Grating Steering Angle

Solve the scalar grating equation for diffraction angle.

Description

The scalar grating equation converts wavelength, period, order and incidence into a principal diffraction angle.

The scalar grating equation converts wavelength, period, order and incidence into a principal diffraction angle. Its sine argument decides whether that order has a returned solution.^[1]

Solve the scalar grating equation for diffraction angle.

When to use Grating Steering Angle

Use this tool to solve the scalar grating equation for diffraction 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 Grating Steering Angle 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 wavelengthMeters, gratingPeriodMeters, diffractionOrder, incidenceAngleDegrees using the field table and calculation rules, then run the tool.
Read diffractedAngleDegrees, physicalOrder. 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
wavelengthMeters	Wavelength (m)	number; minimum: 0	Required
gratingPeriodMeters	Grating period (m)	number; minimum: 0	Required
diffractionOrder	Diffraction order	integer	Required
incidenceAngleDegrees	Incidence angle (°)	number	Required

Enter nonnegative wavelength, positive period, signed integer order and finite incidence degrees. Return angle and true for argument in [−1,1]; otherwise zero angle and false.

sin(output)=order×λ/period−sin(incidence)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
diffractedAngleDegrees	Diffracted angle (°)	number
physicalOrder	Physical diffraction order	boolean

json

{
  "input": {
    "wavelengthMeters": 5e-7,
    "gratingPeriodMeters": 0.000001,
    "diffractionOrder": 1,
    "incidenceAngleDegrees": 0
  },
  "output": {
    "diffractedAngleDegrees": 30.000000000000004,
    "physicalOrder": true
  }
}

Limitations and assumptions

Zero is a no-solution placeholder. No efficiency, polarization, blaze or full order spectrum is calculated.

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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Optical Phased-Array Steering: Calculate phased-array beam steering from wavelength, element spacing, and adjacent phase shift. For a complementary task, use Mode-Hop Tuning Ratio: Calculate the current-to-grating tuning ratio needed for matched frequency change.

References

Grating Steering Angle — tool.io

Similar or alternative tools

Optical Phased-Array Steering
Calculate phased-array beam steering from wavelength, element spacing, and adjacent phase shift.
Mode-Hop Tuning Ratio
Calculate the current-to-grating tuning ratio needed for matched frequency change.