Rayleigh Beam Length Calculator

Rayleigh Range Formula:

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

Rayleigh Range (ZR):

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1. What is Rayleigh Range?

The Rayleigh range (ZR) 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. It characterizes the collimation length of a Gaussian beam in laser optics.

2. How Does the Calculator Work?

The calculator uses the Rayleigh range formula:

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

Where:

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

Explanation: The Rayleigh range represents the distance over which the beam remains approximately collimated. Beyond this range, the beam begins to diverge significantly.

3. Importance of Rayleigh Range Calculation

Details: Calculating Rayleigh range is essential in laser system design, optical communications, and various applications where beam collimation and focus are critical parameters.

4. Using the Calculator

Tips: Enter beam waist in meters and wavelength in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Rayleigh range?
A: The Rayleigh range indicates the distance over which a Gaussian beam remains well-collimated. It's the distance from the beam waist where the beam radius increases by a factor of √2.

Q2: How does beam waist affect Rayleigh range?
A: Rayleigh range increases with the square of the beam waist radius. Larger beam waists result in longer collimation distances.

Q3: How does wavelength affect Rayleigh range?
A: Rayleigh range is inversely proportional to wavelength. Shorter wavelengths result in shorter Rayleigh ranges for the same beam waist.

Q4: What are typical values for Rayleigh range?
A: Values vary widely depending on application. For visible lasers with small beam waists, Rayleigh range can be millimeters to centimeters. For large beam systems, it can be meters or more.

Q5: How is Rayleigh range related to beam divergence?
A: The beam divergence angle is inversely related to the Rayleigh range. A longer Rayleigh range corresponds to a more collimated beam with smaller divergence.