1. What is Rayleigh Range?

Definition: The Rayleigh range is the distance along the propagation direction of a beam from the beam waist to the place where the area of the cross section is doubled.

Purpose: It characterizes how quickly a laser beam diverges and is important in laser optics, fiber optics, and beam focusing applications.

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 is proportional to the square of the beam waist radius and inversely proportional to the wavelength.

3. Importance of Rayleigh Range

Details: Understanding Rayleigh range helps in 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 in meters. Both values must be > 0. For common lasers, wavelengths are often in nanometers (1 nm = 1×10⁻⁹ m).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical beam waist radius?
A: For many lasers, beam waist radius ranges from micrometers to millimeters, depending on the application.

Q2: How does wavelength affect Rayleigh range?
A: Shorter wavelengths result in shorter Rayleigh ranges for the same beam waist, meaning the beam diverges more quickly.

Q3: What's the relationship between Rayleigh range and beam divergence?
A: The far-field divergence angle θ ≈ λ/(πw₀) = w₀/z_R, showing the inverse relationship between divergence and Rayleigh range.

Q4: Can I use this for non-Gaussian beams?
A: The formula is strictly for Gaussian beams. Other beam profiles require different calculations.

Q5: How do I measure beam waist radius?
A: Typically measured using beam profilers or by analyzing the beam diameter at multiple positions along the propagation axis.