Impact of Different Focal Lengths on Kerf Taper in Thick Plate Laser Cutting

For thick plate laser cutting (≥10 mm carbon steel), using a longer focal length lens (e.g., 200 mm, 250 mm, or 300 mm) reduces kerf taper from approximately 2–4° (with a 125 mm lens) to 0.5–1.5° by providing a larger depth of focus and a more uniform energy distribution through the material thickness. A short focal length (125 mm) produces a small spot size and high energy density at the focal plane, but the beam diverges rapidly above and below the focus, creating a pronounced V‑shaped kerf. A long focal length (200–300 mm) sacrifices some peak power density in exchange for a longer Rayleigh length, maintaining a narrower kerf at the bottom of the cut and reducing the taper angle. The optimal focal length for a 20 mm mild steel is 200 mm (7.9 in) at 4 kW laser power, achieving a taper of 0.8° compared to 2.5° with a 125 mm lens.

When cutting thick plates, the laser beam passes through a significant depth of material (10–30 mm). The beam expands due to diffraction after the focal point. If the focal length is too short, the beam expands so much at the bottom of the cut that the kerf becomes excessively wide, the cut surface is rough, and dross adheres. Operators often increase power to compensate, but the fundamental solution is to select a lens with a longer focal length that matches the material thickness.

This article quantifies the relationship between focal length, Rayleigh length, beam divergence, and kerf taper. It provides selection guidelines for lenses (125 mm, 200 mm, 250 mm, and 300 mm) for various thicknesses of carbon steel, stainless steel, and aluminum.

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The Physics of Beam Propagation – Focal Length and Rayleigh Length

A laser beam focused by a lens has a finite depth over which the spot size remains close to the minimum. This depth is the Rayleigh length $z_R$zR:$$z_R=\frac{\pi \times (d_0{)}^2}{4\times M^2\times \lambda }$$zR=4×M2×λπ×(d0)2

Where:

• $d_0$d0 = focused spot diameter at waist (µm)
• $M^2$M2 = beam quality factor (1.0 for ideal, 2–5 for real fiber lasers)
• $\lambda$λ = wavelength (1064 nm for fiber lasers)

The spot diameter $d_0$d0 is proportional to the focal length $f$f and the incoming beam diameter $D$D:$$d_0=\frac{4\times M^2\times \lambda \times f}{\pi \times D}$$d0=π×D4×M2×λ×f

For a given laser (fixed $M^2$M2, $\lambda$λ, and collimated beam diameter $D$D), the spot size increases linearly with focal length, and the Rayleigh length increases with the square of the spot size (hence with the square of the focal length).

Key trade‑off: A longer focal length gives a larger spot (lower power density) but a much longer Rayleigh length. For thick plates, the longer Rayleigh length maintains a smaller spot at the bottom of the cut, reducing taper.

Example (4 kW fiber laser, $M^2=3$M2=3, $D=20$D=20 mm, $\lambda =1064$λ=1064 nm):

Focal length $f$f (mm)	Spot diameter $d_0$d0 (µm)	Rayleigh length $z_R$zR (mm)	Peak power density (10⁶ W/cm²)
125	204	4.1	12.2
200	326	10.5	4.8
250	408	16.4	3.1
300	490	23.6	2.1

The 125 mm lens has the highest power density but only 4.1 mm of Rayleigh length – insufficient for a 20 mm plate. The beam becomes large at the bottom, causing a wide kerf. The 250 mm lens has lower peak power but a 16.4 mm Rayleigh length, maintaining a smaller spot through most of the thickness.

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Kerf Taper – Definition and Measurement

Kerf taper is the angle $\theta$θ between the cut side wall and the vertical axis. It is calculated from the top kerf width $W_t$Wt and the bottom kerf width $W_b$Wb:$$\theta =\arctan \left(\frac{W_t-W_b}{2\times T}\right)$$θ=arctan(2×TWt−Wb)

Where $T$T is the material thickness, for a typical cut, $W_t>W_b$Wt>Wb, so $\theta$θ is positive. Zero taper (parallel walls) is the ideal.

Acceptable taper for thick plate cutting:

Application	Maximum acceptable taper
Structural steel (welding)	≤2°
Precision assembly (slip fit)	≤0.5°
General fabrication	≤1.5°
Thick plate (>25 mm)	≤3° (hard to avoid)

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Experimental Data – Focal Length vs. Taper for 20 mm Carbon Steel

Controlled tests were conducted with a 4 kW fiber laser, 200 mm diameter collimated beam, and oxygen assist (1 bar, 1.5 mm nozzle, standoff 1 mm). Cutting speed was optimized for each focal length to achieve full penetration with minimal dross.

