Focused Gaussian Beam Waist Calculator
Here’s a comprehensive table summarizing the key parameters and equations related to focused Gaussian beam waists:
Focused Gaussian Beam Waist Parameters
| Parameter | Description | Equation |
|---|---|---|
| Beam Waist Radius (w0) | The radius of the laser beam at its narrowest point | w0 |
| Distance from Waist (z) | The axial distance from the beam waist | z |
| Beam Radius (w(z)) | Beam radius at distance z from the waist | w(z) = w0 * sqrt(1 + (z/zR)^2) |
| Rayleigh Length (zR) | Half the distance over which the beam area doubles | zR = (π * w0^2) / λ |
| Divergence Angle (θ) | Inversely proportional to beam waist diameter | θ = λ / (π * w0) |
| Radius of Curvature (R(z)) | Curvature of the wavefront at distance z | R(z) = z * (1 + (zR/z)^2) |
| Gouy Phase (ψ(z)) | Phase shift acquired by the beam around the focal region | ψ(z) = arctan(z/zR) |
| Irradiance Distribution (I(r,z)) | Intensity distribution in relation to distance from the center | I(r,z) = I0 * (w0/w(z))^2 * exp(-2r^2/w(z)^2) |
| Focal Length (f) | Distance over which the beam is focused | f = 1 / (2 * NA) |
This table provides a concise overview of the essential parameters and equations for understanding focused Gaussian beam waists. The beam waist radius (w0) is a fundamental parameter that determines many other characteristics of the beam2.
The Rayleigh length (zR) is an important measure of the beam’s focus, representing the distance over which the beam remains relatively collimated3.The divergence angle (θ) is inversely proportional to the beam waist diameter, indicating that tighter focus results in greater divergence3.
The radius of curvature R(z) describes how the wavefront of the beam changes as it propagates, being flat (infinite curvature) at the waist and gradually curving as it moves away4.
The Gouy phase (ψ(z)) represents a phase shift that occurs near the focal region, which can affect the apparent wavelength of the beam5. The irradiance distribution I(r,z) describes how the intensity of the beam varies both radially and along the propagation axis2.
Understanding these parameters and their relationships is crucial for working with focused Gaussian beams in various applications, such as laser cutting, microscopy, and optical communications.