Half Angle Divergence
θ₀ = M² × λ / (π × w₀)
Where θ₀ is the half angle divergence in radians
Laser Beam Divergence Calculator
Calculate laser beam divergence angles, far field beam diameters, and analyze Gaussian beam propagation characteristics. Essential for optical system design and laser safety calculations.
Class 1-4 Compatible
Input Parameters
dimensionless
M² = 1 for ideal Gaussian beam, >1 for real beams Calculation Results
Divergence Angles
Half Angle Divergence - mrad
Full Angle Divergence - mrad
Divergence (degrees) - °
Beam Characteristics
Rayleigh Length - mm
Beam Radius at Distance - mm
Beam Diameter at Distance - mm
Beam Classification
Calculate to see beam type
Formula and Theory
Rayleigh Length
z_R = π × w₀² / (M² × λ)
Distance over which beam area doubles
Beam Radius at Distance z
w(z) = w₀ × √(1 + (z/z_R)²)
For distances beyond Rayleigh length: w(z) ≈ θ₀ × z
Understanding Beam Divergence
- Beam Waist (w₀): Minimum beam radius where wavefront is flat
- Divergence Angle: Rate at which beam expands as it propagates
- M² Factor: Measure of beam quality; M² = 1 for perfect Gaussian beam
- Rayleigh Length: Characteristic distance for beam expansion
- Far Field: Region where z >> z_R and beam expands linearly
Applications
Laser System Design
Optimize beam delivery systems and determine working distances for laser processing applications.
Optical Component Selection
Choose appropriate lenses, mirrors, and beam expanders based on divergence requirements.
Safety Analysis
Calculate safe distances and beam containment requirements for laser safety protocols.
Beam Quality Assessment
Evaluate laser performance and compare different laser sources based on beam characteristics.