Laser Beam Divergence Calculator
Free calculate laser beam divergence angle from wavelength, beam diameter, and m² beam quality factor.
Input Parameters
Beam waist diameter (2w₀)
M² = 1 for ideal Gaussian beam, >1 for real beams
Results
Enter parameters to calculate
What is Laser Beam Divergence?
Laser beam divergence is the angular spread of a laser beam as it propagates through space. Even well-collimated laser beams expand due to diffraction, with the divergence angle depending on wavelength, beam diameter, and beam quality.
Divergence is typically measured as the half-angle (θ) in radians or milliradians. Smaller divergence means a more collimated beam that stays focused over longer distances. Ideal Gaussian beams have the minimum possible divergence for a given beam diameter.
The M² factor (beam quality factor) quantifies how close a real beam is to an ideal Gaussian beam. M² = 1 for perfect Gaussian beams, while M² > 1 indicates deviations from the ideal, resulting in larger divergence.
Laser Beam Divergence Formula
Where:
- • θ = Half-angle divergence (radians)
- • M² = Beam quality factor (≥ 1)
- • λ = Wavelength (m)
- • D = Beam waist diameter (m)
For ideal Gaussian beam (M² = 1):
θ = 2λ / (π × D)
Note: Full divergence angle = 2θ
How to Calculate
-
1
Convert all units to meters
Convert wavelength (nm → m) and beam diameter (mm → m) for consistent calculations.
-
2
Determine M² factor
Use M² = 1 for ideal Gaussian beams, or the measured value for real laser beams.
-
3
Apply the formula
Calculate θ = (2 × M² × λ) / (π × D) to get half-angle divergence in radians.
Practical Examples
Example 1: HeNe Laser
A HeNe laser (λ = 632.8 nm) with 5 mm beam diameter and M² = 1. Calculate divergence.
Solution:
λ = 632.8 nm = 6.328×10⁻⁷ m, D = 5 mm = 0.005 m
θ = (2 × 1 × 6.328×10⁻⁷) / (π × 0.005)
θ ≈ 8.05×10⁻⁵ rad ≈ 0.0046° ≈ 0.08 mrad
Example 2: Real Laser with M² = 1.5
Same laser but with M² = 1.5 (typical for many lasers).
Solution:
θ = (2 × 1.5 × 6.328×10⁻⁷) / (π × 0.005)
θ ≈ 1.21×10⁻⁴ rad ≈ 0.12 mrad (50% larger!)
Applications
Laser Cutting
Understanding beam spread for precision cutting, determining spot size at focus, and optimizing cutting parameters.
Optical Communications
Calculating beam spread for free-space optical links, determining receiver requirements, and link budget analysis.
Medical Lasers
Ensuring precise beam delivery in medical procedures, calculating treatment area, and safety considerations.
Research
Characterizing laser beams, understanding beam propagation, and designing optical systems for experiments.
Frequently Asked Questions
What is the M² factor?
M² (M-squared) is the beam quality factor that compares a real beam to an ideal Gaussian beam. M² = 1 for perfect Gaussian beams, while M² > 1 indicates worse beam quality and larger divergence.
How does wavelength affect divergence?
Shorter wavelengths (blue/violet) have smaller divergence than longer wavelengths (red/IR) for the same beam diameter. This is why blue lasers can be focused to smaller spots.
What is the difference between half-angle and full-angle divergence?
Half-angle (θ) is measured from the beam axis to one edge. Full divergence angle is 2θ, measured from edge to edge. The formula gives half-angle divergence.
Can divergence be reduced?
Yes! Larger beam diameter reduces divergence. Beam expanders increase beam size to reduce divergence. Better beam quality (lower M²) also helps, but is limited by the laser's fundamental properties.
What is a typical divergence value?
Typical values range from 0.1-1 mrad for well-collimated lasers. High-quality lasers can achieve <0.1 mrad, while diode lasers often have 5-20 mrad divergence due to their small beam diameter.