB6", strokeDasharray: "4 3" })
  ]
})