Gaussian Beam Calculator
Enter wavelength, beam waist, and propagation distance. The Gaussian Beam Calculator instantly computes beam radius, divergence, Rayleigh range, and all key parameters.
About the Gaussian Beam Calculator
The Gaussian Beam Calculator is a precise, scientifically accurate tool that computes all parameters of Gaussian beam propagation using the fundamental equations from laser physics. This Gaussian Beam Calculator implements the exact formulas for beam radius w(z), divergence angle θ, Rayleigh range z_R, and wavefront curvature R(z) — the standard model for real laser beams. Proudly supported by Agri Care Hub.
Scientific Formulas
z_R = π w₀² / (λ M²) (Rayleigh range)
θ = λ / (π w₀ M²) (half-angle divergence)
R(z) = z (1 + (z_R/z)²) (radius of curvature)
Why This Calculator Is Essential
Gaussian beams are the fundamental mode of most lasers. Understanding their propagation is critical for: • Laser focusing and mode matching • Optical cavity design • Fiber coupling efficiency • Beam delivery systems • LIDAR and remote sensing • Laser material processing Accurate Gaussian beam modeling is required in every laser application.
How to Use
- Enter wavelength λ in μm (e.g., 0.532 for green, 10.6 for CO₂).
- Enter beam waist w₀ (1/e² radius) in mm.
- Enter M² beam quality factor (1 for ideal TEM₀₀).
- Enter propagation distance z in meters.
- Click “Calculate Gaussian Beam”.
When Should You Use This Tool?
- Laser system design and alignment
- Optical engineering and photonics
- Fiber optics coupling optimization
- Free-space optical communication
- LIDAR and laser ranging
- Teaching Gaussian beam optics
Scientific Foundation
Gaussian beams are the exact solution of the paraxial wave equation for cylindrical symmetry. The formulas are derived from Maxwell's equations in the paraxial approximation and confirmed experimentally. M² accounts for real beam deviations from ideal. Full theory at Gaussian Beam on Wikipedia and Siegman’s *Lasers* (1986).
Conclusion
The Gaussian Beam Calculator brings professional laser beam modeling to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning Gaussian optics, a researcher designing laser cavities, or an engineer optimizing beam delivery, this tool delivers precise results every time. For more optics tools, visit Agri Care Hub.