1. What is a Rayleigh Measurement Calculator?

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

Purpose: It helps optical engineers and physicists determine the characteristic distance over which a laser beam remains collimated.

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 from the beam waist where the beam radius increases by a factor of √2.

3. Importance of Rayleigh Range Calculation

Details: Knowing the Rayleigh range is crucial for laser system design, beam focusing applications, and understanding beam divergence characteristics.

4. Using the Calculator

Tips: Enter the beam waist radius and wavelength in meters. Both values must be > 0. For typical lasers, wavelengths are often in nanometers (1 nm = 1×10⁻⁹ m).

5. Frequently Asked Questions (FAQ)

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

Q2: How does beam waist affect Rayleigh range?
A: Rayleigh range increases with the square of the beam waist - smaller waists produce shorter Rayleigh ranges.

Q3: What's a typical wavelength for visible lasers?
A: Common values are 532 nm (green) or 650 nm (red). Remember to convert to meters (e.g., 532 nm = 532×10⁻⁹ m).

Q4: How is this related to beam divergence?
A: The far-field divergence angle θ ≈ λ/(πw₀), inversely related to Rayleigh range.

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