Rayleigh Length Calculator
Calculate Rayleigh length, confocal parameter, and beam propagation characteristics for Gaussian laser beams. Essential for optical system design and beam quality assessment.
Input Parameters
Calculation Results
Propagation Parameters
Beam Characteristics
Propagation Assessment
Formulas and Theory
Rayleigh Length
Distance from beam waist where beam area doubles. Fundamental parameter for beam propagation analysis.
Confocal Parameter
Total distance over which beam remains near minimum diameter. Practical working distance for applications.
Beam Radius at Distance z
Beam radius evolution along propagation axis. Hyperbolic growth from waist position.
Far Field Divergence
Half-angle divergence in far field region (z ≫ z_R). Asymptotic beam spreading angle.
Understanding Rayleigh Length
📏 Rayleigh Length (z_R)
Characteristic distance for Gaussian beam propagation where beam area doubles from minimum value.
🎯 Confocal Parameter (b)
Length of focus region (2×z_R) where beam remains reasonably collimated for practical applications.
🔍 Near Field Region
Region where z < z_R and beam radius changes slowly, approximately constant beam size.
📡 Far Field Region
Region where z ≫ z_R and beam expands linearly with distance at constant divergence angle.
⚡ M² Beam Quality
Beam quality parameter affecting propagation. M² = 1 for perfect Gaussian, higher values indicate multimode behavior.
🎪 Depth of Focus
Practical working distance for focused applications, typically related to confocal parameter.
Applications
Microscopy & Imaging
Determine depth of focus for laser scanning microscopes and optimal working distances for high-resolution imaging systems.
Laser Processing
Calculate working range for laser cutting, welding, and marking applications to maintain consistent power density and quality.
Beam Shaping Design
Design optical systems with appropriate beam expansion and collimation for specific propagation requirements and applications.
Free Space Communication
Optimize beam propagation for laser communication systems and atmospheric transmission calculations with precise parameters.