Rayleigh Range Calculator

Rayleigh Range Equation:

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

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 waist to the place where the area of the cross section is doubled. It is a fundamental parameter in Gaussian beam optics that characterizes the divergence of the beam.

2. How Does the Calculator Work?

The calculator uses the Rayleigh range equation:

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

Where:

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

Explanation: The equation shows that Rayleigh range increases with the square of the beam waist and decreases with increasing wavelength.

3. Importance of Rayleigh Range Calculation

Details: Rayleigh range is crucial in laser optics for determining beam divergence, depth of focus, and optimal focusing conditions. It helps in designing optical systems, laser cutting, and medical laser applications.

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 range in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Rayleigh range?
A: Rayleigh range represents the distance over which the beam radius remains relatively constant before significant divergence occurs.

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 Rayleigh ranges.

Q3: What is the relationship between wavelength and Rayleigh range?
A: Rayleigh range is inversely proportional to wavelength - shorter wavelengths result in longer Rayleigh ranges.

Q4: How is Rayleigh range used in practical applications?
A: It's used to determine optimal focusing conditions, calculate depth of field in optical systems, and design laser resonators.

Q5: What are typical values for Rayleigh range?
A: Values range from micrometers for tightly focused visible lasers to kilometers for large-beam microwave systems.