1. What is Gaussian Beam Focusing?

The Gaussian beam describes the propagation of electromagnetic waves where the transverse electric field and intensity distributions are described by Gaussian functions. The beam width changes over time due to diffraction effects.

2. How Does the Calculator Work?

The calculator uses the Gaussian beam width equation:

Where:

• \( w(t) \) — Beam width at time t (m)
• \( w_0 \) — Initial beam width (m)
• \( t \) — Time (s)
• \( t_R \) — Rayleigh time (s)

Explanation: The equation describes how the beam width evolves over time due to diffraction, with the Rayleigh time being a characteristic time scale for the beam's expansion.

3. Importance of Beam Width Calculation

Details: Understanding beam width evolution is crucial for laser applications, optical systems design, and predicting beam behavior in free space or through optical elements.

4. Using the Calculator

Tips: Enter initial beam width in meters, time in seconds, and Rayleigh time in seconds. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Rayleigh time?
A: The Rayleigh time is the characteristic time scale at which the beam width increases by a factor of √2 from its initial value.

Q2: How is this related to the Rayleigh range?
A: The Rayleigh time is related to the Rayleigh range (z_R) through the beam's propagation speed. For a beam moving at speed v, t_R = z_R/v.

Q3: What happens when t = t_R?
A: When t = t_R, the beam width becomes w(t_R) = w_0√2, meaning the beam area has doubled from its initial value.

Q4: What are typical values for w₀ in laser systems?
A: Typical values range from micrometers for tightly focused beams to millimeters for collimated beams in laser applications.

Q5: Can this be used for pulsed lasers?
A: Yes, but only if the pulse duration is much longer than the characteristic times involved, otherwise more complex models are needed.