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Optics

Laser Beam Divergence Calculator

Calculate divergence, Gaussian beam propagation, Rayleigh range, M² beam quality, and spot size at distance.

Interactive calculator

Laser Beam Divergence Calculator

Calculate diffraction-limited divergence, Gaussian beam propagation, Rayleigh range, beam quality M², and spot size at distance.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: diffraction-limited divergence, beam diameter at distance, Gaussian beam, Rayleigh range, M², or spot size.
  • Use presets for common laser types (HeNe, Nd:YAG, CO₂, fiber).
  • Click Calculate for detailed results.

Table of Contents

Key Takeaways

  • Gaussian beam divergence: θ = λ/(πw₀) — smaller waist means larger divergence.
  • Rayleigh range zR = πw₀²/λ defines the near-field region where the beam stays collimated.
  • M² ≥ 1 measures beam quality; M² = 1 is a perfect TEM₀₀ mode.
  • Diffraction-limited divergence (1.22λ/D) is the theoretical minimum for a given aperture.
  • Beam expanders reduce divergence but increase beam diameter proportionally.

Laser Beam Divergence

All laser beams spread as they propagate due to diffraction. The divergence angle characterises how quickly the beam expands. Understanding divergence is essential for laser alignment, communication links, material processing, and scientific measurements.

Key Formulas

θ=λπw0\theta = \frac{\lambda}{\pi w_0}
zR=πw02λz_R = \frac{\pi w_0^2}{\lambda}
w(z)=w01+(zzR)2w(z) = w_0\sqrt{1 + \left(\frac{z}{z_R}\right)^2}

Where w₀ is the beam waist radius, λ is the wavelength, zR is the Rayleigh range, and w(z) is the beam radius at distance z from the waist.

Gaussian Beam Optics

A Gaussian beam (TEM₀₀ mode) has an intensity profile that follows a Gaussian distribution. It is the fundamental mode of most laser cavities and represents the lowest possible divergence for a given beam waist. The M² factor quantifies how close a real beam is to this ideal.

How to Use

  1. Select a mode from the dropdown.
  2. Enter beam parameters (waist, wavelength, distance).
  3. Click Calculate. Results include Rayleigh range and expansion ratios.

Examples

HeNe laser (632.8 nm, w₀ = 0.5 mm)

θ = 632.8 nm / (π × 0.5 mm) = 0.40 mrad; zR = π × (0.5 mm)² / 632.8 nm = 1.24 m

CO₂ laser (10.6 μm, w₀ = 5 mm)

θ = 10.6 μm / (π × 5 mm) = 0.68 mrad; zR = π × (5 mm)² / 10.6 μm = 7.42 m

FAQ

What is beam divergence?›

Beam divergence is the angular spread of a laser beam as it propagates. It's measured as the far-field half-angle (for Gaussian beams) or full angle. Lower divergence means the beam stays collimated over longer distances.

What is the Rayleigh range?›

The Rayleigh range (zR) is the distance from the beam waist where the beam area doubles (radius increases by √2). Within the Rayleigh range, the beam is considered collimated. zR = πw₀²/λ.

What does M² mean?›

M² (M-squared) is the beam quality factor. It measures how many times the beam divergence exceeds the ideal Gaussian beam. M² = 1 is perfect. Single-mode fiber lasers typically have M² < 1.1; industrial lasers can be 10-100.

How do I reduce divergence?›

Use a beam expander — it increases the beam diameter by factor M while reducing divergence by the same factor. Alternatively, improve beam quality (lower M²) or use a shorter wavelength.

What is the far field?›

The far field begins at distances much greater than the Rayleigh range (z >> zR). In this region, the beam expands linearly with distance and the divergence angle is constant.

Sources

  1. Saleh & Teich – Fundamentals of Photonics
  2. Thorlabs – Gaussian Beam Optics
  3. RP Photonics – Beam Divergence
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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