1. What is Beam Diameter (4σ)?

The beam diameter is defined as 4 times the standard deviation (σ) of the Gaussian beam intensity profile. This measurement is commonly used in laser physics and optics to characterize the width of a laser beam.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( \sigma \) — Standard deviation of the beam's intensity profile (meters)

Explanation: For a Gaussian beam, 4σ contains approximately 86% of the total beam power.

3. Importance of Beam Diameter Measurement

Details: Accurate beam diameter measurement is crucial for laser system design, optical alignment, and ensuring proper beam delivery in applications like laser cutting, medical lasers, and optical communications.

4. Using the Calculator

Tips: Enter the standard deviation (σ) of your laser beam's intensity profile in meters. The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why use 4σ instead of FWHM?
A: 4σ provides a more comprehensive measure of beam width that includes more of the beam's energy profile compared to Full Width at Half Maximum (FWHM).

Q2: How do I measure σ experimentally?
A: σ can be determined by measuring the beam profile with a CCD camera or scanning slit profiler and calculating the standard deviation of the intensity distribution.

Q3: What's the relationship between 4σ and 1/e² diameter?
A: For a perfect Gaussian beam, the 1/e² diameter is exactly equal to 4σ.

Q4: Does this apply to non-Gaussian beams?
A: The 4σ definition can be applied to any beam, but the physical interpretation may differ for non-Gaussian profiles.

Q5: What are typical σ values for common lasers?
A: This varies widely - from micrometers for fiber lasers to centimeters for high-power industrial lasers.