Gaussian Spot Size Calculator

Formula

To calculate the Gaussian Spot Size:

$w_0 = \frac{\lambda \cdot f}{\pi \cdot D}$

Where:

$w_0$ is the Gaussian spot size
$\lambda$ is the wavelength
$f$ is the focal length
$D$ is the beam diameter

Gaussian Spot Size Definition

The Gaussian spot size refers to the radius at which the intensity of a Gaussian beam falls to $\frac{1}{e^2}$ (about 13.5%) of its peak value. This measurement is crucial in optics and laser physics, as it determines the focus and resolution of laser beams. The spot size is influenced by the wavelength of the laser, the focal length of the focusing lens, and the diameter of the beam before focusing. Understanding and calculating the Gaussian spot size is essential for applications that require precise control of laser beams, such as in microscopy, material processing, and optical communication systems.

Example Calculation 1

Let's assume the following values:

Wavelength ( $\lambda$ ) = 500 nm
Focal Length ( $f$ ) = 0.1 meters
Beam Diameter ( $D$ ) = 0.01 meters

Using the formula:

$w_0 = \frac{500 \times 0.1}{\pi \times 0.01} \approx 1.591 \times 10^3 \text{ nm}$

The Gaussian Spot Size is approximately 1591 nm.

Example Calculation 2

Let's assume the following values:

Wavelength ( $\lambda$ ) = 800 nm
Focal Length ( $f$ ) = 0.05 meters
Beam Diameter ( $D$ ) = 0.005 meters

Using the formula:

$w_0 = \frac{800 \times 0.05}{\pi \times 0.005} \approx 2.546 \times 10^3 \text{ nm}$

The Gaussian Spot Size is approximately 2546 nm.