1. What is a Rayleigh Range Calculator?

Definition: This calculator determines the Rayleigh range (z_R) of a Gaussian laser beam based on its waist radius and wavelength.

Purpose: It helps optical engineers and physicists understand beam propagation characteristics in laser systems.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( z_R \) — Rayleigh range (meters)
• \( w_0 \) — Beam waist radius (meters)
• \( \lambda \) — Wavelength (meters)

Explanation: The Rayleigh range represents the distance over which the beam radius remains within √2 of its minimum value.

3. Importance of Rayleigh Range

Details: Knowing the Rayleigh range is crucial for designing optical systems, determining beam divergence, and calculating depth of focus in laser applications.

4. Using the Calculator

Tips: Enter the beam waist radius and wavelength (default 532nm for green lasers). Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Rayleigh range?
A: It indicates the distance over which a laser beam remains nearly collimated before significant divergence occurs.

Q2: How does wavelength affect Rayleigh range?
A: Longer wavelengths result in longer Rayleigh ranges for the same beam waist, while shorter wavelengths decrease the Rayleigh range.

Q3: What's a typical beam waist size?
A: Common values range from micrometers (fiber optics) to millimeters (free-space lasers).

Q4: How is this related to beam divergence?
A: Beam divergence angle θ ≈ λ/(πw₀), showing an inverse relationship with Rayleigh range.

Q5: Can this be used for non-Gaussian beams?
A: The formula applies specifically to fundamental Gaussian (TEM₀₀) modes. Different modes have different propagation characteristics.