What Is the Gaussian Laser Beam Waist & Rayleigh Range Calculator?
Gaussian beam optics describes the spatial profile and propagation characteristics of focused and collimated laser beams.
How Does the Gaussian Laser Beam Waist & Rayleigh Range Calculator Work?
Calculates the confocal parameter and hyperbolic expansion radius from the diffraction wave equation.
Gaussian Laser Beam Waist & Rayleigh Range Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
z_R = rac{pi w_0^2}{lambda}, quad heta = rac{lambda}{pi w_0}, quad w(z) = w_0 sqrt{1 + left( rac{z}{z_R}
ight)^2}
Rayleigh collimation range and beam radius hyperbolic profile.
How to Use the Gaussian Laser Beam Waist & Rayleigh Range Calculator
- Enter laser wavelength, focused waist radius w0, and distance z from the waist.
Step-by-Step Example Calculation
Green DPSS Laser Collimation
Input Values:
wavelengthNm:532
beamWaistRadiusUm:250
propagationDistanceM:1.5
Worked Steps: Yields Rayleigh range z_R = 0.369 m, divergence 1.35 mrad, and beam radius 1.045 mm at 1.5 m.
Understanding Your Result
Rayleigh range marks distance where beam area doubles; spot radius gives 1/e² intensity radius at target z.
Factors That Affect the Result
- Beam quality factor M² increases real-world divergence over the ideal diffraction limit.
When Should You Use This Calculator?
- Laser cutting nozzle focus design, optical bench alignment, lidar sensor range calculation, and fiber coupling.
Assumptions & Limitations
- Assumes ideal diffraction-limited fundamental TEM00 mode with M² = 1.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard paraxial Gaussian beam formulation.