Laser Beam Expander Calculator
Calculate beam expansion ratio and output beam diameter
How to Use This Calculator
Select Calculation Type
Choose whether you want to calculate the expansion ratio from input and output diameters, or calculate the output diameter from input diameter and magnification.
Enter Values
Input the input beam diameter and either the output diameter (for expansion calculation) or the magnification (for output calculation). All diameters should be in meters.
Calculate
Click the "Calculate" button to get the expansion ratio or output beam diameter.
Formula
M = D_out / D_in
Where:
- M = Magnification (expansion ratio)
- D_out = Output beam diameter (in meters)
- D_in = Input beam diameter (in meters)
Rearranging:
D_out = M × D_in
Example Calculation:
Expanding a 1 mm beam to 5 mm:
D_in = 0.001 m (1 mm)
D_out = 0.005 m (5 mm)
M = 0.005 / 0.001 = 5×
The beam expander has a 5× magnification.
About Laser Beam Expander Calculator
A laser beam expander is an optical device that increases the diameter of a laser beam. This reduces the beam's divergence and increases the beam's collimation, making it useful for long-distance applications, laser cutting, and optical systems where a larger beam is needed. This calculator helps you determine the expansion ratio (magnification) of a beam expander or calculate the output beam diameter given the input diameter and magnification.
When to Use This Calculator
- Optical System Design: Design laser systems with specific beam sizes
- Beam Expander Selection: Choose appropriate beam expanders for your application
- Laser Processing: Calculate beam sizes for laser cutting, welding, or marking
- Research: Plan experiments requiring specific beam diameters
- Educational Purposes: Understand beam expansion principles
Why Use Our Calculator?
- ✅ Bidirectional Calculation: Calculate expansion ratio or output diameter
- ✅ Instant Results: Get accurate calculations immediately
- ✅ Easy to Use: Simple interface with clear input fields
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works perfectly on all devices
Common Applications
Laser Cutting and Material Processing: Beam expanders are used to create larger, more uniform beams for cutting and welding applications. Larger beams provide better power distribution and can improve processing quality.
Long-Distance Laser Systems: Expanding a beam reduces its divergence, keeping the beam size small over long distances. This is crucial for free-space optical communications, laser ranging, and alignment systems.
Optical Measurement: Expanded beams provide larger spot sizes for illumination or measurement applications, improving signal-to-noise ratio and measurement accuracy.
Tips for Best Results
- Use consistent units (meters for diameters)
- Beam expanders typically have magnifications from 2× to 20×
- Expanding a beam reduces divergence by the same factor (M times less divergence)
- Remember that beam expanders also affect beam quality and can introduce aberrations
- For Gaussian beams, both diameter and divergence scale by the magnification factor
- Consider the physical size of the expander—larger magnifications require larger optics
Frequently Asked Questions
Why expand a laser beam?
Expanding a beam reduces divergence, allowing the beam to stay collimated over longer distances. It also provides larger beam sizes for applications like laser cutting, where uniform power distribution is important. Additionally, larger beams can reduce optical damage risks by lowering power density.
How does beam expansion affect divergence?
Beam expansion reduces divergence by the same factor as the magnification. If you expand a beam by 5×, the divergence is reduced by 5×. This is because the beam waist increases by the magnification factor, and divergence is inversely proportional to beam waist.
Can I use a beam expander in reverse?
Yes, beam expanders can be used in reverse to compress beams. However, the optical design may not be optimal for reverse use, and aberrations may differ. Some beam expanders are designed to work bidirectionally.
What's the difference between Galilean and Keplerian beam expanders?
Galilean expanders use a negative lens followed by a positive lens, providing a shorter overall length. Keplerian expanders use two positive lenses, creating an intermediate focus that can be useful for spatial filtering but requires a longer system.
Does beam expansion affect power?
Beam expansion doesn't change total power, but it does reduce power density (power per unit area). The power density decreases by M², where M is the magnification factor. This can be useful for reducing the risk of optical damage.