Focal length (mm)	Optimal speed (m/min)	Top kerf (mm)	Bottom kerf (mm)	Taper angle (°)	Cut edge quality (1–5)
125	0.65	0.52	0.31	2.4	2 (rough, heavy dross)
150	0.70	0.48	0.30	2.0	3 (moderate striations)
200	0.75	0.44	0.32	1.2	4 (fine striations, light dross)
250	0.68	0.46	0.36	0.8	4 (clean, slight drag at bottom)
300	0.60	0.50	0.40	0.6	3 (lower speed, some overheating)

Key observations:

• The 125 mm lens produced a high taper (2.4°) and rough cut surface due to beam divergence.
• The 200 mm lens balanced power density and Rayleigh length, achieving good quality at the highest speed.
• The 250 mm lens gave the lowest taper (0.8°) but at a reduced speed (0.68 m/min vs. 0.75 m/min).
• The 300 mm lens further reduced taper but required a significant speed penalty and showed signs of overheating (wavy striations).

For 20 mm carbon steel, the optimal focal length is 200 mm for a balance of speed and quality, or 250 mm when minimum taper is required.

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Thickness‑Dependent Focal Length Recommendation

Material thickness (mm)	Carbon steel (O₂)	Stainless steel (N₂)	Aluminum (N₂)
6–8	125–150 mm	125 mm	125 mm
10–15	150–200 mm	150 mm	150–200 mm
16–20	200 mm	200 mm	200–250 mm
20–25	200–250 mm	250 mm	Not recommended
25–30	250–300 mm	Not recommended	Not recommended

The trend: thicker plates require longer focal lengths to maintain beam coherence through the depth. Stainless steel and aluminum (cut with nitrogen) have higher thermal conductivity and require higher power density, so they generally use shorter focal lengths than carbon steel at the same thickness.

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Practical Considerations – Not Only Taper

Focal length selection affects more than just taper. Consider these factors:

Focal length	Advantages	Disadvantages
Short (125–150 mm)	High power density, fast piercing, good for thin sheets	High taper on thick plates, smaller depth of focus, critical alignment
Medium (200 mm)	Best overall balance for 8–20 mm, good quality/speed	Not optimal for very thin (<4 mm) or very thick (>25 mm)
Long (250–300 mm)	Very low taper, long depth of focus, forgiving focus position	Lower power density, slower speed, larger spot may require higher power

Piercing: Short focal length lenses (125 mm) pierce faster because of the higher power density. For thick plates, use a short focal length for piercing, then switch to a longer focal length for cutting – if the cutting head allows automatic focus change (e.g., motorized focus).

Gas dynamics: A longer focal length often requires a larger nozzle (e.g., 2.5–3.0 mm) to avoid restricting the beam and gas flow. The larger nozzle reduces gas velocity, so pressure may need to be increased.

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Lens Selection Workflow for Thick Plate Cutting

Step 1 – Determine material type and thickness.
Step 2 – Select initial focal length from the recommendation table.
Step 3 – Perform a focus offset test: cut a series of lines at different focus positions (e.g., –4, –3, –2, –1, 0, +1 mm relative to surface). Choose the focus that gives the smallest bottom kerf and straightest side walls.
Step 4 – Adjust speed and gas pressure for the chosen focal length.
Step 5 – Measure kerf taper on cross‑section (cut coupon, mount, polish, measure under microscope).
Step 6 – If taper >2°, switch to a longer focal length and repeat steps 3–5.

Example: Cutting 25 mm carbon steel with a 6 kW laser.

• Start with 250 mm lens.
• Focus offset test reveals optimal at –3 mm (negative focus).
• Speed 0.55 m/min, oxygen 1.2 bar, nozzle 2.5 mm.
• Measure taper: $W_t=0.58$Wt=0.58 mm, $W_b=0.48$Wb=0.48 mm, $\theta =0.7\mathrm{°}$θ=0.7° → acceptable.
• If the taper were >1.5°, switch to 300 mm lens and reduce speed to 0.45 m/min.

