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Laser Gaussian Beam Waist, Divergence & Rayleigh Range Calculator

Easily calculate and compute laser gaussian beam waist, divergence & rayleigh range calculator with accurate equations, live formulas, and expert guidance.

e.g., Nd:YAG = 1064 nm, He-Ne = 632.8 nm.

1/e² intensity beam radius at narrowest focus.

Ideal diffraction-limited TEM₀₀ Gaussian beam M² = 1.0.

Calculated Result
1.6 mm

Rayleigh Range (z_R)

Rayleigh Range (z_R)

1.6 mm

Rayleigh Range Mm

1.6

Half Angle Divergence Mrad

15.58

Full Angle Divergence Mrad

31.16

Confocal Parameter Mm

3.2

1.6 — mm

Calculation Breakdown

  1. Applied FormulaComputes the Rayleigh propagation depth of focus, beam divergence angle, and confocal parameter for focused Gaussian laser beams.z_R = \frac{\pi w_0^2}{M^2 \lambda}, \quad \theta = \frac{M^2 \lambda}{\pi w_0}

Gaussian Beam Rayleigh Range Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.40.81.21.6Rayleigh Range (z_R)

What Is the Laser Gaussian Beam Waist, Divergence & Rayleigh Range Calculator?

This tool computes laser gaussian beam waist, divergence & rayleigh range calculator with high precision arithmetic.

How Does the Laser Gaussian Beam Waist, Divergence & Rayleigh Range Calculator Work?

Computes the Rayleigh propagation depth of focus, beam divergence angle, and confocal parameter for focused Gaussian laser beams.

Laser Gaussian Beam Waist, Divergence & Rayleigh Range Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

zR=πw02M2λ,θ=M2λπw0z_R = \frac{\pi w_0^2}{M^2 \lambda}, \quad \theta = \frac{M^2 \lambda}{\pi w_0}

Computes the Rayleigh propagation depth of focus, beam divergence angle, and confocal parameter for focused Gaussian laser beams.

How to Use the Laser Gaussian Beam Waist, Divergence & Rayleigh Range Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Laser Gaussian Beam Waist, Divergence & Rayleigh Range Calculator Example

Input Values:

wavelengthNm:1064
beamWaistRadiusUm:25
m2Factor:1.15
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required mm.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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