Axicon Bessel Zone
Estimate geometric Bessel-zone length from beam radius and axicon cone angle.
Description
An axicon’s geometric Bessel zone relates beam radius to cone angle.
An axicon’s geometric Bessel zone relates beam radius to cone angle. The cone angle in this formula is the propagation cone used by the model.1
Estimate geometric Bessel-zone length from beam radius and axicon cone angle.
When to use Axicon Bessel Zone
Use this tool to estimate geometric Bessel-zone length from beam radius and axicon cone angle.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Axicon Bessel Zone and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter inputBeamRadiusMeters, coneAngleDegrees using the field table and calculation rules, then run the tool.
- Read besselZoneLengthMeters. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| inputBeamRadiusMeters | Input beam radius (m) | number; minimum: 0 | Required |
| coneAngleDegrees | Axicon cone angle (°) | number; minimum: 0; maximum: 89.999 | Required |
Enter nonnegative radius meters and angle strictly above zero through 89.999°. Return length meters.
zoneLength=radius/tan(coneAngle) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| besselZoneLengthMeters | Geometric Bessel-zone length (m) | number; minimum: 0 |
{
"input": {
"inputBeamRadiusMeters": 0.005,
"coneAngleDegrees": 5
},
"output": {
"besselZoneLengthMeters": 0.05715026151380671
}
}Limitations and assumptions
No axicon material-angle conversion, diffraction, central-lobe size or nonideal beam profile is modeled.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Astigmatic Collimator Design: Estimate separate fast- and slow-axis collimator focal lengths from divergence and target diameter. For a complementary task, use Focused-Beam Waist Location: Propagate a Gaussian beam q parameter through a thin lens to locate the new waist.
References
-
Axicon Bessel Zone — tool.io
Similar or alternative tools
- Astigmatic Collimator Design
Estimate separate fast- and slow-axis collimator focal lengths from divergence and target diameter.
- Focused-Beam Waist Location
Propagate a Gaussian beam q parameter through a thin lens to locate the new waist.