Laser Beam Expander Calculator
Calculate magnification, beam expansion, and divergence reduction for laser beam expander systems
Calculate Laser Beam Expander Parameters
Galilean Design
Negative + positive lens, no internal focus, compact
Keplerian Design
Two positive lenses, internal focus, beam cleaning
Input lens focal length (where beam enters)
Output lens focal length (where expanded beam exits)
Initial beam diameter before expansion
Initial beam divergence angle
Distance to calculate beam size at that point
Beam Expander Results
Magnification Parameters
Beam Parameters
Key Formulas: MP = fO/fI, DO = MP × DI, θO = θI/MP, DL = DO + L × tan(2θO)
Design: Galilean (compact, no internal focus)
Beam Quality Analysis
High expansion - excellent for reducing divergence
Example Calculation
Galilean Beam Expander (6X)
Image lens: fI = -25 mm (negative focal length)
Objective lens: fO = 150 mm (positive focal length)
Magnifying power: MP = 150/25 = 6X
Input beam: 2 mm diameter, 0.4 mrad divergence
Output: 12 mm diameter, 0.067 mrad divergence
At 5 meters distance:
• Beam diameter: DL = 12 + 5000 × tan(2 × 0.067 × 10⁻³) ≈ 12.67 mm
• Lens separation: 150 + 25 = 175 mm
• Beam quality: Excellent collimation with minimal spread
Design Comparison
Galilean
- • Negative + positive lens
- • No internal focus point
- • Compact design
- • High power applications
- • Lower cost
Keplerian
- • Two positive lenses
- • Internal focus point
- • Beam cleaning capability
- • Higher expansion ratios
- • Pulsed laser applications
Common Applications
Laser machining and material processing
LIDAR and rangefinding systems
Optical pumping and laser arrays
Beam shaping for uniform illumination
Telescope and astronomical instruments
Laser communication systems
Understanding Laser Beam Expanders
What is a Beam Expander?
A laser beam expander is an optical device that increases the diameter of a laser beam while maintaining the collimation (parallel rays). It consists of two lenses arranged to expand the beam by a controlled factor, simultaneously reducing the beam's divergence angle.
Why Use Beam Expanders?
- •Reduce beam divergence for long-distance applications
- •Improve beam quality and spatial coherence
- •Overfill optical components for uniform illumination
- •Reduce power density to prevent damage
Key Formulas
- MP = fO / fI (Magnifying Power)
- m = 1 / MP (Magnification)
- DO = MP × DI (Output Diameter)
- θO = θI / MP (Output Divergence)
- DL = DO + L × tan(2θO) (Diameter at Distance)
- MP: Magnifying power (expansion factor)
- fO, fI: Objective and image focal lengths
- DO, DI: Output and input beam diameters
- θO, θI: Output and input divergence angles
- L: Distance from expander
Design Considerations
Magnification Factor
Higher magnification provides better collimation but requires larger optics and more precise alignment. Common factors: 2X, 5X, 10X, 20X.
Wavelength Compatibility
Lens coatings and materials must match laser wavelength. AR coatings minimize reflections and maximize transmission efficiency.
Power Handling
Keplerian designs create internal focus requiring careful power management. Galilean designs handle continuous high power better.