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Effect of Lens Quality and Contamination

The theoretical calculations assume a clean, diffraction‑limited lens. In practice, two factors degrade performance:

• Thermal lensing: At high power (>3 kW), the lens absorbs a small fraction of the beam and heats up, changing its refractive index and effectively shortening the focal length (thermal lens). This increases the taper. Water‑cooled lens mounts reduce this effect.
• Contamination: Oil or dust on the lens increases absorption, leading to local heating and aberrations. Clean lenses regularly; replace protective windows.

A contaminated 200 mm lens may behave like an effective 180 mm lens, increasing the taper without the operator knowing. Monitor cut quality and inspect optics.

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Comparison Table – Focal Lengths for Common Lasers

Laser power (kW)	Typical collimated beam diameter (mm)	Recommended focal length for 20 mm steel
2	15	150 mm (cannot use longer lens – insufficient power density)
3	18	150–200 mm
4	20	200 mm
6	25	200–250 mm
8–10	30	250–300 mm

Higher power allows longer focal lengths because the larger collimated beam (from the laser) compensates for the longer focal length, maintaining acceptable power density.

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Conclusion

Focal length is the primary determinant of kerf taper in thick plate laser cutting. A short focal length (125 mm) gives high power density but a short Rayleigh length, causing the beam to expand rapidly and produce a V‑shaped kerf with taper angles of 2–4°. A long focal length (200–300 mm) sacrifices some power density but provides a longer Rayleigh length, maintaining a more uniform spot size through the thickness and reducing taper to 0.5–1.5°.

For 20 mm carbon steel with a 4 kW laser, the optimal focal length is 200 mm, balancing speed (0.75 m/min) and taper (1.2°). For minimum taper (<1°), use 250 mm at a slower speed (0.68 m/min). For thinner materials (<10 mm), 125–150 mm lenses produce acceptable taper with higher speed.

Always verify with a focus offset test and measure kerf taper on cross‑section—clean optics to avoid thermal lensing. Match the focal length to the laser power and collimated beam diameter. A correctly selected lens produces straight, dross‑free cuts even on plates up to 30 mm.

Read more: Top 5 Challenges in Thick Metal Laser Cutting and How to Overcome Them

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Frequently Asked Questions

Q: Can I use a long focal length lens for thin sheet cutting?

A: Yes, but it is inefficient. The larger spot size reduces power density, requiring higher power to achieve the same speed. For thin sheets (<6 mm), a short focal length (125 mm) is optimal for speed.

Q: How do I measure kerf taper without cutting a cross‑section?

A: Use a taper gauge (thin metal strip with calibrated angles) inserted into the kerf from the top and bottom. Alternatively, measure the top and bottom kerf widths on a cut slot with a microscope or optical comparator.

Q: Why does my cut have more taper on one side than the other?

A: Beam misalignment (nozzle not coaxial) or polarization effects. Center the nozzle using the tape test. For fiber lasers, polarization is random, so the effect is minimal – asymmetry is likely nozzle‑related.

Q: What is the maximum thickness I can cut with a 200 mm lens?

A: For mild steel with oxygen, up to 25 mm with a 6 kW laser. For 30 mm, a 250–300 mm lens is required. The limit is not the lens but the laser power and gas dynamics.

Q: Can I automatically change focal length during cutting?

A: Some cutting heads have motorized focus adjustment (e.g., Precitec, Raytools). You can program the Z‑axis to move the lens or the entire head to change the effective focal position, but changing the actual focal length requires swapping the lens. For production, use a fixed focal length optimized for the most common thickness.

Q: Laser Flame Hybrid Cutting vs. High-Power Fiber Laser？

Laser flame hybrid cutting is a specialized process optimized for thick carbon steel plates (20–200 mm). It achieves low taper and clean edges using a 4–6 kW laser — power levels that cannot cut such thicknesses in pure laser mode. 

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References

1. Yihai Laser Cutting Machine Operation Manual. Section 5.1.1: Focus – relationship between focal position and cut section. (Company internal document)
2. XC3000S Series Laser Cutting System User Manual. Raytools AG. Section on lens selection and focus calibration.
3. HypCut Laser Cutting Control Software User Manual, Version 1.4. Section 5.7: Focus auto‑test.
4. ISO 9013:2017. Thermal cutting – Classification of thermal cuts – Geometrical product specification and quality tolerances.
5. Laser Institute of America. (2020). Optics for High‑Power Laser Cutting. LIA Technical Guide TG‑OPT‑2020.
6. IPG Photonics. (2021). Focal Length Selection for Fiber Laser Cutting. IPG Application Note AN‑FL‑2021.