Interactive Laser Beam Expander Calculator
How to Use This Calculator
This calculator determines the properties of a laser beam after passing through a two-lens beam expander.
- Enter the Wavelength (λ) of the laser light and select its units.
- Enter the Input Beam Waist Diameter (D0,in) (diameter at the narrowest point before the expander) and select its units.
- Enter the Beam Quality Factor (M²) (use 1 for an ideal TEM00 Gaussian beam).
- Enter the Focal Length of the First Lens (f1) (objective lens, light enters this first). Use a negative value for a concave lens. Select its units.
- Enter the Focal Length of the Second Lens (f2) (eyepiece/output lens). Use a negative value for a concave lens. Select its units.
- Click the "Calculate Beam Expander Properties" button.
- Results (magnification, output diameter, output divergence, expander type, and length) and a step-by-step solution will be displayed.
Theory: Laser Beam Expanders
A laser beam expander is an optical device that takes a collimated beam of light and increases its diameter (or cross-sectional area) while decreasing its divergence angle. This is typically achieved using a pair of lenses.
Purpose:
- Decrease beam divergence for long-distance propagation.
- Increase beam diameter to reduce power density on optical components.
- Focus to a smaller spot size (a larger collimated beam can be focused more tightly).
Magnification (Mexp): The ratio of the output beam diameter to the input beam diameter. For a two-lens system, $M_{exp} = |f_2 / f_1|$.
Output Divergence (θout): If the input beam divergence is θin, the output divergence is θout ≈ θin / Mexp. Thus, expanding the beam diameter reduces its divergence.
Types of Expanders (Two-Lens):
- Keplerian: Uses two convex (positive focal length) lenses. It has an internal focal point, which can be problematic for high-power lasers due to potential air breakdown. The lenses are separated by $L = f_1 + f_2$. Output beam is inverted.
- Galilean: Typically uses a convex (positive) objective lens (f1) and a concave (negative) eyepiece lens (f2). It has no internal focus, making it suitable for high-power applications. The lenses are separated by $L = f_1 + f_2$ (where f2 is negative, so $L = f_1 - |f_2|$). Output beam is non-inverted.
Formulas Used
- 1. Input Beam Waist Radius:
w0,in = D0,in / 2 - 2. Input Divergence Half-Angle (θin):
θin = M²λ / (πw0,in)(radians) - 3. Expander Magnification (Mexp):
Mexp = |f2 / f1| - 4. Output Beam Waist Diameter (D0,out):
D0,out = D0,in × Mexp - 5. Output Divergence Half-Angle (θout):
θout = θin / Mexp(radians) - 6. Expander Length (L):
L = f1 + f2(using signed focal lengths for physical separation producing collimated output from collimated input)