Gaussian Beam Divergence Calculator
Here’s a comprehensive table summarizing the key aspects of Gaussian Beam Divergence:
Gaussian Beam Divergence: Essential Parameters and Formulas
| Parameter | Description | Formula |
|---|---|---|
| Wavelength (λ) | The wavelength of the light used in the Gaussian beam | – |
| Beam Waist (w0) | The minimum beam radius at the focal point | – |
| Rayleigh Range (zR) | Distance over which the beam maintains a good focus | zR=πw02λzR=λπw02 |
| Divergence (θ) | The angle at which the beam diverges as it propagates | θ=λπw0θ=πw0λ |
| Beam Quality Factor (M²) | Measures how much the beam deviates from an ideal Gaussian beam | – |
| Confocal Parameter | Twice the Rayleigh range; represents the depth of focus | Confocal Parameter = 2 * zR |
| Beam Parameter Product (BPP) | The product of the waist radius and the divergence angle, relates to beam quality | BPP = w0 * θ |
Key Points on Gaussian Beam Divergence
- Relationship to Beam Waist: The divergence is inversely proportional to the beam waist. A smaller waist results in larger divergence, while a larger waist leads to smaller divergence2.
- Wavelength Dependence: Longer wavelengths result in stronger divergence for a given beam waist1.
- Far-field Behavior: The divergence angle θ is a far-field approximation, becoming more accurate as the distance from the beam waist increases4.
- Diffraction Limit: A Gaussian laser beam is considered diffraction-limited when its measured divergence is close to the theoretical minimum value3.
- Beam Quality: The M² factor quantifies how close a real beam is to an ideal Gaussian beam. An M² of 1 represents a perfect Gaussian beam, while real beams have M² > 12.
- Numerical Aperture: For a Gaussian beam, the numerical aperture (NA) is related to the divergence by NA = n * sin(θ), where n is the refractive index of the medium2.
- Beam Expansion: Laser beam expanders can reduce beam divergence by increasing the beam diameter4.
- Paraxial Approximation: The Gaussian beam model is accurate for beams with waists larger than about 2λ/π, as it relies on the paraxial approximation2.
Understanding these parameters and their relationships is crucial for designing and optimizing optical systems that utilize Gaussian beams, such as laser-based instruments and fiber optic communications.