Laser Beam Profiling Inputs
Sample Measurement Set and Output
These values illustrate typical near-infrared lab settings.
| Parameter | Example input | Typical meaning |
|---|---|---|
| Wavelength | 1064 nm | Nd:YAG fundamental |
| Waist radius | 50 um | 1/e^2 intensity radius at focus |
| M^2 | 1.20 | Beam quality above diffraction limit |
| Evaluate at z | 50 mm | Distance from waist along propagation axis |
| Power | 2.0 W | Used to estimate peak intensity |
Gaussian Beam Relations
w(z) = w0 * sqrt(1 + (z / zR)^2)
zR = (pi * w0^2) / (M^2 * lambda)
theta = (M^2 * lambda) / (pi * w0)
I0 = (2P) / (pi * wx * wy)
dFWHM = w * sqrt(2 ln 2) and D1/e^2 = 2w.Steps for Accurate Profiling
- Pick a method: propagation, M^2 estimation, or diameter conversion.
- Enter wavelength and measured values using the displayed units.
- Optionally enter power to compute peak intensity estimates.
- Set the z-range and number of table points for your report.
- Click Calculate, then export CSV or PDF for documentation.
Professional Notes on Laser Beam Profiling
1) What a profiler actually measures
Most profilers record a 2D intensity map and report widths using common conventions such as 1/e^2 and FWHM. For a Gaussian intensity profile, the conversion is fixed: dFWHM = w * sqrt(2 ln 2) and D1/e^2 = 2w. This calculator keeps those definitions consistent for reporting.
2) Typical lab wavelengths and unit discipline
Industrial and research beams often fall between 405-1550 nm. The same beam diameter can look better or worse depending on unit handling. Here, wavelength is entered in nm, radii in um, and distances in mm, then converted internally to SI for stable results and clean exports.
3) Rayleigh range as a quick stability indicator
Rayleigh range (zR) marks the distance over which the radius grows by sqrt(2). For a 1064 nm beam with w0 = 50 um and M^2 = 1, zR is about 7.38 mm. A higher M^2 reduces zR, so alignment and focus become more sensitive.
4) Divergence: what mrad really means
Far-field divergence is usually quoted in milliradians. Diffraction-limited half-angle divergence is theta0 = lambda/(pi w0). With 1064 nm and 50 um, theta0 is about 6.77 mrad. If your measured divergence is larger, M^2 increases proportionally.
5) M^2 estimation from waist and divergence
The calculator uses M^2 = (pi w0 theta)/lambda (theta as half-angle). For example, w0 = 50 um, theta = 10 mrad at 1064 nm yields M^2 about 1.48. This helps compare sources, resonators, and fiber delivery quality.
6) Elliptical beams and axis-by-axis reporting
Diode lasers and imperfect optics often produce different x/y radii. This tool computes wx(z) and wy(z) independently, giving separate diameters and an elliptical intensity estimate. That prevents misleading single-number summaries when the beam is astigmatic.
7) Power and peak intensity for safety checks
If you enter optical power, peak intensity is estimated using I0 = 2P/(pi wx wy) for TEM00. For tight waists, intensity can climb rapidly; exporting the table helps document operating points before changing focusing lenses or power setpoints.
8) Recommended table settings for repeatable reports
For routine documentation, 11-21 points across a 0-100 mm span is typically readable and export-friendly. Use higher point counts (up to 200) only when you need smoother curves for plotting. Keep the same z-range across runs for fair comparisons.
FAQs
1) Should I enter beam radius or diameter?
Enter radii for waist fields (w0). The reported table shows diameters (2w) to match many profiler readouts. Keep your convention consistent across measurements.
2) What does M^2 = 1 mean?
M^2 = 1 represents an ideal diffraction-limited Gaussian beam. Values like 1.1-1.5 are common for high-quality lasers; larger values indicate more divergence or higher-order structure.
3) My profiler reports FWHM. Can I use this?
Yes. Use the conversion method to translate FWHM diameter into 1/e^2 diameter (or vice versa). Then use the propagation method with 1/e^2 radii.
4) Half-angle vs full-angle divergence: what should I pick?
If your instrument states full-angle, select full-angle so the calculator halves it internally. Many standards use half-angle for the M^2 relation.
5) Does the intensity estimate include losses or clipping?
No. Intensity uses the entered power and the Gaussian TEM00 model. Optical losses, aperture clipping, and non-Gaussian hotspots can change real peak intensity.
6) Can I profile beams far from the waist?
Yes, as long as z is measured from the waist location. If the waist position is uncertain, measure multiple planes and refine your waist estimate before relying on the table.
7) Why do x and y diameters differ?
Different x/y diameters indicate ellipticity or astigmatism, often caused by diode emitters, tilted optics, or thermal lensing. Reporting both axes is the most reliable way to document such beams.