Rayleigh Limit Calculator

Rayleigh Range Equation:

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

Rayleigh Range (ZR):

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1. What is the 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 an important parameter in Gaussian beam optics that characterizes the depth of focus of a laser 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: Calculating Rayleigh range is essential in laser optics for determining the depth of focus, beam divergence, and designing optical systems with specific focusing requirements.

4. Using the Calculator

Tips: Enter beam waist in meters, 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 a laser beam remains approximately collimated before significant divergence occurs.

Q2: How does beam waist affect Rayleigh range?
A: Rayleigh range increases with the square of the beam waist radius, meaning larger beams stay collimated over longer distances.

Q3: What units should I use for the inputs?
A: Both beam waist and wavelength should be entered in meters for consistent results. Convert from other units if necessary.

Q4: How is Rayleigh range related to beam divergence?
A: Beam divergence angle is inversely proportional to the Rayleigh range, with smaller divergence corresponding to longer Rayleigh ranges.

Q5: Can this calculator be used for non-laser beams?
A: The equation applies to any Gaussian beam, but is most commonly used for laser beams which typically have Gaussian intensity profiles.