What Is the Gaussian Laser Beam Waist & Divergence Calculator?
A Gaussian beam is an electromagnetic wave whose transverse electric field and intensity distributions are described by Gaussian functions.
How Does the Gaussian Laser Beam Waist & Divergence Calculator Work?
Computes Rayleigh range z_R, the distance over which beam cross-section area doubles.
Evaluates spot radius w(z) at distance z.
Computes asymptotic far-field divergence half-angle θ.
Gaussian Laser Beam Waist & Divergence Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
z_R = (π · w₀²) / λ, w(z) = w₀ · √[ 1 + (z / z_R)² ], θ = λ / (π · w₀)
Paraxial Helmholtz diffraction equations for TEM₀₀ Gaussian laser modes.
How to Use the Gaussian Laser Beam Waist & Divergence Calculator
- Enter laser wavelength in nm.
- Specify minimum waist radius w₀ in microns.
- Provide target propagation distance in meters.
Step-by-Step Example Calculation
Focused 1064 nm Nd:YAG Laser
Input Values:
wavelength:1064
waistRadius:20
distance:0.5
Worked Steps: Infrared laser focused to 20 µm spot propagating 0.5 meters.
Understanding Your Result
Primary output indicates spot radius at specified distance.
Summary displays Rayleigh depth of focus and full divergence angle.
Factors That Affect the Result
- Wavelength (shorter wavelengths diverge less for the same waist).
- Beam quality factor M² (real beams diverge faster than ideal M² = 1.0 Gaussian modes).
When Should You Use This Calculator?
- Laser cutting, optical communications, microscope objective design, and laser collimation.
Assumptions & Limitations
- Assumes fundamental paraxial TEM₀₀ mode (M² = 1).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical paraxial wave solution.