Rayleigh Beam Calculator

Rayleigh Length Formula:

\[ z_R = \frac{\pi w_0^2}{\lambda} \]

Rayleigh Length (zR):

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1. What is Rayleigh Length?

The Rayleigh length (zR) is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. It's a fundamental parameter in Gaussian beam optics that characterizes the beam's divergence and focusing properties.

2. How Does the Calculator Work?

The calculator uses the Rayleigh length formula:

\[ z_R = \frac{\pi w_0^2}{\lambda} \]

Where:

\( z_R \) — Rayleigh length (m)
\( w_0 \) — Beam waist radius (m)
\( \lambda \) — Wavelength (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The Rayleigh length represents the distance over which the beam radius expands by a factor of √2 from its minimum value at the beam waist.

3. Importance of Rayleigh Length

Details: Rayleigh length is crucial in laser optics, fiber optics, and optical system design. It determines the depth of focus, beam divergence, and helps in designing optical systems for optimal beam quality and focusing characteristics.

4. Using the Calculator

Tips: Enter beam waist radius and wavelength in meters. Both values must be positive numbers. The calculator will compute the Rayleigh length in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Rayleigh length?
A: Rayleigh length indicates the distance over which a Gaussian beam remains approximately collimated. Beyond this distance, the beam begins to diverge significantly.

Q2: How does wavelength affect Rayleigh length?
A: Shorter wavelengths result in longer Rayleigh lengths for the same beam waist, meaning the beam stays collimated over a greater distance.

Q3: What is the relationship between Rayleigh length and beam divergence?
A: The beam divergence angle is inversely proportional to the Rayleigh length. Longer Rayleigh length means smaller divergence angle.

Q4: Can this formula be used for non-Gaussian beams?
A: This specific formula applies to fundamental Gaussian beams. Different beam profiles may require modified calculations.

Q5: How is Rayleigh length used in practical applications?
A: It's used in laser cutting, optical communications, microscopy, and any application where beam focusing and collimation are critical.