Science calculator
Rayleigh range.
Enter a Gaussian beam's waist radius and wavelength to find its Rayleigh range zR and confocal parameter 2zR.
Rayleigh range zRTEM₀₀
—
distance from waist to w = √2w₀
- Confocal parameter 2zR
- —
- w₀ 1/e² intensity waist radius · λ wavelength in the medium · zR Rayleigh range
Assumptions
- Fundamental TEM₀₀ Gaussian beam with M² = 1.
- Paraxial propagation in one homogeneous medium.
- w₀ is the 1/e² intensity radius at the true beam waist.
- Use the wavelength in the propagation medium; the model neglects apertures and aberrations.
How it works
The Rayleigh range sets the natural axial scale of a Gaussian focus. At one zR from the waist, the beam radius has grown to √2 times w₀.
A wider waist gives a much longer Rayleigh range because zR scales with w₀². A longer wavelength shortens it for the same waist.
The confocal parameter 2zR spans from −zR to +zR and is often used as a Gaussian-beam depth-of-focus measure. Display rounding does not reduce calculation precision.
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